[HN Gopher] Music theory for nerds (2016)
___________________________________________________________________
Music theory for nerds (2016)
Author : marianoguerra
Score : 298 points
Date : 2022-02-16 11:58 UTC (11 hours ago)
(HTM) web link (eev.ee)
(TXT) w3m dump (eev.ee)
| bannedbybros wrote:
| >Not counting the octave, there are seven fairly nice fractions
| here. Hmm. Seven. What a conspicuous number.
|
| There's seven nice fraction because of how they were rounded.
|
| But there's no explanation of why he rounds 1.682 to 5/3 but
| doesn't round 1.587 to the even closer 8/5.
|
| It's because scales are a social construction, not a result of
| vague math.
| taubek wrote:
| Math and music are similar in so many aspects. Are the people
| good at one also good at other? I mean, do mathematicians
| understand musical theory better than those that have no
| background in mah?
| schwartzworld wrote:
| I don't know about mathematicians, but there's definitely an
| overlap with programmers and musicians.
| scottious wrote:
| I don't really think so. The stuff that's covered in the first
| half of this article is certainly very math-y, but you can be a
| great musician and not know this stuff. I really think all you
| need to know is basic arithmetic and the absolute basics of
| modular arithmetic (akin to learning how 12 o'clock + 1 hour =
| 1 o'clock, not 13 o'clock).
|
| Becoming a great musician is more about developing your ear,
| technique, repertoire, etc. It's more similar to learning a
| foreign language than learning math, in my opinion.
| lelandfe wrote:
| My family is full of music theorists, including a professor of
| it. I've asked this before, and they're of the thinking that
| _no_ , one's aptitude at music theory is not related to a
| knowledge of mathematics. The professor in my family has in
| particular seen no relationship between the two in their
| decades of teaching.
|
| But - importantly - a background of math can be a tremendous
| asset later in one's career as a music theorist. It can help
| provide a unique way of looking at and improving on theory.
| karmakaze wrote:
| I've read that Einstein often improvised on violin. Here's a
| search result[0].
|
| > Einstein's violin playing took a gypsy turn when he
| improvised, often while thinking about mathematics. He was a
| very good musician. He could navigate the piano well enough.
| But his real love was for the violin. Even so, Einstein's
| violin playing was not of the first rank. Yet such was his love
| for the violin that he played and practiced anyway. Such is the
| spell that musical instruments cast on people's minds.
|
| > In addition to studying the classic violin pieces of Bach and
| Mozart that he adored, Einstein was also given to
| improvisations. Some have told of the haunting, gypsy-like
| quality of these rhapsodies. Einstein himself stated that many
| of his greatest mathematical ideas came when he was improvising
| on the violin.
|
| [0] https://pianobynumber.com/blogs/readingroom/einsteins-
| violin...
| Rochus wrote:
| > _Einstein often improvised on violin_
|
| Improvisation has little to do with music theory; most Folk
| and Jazz music is improvised; even what we know today as
| "classical music" was often improvised in the past; many
| great composers were also great improvisers.
| danShumway wrote:
| Jazz theory is a way of condensing down and describing to
| each other what a collective group of musical geniuses did
| across multiple years.
|
| I don't think theory is strictly necessary, there are great
| musicians who don't know anything about theory. Theory
| should never be used as a way of gatekeeping or deriding
| people's efforts to build things. However, unless you are
| also a musical genius who has spent decades honing your
| craft, there will probably be some benefit from learning
| from the people who came before you.
|
| It's not necessary essential, but very little theory is
| essential. You can technically be a great game designer
| without ever looking at other games, you can technically be
| a great UX designer without learning UX rules. The rules
| just make it _much, much_ easier to get to that point --
| because the rules allow you to more quickly learn from a
| large body of extremely talented individuals who shaped the
| entire genre.
| watwut wrote:
| Wut? Jazz is heavy on theory from the start precisely to
| facilitate the improvisation. You need theory to improvise,
| basically.
|
| You do not need theory to perform existing pieces all that
| much. Which is why you can learn to play classical music
| while ignoring theory.
| Rochus wrote:
| Music theory is always "after the fact"; it's a way to
| teach people what their idols did, even if the idols
| didn't know or didn't apply the theory. To improvise you
| first of all require musical talent on both harmonic and
| rhythmic dimensions, and you need practice. Theory might
| help, but it is not a prerequisite.
| watwut wrote:
| This is not even true across history. "The idols" in jazz
| did knew and did applied theory.
|
| > To improvise you first of all require musical talent on
| both harmonic and rhythmic dimensions
|
| I mean, you need ability to keep rhythm and play notes.
| But beyond that, you absolutely can get away with theory
| only with basically zero special talent. You wont become
| world famous, but you will be able to match what the rest
| of group is playing.
|
| > even what we know today as "classical music" was often
| improvised in the past; many great composers were also
| great improvisers.
|
| Also going back to original comment, you seem to put
| theory and improvisation into some kind of dichotomy.
| But, both being great composer and great improviser are
| heavily facilitated by understanding theory.
| jseban wrote:
| Yeah it's not true at all, just look at russell's lydian
| chromatic concept for example, and how much new ideas for
| jazz and improvisation that it spawned. Theory does not
| only come after practice. Oh how I wish people would stop
| venting their fantasies of the god gift whenever the
| subject of music comes up
| Rochus wrote:
| > _" The idols" in jazz did knew and did applied theory_
|
| When jazz music appeared, there were no conservatories or
| theory for it. The first jazz conservatories emerged
| fifty years later. Today they find many graduates, for
| example, from Berklee. But this is a development that has
| only begun in the last forty years. It didn't make the
| music better, it just made it different.
|
| > _You wont become world famous_
|
| Very very few world famous exponents of popular music
| have a formal musical education.
| lewispollard wrote:
| > When jazz music appeared, there were no conservatories
| or theory for it. The first jazz conservatories emerged
| fifty years later.
|
| Yes, to study the tropes and patterns of theory applied
| by the great jazz musicians, who certainly knew what they
| were doing with theory, even if "the theory of jazz"
| didn't exist. You don't have to know "jazz theory" in
| order to use theory to create a new genre of music that
| became known as "jazz". There were a community of
| performing musicians who had at least some formal theory
| knowledge (if not to a rigorous Berklee standard), who
| shared ideas and patterns and tropes, which eventually
| became a recognised genre, and later on an academic field
| of study.
|
| It's funny, because out of all the niche subgenres of
| music out there today, jazz is almost certainly one of
| the most "theory influenced" genres of the last century.
| jseban wrote:
| > Very very few world famous exponents of popular music
| have a formal musical education.
|
| This is just false. If you start to dig into this a
| little bit, you will easily find connections between
| almost all famous musicians, and universities. If they
| didn't have formal education themselves, they often had
| private lessons from someone with a degree. Or someone in
| the band had a degree etc. Or in the case of the beatles,
| the "producer" just happened to be a trained composer who
| was giving a lot of "suggestions".
|
| Other examples: punk band green day songwriter billie joe
| had 15 years of lessons with a jazz guitarist with a
| university degree. Bluegrass guitarist tony rice had
| private theory lessons with a berklee graduate. etc etc.
|
| It's part of the marketing to downplay the theory and
| knowledge involved, people want to relate to musicians,
| and not feel like their being outsmarted, or manipulated
| by "some formula".
| Rochus wrote:
| > This is just false
|
| Are you from the industry? I am, with forty years of
| experience under my belt. Believe me, there is no
| correlation between success and formal musical education.
| acjohnson55 wrote:
| I think their point is more that in many cases, you can
| trace the chain of direct influence to someone with
| formal training, even if the musicians themselves don't
| have it.
|
| Obviously, there are also plenty of artists who only have
| this influence indirectly, through other artists that
| inspire them. Or in the case of hip hop and electronic,
| through sampling. So I think their point was overstated.
| sornaensis wrote:
| Jazz theory came decades after jazz.
| danShumway wrote:
| That's why jazz theory is valuable, sometimes people
| don't want to spend decades re-learning things that other
| people have already learned.
|
| Also, I'm just plain not as good a musician as, say, Duke
| Ellington was, and there's a benefit to being able to
| understand what he was doing so I can try to imitate that
| style and incorporate his techniques into my own playing
| -- I don't want to rediscover all of his lessons
| completely on my own because I'm not talented enough to
| do that; very few people are.
| lewispollard wrote:
| Yes, to describe and group together the specific music
| theory elements that jazz musicians tended to use:
| sevenths, avoiding triads, modulation, etc. Not because
| there was no theory intentionally used in jazz music. If
| you think those guys didn't know what they were doing...
| lewispollard wrote:
| Good luck improvising without any theory knowledge,
| especially against a backing band.
|
| Pro folk musicians are some of the most theory adept people
| I know, my uncle is one and he knows 1000s of songs, and
| can basically play any song in any key through his theory
| chops.
|
| Jazz musicians... I mean, cmon, Jazz is all about doing
| wild things with theory that surprise and amaze you. Good
| luck being a jazz musician without understanding seventh
| chords, modal/metric modulation, etc.
| Rochus wrote:
| No problem if the band operates on known pieces, even
| possible when the band is from another culture and the
| specific pieces are not known to the improviser.
| lewispollard wrote:
| Yes, but how does the improviser know which notes are
| concordant and which dissonant against the chords of the
| known song without theory? How do they know how to create
| tension and resolution within the harmonic/melodic
| progression?
|
| Improvisation doesn't mean "making up random stuff", it
| means knowing your instrument and the ways in which
| chords, melodies, harmonies interact, knowing changes and
| progressions, inside out so well that you naturally can
| use that knowledge to come up with something unique.
|
| If what you mean is "some musicians can implicitly
| understand this stuff without knowing the academic
| language", well yeah, music theory isn't prescriptive,
| it's a language used to communicate with other musicians.
| You can get away without knowing the terms, but knowing
| what it's _describing_ is important.
|
| Edit: I should add, knowing what it's describing is
| important up until the point that you want to readily
| communicate with other musicians and have them
| communicate with you with full understanding, as quickly
| as possible, sometimes during performance - then the
| language of music theory becomes very useful.
| Rochus wrote:
| > _how does the improviser know which notes are
| concordant and which dissonant against the chords of the
| known song without theory?_
|
| A skilled/talented musician just hears that. It's like
| cooking: a good cook knows from experience which spices
| go with which dishes, without having to know the basic
| physics.
|
| > _making up random stuff_
|
| It always has random components, that's how humans
| operate; but good improvisers can produce music in real-
| time which sounds like composed/arranged music; the
| purpose of music is to entertain and please people; this
| goal can be fully achieved without any theory or prior
| arrangement.
| lewispollard wrote:
| But music theory isn't on the level of _physics_ , it's
| not what music is _made of_ , it's more like a recipe -
| yes, you can intuitively cook a dish from experience, but
| at some point if you want to communicate that with others
| you have to write down the names and quantities of the
| things you're using, the temperatures and timings, and so
| on. And knowing lots of recipes allows you to much better
| understand how to tweak and improvise on your existing
| knowledge by adding new elements or substituting
| ingredients.
| Rochus wrote:
| There is a famous quote from Goethe, that aptly describes
| the situation: " _Wenn ihr 's nicht fuhlt, ihr werdet's
| nicht erjagen_"
|
| > _And knowing lots of recipes allows you to much better
| understand how to tweak and improvise on your existing
| knowledge_
|
| Sure, practice is helpful. And it is to be hoped that the
| conservatories are also helpful for something, if society
| invests so much money in them and so many professional
| musicians come out of them.
| parenthesis wrote:
| It's both.
|
| Last night I was improvising a melody based on a chord
| progression I had just come up with. I heard the chord
| progression in my head without thinking about what the
| chords were. But then when I thought about it, I knew
| what they were, tested on my instrument, and wrote them
| down.
|
| Beginning to melodically improvise on the progression
| (with no backing) I was initially looking at my chart the
| whole time and thinking in theoretical terms. But, before
| long, I was having moments of losing track of where I was
| in the chart, but my mind's ear and my fingers still knew
| what to do to keep going within the harmony.
|
| I.e., you reach a point where you have internalised the
| sound of the chord changes, and you can just hear the
| lines you want to play, and your fingers just know how to
| play the notes that you hear.
|
| But to get to the point of being able to do that in a
| reasonably sophisticated way, one is mightily helped by
| thinking about things and practising things in a theory-
| informed way.
| Rochus wrote:
| An experienced musician with improvisation skills doesn't
| have to write down chords to be able to improvise. If you
| have a look at the non-academic music culture as you can
| still find it e.g. on the country side or in other
| popular music pieces are passed on by playing them and
| having the other musicians play along with them and
| repeat them. Music theory can be helpful, but it's not a
| "conditio sine qua non".
| parenthesis wrote:
| Oh, absolutely. In fact, I can recall improvising over a
| song purely by ear, and then coming up with some worse
| lines once I'd worked what the chords were and written
| them out.
| Kye wrote:
| Music theory is both the languages of music and the formal
| study of those languages. Improv musicians communicate with
| _something_ , and it often looks like the body of music
| theory around that tradition because the body comes from
| the tradition.
|
| Trying to separate theory from its basis is folly. Like the
| scientific method and the body of scientific knowledge,
| it's important to remember one follows the other, but I'm
| still employing centuries of science every day even if I
| can't name it all.
|
| Jazz musicians who can't cite theory don't use 7ths by
| accident.
| Rochus wrote:
| That's a very academic perspective which I cannot share
| as a musician. Music needs no formal specification to
| exist. It's like a language, but a language for
| emotional, not rational communication. Btw. science
| exists by itself as well and doesn't depend on a
| "scientific method". Like in music, philosophers tried to
| understand how science works after the fact, and there is
| a plethora of philosophic optinions how science works.
| And we can pretty well do science without caring much of
| all those opinions. The same applies to music.
|
| > Jazz musicians who can't cite theory don't use 7ths by
| accident.
|
| I don't understand this argument. It's unavoidable to use
| 7ths, regardless whether the musician can name the
| interval or not.
| Kye wrote:
| I think we're closer than you realize, and I just did a
| poor job laying out my position. Unfortunately, I lack
| the language to get closer to what I mean.
| wcarss wrote:
| My very amateur musician take: it can have little, or it
| can have a lot.
|
| One way to 'improvise' is to have an understanding of the
| relationships between keys and while moving around at
| pleasing intervals and making interesting chords, regularly
| jump keys at points where they overlap -- that's .. pretty
| music-theory driven, and can be very mathematical! There's
| a lot of fun math in jazz.
|
| It's not the only way to improvise, certainly. But someone
| who knows the rules can make them run a long way.
| Rochus wrote:
| Improvisation is like talking. Not all people can do it
| equally well, and you learn to speak as a child without
| theory, and without knowing or being aware of the
| physiological or physical processes, or the syntactic or
| semantic features of language. You can listen to
| discussion groups and be well entertained without the
| speakers following any script or theory.
| jseban wrote:
| Can you give an example of a master speaker who doesn't
| know how to read or write, and are completely ignorant of
| grammar and how language works? And can you really say
| that one such example would make speaking mostly
| unrelated to language theory?
| Rochus wrote:
| Did you learn to read or write and the grammar and how
| language works before you learned to talk?
| jseban wrote:
| Of course your first exposure is not formal education,
| but the things I picked up by ear, the speakers had
| learned in formal education. Nobody becomes an expert in
| a field, completely detached from the existing body of
| knowledge. You could learn it only by immersion if you,
| for some reason, really want to avoid formal education,
| but you're still using an existing body of knowledge,
| even though mentally you might not call things "adverbs".
| And the likely, going that route will be much longer and
| harder, and also put a limit on how far you can go.
| Rochus wrote:
| Well, you didn't learn to talk on your own, but from your
| parents and other people around you. It's the same with
| music.
| lewispollard wrote:
| Right, and when you asked your parents/teachers/those
| around you about aspect of the language you were
| speaking, did they tell you to not worry about it and
| just feel it? Or did they explain, well this part of
| grammar is called an X, and we use it to modify Y, which
| in turn is a part of Z - such that you could better
| understand it, communicate it to others better, and
| generalise the specific thing you'd intuitively learned
| to a wider aspect of language?
| trasz wrote:
| Ever tried to explain (or learn) when to use word "the"
| using grammar rules?
|
| Some of the grammar rules are sometimes useful to general
| public.
| Rochus wrote:
| > _Are the people good at one also good at other? do
| mathematicians understand musical theory better than those that
| have no background in math_
|
| Music and music theory are two different things. A person who
| is an expert in music theory is not necessarily a good musician
| and vice versa. There are approaches to music theory based on
| mathematics (see book list below); here at the latest, your
| assumption is likely to be correct, but hardly in general.
|
| Book list:
|
| Mathematics and Music - Composition, Perception, and
| Performance
|
| Musimathics Volume 1 and 2
|
| Music and Mathematics - From Pythagoras to Fractals
|
| Mathematical and Computational Modeling of Tonality - Theory
| and Applications
| taubek wrote:
| Yeah, I meant music theory. Playing a music instrument is a
| skill that can be learned (if you have what it takes :) ).
| watwut wrote:
| Music theory can be learned too. I mean, there is not other
| way how to get it then by learning.
| Rochus wrote:
| > _Music theory can be learned too_
|
| Sure, but it's an add on. Music theory is developed after
| the fact by analyzing music created by people who
| (mostly) didn't know the theory. It's a (more or less
| useful) means to understand what the original creator
| did.
