[HN Gopher] Tritone Substitutions
___________________________________________________________________
Tritone Substitutions
Author : chmaynard
Score : 172 points
Date : 2024-07-27 19:52 UTC (1 days ago)
(HTM) web link (johncarlosbaez.wordpress.com)
(TXT) w3m dump (johncarlosbaez.wordpress.com)
| NickC25 wrote:
| neat!
|
| Always love to see music theory content here. Nice find!
| 082349872349872 wrote:
| Does Joanie Baez have a blog? Now I'm curious to see if she's
| ever written (sung?) anything about the symmetries of the
| icosahedron...
| vinnyvichy wrote:
| To answer for the other JCB, no, because (my inference) she
| in her own words was abused by her mathematician
| (mathematical physicist?) father Albert Baez.
| 082349872349872 wrote:
| Yikes! Every now and then I have to figure PKD was really
| talking about earth[0] in _Clans of the Alphane Moon_
| (1964)[1].
|
| [0] thank you RWR (1981)
|
| [1] (wrt AG) note that Alphane saints tend to come from the
| Heebs
| vinnyvichy wrote:
| >[1]
|
| not sure why you had to prefix.. :)
|
| Thanks for the PKD tip!!
|
| (EDIT: this is the only dried bark PKD in my possession,
| which suggests that while PKD admired the schizos he
| might have selfdiagnosed as OCD?)
|
| https://en.wikipedia.org/wiki/Confessions_of_a_Crap_Artis
| t)
| beefman wrote:
| The earliest tritone substitution I know of appears in Scarlatti
| K420
|
| https://www.youtube.com/watch?v=Nf3_NfuvK8Y
|
| There are two tritones in 7-limit just intonation (7/5 and 10/7)
| and therefore two possible tritone substitutions. Here they're
| played successively
|
| http://lumma.org/music/theory/demo/progs/TritoneProgressions...
| pclmulqdq wrote:
| I didn't hear that spot as a tritone substitution, personally,
| but a sort of non-harmonic counterpoint move ("passing tones"
| or "setup tones" to 19th century theorists).
|
| More broadly, a lot of people like to point out wild 20th
| century chords in baroque music, but they really didn't think
| in terms of chords, and as such these pseudo-chords don't have
| the same function that modern versions of chords do. In
| particular, Scarlatti was a prolific user of the partimento
| method of composition, which is a slightly of abstracted
| version of counterpoint, and his sonatas are pretty good
| examples of pieces written with this in mind. The method
| revolves around intervals and movement between voices rather
| than chords. It's normal for someone thinking in counterpoint
| to produce some very "modern" "chords" because that's a common
| consequence of following nothing but voice leading to produce a
| piece of music.
|
| https://en.wikipedia.org/wiki/Partimento
|
| See also Rick Beato mis-analyzing Bach's counterpoint as
| containing a very "modern" maj7#5 chord:
| https://www.youtube.com/watch?v=d1f_tzBx6ko&t=1s
| briffid wrote:
| But JS Bach apparently did love those modern sounds, see BWV
| 542/I But indeed it doesn't make much sense to apply jazz
| theory on classical or early music.
| AlbertCory wrote:
| I've never quite understood that POV, although my piano
| teacher had it. Clearly she had another way of
| understanding it which I'm sure is _more_ useful. I lack
| that training.
|
| Pick an example everyone knows: Bach's Prelude in C. I
| wrote in chord symbols over every bar of that, except for
| that one very weird bar near the end. It helped me a lot in
| memorizing it.
| pclmulqdq wrote:
| IMO when you're playing music, everything you want to do
| is on the table. If you're going to make music theory and
| music history arguments, you should be sensitive to the
| theory and history you are arguing about.
|
| By the way, a 19th century functional harmonist would
| also find that prelude sort of odd. Not in terms of the
| chords themselves, but they don't always obey their usual
| functions.
|
| Also, many modern players and theorists reach toward
| Schenkerian analysis and its derivatives to sort of
| explain why music sounds the ways it does. Unlike
| counterpoint and harmony, Schenkerian analysis is almost
| entirely descriptive, not prescriptive. I have no idea
| what your teacher would have suggested.
| AlbertCory wrote:
| > IMO when you're playing music, everything you want to
| do is on the table. If you're going to make music theory
| and music history arguments, you should be sensitive to
| the theory and history you are arguing about.
|
| I don't even understand this paragraph. I'm not arguing.
| pclmulqdq wrote:
| That wasn't directed to you, but rather toward your
| teacher and the OP. The intent was that as a player, I
| think you should go ahead and use roman numerals or jazz
| theory or any other form of analysis that helps you think
| about things. However, if you are publishing an analysis
| of a piece (which you did not do), you should be thinking
| differently than that.
|
| As someone with a significant background in historical
| performance, my books of Bach preludes are still full of
| Roman numerals because that is a really good way to
| "compress" information about what notes to play.
| AlbertCory wrote:
| OK. For sure I wouldn't publish that set of chords, since
| anyone could create it as a shorthand.
|
| I'm actually interested in other ways of analyzing it.