| nescioquid wrote:
| For Western classical music, this is often claimed and is
| probably only a little true these days (e.g. Schenker is
| truly post facto, though illuminating).
|
| However, the theory really was deeply tied to the
| practice of composition and performance. One of the first
| exercises Mozart set his composition students was to
| write out various cadences. Likewise, Bach started his
| pupils with voice-leading. Theory was also needed for
| various forms of performance -- look at any manual on
| continuo playing (this is where the figures on roman
| numeral notation come from). Handel wrote a manual on
| continuo playing in which he touches on how to improvise
| a fugue!
| rotten wrote:
| There is also "The Geometry of Musical Rhythm"
| gjulianm wrote:
| I have a degree in mathematics and have studied music for some
| years. My personal opinion is that they're quite different
| things. Yes, the underlying theory of music requires some
| mathematics, but that's it. Once you get into it there's much
| more "feeling" and "intuition" and "subjectiveness" than math
| could ever accept.
| dan_mctree wrote:
| When I listen to the three sinewaves, two of which are supposed
| to feel more similar because they a factor two apart, I don't
| actually get any such similarity effect. They all seem just about
| equally similar to each other, even when played together. Is
| everyone here picking this sameness up? I'm curious what kind of
| mechanic underlies those feelings of sameness and what it feels
| like.
| OscarCunningham wrote:
| Right. Octaves sound consonant because the harmonics of one
| note line up with the harmonics of the other. Without the
| harmonics you expect to hear no effect.
| whiddershins wrote:
| Its very hard to hear this with sine waves.
|
| Sine waves work to visualize the concepts but real instrument
| notes almost always are better modeled as a large number of
| sine waves with a mathematical relationship that sound
| simultaneously and in varying amplitudes that combine to create
| the _timbre_ of the note.
|
| Then when those notes sound together we get combinations of all
| those sine waves together to create a very complex wave that
| sounds a certain way to our ear based on the interactions
| between _all_ of these waves at once.
|
| So to visualize it or reason about it, my comment here makes
| sense:
|
| https://news.ycombinator.com/item?id=30363653
|
| But to _hear_ it you would be much better off with triangle or
| sawtooth waves or samples of actual musical instruments.
| dataspun wrote:
| As an amateur musician (and amateur nerd) I found this article to
| be insightful in many ways. The author's opening disclaimer
| renders most of the HN criticism moot.
| srcreigh wrote:
| > I don't know why twelve in particular has this effect, or if
| other roots do as well
|
| Here's a 31-equal temperament song. Microtonal music has a
| reputation for sounding bad, but it doesn't have to.
|
| https://www.youtube.com/watch?v=u-PEhbSOh74&list=PLC6ZSKWKnV...
|
| > ... but it's probably why Western music settled on twelve.
|
| The curious part is that Western music settled on twelve a long
| time before equal temperament. They used to have 12 notes but use
| for example quarter-comma meantone. Great mozart meantone piano
| piece (mozart never used equal temperament):
|
| https://youtu.be/lzsEdK48CDY?t=700
| hammock wrote:
| What am listening to? Long time musician here, just not
| familiar with untraditional scales. I assume 31edo but using
| Bach means you are ignoring 19 of 31 possible semitones-
| correct? Less? (I could imagine leading tones going in the
| opposite direction, or something)
|
| To my ear it sounds like there are way more major thirds than
| there normally would be in a Bach piece like this... anything
| else I ought to be hearing?
| srcreigh wrote:
| I would guess you're right but I'm not 100% sure! This
| channel is pretty responsive, you ask on the video.
|
| This one is fascinating too - it's just intonation vs 12edo
| comparison. You can really hear all the beating in the
| harmonics in the EDO one.
|
| https://www.youtube.com/watch?v=AgB4TrV57AU
| [deleted]
| lewispollard wrote:
| I haven't listened to the piece, but afaik typically
| transposing existing 12TET pieces into microtonal tunings are
| taking the intervals in the original piece and applying them
| to scales in the new tuning, with some creative license/taste
| to embellish where it doesn't sound so good. So it's not
| ignoring or limiting any pitches to my (limited)
| understanding, other than the natural way that pieces written
| in a particular key/mode will skip over some tones in favour
| of others for harmonic or melodic reasons.
| jacquesm wrote:
| Interesting, that sounds like music from some kind of medieval
| castle that somehow got stuck in a timewarp. I can't listen to
| it for very long but it sounded a lot better than I thought it
| would.
| streamofdigits wrote:
| > That problem is that sheet music is terrible.
|
| Something that people with casual exposure to musical notation
| probably don't know is that before the standard 5-staff notation
| became ubiquitus there were quite a few alternatives, maybe the
| most interesting from a mathematical perspective being the
| Byzantine notation
|
| Broadly speaking, while the modern system focuses on pitch
| _values_ and an elaborate (modulated) map from frequency space to
| physical space (paper), older systems used in the Byzantium used
| "deltas" or the first differences of pitch values.
|
| So you start with a base note (lets say C) and then you go +1,
| +1, -2 to indicate pitch changes (in semitones). This is quite
| well adapted to monophonic chant. This notation was never
| developed to cope with the complexity of modern music but its not
| immediately obvious that it can't be done
|
| There is no easily accessible exposition of this musical notatin
| style, this cheatsheet gives a flavor
| http://www.byzantinechant.org/notation/Table%20of%20Byzantin...
| throw7 wrote:
| "This has got to be some of the worst jargon and notation for
| anything, ever."
|
| Ummm, do you math? ;)
|
| My point of view of music theory is: sound is objective. music is
| subjective. where the two meet is music theory.
| H8crilA wrote:
| Yeah, no, modern math notation is a lot cleaner than musical
| notation, and completely free of historic conventions.
|
| Pretty much the only thing "forced" into it by human preference
| is the standard of using base-10 numbers.
|
| Prove me wrong please :)
| KineticLensman wrote:
| > and completely free of historic conventions
|
| > Prove me wrong please :)
|
| Some of the notation goes back centuries [0]. Our current
| representation of calculus reflects a convention that was
| hammered out following significant disputes in the early 18th
| Century.
|
| [0] https://en.wikipedia.org/wiki/History_of_mathematical_not
| ati...
| navane wrote:
| Why did we settle on 12 notes?
|
| Rule 1 (also stated in the article): Doubling frequency gives us
| practically the same note. It is so pleasant together with the
| original note, that it is boring.
|
| Lets make a set of notes that sound nice together, and are more
| or less equally distributed between a note and its frequency
| double (octave).
|
| The next most pleasant note, is a note with 3 times the
| frequency, then 4, etc...
|
| (Why is this pleasant? Because its a close natural harmonic. When
| you vibrate a string with frequency 1, it will start vibrating
| with a frequency of 2 as well, but softer. This doubling in
| frequency is because the string will behave both as a string with
| length L, and as two separate strings with length L/2. Because
| the length is halve, the frequency is doubled.)
|
| Now, 3 times the frequency, is the same as 1.5 times the
| frequency. If we do the same from that base note, we get 1.5 *
| 1.5 = 2.25 times the frequency. You could decide that that 2.25
| is close to 2, call it a day, and settle on a two note scale.
|
| Or, you go further. 2.25/2 = 1.125, so now we have the notes 1,
| 1.125, 1.5 and 2. Not really evenly spaced yet.
| 1.125*1.5=1.6875...: [1, 1.125, 1.265, 1.5, 1.687, 1.89]. Oh,
| 1.89 is almost 2. Let's call it a day and settle on a five note
| scale. (there are plenty of cultures with a five not scale folk
| music tradition).
|
| Note that the error gets smaller, it was 2.25/2 for our 2 note
| scale, it's 1.89/2 for the 5 note scale. Now it happens that the
| next smallest error is with a 12 note scale. But there's still an
| error, you don't arrive at exactly 2. The intervals between your
| notes are not even, and your last interval is all retarded.
|
| That's why people settled on "equal temperament", where all the
| intervals between the notes are made equal, and the number 12
| looks seemingly arbitrary.
|
| I did the math, see table below. The first column are the
| frequency of the notes, with base frequency 1, where I multiplied
| by 1.5, and divided by 2 to keep the notes between frequency 1
| and 2. The 4th column gives you the "error", how close is the
| last note of the scale, to the octave of the base note. The
| closer it is, the better, it means we have an equally divisible
| range of notes that all have nice (with ratio 1.5) intervals with
| each other.
|
| The arrows indicate where we could stop adding notes to our
| scale, because we arrived at a local optimum: a five not scale is
| small but has quite an error. The 12 note scale is quite
| elaborate, but reduces the error a lot. The next best scale would
| be a 41 note scale, with only a slightly diminished error
| compared to the 12 note scale. Freq. n/1 2/n
| min(n/1;2/n) 1.500 1.50 1.33 1.333 1.125 1.13 1.78
| 1.125 1.688 1.69 1.19 1.185 1.266 1.27 1.58 1.266
| 1.898 1.90 1.05 1.053 <-- (5 notes) 1.424 1.42 1.40 1.405
| 1.068 1.07 1.87 1.068 1.602 1.60 1.25 1.249 1.201
| 1.20 1.66 1.201 1.802 1.80 1.11 1.110 1.352 1.35
| 1.48 1.352 1.014 1.01 1.97 1.014 <-- (12 notes)
| 1.520 1.52 1.32 1.315 1.140 1.14 1.75 1.140 1.711
| 1.71 1.17 1.169 1.283 1.28 1.56 1.283 1.924 1.92
| 1.04 1.039 1.443 1.44 1.39 1.386 1.082 1.08 1.85
| 1.082 1.624 1.62 1.23 1.232 1.218 1.22 1.64 1.218
| 1.827 1.83 1.09 1.095 1.370 1.37 1.46 1.370 1.027
| 1.03 1.95 1.027 1.541 1.54 1.30 1.298 1.156 1.16
| 1.73 1.156 1.734 1.73 1.15 1.153 1.300 1.30 1.54
| 1.300 1.951 1.95 1.03 1.025 1.463 1.46 1.37 1.367
| 1.097 1.10 1.82 1.097 1.646 1.65 1.22 1.215 1.234
| 1.23 1.62 1.234 1.852 1.85 1.08 1.080 1.389 1.39
| 1.44 1.389 1.041 1.04 1.92 1.041 1.562 1.56 1.28
| 1.280 1.172 1.17 1.71 1.172 1.758 1.76 1.14 1.138
| 1.318 1.32 1.52 1.318 1.977 1.98 1.01 1.012 <-- (41 notes)
| cartucho1 wrote:
| I'm far from an expert on the subject, but I think this is a
| better explanation than the author's of why we settled on a
| 12-note scale.
|
| However, the history of the adoption of "equal temperament"
| (distributing the .014 "comma" equally among the twelve notes)
| is more complicated. In fact, many classical composers used
| other systems for distributing it (called "temperaments").
|
| In those other temperaments, transposing a music piece to
| another tonality (i.e. moving every note upwards or downwards
| by the same amount, for example, changing every C to a D, every
| D to an E, etc.) didn't sound "the same, but starting from a
| different place", it changed the piece more substantially (e.g.
| it might make it sound brighter or darker in character).
| andrewzah wrote:
| Ultimately a lot of things around music are cultural and/or
| arbitrary. It's like languages in that sense. Personally I don't
| find this sort of analytical study to be that helpful for
| actually playing or improvising music, but it is neat
| information. You don't have to clinically study grammar and
| language theory in order to be a great writer; it's the same with
| music.
|
| Something that's very important to note is that music theory and
| playing music are very different. Music theory allows us to
| understand what someone played, and lets us communicate to other
| musicians in a compact manner. Theory by no means imposes rules,
| unless you are specifically wanting to write music exactly like
| Bach or something.
|
| As a logical-minded person myself, it's tempting to really dive
| into theory and the root of things, but I've found that it's a
| trap most of the time. For getting better at songwriting or
| composing, I've found the best thing to do is transcribe the
| songs you like (or portions of them) and see what they do, then
| incorporate those ideas into your own playing.
|
| I also get the frustration around enharmonics (e.g. C# vs Db),
| but honestly it's not an issue in practice. I had no opinion
| until I started typesetting songs myself, and it just looks
| cleaner to sometimes have Cb or B# depending on the context. The
| circle of 5ths also neatly puts scales in the order of how many
| sharps or flats they have. Also, C# is not a commonly used key
| anyways.
|
| From a theoretical perspective C major and A minor share the same
| notes, but when I improvise I do find the distinction meaningful.
| Having multiple ways to think about things is helpful. There are
| other things too: C minor 7 is the same as Eb major 6. Or if you
| play a rootless voicing, the harmony could be ambiguous. Etc.
|
| Yes, our music notation system has some issues. But this article
| is overanalyzing it from an armchair. It's mostly fine in
| practice.
| cousin_it wrote:
| The article says: 0 1.000 = 1:1
| (unison) 1 1.059 (semitone; minor
| second) 2 1.122 [?] 1.125 = 9:8 (whole tone; major
| second) 3 1.189 (minor third)
| 4 1.260 [?] 1.250 = 5:4 (major third) 5 1.335
| [?] 1.333 = 4:3 (perfect fourth) 6 1.414 7
| 1.498 [?] 1.500 = 3:2 (perfect fifth) 8 1.587
| (minor sixth) 9 1.682 [?] 1.667 = 5:3 (major sixth)
| 10 1.782 (minor seventh) 11 1.888
| [?] 1.889 = 17:9 (major seventh) 12 2 =
| 2:1 (octave)
|
| This table has many omissions and some errors. The way people
| usually play these intervals on just intonation instruments,
| minor second should be 16:15, major second can be 9:8 or 10:9
| depending on context, minor third is 6:5, minor sixth is 8:5,
| minor seventh can be 9:5 or 16:9 (or 7:4 in barbershop), major
| seventh is 15:8.
| kmill wrote:
| You might like the book "Equal Temperament Ruined Harmony." It
| makes the case that there is a long history of differentiating
| sharps and flats in western music (flats are just a bit sharper
| than sharps), while arguing that in practice the whole tone was
| subdivided into nine parts, with the major and minor half steps
| respectively 5 or 4 of those nine parts. I don't think the
| precise tuning system described by the book really happened,
| but it does collect evidence that "enharmonic" used to mean
| "finesse your intonation to make this sharp be that flat."
|
| In my own experimentation, the just intonation intervals are
| jarringly perfect, and I'd say that the 5:4 major third is too
| narrow. Has anyone checked that barbershop quartets are
| actually singing such narrow major thirds? My understand is
| that many studies have shown that string instrumentalists and
| singers, even when they claim to be using just intonation, play
| their major thirds somewhere between 5:4 and equal temperament.
|
| It's also extraordinarly difficult to really tune basic harmony
| justly. The ii V I progression is a fun one... if you're not
| careful you shift the tonic by a syntonic comma.
| cousin_it wrote:
| I don't think it's very difficult. In the ii-V-I, slightly
| shifting the root of the ii sounds fine, and most other
| problems can be solved similarly. I've made plenty of music
| in just intonation, here's a recent example:
| https://www.youtube.com/watch?v=qkUs-BdxtN8 To me it sounds
| like very standard harmony, but "cleaner".
| tshaddox wrote:
| > Has anyone checked that barbershop quartets are actually
| singing such narrow major thirds?
|
| I don't know if anyone has checked, but why wouldn't they
| want to? Surely the low integer ratios are best going to get
| the intended sound of barbershop harmony, unless there are
| other acoustic reasons why slightly changing the intervals
| would work better (something akin to octave stretching in
| pianos, although I'm not sure that sort of thing would be as
| relevant to barbershop harmony).
| kmill wrote:
| That's a nice thought in theory, but I can assure you that
| string quartets do not play 5:4 major thirds -- they're
| significantly sharper (but not quite equal tempered major
| thirds).
|
| There's more to music than acoustics. Four-part harmony has
| a lot of moving parts (literally and figuratively), and you
| have to make concessions to acoustically pure intervals to
| make it sound like it's in tune through time.
| tshaddox wrote:
| But I was talking about barbershop quartets and the
| specific sound they are generally going for based on my
| experience with and impression of that genre. I don't
| know much about string quartet music so I wouldn't wager
| a guess about what they do.
|
| My impression of barbershop harmony is that they're not
| particularly concerned with how the _melodies_ are tuned.
| I don 't think there's much deliberate intention there,
| other than that you obviously don't want frequencies to
| drift too much throughout a song because you want to be
| in the right ranges for each vocalist. Barbershop harmony
| seems much more concerned about the "vertical" tuning and
| my hypothesis is that they do tend to hit very close to
| the low integer ratios. Can you think of a reason they
| wouldn't intend to do that? The harmonies tend to be
| pretty close (unlike a piano) and I would guess that the
| human voice is less inharmonic than piano strings
| (although bowed string instruments are very harmonic,
| right?).
| kmill wrote:
| I brought up string quartets because I know about tuning
| them, and, like barbershop quartets, it's 4-part harmony
| with extremely harmonic instruments. Bowing a string
| causes a phenomenon called "mode locking," where the
| normally somewhat inharmonic strings are forced to be
| harmonic (my understanding is the human voice also
| exhibits mode locking). You often do microadjustments to
| get chords to sound good vertically and horizontally.
|
| I pulled up a random barbershop recording and looked at a
| spectrogram for the final chord, since the final chord is
| supposed to ring as much as possible, and there are
| _only_ vertical considerations, so you 'd presume they'd
| tune it as justly as possible, right? Here's what I
| found:
|
| They tuned their perfect fifth justly as 3 : 2 almost
| perfectly. That's not unexpected, even equal temperament
| gets perfect fifths close to right (though a little
| flat).
|
| They tuned their major third between 1.253 : 1 and 1.258
| : 1. A just major third is 1.25 : 1, an equal tempered
| major third is about 1.26 : 1, and the 55-EDO system
| mentioned in the book I referenced in my first comment
| would give a major third of about 1.255 : 1. Like I
| expected, they tuned their major third sharp with respect
| to just intonation, but still flat with respect to equal
| temperament.
| tshaddox wrote:
| That's interesting. I would leave to see that analysis
| across a lot of performances. I know that barbershop
| folks often say to "aim high" or "sit on top of" your
| major thirds, but I always thought that's simply because
| it sounds really bad to be even slightly flat.
|
| What's the theory behind why string quartets aim slightly
| sharper than 5:4? Is it something to do with
| inharmonicity or acoustics? Could it also have something
| to do with avoiding going flat? Is it possible that
| listeners are so accustomed to equal tempered thirds that
| a 5:4 third actually sounds flat?
| kmill wrote:
| I can't say I fully understand it, but having compared
| major triads with different intonations, I can only say I
| myself find slightly sharper thirds to sound nicer in
| chords. Here's one thing I've used:
| http://tmp.esoteri.casa/interval-test.html (5-limit is
| "just intonation", Pythagorean uses 81 : 64 for the major
| third, 1/6-comma meantone is 55-EDO, and 12-EDO is
| standard equal temperament.)
|
| One thing I like is that the slight dissonance takes the
| edge off the ringing. I find that to be a rather strong
| flavor.
|
| The book I mentioned offered suggestions why sharper
| major thirds are used, but I don't remember there being
| anything convincing other than observations about how
| harmony works. Maybe your thought that going too flat
| sours the third makes sense: if it's sharp, you have a
| little more freedom to adjust your intonation without
| accidentally going flat. Plus, thirds are fairly
| forgiving anyway since they're corresponding with the
| fifth harmonic, which over two octaves higher.
|
| It's worth mentioning that the Pythagorean major third is
| about 1.266 : 1, which is quite sharp, yet it's still
| just intonation since it's from going up by 3 : 2 fifths.
| zozbot234 wrote:
| This is true, there are even "comma pump" sequences that
| are literally impossible to play fully harmonically,
| being inherently based on conflating "close" ratios! (I
| think in theory, a very detailed Schenkerian-ish analysis
| of a piece would tell you quite a bit about _where_
| ratios should be made "nicer" and where they shouldn't -
| but that's a lot of work and involves a whole lot of
| personal judgment.)
| kmill wrote:
| I think one of the reasons ii V I is so compelling
| (versus IV V I) is that the ii (or ii7) is conflating
| many notes. In C major, using interval terms as a stand-
| in for "tuned justly":
|
| Is the D a fourth below G or a minor (or harmonic)
| seventh below C? Once you've chosen your D, is A a
| perfect fifth above it? If so, what kind of major second
| relation does it now have to G?
|
| Is the F a perfect fourth above C, or is it a major third
| above your D? Or is it supposed to be the minor (or
| harmonic) seventh above G?
|
| I think barbershop tends to skirt these questions by
| instead using a II V I progression (a secondary
| dominant), since the F# doesn't have to stand in careful
| relation to other notes of the plain C major scale.
|
| (That's interesting Schenkerian analysis can help
| understand these issues. I know only about it at a very
| thin surface level.)
| zozbot234 wrote:
| I suppose a good rule of thumb is that "dissonant" notes
| (in the musical syntax sense) should be in a harmonic
| relation with the scale step they will ultimately resolve
| into - so D to C, A to G, F to C etc. This can and will
| create roughness in the vertical dimension, but that
| actually reflects their unstable "energy" that drives
| them to resolution. Of course one could just as well use
| microtonal shifts to play with this kind of stability
| whenever longer-range relations are involved. Perhaps
| this is part of what good performers do intuitively when
| playing a melodic instrument. The relevance of music-
| syntactical dissonance and resolution is what might make
| Schenkerian analysis a very useful tool to understand
| these possibilities!
| whiddershins wrote:
| I love this style of clear, unambiguous writing starting with no
| knowledge assumptions.
|
| [but] The author is missing or skipping key pieces of information
| about why we use the notes we use, how they were derived, and why
| they sound the way they do to us.
|
| Edit. There was zero sarcasm in my comment. I really love this
| style of writing.
|
| The missing concept here is the harmonic series. A pitched note
| is not generally a sine wave, it is properly modeled as a series
| of sines waves combined. These sine waves go up in mathematical
| multiples.
|
| So say we have a note at 100hz. Simplistically it is actually
| 100, 200, 300, 400 etc all at once. So if 100 were A, 200 is A,
| 400 is A, 300 is ... E, so 150 is E. Etc.
|
| None of this is arbitrary because the When the waves combine the
| result is more ordered or more chaotic, depending on the ratios
| of the waves, which our ears hear as consonant or dissonant.
|
| Best I can do from a phone.
| H8crilA wrote:
| This explains why the ear "likes" simple fractions, because
| then the harmonics in the notes will be overlapping more.
| whiddershins wrote:
| Yes. For a slightly more complicated explanation:
|
| When two patterns are overlayed there is a third pattern
| which is the interference of the two patterns, or a pattern
| of the sums and differences of the two patterns.
|
| If the first two patterns have a simple fractional
| relationship you can visualize the resulting pattern in your
| head, and the brain when hearing perceives this as
| predictable and regular, and predictability is boring and
| sounds consonant.
|
| If the fractions are more complicated we end up with a more
| complex combined pattern which is harder for the brain to
| predict and is perceived as richer or more dissonant.
|
| If the patterns get very far from the fractional relationship
| (for example If an instrument is out of tune) these patterns
| start to feel non deterministic or non repeating to the brain
| and we tend to hear this as unpleasant.
|
| If the patterns have no particular mathematical relationship
| we end up with a completely non repeating pattern that is
| indistinguishable to the brain from randomness, and we call
| this unpitched or noise.
| chrisweekly wrote:
| It took a moment to realize your first sentence was derisive
| sarcasm.
|
| From TFA:
|
| > "Here is what I gathered, from the perspective of someone
| whose only music class was learning to play four notes on a
| recorder in second grade. I stress that I don't know anything
| about music and this post is terrible. If you you so much as
| know how to whistle, please don't read this you will laugh at
| me."
|
| ... which makes your comment even more uncharitable and
| unrealistically demanding. As if any mere blog post could
| answer those questions in meaningful depth. IOw, I don't
| understand the point of your complaint.
| whiddershins wrote:
| I was not being sarcastic. The part about how the octave gets
| divided up is just missing some key concepts.
| chrisweekly wrote:
| Ah, ok, thanks for clarifying. (If your 2nd sentence began
| with "But, ", this would have been clear to me.)
|
| PS I love OP's writing style, too. Fearless learning in
| public is to everyone's benefit -- given proper
| disclosure/transparency.
| whiddershins wrote:
| All good. I went back and edited more. I would hate the
| author to think I was denigrating the article.
| buzzwords wrote:
| I have always struggled to learn music theory. If anyone has a
| good source please let me know.
| wildmanx wrote:
| This has about as much to do with "music" as analyzing grammar
| when talking about poetry.
|
| Musical notation, and lots of "rules" that come with it, came
| after the fact. Just like with natural language.
|
| And just like staring at grammar rules is a terrible way to learn
| to speak a new language, analyzing music "theory" at this level
| does not teach you anything about actual music.
| Aidevah wrote:
| Agreed. The author mentioned that the desire to compose music
| is what spurred this post. It would be much quicker to read
| through a music textbook. The basics of western music notation
| can be taught in 15 minutes, and one could get used to it after
| an afternoon. There is no need to interrogate the origins and
| reasons behind conventional notation if creative work is the
| goal, since there are much more important concepts like harmony
| and voice leading which are more worth your time.
| trasz wrote:
| If by "western music notation" you mean the clef and stuff,
| then lol, no. There's a reason most musicians don't use nor
| know it.
| Aidevah wrote:
| The reason most musicians don't use staff notation is
| because most musicians do not need it unless they want to
| engage with the literate tradition of music, and are not
| disadvantaged if they can't. Not because of any inherent
| difficulties in the notation itself.
| zozbot234 wrote:
| > and are not disadvantaged if they can't
|
| Literacy is just as helpful in music as in any other
| artform. One can certainly play and create music without
| learning how to read and write staff notation, but being
| literate can only help!
| lancesells wrote:
| I think even faster is taking whatever instrument you have,
| whether it's physical or digital, and start putting together
| some melodies or notes and making something.
| deckar01 wrote:
| Except the poetry is written in German, but must be read aloud
| in French. This is how I felt as a young trombone player. I was
| playing an instrument that had a nearly linear physical
| relationship with pitch, I was required to memorize the pieces,
| but I was required to translate sheet music in my head during
| practice. It felt like training with one hand tied behind my
| back.
| jacquesm wrote:
| The same goes for the piano keyboard. It's an absolutely
| terrible design for what it tries to do but it is so
| entrenched it will be there long after querty has died.
| zozbot234 wrote:
| The piano keyboard is quite intuitive to many, since it
| physically reflects the complete diatonic scale. Isomorphic
| keyboards may be intuitive as well, but they might pair
| better with a hexachord-based way of thinking with its
| unique half-step _mi_ - _fa_ , and hexachord mutation to
| cope with both "full" diatonicism and
| transposition/chromatic notes!
| jacquesm wrote:
| If you're in the key of C, then yes. But in any other key
| it doesn't work nearly as nice so every chord you have to
| learn many times over. Of course once you have that time
| invested it becomes a barrier to entry for others so
| there is all kinds of inertia at work there.
|
| But have a look at the Janko and other cromatic keyboards
| to see what the alternatives could look like and how nice
| it is to have _all_ version of a chord playable with the
| same fingering.
| zozbot234 wrote:
| > But have a look at the Janko and other cromatic
| keyboards to see what the alternatives could look like
|
| That's the isomorphic keyboard I mentioned. Different
| name, same thing.
|
| > ... But in any other key it doesn't work nearly as nice
| ...
|
| It works nicely enough from a visual POV if you handle it
| via the circle of fifths. The biggest obstacle of course
| is learning basic finger patterns for the new scale;
| that's where isomorphic keyboards could well be
| preferable.
| toolslive wrote:
| Hold on. a C# and a Db are not the same note. They are a comma
| apart.
|
| https://en.wikipedia.org/wiki/Comma_(music)
| commandlinefan wrote:
| Hm - maybe technically, but they _are_ the same on any
| instrument you can play them on.
| rdlw wrote:
| Except for voice [0], any fretless stringed instrument [1],
| any fretted string instrument with separate frets for sharps
| and flats [2], keyboard instruments that allow expression
| [3], keyboard instruments with split flat/sharp keys [4], and
| electronic instruments that allow unorthodox tunings without
| huge hassle [5]... I'm sure I'm missing some, but other than
| that you're totally right ;)
|
| [0] https://youtu.be/XnGqVIW51JA,
| https://youtu.be/mPZn4x3uOac [1] https://youtu.be/PqR36Drhn_k
| [2] https://youtu.be/iRsSjh5TTqI [3]
| https://youtu.be/P14JcRyJCEI [4] https://youtu.be/7GhAuZH6phs
| [5] https://youtu.be/xVZy9GUeMqY
| asdfman123 wrote:
| Everyone knows the C# connects to the DB
| honkycat wrote:
| I read eev.ee's tutorial on platformer physics when doing a
| little gamejam.
|
| Worked great! What a talented person!
| strong_as_oak wrote:
| coldtea wrote:
| > _If we say 440 Hz produces a note called A, then 880 Hz, 220
| Hz, 1760 Hz, 110 Hz, and so forth will also produce a note called
| A. An important consequence of this is that all distinct notes we
| could possibly come up with must exist somewhere between 440 Hz
| and 880 Hz. Any other pitch could be doubled or halved until it
| lies in that range, and thus would produce a note in that range._
|
| That's inaccurate and backwards. 338 Hz is not in that range, and
| it can't be doubled or halved to fit in that, but it's a
| perfectly fine not. The range is more about tuning (which is a
| choice) than about 440-880Hz being something special.
|
| > _All of these things messily overlap and create multiple
| conflicting names for the same things, because they're attempts
| to describe human intention rather than an objective waveform._
|
| Nope, they don't overlap any more messily than 1+2 == 2+1, or in
| how 0.99999... == 1.
| quasisphere wrote:
| 338 * 2 = 676, which is between 440 and 880
| coldtea wrote:
| Yeah, bad wording. 338*2 is in the range, but is nowhere near
| the 12 tones we use when A=440 (and wont be with integral
| doubling or halving). The property "within the range A4=440
| A5=880" doesn't have any particular special musical meaning.
|
| The idea I wanted to convey is that 440-880 is just a
| convention, starting from 440 as concept pitch, but concept
| pitch can be totally different (and outside the range). 432
| is a famous standard which has and is been used today, but
| also tons of others, even widely outside the range...
|
| (also: "but it's a perfectly fine not" --> "note").
| fugalfervor wrote:
| Music was taught as part of the quadrivium (alongside arithmetic,
| geometry, and astronomy), so it has a long history of being
| thought about in mathematical terms. There's nothing wrong with
| looking at music that way. What is so interesting about music is
| its ability to turn mathematical beauty into aesthetic, artistic
| beauty.
|
| Sometimes the math is just there in the background: "This chord
| progression is based on certain physical facts related to the
| harmonic series. That makes it sound good, and I like it".
| Sometimes it is brought to the forefront: "All of this music
| appears to be generated from a short pattern of notes which is
| recognizable even as it is subjected to rotations, elongations,
| truncations, etc. That is beautiful."
|
| Certain types of music play up the lovely-pattern-ness of music,
| and some don't. Neither is better than the other (denigrate the
| art of Justin Bieber who dare), but you can probably guess which
| I prefer :)
|
| Consciousness, pattern-recognition, spatial rotation of abstract
| objects, natural mathematical beauty, poetry, drama,
| acting/performance, nonverbal collaboration, shared rhythm: music
| is a nexus for all of these things. Music is nothing short of
| awesome, in the truest sense of that word.
| holri wrote:
| What is interesting is that master composers often broke the
| "mathematic" rules. Schubert, Beethoven or Chopin for example
| have sometimes very strange and unbelievable beautiful
| harmonics sprinkled in. Whereas mediocre composer do not do
| this, they are predictable.
| fugalfervor wrote:
| I don't think it's helpful to think of music in terms of
| mathematical "rules", but more in terms of cultural variation
| on what is acceptable. Now this is my perspective, after
| spending a long time steeped in this stuff, but feel free to
| disagree: The history of music has been oversimplified and
| done a disservice by its characterization as "great men"
| breaking all the rules. Taken to its extreme, music gets
| better when a greater man breaks more rules. That's obviously
| a little silly if you ask me.
|
| Dissonance (a "broken mathematical rule") has as much a right
| to exist in music as consonance does. There is a constant
| tension between consonance and dissonance, and it is that
| dynamic tension which is exploited for affect or structural
| definition.
|
| So what we have in the case of Schubert, Beethoven, and
| Chopin is not so much the breaking of mathematical rules. In
| my opinion, they are just examples of expert judgment applied
| to the tension and release within an artistic work.
| holri wrote:
| Yes, of course, does breaking the rules not lead to better
| music automatically. But strictly adhering to the
| cultural/mathematical rules seems to lead to mediocre
| results.
| Kye wrote:
| One thing I like to do with my sizable sample library is
| smush different samples together that would be "wrong" by a
| strict, surface theoretical view. There's probably theory to
| explain why two samples in two different non-relative scales
| can sound good together, but I don't know it. And if someone
| knows it, I would like to know! Then I can be more
| intentional and rely less on trial and error.
| howLongHowLong wrote:
| Music theory is descriptive rather than prescriptive. Its
| purpose is not to tell you what sounds good, but to have a
| common language to describe what you've heard.
| calebm wrote:
| My quick notes on music theory: https://calebmadrigal.com/music-
| theory-notes/
| adamnemecek wrote:
| I'm working on an IDE for music composition https://ngrid.io
| ben7799 wrote:
| I guess I fell into the same trap as a lot of others reading this
| and commenting it and having the programmer side of my brain see
| one thing and the musician side see something else.
|
| Computer programs must follow the rules... the rules get made up
| first and the programs get built to conform to the rules.
|
| Music theory isn't like that. The music comes first. The theory
| gets made up to try and describe & understand what is going on
| with the music. It's not at all like a program where the rules &
| theory come first and you build something that fits into that.
|
| If you write a piece of music that doesn't conform to some kind
| of arbitrary rule in music theory that's fine. If your music is
| successful and important enough someone will modify music theory
| to explain why your music was successful and important.
|
| There is a cycle where you learn some music theory to help learn
| music but the theory just helps you understand what's going on,
| it doesn't force you to do anything a certain way. You can't come
| at music and think about it like you're building a computer
| program.
| quaintquant wrote:
| > You can't come at music and think about it like you're
| building a computer program.
|
| I think the absolutionist take here is unproductive.
|
| I would argue a writing a fugue is analogous to "building a
| computer program"; to say little of 12 tone chromatic atonal
| music compositions that usually sacrifice 7 tone based
| harmonies for interesting structure, like palindromic
| reflection of ascending and descending musical ideas, and
| optimising for a high number of pitches in a melody.
|
| Additionally, 7 note diatonic music theory can be completely
| summed up with two statements:
|
| 1) tick-tick-tock-tick-tick-tick-tock
|
| 2) permuate all the things!
|
| Most common western instruments are literally built to only
| play 7 tone diatonic music theory.
|
| Look at a piano. It can literally ONLY play "semi-tones". It's
| impossible to explore music beyond the 12 note chromatic scale
| without first modifiying the physical construction of the
| piano.
| chrisweekly wrote:
| Love it! Learning in public FTW. (I've been making music for over
| 40 years, and some of this gave me a fresh appreciation for how
| convoluted and borderline impenetrable music theory can be.)
| ben7799 wrote:
| He left off right where it starts to get really interesting.
|
| Most of what he covered is stuff you learn the first day playing
| and never really need to worry about again.
|
| The interactions of how different notes & chords in a scale draw
| our ears, how 7ths and other intervals work/sound. Modes, chord
| voicings, inversions, modulations.. all that stuff gets
| incredibly fascinating.
| iamevn wrote:
| (fyi, it's she)
| PaulDavisThe1st wrote:
| > Modes, chord voicings, inversions, modulations
|
| In defense of the article, I'd note that these are all choices
| you make _within_ the framework set up by 12TET, not the
| framework itself.
| mtalantikite wrote:
| > More "fake" notes exist than E#, too; I hear rumor of such
| nonsense as G, "G double sharp", which I would rather call "A".
|
| It starts making more sense when you're working with harmony and
| chords. The wikipedia example section on enharmonic equivalents
| has a nice example of a Shubert sonata that makes use of this
| [1].
|
| [1]https://en.wikipedia.org/wiki/Enharmonic
| [deleted]
| zozbot234 wrote:
| Yes, if you think enharmonic notes are pointless or "fake" you
| should look into the derivation of diatonic and chromatic
| scales via "stacking" fifths, and what that implies for
| modulation along the circle of fifths. Also how sharp and flat
| are often theoretically conflated with _mi_ and _fa_ , since
| both proceed by half-step to their neighbor note.
| abetusk wrote:
| I really don't understand all the hate in the comments for this
| article. This seems like a really fine introduction to a lot of
| the concepts. I had to scour the web a long time before
| understanding that the scales were constructed because of the
| simple/reduced ratio of root note to the others, which is clearly
| spelled out in this article.
|
| Music theory is, in my experience, typically taught as a list of
| facts to remember. Deriving it from first principles, insofar as
| it can be, is not common. This article is attempting to start
| that process.
|
| Some commentators are saying that the article doesn't address why
| we have 12 notes but I wonder if they even know why (one answer
| is because it's a good compromise between number of notes and
| that have simple/reduce ratios to each other [0]). I'm also
| skeptical of music theorists that can't even attempt an answer to
| basic questions about note length frequency, why some chords are
| "sad" or "happy" and other basic questions. It's difficult
| because music theory is a hodge podge of theory that's attempting
| to describe what's effectively an evolved language (with
| different music evolution for different regions), but there are
| some basic tenets that probably apply.
|
| I don't claim to have deep knowledge but there are a few key
| facts about music and music theory that are really obscure unless
| you know where to look. Any attempt at coming to music theory
| from a more rigorous foundation should be encouraged.
|
| [0] "Measures of Consonances in a Goodness-of-fit Model for
| Equal-tempered Scales" by Aline Honigh
| (https://github.com/abetusk/papers/blob/release/Music/measure...)
|
| EDIT: corrected spelling (thanks for the comments pointing it
| out)
| Infernal wrote:
| > basic tenants
|
| Just in case it's helpful - "tenets"
| chrisweekly wrote:
| +1 / agreed.
|
| Also (tangent / tiny nit): "tenants" (inhabitants) -> "tenets"
| (rules)
| criddell wrote:
| You seems to know a lot about the art and science of music so
| maybe you can answer a question I've had lately: what's the
| difference between pitch and frequency? When a person talks
| about middle C on a piano, is that 'C' more closely related to
| pitch or frequency?
| sevagh wrote:
| Frequency is the repetition rate of the sound wave created by
| the instrument.
|
| Pitch is the perceptual (i.e., human auditory perception)
| correlate of frequency. Pitch is what your brain/auditory
| system interprets that it hears from the sound wave at that
| frequency.
|
| For a piano chord, there is likely the fundamental frequency
| (or f0, the lowest frequency), and its upper harmonics
| (integer multiples of the fundamental). That's why musical
| instruments (like the piano) sound richer than simple sine
| waves: their physical bodies create richer, more complex
| waveforms from the harmonics, giving it a unique timbre.
|
| There are some subtle differences. For example, (very
| oversimplified), if you were made to listen to a waveform
| containing the frequencies of 60 Hz and 90 Hz, your auditory
| system would "hear" a pitch corresponding to a fundamental
| frequency of 30 Hz, since 60 Hz and 90 Hz are integer
| multiples of 30 Hz.
| criddell wrote:
| Is the phenomenon you describe in your last paragraph the
| thing that makes a Shepard scale work?
|
| If one were to make a pitch classifier machine, would it
| always agree with the human ear?
| sevagh wrote:
| I don't know much about the Shepard scale.
|
| Regarding a pitch classifier machine, typically
| algorithms for pitch classification/tracking/detection
| focus only on the fundamental frequency (or f0) of the
| input sound wave. So, _technically_ pitch and f0 are used
| interchangeably where they shouldn't be.
|
| I have yet to see a pitch classifier machine that tries
| to implement the special workings of the human auditory
| system.
| pvarangot wrote:
| > There are some subtle differences. For example, (very
| oversimplified), if you were made to listen to a waveform
| containing the frequencies of 60 Hz and 90 Hz, your
| auditory system would "hear" a pitch corresponding to a
| fundamental frequency of 30 Hz, since 60 Hz and 90 Hz are
| integer multiples of 30 Hz.
|
| Eh, so if you add 60hz and 90hz you get a wave that repeats
| every 33ish milliseconds. You don't "hear a 30hz sine wave"
| that your brain is inventing, that's a very common
| misconception. You just hear a 30hz "thing" that is not a
| sine wave because there's a 30hz thing that is not a sine
| wave playing. Just try adding an actual 30hz sine wave to
| the 60+90 thing and you'll see it sounds very different to
| what you hear when you add those two sine waves. If you
| keep on adding waves spaced 30hz adding the 30hz or 15hz
| one wouldn't make much of a difference because what you are
| listening to is something very similar to a low pass
| filtered 30hz pulse wave.
| sevagh wrote:
| When did I say you'll hear a 30 Hz sinewave?
| pvarangot wrote:
| I thought that's what you meant with:
|
| > your auditory system would "hear" a pitch corresponding
| to a fundamental frequency of 30 Hz
| [deleted]
| parenthesis wrote:
| Frequency is measured in hertz (Hz), where 1 Hz means 1 cycle
| per second, 440 Hz means 440 cycles per second etc.
|
| Periodic sounds above about 20 Hz are perceived is being
| `pitched'. Our perception of pitch is logarithmic. I.e. if
| you keep multiplying the frequency of a sound by the same
| number we perceive the pitch as going up in equal steps.
|
| For example, to go up (an equally-tempered) semitone (aka
| half step or half tone) -- which is usually the smallest
| pitch distance used in music -- you multiply the frequency by
| 2^(1/12) (roughly 1.059463).
|
| To go up an octave in pitch, you multiply the frequency by 2.
| But going from the pitch A3 (220 Hz) to the note an octave
| higher, A4 (440 Hz), sounds like the same `size' of increase
| in pitch as going up an octave from A4 (440 Hz) to A5 (880
| Hz), even though you are now going up 440 Hz instead of 220
| Hz for the previous octave.
| acjohnson55 wrote:
| Pitch is a perceptual feature of sound, quantized within a
| musical scale. It is relational, in the sense that pitch
| probably wouldn't have meaning outside of a musical context
| that defines multiple pitches.
|
| Frequency is a physical measurement of a periodic waveform.
|
| Generally, a tone is composed of harmonics, which have
| frequencies that are integer multiples of a fundamental
| frequency. The pitch physically corresponds to the
| fundamental frequency of harmonic sound (or a sound that is
| mostly harmonic). But the relationship is complicated, as we
| can perceive two tones as having the same pitch (and
| fundamental frequency) even if the actual spectrum of one of
| them does not actually contain a component at the fundamental
| frequency (see
| https://en.wikipedia.org/wiki/Missing_fundamental).
|
| This is because our brain will fill in the fundamental
| frequency if a tone has most of its harmonics. This is why
| you can hear bass notes of a song even if the speaker you're
| listening to doesn't have the frequency response to actually
| reproduce the fundamental frequency.
|
| I hope some of this nuance is making this make sense.
|
| There's also a concept of "pitch class", which is the idea of
| what you might call "C-ness" of every C note on the piano. In
| other words, octave equivalance, or the fact that you can
| substitute nearby C for each other without ruining harmony.
| Pitch, in some ways, is the intersection of pitch class and a
| specific fundamental frequency.
| pvarangot wrote:
| The reason some chords or progressions sound "sad" or "happy"
| for some people is mostly cultural and based on association.
| And you can rewire your brain to get rid of those associations.
| It's like saying chocolate taste is happy and lead taste is
| sad, and complaining chemistry doesn't have an answer as to
| why.
|
| I've never met a jazz pianist that for example will work under
| the assumption that a 2-5-1 sounds sad-transition-happy, it
| sounds like a 2-5-1 because the pianist has a sophisticated
| enough musical understanding to have a concept on their brain
| that is a 2-5-1 and has a specific sound that is associated to
| it. It's the whole deal with ear training intervals, scales and
| chords. The whole major happy minor sad thing is like a
| pedagogy trick to get people started into getting those kind of
| sounds into their language. Same thing with intervals, a minor
| third is maybe sad but then a whole or a half step on the major
| scale are what? super sad? they sound like a train wreck
| harmonically but happy when you play them all together on the
| scale? What's happening is that people just associate musical
| phrases, sounds, harmony, to stuff and that's kinda outside of
| musical theoretic research and more like getting into the
| fields of cognitive science or psychology.
|
| Have you actually asked any music theorist about this? I would
| be surprised if you hadn't gotten this kind of answer because
| in my experience talking to working theorists over lunch or on
| social events they usually agree on this.
| andrewzah wrote:
| Major = happy seems like a lesson for really young kids that
| somehow got internalized by a lot of people. It's so bizarre.
| In a major 7 chord, the 1 to major 7 interval is quite
| dissonant... Never mind that a major 7 chord has a minor
| chord in it, and a minor 7 chord has a major chord in it.
|
| I tend to think of things in consonance vs dissonance, and
| different colors for chord qualities and voicings. Where the
| goal is managing contrast/tension and release.
| tarentel wrote:
| _I 'm also skeptical of music theorists that can't even attempt
| an answer to basic questions about note length frequency, why
| some chords are "sad" or "happy" and other basic questions._
|
| I am no expert in music theory but I've been playing for most
| of my life and write music for fun. I know that A4 is 440 and
| that's about it. I don't know how knowing any other frequency,
| or even that one for that matter, would ever be helpful in me
| reading a chord sheet and walking a bass line to it nor would
| it be very helpful in me writing a melody or chord progression
| for a song I might be working on.
|
| As far as I know, the happy/sadness qualities of chords isn't a
| universal thing. It's likely not a question for music theory to
| explain.
|
| I read through the article a bit and I think it's fine but the
| way most people learn music theory is by first learning an
| instrument and learning the relevant ideas associated with it
| and if still interested will likely move onto more advanced
| concepts. It's like any other field really it all sort of
| builds on each other. Some of it has to be rigorous I think. If
| you can't read music it's probably not going to be very useful
| to know G->B is a major 3rd. The author says they want to write
| music which you don't really need to know music theory to do
| but you need to learn to walk before you run and it's not clear
| to me whether the author even knows how to play an instrument.
| abetusk wrote:
| Not everyone learns the same. Some programmers and math
| centered folks need a guiding "first principles" approach
| before being able to move past to higher level understanding.
| This was the case for me. Without some way to organize
| knowledge, it's hard to understand which pieces of
| information are important, which are redundant and which
| should be applied (and why).
|
| This learning style is not universal and, in my view, why
| this article is specifically titled "Music theory for nerds".
| Programmers especially can make highly complex music without
| ever learning a classic instrument. Algoraves, chiptune,
| generative music, DAWs, real-time music programming
| environments etc. are all a thing and participants often
| don't need any concept of a "real" instrument to create
| quality music therein.
|
| I think you're right about the happy/sad being a cultural
| quality but there might be portions of it that might be
| explained by other means. Here's my attempt, which is almost
| surely at least partly wrong: "Major" chords have more
| constructively interfering waves than do "Minor" chords,
| especially in the lower frequencies, where more of the power
| lays.
| analog31 wrote:
| Some people might be a lot happier if they skip theory
| altogether and instead, choose an instrument and learn to
| play it. That's what most musicians do. I'm a fairly
| successful jazz musician, and have barely learned any
| theory. The "first principles" are the history of the
| musical style, and the mechanics of my instrument.
| tarentel wrote:
| Definitely agree. I think that's what makes it such a
| tricky subject for people to get into. You don't need to
| play an instrument to learn music theory, you don't need
| music theory to write good music, although you will be
| applying it without knowing it, you technically don't need
| to know how to play any instrument to write music, etc.
|
| Also, I guess my comment does sort of imply that I meant a
| classical instrument but arguably some of the things you
| listed could also be described as instruments, in which
| case, my point still stands. If you want to learn western
| music theory with the intentions of writing music, which is
| what this article is describing more or less, you need to
| have a way to make western music, whether that be a cello,
| a tracker, or a gameboy it doesn't matter.
|
| You're absolutely correct that we all learn differently but
| I would bet the people who learned and understood music
| theory well prior to learning and/or experimenting with
| some sort of sound generation first are in the minority.
| Most people will learn both at the same time. Playing music
| goes along way with reinforcing why things are done the way
| they are done and reading about the concepts after hearing
| them, playing them, experimenting with them goes a long
| way.
| holri wrote:
| There are twelve tones because the pitch between them is the
| smallest one that our ear can differentiate as two distinct
| tones. Is the pitch smaller, you hear only beats.
| dekhn wrote:
| No. Go look at Ragas in indian music.
|
| "Ragas are precise melody forms. A raga is not a mere scale
| nor is it a mode. Each Raga has it's own ascending and
| descending movement. And those subtle touches and uses of
| micro tones and stresses on particular notes like this..."
|
| Microtones are less than the difference between two adjacent
| pitches in western scales and are discernable, even to people
| like me who have a hard time telling adjacent pitches apart.
| andrewzah wrote:
| No.
|
| There are systems that have more than 12 notes.
|
| Plenty of instruments hit these "microtones". E.g. string
| instruments with frets can bend strings, and string
| instruments without frets can just play those notes.
|
| Genres of music like the blues frequently utilize these
| microtones.
|
| 12TET is just the custom in western music, but we can
| absolutely discern smaller intervals.
| holri wrote:
| yes, there are more than 12 tones, obviously. But If you
| play two neighbor microtonal tones together, you hear only
| one beating.
| andrewzah wrote:
| You can play with a 31/43/53 note keyboard yourself to
| see that you're incorrect.
|
| http://terpstrakeyboard.com/web-app/keys.htm
| proposicion47 wrote:
| Wait until you learn about live beyond 12TET
|
| In short: no you're factually wrong. Human ear can discern
| smaller pitch changes and there actually music composed on
| smaller subdivisions than 12
|
| For instance
| https://en.wikipedia.org/wiki/19_equal_temperament
|
| You can check done pieces on YouTube.
|
| Yes it sounds unusual. Yes it sounds strange. But thats just
| because you've been conditioned to listen 12 tet all your
| life.
|
| But saying 12 notes because we can't perceive smaller changes
| is, again, wrong and there's actual counterexamples of music
| done with smaller changes
| holri wrote:
| You can test this in the Vienna museum of music. There is a
| live demonstration with a headphone and with two knobs for
| the frequency of two separate tones playing together. Also,
| it visually shows the pitch of those two. If you go below
| the 12 tone pitch you hear only one tone, near the 12 tone
| pitch this one tone becomes suddenly to two separate tones.
| tarentel wrote:
| While you are 100% correct a very simple counter example to
| the op that a lot of people have likely heard in their life
| is someone tuning a guitar. It would have saved me a lot of
| time if people couldn't tell the difference. :D
| parenthesis wrote:
| In melodic performances that take a `bluesy' approach to
| pitch, it can absolutely by heard when a note is somewhere in
| between two equal tempered pitches.
|
| For example, lots of the notes in the vocal of the Beatles
| `Come Together' are clearly (often very) flat -- wonderfully
| so, subversively so, even, in our pitch-corrected age!
| holri wrote:
| If they sound together, you hear only one beating tone. One
| after another, you can distinguish them below the 12 tone
| pitch.
| jacquesm wrote:
| This doesn't ring (pun intended) true:
|
| https://www.sciencedirect.com/topics/medicine-and-
| dentistry/...
| gnud wrote:
| It's a fine article, but not a fine introduction. I read more
| as a list of all the things the author didn't understand (or
| pretended not to understand), because they couldn't describe
| them mathematically.
|
| I assume it's written partly tongue-in-cheek, to show how
| arbitrary a lot of music tradition is, and how it creates a
| barrier to entry.
|
| And the article didn't even mention different clefs or
| transposing instruments!
| twelvechairs wrote:
| Music can be analysed in many different ways. People often
| respond poorly to an explanation of 'music' that doesnt cover
| what they see as important or what/how they have learned.
| Kye wrote:
| Music rage made sense once I understood most people learn One
| Way, and don't learn there are many convergent cultures and
| applications that work with the same underlying wiggly airs,
| and there's often animus between those traditions. Hip-hop
| has as much potential for exploration in theory as anything
| else, but a _lot_ of people raised on Western music theory
| consider it inferior mumbling.
|
| An electronic musician working in a DAW needs to understand
| notes as ratios and frequencies lest they produce a mix that
| sounds like goop on club speakers, but a pianist can get away
| with not having any idea. Put them in a room and ask them to
| explain the difference between a mode and a scale, and you'll
| need a hazmat crew.
|
| Realizing all this led to a handy heuristic: the best
| musicians to know and work with are those who can navigate
| those different conceptions and traditions without fear or
| judgement. There's no reason an orchestral composer can't
| learn from riddim without tripping over triplets.
| bityard wrote:
| I only dabble in music as a hobby, started later in life,
| never had any professional instruction whatsoever. So
| occasionally I find myself on forums populated in part by
| people who have been taking formal music lessons from
| strict teachers since the age of three and OH BOY do they
| get fired up when someone suggests anything that differs
| even slightly from their training.
|
| There is definitely some subset of musicians that cannot
| conceive the notion that someone somewhere on the planet
| might be learning music just for fun and don't WANT to take
| it uber-seriously.
| danShumway wrote:
| Agreed, the pushback on this reminds me ironically of some of
| the pushback I see towards people who try to break apart math
| notation to make stuff like science papers more accessible.
|
| My experience with being taught music theory lines up with your
| experience, and I spent a lot of time learning both piano and
| instrumental music leading up to college, to the point where I
| considered myself to be a fairly decent-ish musician. I was not
| taught why anything exists I was taught rules: rules that I
| constantly saw being broken around me, and that I was
| constantly told, "well, it's OK for _them_ to break the rules
| once they understand them. " It was not until I started to
| think of music-theory as a grammar based on conventions and
| social norms that any of it clicked for me, before that point I
| hated music theory. Certainly it was rare for people to try and
| break things down to first principles or to describe why things
| were the way they were.
|
| What happens as an early musician (in my experience) is that
| over time you just kind of get used to the social conventions
| and it becomes intuitive because you've spent a lot of time on
| it. I learned about stuff like ratios once I started getting
| into intermediate jazz on the saxophone; it was not an early
| concept taught to me in piano lessons.
|
| And then people look at articles like this and say, "well,
| that's all super-basic stuff, and it's not completely right,
| and she's doing a bad job of explaining..." Nonsense, she's
| doing fine. Even if there are a few inaccuracies, this is a
| good article: it's written in a way that's sympathetic to
| people who know nothing about music theory, it gets across the
| immediate points that musicians might not even realize are
| problems (why is a C a C, why is B# C), it is a (mostly
| successful) attempt to tie music theory to something that
| readers might already understand. It's helping bridge this gap
| of "repeat this rule until it becomes intuitive", and that's a
| good thing to do.
|
| Even with really simple concepts, people forget how big the
| barrier of entry is around notation. It's extremely common for
| me to run into people who say they would read more scientific
| papers or statistical research if the math notation didn't
| throw them off. Music is the same, there is a common language
| that is very efficient and nice for people who know it, and is
| indecipherable for everyone else. Anything that helps lower
| that gap is good, and looking at this article as someone who
| knows the notation already my immediate reaction is that it
| seems pretty helpful and a lot of "intro" music courses won't
| explain these concepts, they'll expect you to tough it out and
| just memorize the rules.
| xhevahir wrote:
| > Music theory is, in my experience, typically taught as a list
| of facts to remember.
|
| Yes, but accompanying those facts is a set of phenomena that
| you're supposed to experience physically.
| gjulianm wrote:
| > Some commentators are saying that the article doesn't address
| why we have 12 notes but I wonder if they even know why
|
| Is there an actual reason or are all of these post-hoc
| explanations? Depending on the culture you'll have different
| scales and ways of organizing the sound. From what I understand
| it always comes down to "some people thought it sounded good
| and from there they made music and people got used to it and it
| snowballed".
| abetusk wrote:
| I'm trying to walk a fine line. On the one hand the 12 note
| equal tempered scale has almost surely a societal component
| to it. That is, it was one that won out for weird cultural
| reasons that don't have a lot to do with some idea of
| correctness or utility (like why 'qwerty' won out over Dvorak
| keyboards).
|
| _But_ there is an explanation that does try and get at it a
| bit more analytically and that 's in the paper I linked to.
| With the above caveats about the cultural momentum, the 12
| not equal tempered scale provides a happy compromise between
| the number of notes to provide a basic building block for
| music (characters or digits would be an analogy to notes in
| an octave) vs the number of "good" note pair combinations
| (where "good" is if the frequencies have a small/simple
| fraction approximation).
|
| Some of it is hand-waivey, to be sure, but at least it
| provides a potential reason and a starting point.
| scythe wrote:
| The use of pentatonic scales is extremely cross-cultural,
| with independent discovery on at least four continents:
|
| https://en.wikipedia.org/wiki/Pentatonic_scale#Use_of_penta
| t...
|
| As far as I can tell, 12 ET is the smallest equal
| temperament that acceptably encodes the common variants of
| pentatonic scale. Meanwhile, the pentatonic scale probably
| appears because (3/2)^5 [?] 8.
| ben7799 wrote:
| It's only taught as a series of facts to remember if you're not
| involved in practical application.. AKA actually playing music.
|
| If you're getting a practical education in this stuff you learn
| bits of theory right at the point they make perfect sense and
| you "Grok" them quickly and internalize them without having to
| think of them as memorizable facts.
|
| E.x. you are directly associating a particular part of the
| music theory with a direct link to muscle memory on your chosen
| instrument. It's burned into your muscle memory already and now
| you have just associated the theory with the practice. Every
| time you perform that technique or type of passage it just
| reinforces the theory.
|
| Another example.. understanding the difference between a minor
| chord and major chord or 7th/diminished/augmented chord, or the
| difference in how two different intervals relate means a
| totally different thing to a person who has practiced those
| things till they can differentiate them by ear than a person
| who cannot differentiate them by ear.
|
| Perhaps all this is a weakness in an age where a lot of people
| are making music on computers in ways that break this type of
| link.
|
| It's all very analogous IMO to someone who has read a book
| about a sport but has never actually played the sport.
| danShumway wrote:
| > It's only taught as a series of facts to remember if you're
| not involved in practical application.. AKA actually playing
| music.
|
| First, no. I went hard into music in my early life, I both
| learned basic piano and intermediate saxophone, and I went
| through the full suite of band/orchestra/jazz/soloing, to the
| point where I was a fairly decent-ish musician. It's not
| until later that people get taught this stuff in my
| experience, I struggled with any practical connection to
| music theory probably until late middle-school.
|
| But second, what you're describing is exactly why the article
| is useful; because the people who are trying to get into
| music _haven 't_ played an instrument for so long that they
| can improvise on it and start to put together intuitively
| that certain ratios or key signatures or whatever sound good.
|
| What happens with people who are taught to play instruments
| is that they spend a lot of time honing those instincts by
| playing the instrument, but at the same time, what they're
| playing is constantly attached to this notation so that when
| they intuitively connect that minor/major/augmented chords
| sound good or bad in different situations, they
| simultaneously connect them to the notation as a way of
| expressing those concepts.
|
| People who don't have formal instruction don't go through
| that process the same way. They might be composing music
| without ever thinking about the notation. And when they go to
| seek out instruction or learn more about techniques, they
| don't have a bridge to connect their intuitions about what
| does and doesn't sound good with the notation, everyone just
| expects them to find the notation intuitive.
|
| I had a lot of formal instruction on playing jazz. A lot of
| it was about honing intuition, listening to jazz, replaying
| other famous improve tracks, improving over those tracks,
| memorizing licks. But that intuition and practical experience
| was also coupled with being able to break down and describe
| what those other musicians were doing. That required a shared
| notation that I could understand, it required being able to
| understand what an instructor meant when they talked about
| why certain riffs worked or common ways to resolve a run of
| notes if I got lost in the middle of an improv solo and
| didn't what to do next. But I could follow that instruction
| because I knew the notation and I had a connection between my
| practical experience of how music sounds and the formal
| notation about key signatures and chords and crud.
|
| A lot of people don't have that because they haven't spent X
| years learning to read sheet music. Articles like this are
| helpful for them.
| AlbertCory wrote:
| I got to ask The Alexander String Quartet at their Q&A about
| microtones and whether F# is really the same as Gb (answer:
| it's not for them).
|
| There IS a notation that they use among themselves about
| microtones above and below the standard pitch, and they have
| to agree what pitch, exactly, they're playing at any given
| note.
|
| Furthermore, the pitch they would use depends on whether the
| musical line is going up or down; in other words, it could be
| different in different parts of the same piece.
|
| There are a lot of things that serious musicians know well
| enough to explain, but almost no one ever asks them.
| TheOtherHobbes wrote:
| There are no first principles in music. The harmonic series is
| relevant, but _you can 't start from the harmonic series and
| find your way to Western classical music._
|
| It just doesn't work like that. Music could have gone in
| various directions, and Western music happened to pick the
| various directions it developed in, more or less arbitrarily.
|
| They happen to emphasise a combination of parallel blocks and
| horizontal lines, and various quite complex kinds of motivic
| and structural elaboration and development.
|
| Post-classical music - especially electronica - is much more
| focused on rhythm and timbre. It has more complex sounds and
| sound combinations and less complex structures.
|
| There isn't much in the way of rhythm-and-timbre theory yet,
| but it's on its way and will be a thing within a few decades.
|
| All of it is a mess because music has always been about styles,
| experiments, and conventions, and those have changed over time.
|
| And it's also written from the musician's POV. Not a
| mathematician's POV. Or a dabbler's POV. Or a nerdy POV.
|
| For example - sooner or later people get to transposing
| instruments and the obvious question is "Why would anyone sane
| do that?" And the answer is because it's convenient for the
| players.
|
| That's it. That's the rationale. For all of it.
|
| So while it's awkward and not very elegant, it has a kind of
| consistency that's somewhat useful across multiple styles.
|
| It's impossibly hard to invent a system that is so much better
| for this that it's worth throwing the old system away. People
| keep trying and failing, because you can't just rationalise
| part of it, you have to improve all of it. And it's such a huge
| thing that's not a practical project.
|
| So it persists - partly as a relic, partly as a developing
| system.
| BeFlatXIII wrote:
| RE: transposing instruments
|
| It's not just a "convenient for the players" moment. It's
| also because changing over to non-transposing instruments
| would create a generation-long transition period of broken
| pedagogy. It's the same reason oboe fingerings are so
| nonsensical. It's backwards compatibility to preserve
| previous fingerings that makes the new fingerings awkward and
| arbitrary.
| natechols wrote:
| As a software developer, I think of bassoon fingerings as a
| classic example of "technical debt", and also the kind of
| design that if someone thought it up de novo, the only
| appropriate response would be "you're fired."
| abetusk wrote:
| This type of reply is indicative of precisely why it's so off
| putting for programmers to get into music. The attitude of
| "there are no rules!" is espoused while artist after artist
| that produce music that we like are clearly following some
| type of ruleset, at least to some extent.
|
| Electronica might be rhythm and timbre based but even looking
| at rhythm you can start to ask some basic questions (what
| note length frequency is more pleasing? Why? What frequency
| of two underlying beats sounds good? Why?).
|
| Sometimes theory can be nothing more than a collection of
| discovered tricks. Sometimes it can be something more
| fundamental. To waive your hands and say that all of it is
| arbitrary is doing a disservice to anyone trying to learn and
| understand.
| scrozier wrote:
| I understand your frustration. However, as a trained
| musician and working programmer, I get very frustrated with
| programmers posting here in HN that want to somehow fit
| music into their programmer worldview. Although I
| understand that it's _hard_ , the answer is to study
| classical Western music theory. (Or Eastern or whatever; I
| come from the Western tradition.) It's not simple, but it's
| not rocket science either. When you have this basic
| theoretical grounding (intervals, scales, chords, music on
| staves, etc.) then the "world of music" won't seem obscure
| and magical. It's really not terribly important to know
| "what frequency of two underlying beats sounds good."
| You'll discover things like this for yourself if you allow
| yourself to study _music_ rather than studying music as
| applied programming.
| fknorangesite wrote:
| > I get very frustrated with programmers posting here in
| HN that want to somehow fit music into their programmer
| worldview
|
| I sometimes feel like one could take this sentence and
| substitute just about anything for "music."
| dudeman13 wrote:
| >It's really not terribly important to know "what
| frequency of two underlying beats sounds good."
|
| And yet I get the feeling that if someone does
| investigates that (and adjacent topics) in depth with
| success there would be a bunch of interesting
| consequences to it.
|
| Maybe, I have got no knowledge in the field - it just
| sound like something interesting, why the heck wouldn't
| we want to know it?
| scrozier wrote:
| Many people in music know the answer to that and related
| questions. Sometimes the answers prove interesting, as
| you say. What _I 'm_ saying is that I don't think
| questions like that are a useful/effective route to
| understanding music more broadly. They (questions like
| that) _seem_ like they 're interesting, because they
| appeal to us as programmers somehow (math-y), but they
| are largely on the fringe of the broad body of knowledge
| that makers of current popular music (say) operate with.
| You wouldn't expect a musician to come into programming
| saying, "so what's the equivalent of sonata allegro form
| in a typical computer program?" It would be applying the
| wrong paradigms/framework to the topic at hand.
| dudeman13 wrote:
| >What I'm saying is that I don't think questions like
| that are a useful/effective route to understanding music
| more broadly.
|
| Thanks, I misunderstood you.
| Ma8ee wrote:
| My problem is that I quite early learned most basic music
| theory. But I've never really figured out how to use it.
| I read sheet music and I can play several instruments
| (not particularly well any of them). It feels like I
| learned a list of keywords and syntax rules, but never
| figured out how to program.
| scrozier wrote:
| Ah. That's a very interesting way to put it! I think it's
| possible that some people just don't have a "feel" for
| creating music (call it talent, something you're born
| with, etc.). But I sense that you enjoy music and maybe
| feel like you have things you'd like to "say," musically,
| but are frustrated by your inability to wrestle the tools
| into doing what you hear in your mind.
|
| Do you play the piano? I think the piano is the best
| vehicle for grokking music--it allows for melody and
| harmony (and rhythm) all in one instrument, in sort of a
| visual way, that is hard to get in monophonic
| instruments, or even with guitar (for more complicated
| reasons). I think I developed my musical sense in two
| main ways: 1. listening to songs on records and on the
| radio, and figuring out how to replicate them at the
| piano, and 2. playing lots of music on the piano from
| sheet music, where I was constantly exposed to chord
| progressions and the like in other people's music; the
| "tropes" of Western classical and popular music, if you
| like. Neither of these are trivial, but both are within
| reach of most people, I think. I will posit that there
| are few shortcuts to musical mastery. Grokking music is
| definitely _not_ like (as easy as) learning a new
| programming language.
| [deleted]
| [deleted]
| crawfordcomeaux wrote:
| I started out my musical explorations as a kid in piano
| lessons, then playing sax in school until halfway through
| high school. I never felt confident in playing, didn't
| feel free to explore, and judged every sound I made as
| right/wrong.
|
| 6 years ago, I accidentally abandoned my preferences and
| disengaged disgust in an attempt to stop automatically
| judging. And then I returned to music for the first time
| in 18 years with the idea that there is no wrong note.
| Here are some of my observations:
|
| - I wasn't deeply/actively/mindfully listening to music
| when I was younger. This was part of a cycle of an
| attention-degrading cycle where I'd hear music and then
| distract myself with judgements of it, emotions that
| followed the judgments, and judgments about those
| emotions.
|
| - Songs that "feel sad" don't. How a person hears/attends
| to music, how their body has been conditioned to receive
| different notes/chords/progressions, the meaning given to
| the sounds/words, the judgments around those things, and
| how they learned to feel in response to those judgments
| is what's being described when someone says a song feels
| a certain way to them. It's not universal and those
| feelings can be disengaged.
|
| - How I feel in response to music has gotten way deeper
| and more expansive as a result of releasing all those
| conditioned feelings. I did this, in part, by pressing a
| bunch of random keys down on an organ and sitting with
| the feelings that came up and let them pass. Part of the
| practice involves letting up on one key at a time and
| then pressing it again, back and forth, until I can
| distinguish the note in the cacophony and have reached a
| feeling of contentment with the sounds. Rinse and repeat
| for each note.
|
| - Music theory is absolutely unnecessary and in many ways
| hinders the learning process. I play improvisationally
| and not necessarily to play a song I've heard. Doing this
| for a year led to the emergence of a skill where I can
| start picking out melodies I remember.
|
| - Styles and genres are largely based around preferences.
| I have a friend whose connective tissue disease (Ehrler-
| Danlos Syndrome) keeps them from feeling music. As a
| result, they've developed a strong liking of noise music,
| which would likely feel very uncomfortable in the body to
| people whose bodies have been trained on more traditional
| forms of music.
|
| - The discomfort with dissonance is largely a learned
| thing, due to cultures of being unwilling to sit with
| dissonance. It can be turned off.
|
| - If what you're looking to do is make music people can
| easily like based on commonly cultivated body feels
| around different sounds and preferences, focus on rhythms
| that don't change much, avoiding dissonance by default,
| repetition and also on novelty.
|
| - If you want to make music people can easily ENJOY,
| repetition, improvisation, and novelty are keys. If you
| don't know any music theory, novelty will be easy. If you
| can make some sounds and then vaguely make the same
| sounds again, repetition will come (this can take a bit
| of practice, especially if not very connected with the
| body). Improvisation is such a broad idea because there's
| improvising around a melody or theme, around rhythm,
| around volume, around whatever the inspiration is
| (whether it be sounds, rhythms, feels, words, stories,
| colors, whatever), and probably more. Allowing and
| accepting whatever happens is a key to improvisation.
|
| - Music can be enjoyable, even with abrupt transitions
| from slow to fast, soft to loud, harmonious to dissonant,
| rhythmic to droning.
|
| - If I want to play what's in my mind, I can sing it and
| play along with how I'm singing.
|
| - "Wrong notes" played rhythmically can fit into
| anything.
|
| - If there's no wrong sound, I can play any instrument.
|
| - Everything is a drum.
|
| - Everything is music. Including silence. They cannot
| compel the silence to cease. So you are music trying to
| music in some ways and making music without trying.
| Trying to do that in a way that gains approval or caters
| to preferences is one way to live. Experimenting in the
| ways I describe here is another.
| scrozier wrote:
| I love the direction you took this. I happen to love
| experimental music and agree that it is a wonderful and
| fruitful avenue for musical exploration. I'm fascinated
| by your process of disassociating your emotional
| responses from what you heard.
|
| I happened to go to an experimental concert just last
| week, involving organs (since you mentioned them). You
| might enjoy it. It's available for streaming here:
| https://roulette.org/event/cleek-schrey-and-weston-
| olencki-o...
| crawfordcomeaux wrote:
| Thanks for this! Gonna watch it right now if the 3yo
| wants to. Update: they do.
|
| Here's the instructions for doing the nonjudgment
| practice that led to all these realizations. I highly
| recommend them. The effects are quite literally
| lifechanging, unlocking/unblocking joys I didn't even
| know were possible.
|
| https://news.ycombinator.com/item?id=29764591
| crawfordcomeaux wrote:
| We have a pump organ in our living room. This music is
| incredibly affirming for me because it sounds very much
| like music I first started playing when I started playing
| again AND I started on the pump organ (which at least one
| of the musicians at the start of the music is playing
| on).
|
| I've had to really staunchly stand up for myself and my
| music to other musicians and to my past notions of music,
| and have definitely gotten defensive around playing music
| like this.
|
| No more. I'll just send people to this. And I'm
| definitely going to focus on playing more like this
| again.
|
| Thanks again for bringing this into our lives! <3
| scrozier wrote:
| There were about 250 people in the audience that night,
| which I thought was amazing for a program of experimental
| music involving pump organs, a banjo, and a Korean mouth-
| blown reed instrument.
| scrozier wrote:
| Addendum to the above: I also had lots of direct
| instruction in music: piano lessons, theory classes,
| music history classes, various instrument lessons,
| composition classes, etc. It all adds up.
| NikolaNovak wrote:
| I'm a programmer that got into Music.
|
| I hit my head... and other people's heads... and tables and
| walls... until I realized that:
|
| 1. Yes, there are "rules"
|
| 2. They are far far far more arbitrary than I realized
|
| 3. They are far from universally applicable.
|
| Personally, I expected music to be heavily math based, with
| universal rules.
|
| But my current understanding is that while there IS a lot
| of math, what sounds good / what people in any given
| culture like, is all arbitrary. You can use math to
| describe some of it, but not to derive it.
|
| As well, unfortunately, when people say "Music Theory",
| they largely mean a variation on one or both of:
|
| 1. Note reading - Western music notation, which I don't
| consider "Music Theory" but rather notation, but many will
| disagree
|
| 2. Western Music Theory, largely though not entirely put
| down by 18th century old cranky europeans based on what
| they happened to like at the time
|
| There is FAR less "universalness" in Western Music theory
| than I thought.
|
| So there is this combination of:
|
| * Huge englightnment and pattern recognition and increased
| understanding as I learned more music theory
|
| and
|
| * tremendous frustration at inconsistency and
| arbitrariness, until I realized it wasn't my music teacher
| who hated me, it's that what they are teaching me is
| arbitrary
|
| So personally, I think it's important for programmer to
| accept "there are no rules (in the sense that we think of
| "rules", boolean logic and math etc), though there are
| guidelines and recommendations (which are completely
| arbitrary and cultural-based)"
|
| It turns out "what rhythm / note / combination / frequency
| is more pleasing" is 99% how you were brought up / what you
| are used to, rather than some math/physics correlation.
| Move to another part of the world and throw out your 4/4
| and 12-note equal temperament and I-V-vi-IV
| tomjakubowski wrote:
| Based on how many fellow programmers I know who play
| instruments or write compositions or otherwise produce
| music... it doesn't actually seem off putting for
| programmers to get into music. Is your experience
| different?
| danShumway wrote:
| It's technically correct while also being practically
| useless.
|
| There are no fundamental rules to grammar, but we still
| teach writers what a simile is. Even in spelling, English
| has no consistency about a lot of this stuff. Are spelling
| rules useful though for non-native learners? Heck yes. Do
| we still have grammar books? Yes. It turns out that
| learning the exceptions is sometimes faster than memorizing
| everything. Music is a communicative medium based in large
| part around social norms of what combinations of sounds
| tend to feel good to people who grew up in a specific
| environment, and music theory is an attempt to break apart
| that social consensus into basic rules that can be imitated
| and built up into more complicated genres.
|
| The rules are somewhat arbitrary and made up, but that
| doesn't mean they're not real, and that doesn't mean you
| can't sort-of derive some of them from more basic rules or
| from basic principles.
|
| Music could have gone in multiple directions, but for
| whatever reason Western music went in the direction it did,
| and many people who are trying to learn music aren't trying
| to learn the full spectrum of every direction music could
| have gone. They're trying to learn how to imitate Western
| sounds, and for that purpose specifically music has rules
| -- many of them derivable from other rules, flexible and
| breakable as they may occasionally be.
| hannasanarion wrote:
| When giving this type of explanation, we want to
| emphasize that the rules are arbitrary and made up
| because the dominant way of teaching music theory from
| the 1920s through to the last decade or two has been to
| claim it as scientifically or mathematically "optimal" in
| some way. It isn't.
|
| Starting off an explanation of music theory by talking
| about whole number frequency ratios is like starting off
| English class with a diagram of the glottis.
| danShumway wrote:
| Do you feel like the article isn't doing a good enough
| job getting that lesson across?
|
| > Western music has twelve distinct pitches. This is
| somewhat arbitrary -- twelve has a few nice mathematical
| properties, but it's not absolutely necessary. You could
| create your own set of notes with eleven pitches, or
| seventeen, or a hundred, or five. There are forms of
| music elsewhere in the world that do just that.
|
| [...]
|
| > I get the feeling that treating the whole chord/key
| ecosystem as a set of rules is like studying Renaissance
| paintings and deciding that's how art is. It's not. Do
| what you want, if it sounds good. I'm gonna go try that.
| Consensus seems to be that the real heart of music is
| managing contrast -- like every other form of art.
|
| ----
|
| > Starting off an explanation of music theory by talking
| about whole number frequency ratios is like starting off
| English class with a diagram of the glottis.
|
| I would say it's more like starting out an explanation of
| color theory by talking about wavelengths, even though
| you don't really need to know any of that to understand
| composition, and even though most of the rules of image
| composition are contextual to specific cultures and
| aren't hard requirements that artists have to obey.
|
| The math behind color is definitely not a requirement
| that artists should be forced to learn, but some people
| find it helpful to know what mathematical formulas were
| used to create a given color wheel.
| PaulDavisThe1st wrote:
| They're not rules unless your teacher is an asshole.
|
| Music theory is a _language_ used to be able to have
| conversations about harmonic and melodic aspects of a
| piece of music. Rythmic aspects are less well supported
| (that 's putting it mildly) by western musical theory,
| but the same is true there for whatever formalism or
| terminology/nomenclature you might pick: it's not a set
| of rules, it's a language to facilitate non-musical
| discusison.
| danShumway wrote:
| I think this is a distinction that only matters if your
| definition of rules is such that they can never be broken
| or played with. That's not typically the way I think of
| rules, and I don't think I'm alone in that. Even
| programmers understand that a lot of programming "rules"
| are actually just heuristics about how to produce good
| code.
|
| As another example, I've spent a ton of time learning
| game design rules, and all of them are optional, but
| they're still useful. "Rules" in this context means, yes,
| communicative terminology, but communicative terminology
| about particularly effective ways to build commonly
| understood musical motifs/phrases that affect Western
| listeners in somewhat predictable ways.
|
| Music theory is a language for talking about a language,
| music itself. It is partially social convention that
| leads us to have a 12 tone scale, and it is definitely
| social convention that leads us to call that a "scale".
| However, the average Western listener will respond to the
| notes of that scale in predictable ways, and there are
| "rules" that you can learn that will allow you to more
| easily and predictably manipulate that listener's
| emotions and communicate broader ideas through your music
| -- many of those underlying rules about tuning, ratios
| between notes, and so on are derivable from mathematical
| principles or at least describable in mathematical terms,
| even if ultimately the reason why listeners respond to
| some of those ratios is social and arbitrary.
|
| Of course, the rules are not concrete or immutable, they
| can be broken and often are. But the majority of rules we
| learn in most subjects are not concrete.
|
| Similarly, there are no concrete rules in writing, and
| the terminology we use to describe story structure is
| arbitrary and made up. However, learning the "rules" of
| writing will make you a better writer for typical
| audiences that live near you, and those rules are
| expressed through common set of terms and concepts that
| many professional/hobby writers have decided to use --
| many of which can be partially derived or explained by
| talking about psychology or history or whatever.
|
| Sure, these are not immutable, scientific principles
| baked into the heart of the universe, but:
|
| A) the author goes out of her way to say that she isn't
| claiming that, and
|
| B) breaking down rules and building them back up from
| different starting points or looking at them
| mathematically is still a reasonable thing to do with
| rules that have a social origin, and
|
| C) even though a lot of why certain chords sound good is
| baked into culture rather than biology, it's also a kind
| of strong claim to say that _all of it_ is purely social.
| But I don 't think it would matter much even if it was
| purely social, people who do music theory for a living
| still talk about math sometimes.
| PaulDavisThe1st wrote:
| Well, I wasn't really thinking of much in TFA as "the
| rules of western music theory" - it didn't really get
| that far. There was another comment that talked about how
| TFA didn't cover things like chord voicing and inversion,
| and there is just so much more that wasn't covered that
| really forms the meat of "the rules of western music
| theory". TFA really just covered "one basis for 12T, what
| scales and chords are", which is barely anything to work
| with.
|
| "Western musical theory" is full of ideas about harmony
| (OMFG, so many rules), often with non-musical semantics
| overlaid on top of the actual musical elements. These are
| the "rules" that you get play with as a musician, and the
| very best of them do in fact break them frequently (but
| expertly). Why do so many people remember "Take 5" ...
| because it's in 5 not 4! Why do people consider Coltrane
| to be a genius ... because of the games he played with
| harmonic relationships mostly connected to the circle of
| fifths but deeply subverted. Why do some of us still
| celebrate the "genius" of Schoenberg, Stravinsky or
| Bartok ... they upended traditional rules about harmonic
| resolution, even the very notion of tonal harmony in some
| cases. Even within this thread, we see people noting a
| striking detail of a recent Adele song that consists of
| (almost certainly deliberately) singing somewhat off-key
| to strong effect.
|
| There is a huge amount of recorded music that plays
| entirely by "the rules" (the ones that go way beyond
| TFA), but a lot of what people think of as musical genius
| is precisely the stuff that flouts the rules (with enough
| knowledge of the rules to make this work).
| danShumway wrote:
| > There was another comment that talked about how TFA
| didn't cover things like chord voicing and inversion, and
| there is just so much more that wasn't covered that
| really forms the meat of "the rules of western music
| theory". TFA really just covered "one basis for 12T, what
| scales and chords are", which is barely anything to work
| with.
|
| I've commented to the same effect elsewhere, but people
| really underestimate how much the "barely anything"
| notation concepts are a real barrier to people who are
| unfamiliar with the domain. https://xkcd.com/2501/ comes
| to mind here; TFA is 5000 words and ends with multiple
| links to further tutorials and reading. That's a
| completely fine place to start. If you want to learn the
| rules of western music theory and get into the meat of
| what you're talking about, it is going to be a lot more
| work if you don't know what a scale or a chord is, and I
| don't see anything wrong with teaching those basic
| concepts from a mathematical perspective.
|
| ----
|
| > with enough knowledge of the rules to make this work
|
| That's the part that the author's target demographic
| wants. They want to be able to either:
|
| A) imitate the rules well enough to write something
| passable (say for game soundtracks), but aren't looking
| to innovate, or to
|
| B) learn the rules well enough to innovate.
|
| In both of those cases, even the most basic notation
| concepts like "what scales and chords are" is a serious
| barrier to entry for many people.
| zozbot234 wrote:
| > I don't see anything wrong with teaching those basic
| concepts from a mathematical perspective.
|
| One thing that often goes "wrong" with this is that the
| mathematics of frequency ratios is a huge barrier that's
| most often irrelevant to actual music making. If you
| literally know nothing about music, there's a good case
| for just letting the tuners deal with it for the time
| being, and starting from the old _Do_ , _Re_ , _Mi_ etc.
| that teaches you both solfege (sight reading /aural
| skills) and the musical syntax of scale degrees. Then
| _sing_ a whole lot of music in (movable do; fixed do is
| pointless except for specialists) solfege and try to make
| up simple embellishments and variations on what you sing.
| There 's a "programmer's favorite" way of learning these
| too (these are called _diminutions_ ) based on the scale-
| degree leap that you're traversing, hypothetical
| elementary operations of musical syntax and whatnot; but
| good musical intuition will always be helpful. Guess
| what, now you're well on your way to improvising simple
| music at the keyboard, and later on you can even get
| started on learning counterpoint without being lost in
| all the details. Because, unlike actual college students
| who are forced to take a counterpoint class as part of
| studying bookish "music theory", you'll have the
| fundamentals down pat.
| danShumway wrote:
| If that works for you, great. But I don't think the
| article is implying that learning music has to start with
| teaching people about frequencies, it's just saying that
| some people (like the author) have found it helpful to
| latch onto.
| dragonwriter wrote:
| > If you want to learn the rules of western music theory
| and get into the meat of what you're talking about, it is
| going to be a lot more work if you don't know what a
| scale or a chord is, and I don't see anything wrong with
| teaching those basic concepts from a mathematical
| perspective.
|
| The problem with teaching them from the particular
| mathematical perspective taken in this work is that...it
| doesn't actually teach them, and it throws up it's hands
| and says I don't really know about fairly basic stuff.
| This isn't an alternate pedagogical route chosen by
| someone who has a different view of how to get people up
| to speed for the domain, it's a smattering of trivia that
| isn't directed at learning the rest because the author
| doesn't understand the basics, much less have a
| particular pedagogical approach to them.
| danShumway wrote:
| There's a bit of jumping around here, because I'm
| responding to people who are telling me that mathematical
| models for music shouldn't be taught at all and that we
| shouldn't use the word "rule" in music theory.
|
| I think that's a separate conversation from whether this
| article specifically should be the entire basis for
| someone learning how to compose music. I agree that I
| would not point someone at this article and say, "this
| will be enough to get you on the road to learning how to
| compose music", I would want something more involved by
| someone who has more experience.
|
| But that's different from saying it's wrong for the
| author to talk about sound frequencies.
|
| ----
|
| To your point in specific, I don't see where the author
| ever claims that this is an alternate pedagogical route
| to learning music, the author actively discourages people
| who already know music from reading the post. The post
| explains a few basic concepts like what a scale is -- and
| fairly accurately (or at least about as accurate as most
| of the other explanations that you'll find online). It
| openly works through the stuff that the author
| understands, and openly admits what the author doesn't
| understand, while sympathizing with the target reader
| that it's hard to pick up a new subject when it sounds
| like everyone else is speaking a different language from
| you.
|
| So basically, it is every single technical blog post
| written on any subject by anyone who is openly learning
| about a thing online, and that is something that should
| be encouraged, not derided.
|
| I also still kind of disagree with people who are saying
| that this is just trivia or too basic to even talk about,
| commenters are _still_ underestimating how little normal
| people know about music.
|
| If people come out of this article understanding stuff
| like:
|
| - There are 12 "steps" in an octave
|
| - An octave is doubling the frequency of a pitch
|
| - Written down on a staff, we compress those 12 "steps"
| into roughly 7 spaces.
|
| - A scale is 7 different notes.
|
| - Because of weird ratio stuff and social consensus about
| which "steps" in an octave are most commonly used, some
| parts of the scale move 2 "steps" and some move 1
|
| - Transposition exists as a concept, you can play the
| same song starting at different pitches
|
| - Notes like B# and C can overlap, except some really
| professional players might treat them differently because
| it turns out the math we use for different pitches
| doesn't _completely_ work out correctly in all scenarios.
|
| That's all stuff that people who are unfamiliar with
| music don't know. Okay, the author doesn't really
| understand what's going on with minor keys, but this
| isn't a textbook, and there is value even in something as
| simple as "an octave is doubling the frequency of a
| pitch."
|
| I'm weirded out by how upset HN is being about an amateur
| blog post with reasonably correct information by someone
| who is actively trying to teach themselves how to write
| music. This is exactly the content that we should want
| people to write about online, and it's written in exactly
| the style that we regularly encourage bloggers to write
| in when they're exploring new concepts/domains.
| dekhn wrote:
| I remember Take Five mainly for the bass in the
| background during the drum break. But then, I like
| listening to rock music in Just Intonation, so I'm not
| typical.
| pinneycolton wrote:
| Wholeheartedly agreed w/@danShumway - wish I read this
| before typing my own response. I might have saved myself
| some time :)
| pinneycolton wrote:
| That's not entirely true. In fact, the Sound-Harmony-
| Melody-Rhythm-Growth model for analysis explicitly calls
| it out as a critical building block of the music that we
| hear and experience. Like any subject, it takes some
| study to get to the interesting bits.
|
| For example, the vast majority of people who have taken
| Music Theory 101 have completed coursework that is the
| equivalent of "Hello, World!". That is barely scratching
| the surface and certainly give the aspiring programmer
| the skills necessary to create something non-trivial. The
| same is true of music theory. You don't instill in
| someone the musical understanding of Brahms with one
| music theory class.
|
| I think that there are rules, but they're less about a
| teacher being an asshole. Musical styles evolve over
| time. We wouldn't have classical without baroque, and we
| wouldn't have romantic without classical. The style
| itself imposes a "rule" that is really a best practice.
| How do we in technology treat best practices? Well,
| they're basically rules that we shouldn't violate without
| careful thought. The same is true of music. People who
| study basic music theory learn about the cadences used
| most commonly in church music ... V-I ... IV-I ... and
| the deceptive I-IV-V-vi cadence! You feel where music is
| going because you've learned the rules by listening to
| other music and embedding yourself within its best
| practices. V-vi is deceptive because it violates a best
| practice, but used effectively, it works.
|
| As music evolved, and as the world became smaller in
| terms of ease of travel and exposure to other cultures'
| music, we started to see new influences. Debussy and
| others were influenced by indonesian gamelan music.
| Without that influence, we might not have the jazz that
| we have today. Why? The impressionist style that Debussy
| practiced created floating pillars of sound,
| chromaticism, etc. that became important elements of
| early Jazz.
|
| It's all connected and has evolved over time, just like
| technology. Personally, I do think they are rules, but
| like most rules, they're meant to be broken.
| Kye wrote:
| There's a world where no one thought to put the Amen
| break in a sampler, and that's a much less interesting
| world.
| zozbot234 wrote:
| > The attitude of "there are no rules!" is espoused while
| artist after artist that produce music that we like are
| clearly following some type of ruleset, at least to some
| extent.
|
| It's a craft, not a rigid system that you _have_ to follow.
| What 's called 'Rules' in music is more like patterns that
| have been found to sound good. For example, the famous
| 'Rule of the Octave' is a _pattern_ based originally on
| playing thirds and sixths ( "first inversion chords" if you
| want to phrase it that way) over a "walking" baseline. But
| the rule is far from fixed, and almost immediately the
| basic pattern using thirds and sixths was altered to use
| thirds and fifths ("root position chords") on the tonic and
| dominant degrees. Then the other chords were altered in
| turn, giving each bass scale degree a sonic identity of its
| own, with ascending and descending, major and minor
| varieties etc. Thus what literally started as a simple and
| basic rule has become incredibly complex. This just shows
| how a _craft_ can evolve to become more interesting; rigid,
| foolproof rules cannot. And the "rule of the octave" is a
| tiny part of music as a whole (though it's pretty
| foundational, all things considered); but guess what, other
| "rules" work the exact same way!
| teawrecks wrote:
| As someone who is firmly on the math side and knows very
| little about music theory, it seems like you should never
| expect music theory to answer subjective questions like
| "Why does x sound better than y?" There are so many factors
| for why someone will find a sound pleasing or not, and most
| of them are biological/psychological.
|
| IMO asking why a melody sounds pleasing would be like
| asking why a plot of the Mandelbrot set is interesting;
| math isn't going to be able to answer that.
|
| I would be fine with a music theory that is a set of tools
| to deal with sounds, just as math is a set of tools to deal
| with numbers. Whether certain properties are desirable are
| up to the theorist.
| pvarangot wrote:
| I agree with OPs sentiment only that it's not true there's
| no theory on rhythm or on timbre. I can share rhythms and
| patches with anyone in the world even if we don't speak the
| same language and we can work on them together, there's a
| rudimentary symbolic language for them that is universal.
| Maybe we don't have an algebra of timbre but we definitely
| have an algebra for rhythm. Theory is also taxonomy and
| categories of things.
|
| What "there are no rules!" is kinda the excuse for music
| theorists to keep on working on a field that has had so far
| little applications on how music is created. Maybe yeah on
| how some people learn it, but that's it. It's basically
| them admitting that actually successful musicians usually
| work under a set of rules and techniques so simple from the
| theoretical standpoint that the whole field gets
| invalidated.
| zozbot234 wrote:
| > successful musicians usually work under a set of rules
| and techniques so simple from the theoretical standpoint
| that the whole field gets invalidated.
|
| If anything, it's just the opposite. The 'rules' (again,
| this should be understood as patterns, or perhaps rules
| of thumb) practitioners implicitly rely on are far more
| _complex_ than most theorists are implicitly comfortable
| with. This is why bookish music _theory_ was mired for
| centuries in pointless discussions about acoustics and
| ratios, or some incredibly weird formalisms for
| representing meter, whilst practitioners got on simply
| focusing on what sounded good.
| pvarangot wrote:
| I've gotten instruction from very prodigious
| practitioners and their opinion on the rules they are
| following is what I stated. You can get through
| introductory jazz or classical piano and also basic
| orchestral composition and the patterns or rules you'll
| know are about are going to be super basic and even very
| sophisticated niche and "intellectual" music is not being
| created by people with more theoretic knowledge than
| that.
| zozbot234 wrote:
| That's why I talked about implied reliance, as opposed to
| what people explicitly "know about". Surfacing the actual
| practical rules behind what practitioners are doing is
| arguably a theorist's job, but many theorists are not
| fully comfortable with the kind of thinking that this
| would require.
|
| (The 'Rule of the Octave', which _is_ the kind of rule I
| 'm pointing to, was quite exceptional in being explicitly
| _taught_ in actual published treatises about music - and
| even that was practically forgotten later on; it 's not
| usually taught in "introductory music theory" classes
| even though it arguably should be!)
| analog31 wrote:
| Oddly enough I'm a programmer and musician. But I learned
| music before I learned programming.
| giraffe_lady wrote:
| They are not saying it's arbitrary, they're just saying it
| can't be consistently derived from some fundamental,
| smaller set of principles.
|
| 'Music theory' is much more of a working practice musicians
| use to communicate with each other and document their work
| and discoveries. How programmers feel about their notation
| systems isn't something working musicians should be
| concerned with, I don't think.
|
| There is no fundamental thing that makes some notes or
| combinations pleasing and others not. It is _all_
| culturally mediated. I know that possibly seems unlikely
| and uncomfortable, but nonetheless it is true. If you drill
| down far enough into music you find the harmonic ratios,
| and human culture. That 's it, there is nothing else down
| there at the foundations.
| dragonwriter wrote:
| > The attitude of "there are no rules!"
|
| GP didn't say there are no rules.
|
| "The rules are culturally, and path, dependent and are not
| derived or derivable from a simple set of universal first
| principles" is very far from "there are no rules".
|
| It does mean that certain approaches to _learning_ the
| rules that might fit well with people 's abstract
| preferences for how they'd like to approach the field don't
| work well in practice, though.
| PaulDavisThe1st wrote:
| > but you can't start from the harmonic series and find your
| way to Western classical music.
|
| You absolutely can, because that's essentially exactly what
| western classical music (and more or less all other forms of
| music) already did, just spread out over a very long period
| of time.
| maldusiecle wrote:
| That's the wrong way about thinking about it, though.
| Historical processes don't operate solely based on first
| principles, they operate according to contingency.
|
| Take Western music. Early music is mostly vocal, and early
| principles of music theory evolved around what would be
| possible (and practical) to sing. Different people have
| different vocal ranges, and the constraints that puts on
| the music lead to certain constraints in counterpoint.
| Eventually instrumental music becomes more socially
| important, and that changes what kinds of music can be
| made. Mathematics progresses in such a way that new tuning
| systems (12 tone equal temperament, and its precursors)
| make it easier to modulate between keys, and more
| modulation (and chromaticism) becomes common.
|
| Even things like the way the music is structured depend on
| social practices, they're not spontaneous. The sonata form
| depends on an audience that listens attentively to music so
| that they can perceive the way the themes are gradually
| transformed.
|
| I could go on, but nearly everything in music goes this way
| --there are principles, but they only have a limited
| explanatory power, you need to get into historical
| contingency to really understand why things evolve the way
| they do.
| PaulDavisThe1st wrote:
| I never said that it was necessarily a smart way to think
| about it. But just as we don't reach the periodic table
| by taking children through every process and discovery
| that led to uncovering a new element, it's not necessary
| to teach this subject (whatever we call it) as a
| historical process either.
|
| I certainly agree that historical context has always been
| central to the way music has developed. It's not for
| nothing that most of Europe refers to "the church modes"
| rather than using a more abstract term for a set of
| interval rotations. But that historical context is only
| absolutely necessary if you want to try to understand
| _why_ music evolved in the way that it did. It 's not
| necessary if your goal is to understand the way we
| understand, compose and perform music today.
|
| Of course, I'm all for more understanding of music, so
| I'd favor historical context every time. It's just that
| it's not a necessary feature for understanding where we
| currently are.
| hannasanarion wrote:
| The analogy with chemistry doesn't work. There is only
| one "chemistry theory": the one that describes reality.
| The table of elements changes because our experimental
| understanding of reality improves.
|
| There is no one true "music theory". Music theory as it
| is typically taught is no more than an elaborate system
| of nomenclature of the stylistic preferences of European
| music in the last three centuries. It is a cultural
| description of a cultural phenomenon.
|
| To get into more specifics, when explaining music theory
| at an elementary level, you might say that a frequency
| ratio of 1:2 is called an octave and all the notes with
| an octave relationship to each other are considered
| equivalent. That is true, if you are making European-
| style music. Most other cultures around the world have a
| name for the interval called the octave, but most of them
| don't consider all octaves to be the same note. "octave
| equivalency" is fundamental to Western music, but it's
| not a universal law, it's a stylistic choice. To imply
| otherwise by claiming that your explanation of this
| European convention is essential to music writ large is
| to do a disservice to the many musical cultures around
| the world that don't follow that convention.
| PaulDavisThe1st wrote:
| Somewhere upthread, that I replied to, said:
|
| > The harmonic series is relevant, but you can't start
| from the harmonic series and find your way to Western
| classical music.
|
| As big as fan as I am of being aware of non-western
| musical culture, I was commenting on the specific idea of
| moving from the harmonic series to a _specific musical
| culture_ (the western classical one). This is why the
| chemistry analogy is (roughly) appropriate, because there
| are in fact a substantial number of (western) music
| theorists who consider there to be only a single western
| classic music theory.
|
| I try to almost never use the words "music theory"
| without prefixing them with a temporal and/or geographic
| cultural qualifier (though I likely often fail here).
| whycombs wrote:
| Sorry, a lot of this is wrong. A major 7th is not 17:9 but 15:8.
| Our ear tries to represent all these rich resonances in as simple
| primes as possible (Think, combos of 2's 3's and 5's - and
| _occasionally_ 7 's in blue notes).
|
| A minor 6th isn't just a note in between, but a simple 4:5, The
| _minor_ sound that we associate with sadness is simply the
| reciprocal nature of the ratio - the more complicated prime is in
| the denominator (as opposed to the overtonal nature of the M7
| above)
|
| Short answer: read Harmonic Experience by W.A. Mathieu
| srcreigh wrote:
| It's not always just about simplicity of primes. Some intervals
| correspond to harmonics too.
|
| Major 2nd: 9th harmonic (9/8)
|
| Major 3rd: 5th harmonic (5/4)
|
| Perfect 4th: inverted 3rd harmonic (4/3)
|
| Perfect 5th: 3rd harmonic (3/2)
|
| Major 7th: 15h harmonic (15/8)
|
| In fact one of my fav tunes Easy on Me by Adele has a
| suspiciously sharp perfect 4 in the chorus melody... I think
| she was tuning a bit towards the 11th harmonic which is sharper
| than a perfect 4. Someone measured her pitch and it's actually
| somewhere in between perfect 4 and 11th harmonic. So cool how
| it works!
|
| https://youtu.be/U3ASj1L6_sY?t=145
| whycombs wrote:
| Harmonics are the stacked ratios of primes. There's no 9th
| harmonic, there's the overtonal stacking of the two 5th
| harmonics. Or more literally, when you play a maj 9th on the
| piano, your ear is filling in the missing perfect 5th between
| them.
| srcreigh wrote:
| Every part of what you said confuses me so much!
|
| How does 5+5=9? (Wrong I know but what is right?)
|
| Isn't the 9th harmonic a distinct frequency in a musical
| note? I thought it was side effect of how physical
| vibrations ripple out or something...
|
| Where can I learn more about what you're talking about?
| It's very interesting. Thanks.
| mrob wrote:
| The ear does not care about ratios. Dissonance can be modeled
| using Plomp and Levelt's curve, which predicts the perceived
| dissonance of a pair of sine waves. Dissonance is minimum at
| unison, smoothly increases to a maximum at a narrow interval
| (dependent on absolute frequency), and smoothly decreases again
| as the interval increases.
|
| Sethares extended this model to arbitrary sounds by decomposing
| them into their sine-wave partials with a Fourier transform and
| then taking an amplitude-weighted average of the predicted
| dissonance of each pair of partials. If you apply this
| procedure to intervals using harmonic timbres (timbres composed
| of partials with frequency an integer multiple of the
| fundamental frequency), the dissonance curve has minima that
| happen to be at small integer frequency ratios.
|
| Harmonic timbres are most common in music, but there is an
| important class of musical instruments that are naturally
| inharmonic: tuned percussion. Unless substantial effort is put
| into designing them to approximate harmonic timbres, these
| sound most consonant when tuned outside small integer ratios.
| Indonesian gamelan music is a well known example of this. And
| with synthesized timbres you can have whatever inharmonicity
| you like, so timbres can be designed to suit any arbitrary
| tuning system.
|
| Non-technical explanation of Sethares' model:
|
| https://sethares.engr.wisc.edu/consemi.html
|
| Full mathematical details:
|
| https://sethares.engr.wisc.edu/paperspdf/consonance.pdf
| PaulDavisThe1st wrote:
| > Sethares extended this model to arbitrary sounds by
| decomposing them into their sine-wave partials with a Fourier
| transform and then taking an amplitude-weighted average of
| the predicted dissonance of each pair of partials.
|
| This is not entirely fair to Plomp & Levelt: they were the
| first to consider a timbre as a set of sine-wave partials and
| do the pair-wise partial average. Sethares' extension was to
| consider inharmonic sine wave series and reason about the
| implied relationship between timbre and consonance.
|
| As others have noted, I think that that "The ear does not
| care about ratios" is pushing the implications of Plomp &
| Levelt's and Sethares' work a little too far. They have made
| a convincing case that our experience of dissonance and
| consonance is based on a more complicated set of
| relationships that just the harmonic series, but it's still
| fundamentally all about ratios (just more of them, and they
| cannot be considered independent of each other). Even the P&L
| dissonance curve is in some senses a ratio plot.
| notahacker wrote:
| > If you apply this procedure to intervals using harmonic
| timbres (timbres composed of partials with frequency an
| integer multiple of the fundamental frequency), the
| dissonance curve has minima that happen to be at small
| integer frequency ratios.
|
| In practice that's pretty much "the ear cares about ratios"
| isn't it? Sure, it's caring about the ratios because they
| align with harmonic timbres in non-percussive instruments,
| but various human cultures _do_ listen to a wide variety of
| instruments and voice with harmonic timbres, and perceive
| melody and chords based around [reasonably close
| approxiaations] of simple integer ratios sounding more
| consonant.
|
| The implications for creating chordal music with synthesised
| inharmonic timbres designed to be consonant are interesting,
| but not widely applicable to what we actually listen to as
| music; and much of what we hear that goes outside simple
| ratios with the express intent of sounding dissonant...
| whycombs wrote:
| Take one minute and try to sing a perfect 5th over a drone
| note. You'll waver around that beautiful sturdy 3:2. And if
| you're lucky, or if you practice you'll eventually lock in to
| that resonance/ratio and feel a universal truth as important
| as the right triangle.
|
| All of music is based on resonance. And resonance is a ratio
| mrob wrote:
| Voice is a harmonic timbre. If you could sing with
| inharmonic partials that perfect 5th would not sound so
| consonant.
|
| And this is relevant even in Western music. The piano is
| technically tuned percussion, and although it's very close
| to harmonic, it's inharmonic enough that you have to
| deviate from small integer ratios (beyond any deviation
| required for tempered scales) if you want the most
| consonant sound:
|
| https://en.wikipedia.org/wiki/Stretched_tuning
| jacquesm wrote:
| Some people can do that all by themselves:
|
| https://www.youtube.com/watch?v=vC9Qh709gas
| ben7799 wrote:
| Knowing the mathematical ratio of the root to it's Major 7th is
| of course far less important than knowing what they sound like,
| being able to hear the difference between a
| minor/major/diminished/augmented 7th, and knowing what effect
| using each has in getting to where you want to be.
|
| The focus on this in these articles is missing the forest so
| you can focus on a single tree.
|
| A lot of the ratios have not been fixed in time either, or
| can't be fixed correctly across all instruments.. the article
| doesn't get into that.
| srcreigh wrote:
| There's a simple reason for 15/8 being the major 7th. It's
| the 15th harmonic. The 15th harmonic is not changing anytime
| soon!
| zoltar wrote:
| I really like 12tone's breakdown of pop songs. Here's an example
| with The Immigrant Song:
| https://www.youtube.com/watch?v=gwsfR5sJPbM
| PaulDavisThe1st wrote:
| On the question of "why 12 notes", I _STRONGLY_ recommend this
| video by David Bennett:
|
| https://www.youtube.com/watch?v=lvmzgVtZtUQ
|
| There's a really important step missing in the article which has
| been aluded to by a couple of comments already. It's the step
| between: 1. a series of notes defined by the
| harmonic series, that is, exact integer multiples (or ratios, if
| you prefer) of a base frequency, a physical phenomena found in
| nature
|
| and 2. the well-tempered scales used by most
| western music, which adjusts the ratios to allow certain
| compositional "tricks" to be used without sounding dissonant.
|
| The set of notes defined by (1) are typically referred to as
| "Just Intonation", and was the basis for most western music (and
| some non-western music) until somewhere between about 1400 and
| 1600 (lots of room for discussion/debate there).
|
| The "problem" with just intonation, if indeed it is a problem, is
| that if you define two series of notes (call them a scale, if you
| like) using these integer ratios but starting from two different
| notes, you will trivially find cases where "the next higher E" is
| a different frequency. So starting from (say) A and moving by
| integer ratios gets you to a different (say) F than if you start
| from (say) B.
|
| This means that if you are writing in a just intonation scale
| with (say) A as the root, you have a set of notes that are not
| actually the same frequencies as if your scale started on (say)
| B.
|
| By itself, this is not a problem at all - there is all kinds of
| lovely music written through history that works just fine with
| notes and scales defined this way. You just stay in the same
| scale throughout, and there are no issues. There are even some
| scale changes you can make that still work, you just have to know
| what they are (and they depend on the root note and the set of
| integer ratios you're using, so it gets complicated).
|
| But ... somewhere in the period mentioned above, a subset of
| western musical culture started to want to experiment with
| "modulation" - changing from one scale to another in the midst of
| piece. On continuous pitch instruments (e.g. violin, voice), this
| is entirely possible to do, since they can play any frequency in
| their range at all. However, it does require significant skill on
| the part of the performer, since the pitch of a (say) "F" will
| differ depending on the scale currently in use in the piece.
|
| The breaking point, such as it was, came with the development of
| fixed pitch instruments (keyboards). These can only play the
| notes they are currently tuned to, and so if the (say) F in two
| scales is a different frequency, you cannot play in both scales
| without retuning - an obvious impossibility in the middle of a
| piece.
|
| So, "well-tempered" tuning was developed - the ratios described
| in TFA. These are tweaked by relatively small amounts so that the
| notes are close to where Just Intonation (integer ratios) would
| have placed them, but not precisely the same. These small shifts
| mean that the (say) "F" is the same frequency whether your scale
| began on (say) A or B. You can now play a fixed-tuning instrument
| like a harpsichord or a piano, change from one scale to another,
| and everything remains "in tune".
|
| Of course, to ears used to Just Intonation, "well-tempered"
| tuning sounds out of tune. But in the west, most people (even
| within our musical academies) have grown up used to the sound of
| well-tempered tuning, and it is Just Intonation that sounds
| "off".
| acjohnson55 wrote:
| > But ... somewhere in the period mentioned above, a subset of
| western musical culture started to want to experiment with
| "modulation" - changing from one scale to another in the midst
| of piece. On continuous pitch instruments (e.g. violin, voice),
| this is entirely possible to do, since they can play any
| frequency in their range at all. However, it does require
| significant skill on the part of the performer, since the pitch
| of a (say) "F" will differ depending on the scale currently in
| use in the piece.
|
| Does it really? Listeners are pretty forgiving, so I think in
| practice, you will just have drift away from concert pitch, and
| you maybe just have to be a bit careful because the open
| strings will jolt you back to concert pitch.
|
| But in a capella vocal singing, there's no such forcing
| function, so you just need the ensemble to be good at locking
| in with each other, especially on long chords where you really
| want the audience to feel the consonance or dissonance. Which
| isn't simple, but it's also not rocket science.
|
| It would be very hard to perform exact pitches within a couple
| cents of exact frequencies, if that were necessary. I just
| think theorists vastly overstate how much listeners care about
| tuning in most cases. I made this mistake myself. For research,
| I was interested in creating a sythesizer that allowed
| composers to switch between tuning schemes mid piece. And I
| could barely hear the difference, and much to my
| disappointment, it wasn't very compositionally useful.
| PaulDavisThe1st wrote:
| I used the term "significant skill" to refer to something
| that I don't think an untrained person could do, but that a
| reasonably well trained performer could (whether on violin or
| with their voice). Certainly not rocket science. As a
| reference, it took my wife about a month of twice-weekly
| singing Bulgarian music to really be able to "hear" the
| correct tones, which of course were even further from her own
| musical practice (she had been a professional singer earlier
| in life) due to not just JI/WT but quarter tones etc.
|
| Good point about the open strings though. Less of an issue on
| instruments from other cultures like the kamancheh, where you
| would rarely play an open string, but certainly true on
| multi-strings where the open string situation is "oft-used".
| hannasanarion wrote:
| The first point is just really wrong. The harmonic series is
| not integer multiples, and you don't have to get very far in
| the harmonic series before you encounter radical microtones
| that no European musician would have ever considered in-tune
| for the last thousand years.
|
| The order of intervals in the harmonic series is:
|
| Octave
|
| Perfect Fifth
|
| Perfect Fourth
|
| Major Third
|
| Minor Third
|
| Subminor Third
|
| Diminished Third
|
| Supermajor Second
|
| Major Second
|
| Neutral Second
|
| Minor Second
|
| And that's just the leading edge of the series. Between distant
| notes in the series you will find the neutral third, subfourth,
| superfourth, superaugmented fourth, subfifth, superaugmented
| fifth, supermajor sixth, and neutral seventh.
|
| If you want to claim that our intervals all come from the
| harmonic series, then in order to include the Minor Second,
| which everyone would agree is pretty dang important for our
| music, you must also include all the intervals listed above
| that nobody's ever heard of. It's simply wrong.
|
| The major scale has nothing to do with the harmonic series
| except by coincidence. The Tritone for instance, never appears
| in the harmonic series, and any music theorist will tell you
| that's way more important to our music than the Minor Second.
| Aidevah wrote:
| Thank you. The insistence on using the harmonic series to
| explain the source of the notes diatonic scale is
| anachronistic, post hoc and never really made any sense even
| on its own terms. There is nothing inherently "natural" about
| the seven basic notes that make up the diatonic scale, and
| there are even more problems than the major omissions that
| have been made in order to fit the members of the harmonic
| series into a diatonic mold that you have mentioned. The
| harmonic series cannot explain frequency ratios which does
| not have a power of 2 as a denominator, unless you invoke
| reciprocals. Furthermore the association of dissonance and
| consonance to the simplicity of the ratios is not consistent
| since the idea of dissonance is a social category, not a
| scientific one.
| PaulDavisThe1st wrote:
| > The Tritone for instance, never appears in the harmonic
| series,
|
| The tritone is the eleventh harmonic of the series, folded
| back down into the octave to give a ratio of ... "well, it
| depends".
|
| Again, from wikipedia:
|
| > The ratio of the eleventh harmonic, 11:8 (551.318 cents;
| approximated as Fhalf sharp4 above C1), known as the lesser
| undecimal tritone or undecimal semi-augmented fourth, is
| found in some just tunings and on many instruments. For
| example, very long alphorns may reach the twelfth harmonic
| and transcriptions of their music usually show the eleventh
| harmonic sharp (F# above C, for example), as in Brahms's
| First Symphony
| hannasanarion wrote:
| The eleventh harmonic is a neutral second. Even according
| to the wikipedia section you quoted, you have to round up
| from F half-sharp to F sharp to get it, which doesn't make
| sense if you're trying to derive a musical scale from the
| harmonic series, as you would have already passed over the
| neutral third, diminished third, supermajor second, and all
| the rest of the intervals listed above which require no
| rounding at all.
|
| The actual 11th harmonic is the neutral second against the
| 10th harmonic, which corresponds to the super-fourth
| compared to the root.
| PaulDavisThe1st wrote:
| You are confusing the physical harmonic series with the
| series of "harmonics" typically named in western music.
| hannasanarion wrote:
| You're the one saying that F half-sharp (the actual 11th
| harmonic of C) is the same thing as F-sharp.
| PaulDavisThe1st wrote:
| The problem here is that "tritone" has varying
| definitions, including at least: half an octave, three
| whole tones, two minor thirds, and that particular in JI,
| that leaves things a bit wooly to say the least.
|
| It appears fairly conventional to say at least that the
| _lesser undecimal_ tritone is the 11th harmonic, which
| corresponds to a ratio (folded into the octave) of 11 /8,
| but other defintions (64/45 or 45/32 for example) also
| exist.
| PaulDavisThe1st wrote:
| This is just wrong. You are using western musical culture
| terms for what are actually physical phenomena.
|
| I will quote to you from wikipedia:
|
| > The harmonic series is an arithmetic progression (f, 2f,
| 3f, 4f, 5f, ...). In terms of frequency (measured in cycles
| per second, or hertz, where f is the fundamental frequency),
|
| > The second harmonic, whose frequency is twice the
| fundamental, sounds an octave higher; the third harmonic,
| three times the frequency of the fundamental, sounds a
| perfect fifth above the second harmonic. The fourth harmonic
| vibrates at four times the frequency of the fundamental and
| sounds a perfect fourth above the third harmonic (two octaves
| above the fundamental). Double the harmonic number means
| double the frequency (which sounds an octave higher).
|
| > The frequencies of the harmonic series, being integer
| multiples of the fundamental frequency, are naturally related
| to each other by whole-numbered ratios and small whole-
| numbered ratios are likely the basis of the consonance of
| musical intervals
|
| https://en.wikipedia.org/wiki/Harmonic_series_(music)
|
| What you are describing is a musically significant set of
| intervals that are merely a subset of the harmonic series,
| created by what the wikipedia page describes as:
|
| > If the harmonics are octave displaced and compressed into
| the span of one octave, some of them are approximated by the
| notes of what the West has adopted as the chromatic scale
| based on the fundamental tone
| hannasanarion wrote:
| > some of the pitches in the harmonic series are
| approximated by the notes of the chromatic scale
|
| is not the same thing as
|
| > the chromatic scale is derived from the harmonic series
|
| which is what the OP article claims.
|
| You can find the chromatic scale in the harmonic series,
| yeah, _if you ignore the majority of the notes in the
| harmonic series_.
|
| To find the chromatic scale in the harmonic series, you
| need to take the 2nd, 3rd, 4th, 5th, 9th, 15th, and 44th
| harmonics, and ignore of the rest. That's not a
| mathematically justified derivation, that's a post-hoc
| rationalization built on coincidence alone.
| whiddershins wrote:
| It does somewhat though. You build it by taking the 3rd
| harmonic (perfect fifth) cut it in half to get it back into
| the octave, rinse, repeat.
| hannasanarion wrote:
| That's not the harmonic series though, that's the first 3
| members a bunch of different harmonic serieses smooshed
| together. It's extremely arbitrary.
|
| Like, if you want to say that our musical system revolves
| aroundt the frequency ratios of the octave (1:2) and fifth
| (2:3), then that's one thing and it's basically correct.
|
| But that's very different from claiming that western music
| is derived from the universal mathematical properties of
| the harmonic series, and is entirely irrelevant for making
| progress towards actual important concepts in music theory,
| like octave equivalence, let alone scales or dominant
| resolutions.
| whiddershins wrote:
| Sure. Just saying the harmonic series is not completely
| and utterly irrelevant.
|
| Even as you pointed out some of the harmonic series
| tracks closely to the scale tones, and the relationship
| between the harmonic series and the scale tones is a
| useful unit of analysis towards understanding consonance
| and dissonance and such things.
| PaulDavisThe1st wrote:
| > But that's very different from claiming that western
| music is derived from the universal mathematical
| properties of the harmonic series,
|
| Western (classical) music is marked (one might even say
| "distinguished") by its attention to harmonicity, which
| in turns is rooted in ideas about consonance and
| dissonace. These ideas are _absolutely_ rooted in the
| mathematical properties of the harmonic series. As noted
| elsewhere in the comments, the work of Plomp & Levelt
| and then Sethares has shown how human perception of
| consonance (with dissonance being its reciprocal) is
| rooted in the averaged amplitude-weighted sum of the
| pair-wise disonnances between all the partials.
| hannasanarion wrote:
| They are _related_ to the mathematical properties of the
| harmonic series, but they are definitely not _rooted_ in
| it.
|
| If it was true that western musical ideas of consonance
| is rooted in simple harmonic ratios, and that our musical
| scales were based on the harmonic series, then we should
| be seeing subminor thirds (6:7) and supermajor seconds
| (7:8) _everywhere_. They are way more "consonant" than
| major seconds (9:10), or minor seconds (15:16). But in
| reality, they are seen as exotic and wrong.
| PaulDavisThe1st wrote:
| Unfortunately, nobody said "western musical ideas of
| consonance is rooted in simple harmonic ratios". The
| whole point of Plomb & Levelt's work (recommended if you
| have no read it) is that provides an explanation for
| consonance that has simple harmonic ratios as an
| existential but insufficient component. From their work,
| what matters is not the ratios of the two fundamentals,
| because there are essentially no natural tones that
| consist of only the fundamental (1). Instead,
| consonance/dissonance is a result of the _sum_ of the
| consonsance relationships between each pair of partials
| in the two tones.
|
| This is a good overview (linked elsewhere in the
| comments): https://sethares.engr.wisc.edu/consemi.html
|
| Sethares extended their conclusions a bit by noting that
| since the partial spectrum is the definition of timbre,
| the most consonant/dissonant intervals would vary by
| timbre, which they claimed is observed in the real world.
|
| (1) Indeed, the first step of their work, defining the
| "human dissonance response curve" relies on being able to
| use a signal generator to create pure sine tones.
| Aidevah wrote:
| Sethares showed shocking ignorance towards the history of
| the actual usage of dissonance and consonance by
| practicing musicians and theorists in the history of
| Western music. The most obvious being that the category
| of dissonance and consonance has _shifted_ over time. The
| most famous example being the perfect 4th, which has a
| simple ratio of 4:3 and should be a consonance but was
| treated as a dissonance against the bass for most of
| music history in the west (even though Sethares ' graph
| categorise it clearly as a consonance, contrary to common
| practice). At around around the same time, the thirds and
| sixths began to be considered as consonances either,
| whereas previously they were regarded as dissonant and
| were used sparingly (composers generally avoided thirds
| in the final chord until around the end of the 15th
| century).
|
| There's nothing inherently "good" or "bad" about
| dissonances and consonances, the Western ear has been
| trained to recognise instability in dissonances and
| stability in consonances, hence the ancient prohibition
| of dissonances in the final chord of the piece (a rule
| that has since been discarded). The trajectory of
| classical music in the 20th century shows that people can
| indeed get used to music which do not take that as
| granted. In fact, the almost unspeakable secret about
| dissonances is that they sound as good, even better than
| consonances. How else can the suspension play such an
| important part in western music up until then?
|
| Sethares is of course free to define consonance and
| dissonance in his idiosyncratic way unconnected to common
| usage, but of course his definition and discoveries would
| then be of no use to those who use the ordinary
| definition.
| parenthesis wrote:
| > The "problem" with just intonation, if indeed it is a
| problem, is that if you define two series of notes (call them a
| scale, if you like) using these integer ratios but starting
| from two different notes, you will trivially find cases where
| "the next higher E" is a different frequency. So starting from
| (say) A and moving by integer ratios gets you to a different
| (say) F than if you start from (say) B.
|
| A nice example is this:
|
| On an 7 octave (85 key) piano, if you start on the lowest note
| and go up in perfect fifths, after going up 12 fifths you will
| be on the highest note, i.e. up 7 octaves.
|
| In just intonation you multiply the frequency by 3/2 to go up a
| fifth, and you multiply the frequency by 2 to go up an octave.
|
| But clearly (3/2)^12 is not equal to 2^7 (129.7ish versus 128).
| dang wrote:
| Discussed at the time:
|
| _Music theory for nerds_ -
| https://news.ycombinator.com/item?id=12528144 - Sept 2016 (378
| comments)
| ngcc_hk wrote:
| Seems not knowing the struggle with the note system. The struggle
| eg ## which is not really the note above because the # and b is
| not perfect. Bath well pieces probably not in his understanding.
| Not really a music theory.
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