| bonzini wrote:
| I guess you could use figured bass notation. It's more
| complex than modern chord notation because it tells you
| which inversion to use, and it notates secondary
| dominants (e.g. V of V, which you'd write simply as D7 in
| jazz notation if you're in C). Personally I know too
| little about it to use it effectively and therefore I
| would stick with modern chord notation even when talking
| about classical pieces.
| adw wrote:
| While not disagreeing with anything you've said (music
| theory is one part acoustic physics to several parts
| history and sociology), the specific primacy of
| Schenkerian analysis is a particularly American trait.
|
| It's also, interestingly, illustrative of your argument.
| Musical analysis is necessarily socially contextual and
| therefore revealing of the author's values and
| priorities, and Schenkerian arguments often imply, or
| directly come with, some really quite right-wing
| positions. Schenker was very much into motivated
| reasoning to defend his deep-rooted racism; many
| Schenkerian analysts have, deliberately or otherwise,
| wound up following in those footsteps.
| zozbot234 wrote:
| Schenkerian analysis is, broadly speaking, a rediscovery
| and popularization of melodic reduction approaches that
| were well known to composers and performers in the 18th
| century. There's very little that's specifically American
| about it, let alone German. See Nicholas Baragwanath,
| _The Solfeggio Tradition: A Forgotten Art of Melody in
| the Long Eighteenth Century_. And of course, Schenker 's
| "imaginary continuo" is readily understood as a
| popularization of historical partimento (and closely
| comparable approaches such as the so-called _Partitura_
| known from German sources).
|
| It's true though that Schenker's treatises included
| plenty of political asides of such an extreme chauvistic
| character that to call them "quite right wing" is a huge
| understatement. (It's also true that, as scholarly
| research has pointed out in recent years, he seems to
| have expressed similarly extreme views in his private
| correspondence and other private writings.) Part of this
| might perhaps be explained as Schenker's awkward
| overcompensation for what would've been his remarkably
| humble origins back then (he came from a small village in
| what was then Austrian Galicia, now in modern Ukraine).
| Regardless, I think we nowadays have so many sources
| proving the relevance of melodic reduction/elaboration
| approaches (some of them quite early indeed, from the
| 16th-17th centuries) that to tie these analytical
| approaches polemically to Schenker and his specificities
| is really quite pointless, perhaps even misleading.
| pclmulqdq wrote:
| Ah yes, the good old "fascist dog whistle" argument.
| Schenker himself was an outright fascist. However, many
| theorists from the late 20th century who have come up
| with methods for analyzing tonal music have done so
| mostly on the back of Schenker's work. I'm also not
| suggesting you should read Schenker himself - his own
| work on what we call "Schenkerian analysis" is quite
| primitive and limited.
|
| I'm curious what you would suggest to perform a modern
| analysis of Bach (what the original comment chain on this
| was about) if not Schenkerian analysis. I didn't see any
| alternative analysis tools proposed in your post, even
| though it sounds like you are educated on the subject.
| pclmulqdq wrote:
| See also BWV 903 and BWV 1079.
|
| Andras Schiff playing BWV 903 (there are some REALLY bad
| performances of this piece out there):
| https://www.youtube.com/watch?v=SNWOhm5iXxs
|
| BWV 1079 wasn't necessarily written with musical
| instruments proscribed, but here's a good French group's
| performance: https://www.youtube.com/watch?v=tfMQ-AYiuJw
| beefman wrote:
| Scarlatti's sonatas contain many chords, apart from pure
| polyphony. In fact they're particularly notable for their
| early inroads toward functional harmony. The tritone
| substitution in K420 is a clear example of this. Bach much
| less so, and certainly not in the case highlighted by Beato
| there.
| pclmulqdq wrote:
| Whether it contains what a modern ear hears as chords or
| not, he wrote the piece using polyphonic methods. Bach's
| music also contains plenty of chords, but that doesn't
| change how it was written.
|
| When theorists talk about Scarlatti laying the foundation
| of harmony, partimento is probably the foundation they are
| referring to. Functional harmony of the 19th century is
| just a more powerful abstraction.
| ramenbytes wrote:
| Can you recommend any good books or resources for
| learning polyphonic compositional methods and/or about
| the other known methods?
| pclmulqdq wrote:
| Fux's Gradus ad Parnassum is something you can find. A
| lot of the partimento stuff was practical in nature, and
| consisted of some rules and several exercises. A great
| online source on Partimento and historical solfege:
|
| https://partimenti.org/
| ramenbytes wrote:
| Thanks!
| tgv wrote:
| I don't get how it depends on "how it was written."
| First, Bach did write chords. Bar 2 of the famous Toccata
| and fugue ends in a chord. Bar 10/11 has a big chord. Bar
| 12 starts with a chord. There are chords everywhere. In
| case you doubt the authorship, plenty of other toccatas
| have chords. The whole idea of figured bass is chords.
|
| Second, while they did think differently about harmony,
| you can describe it in modern terms. A description like
| Cmaj7 doesn't mean anything else than a set of pitches.
|
| A tritone substitution is somewhat different, since it
| depends on what the analyzer thinks the chord
| could/should have been. There's a recent YouTube video
| (by David Bennett, IIRC) that shows tritone substitutions
| in songs, but he mentions that he doubts Paul McCartney
| knew he was writing one. But does that mean it isn't? No,
| it means _you_ can see it as a tritone substitution.
|
| Music theory is a subjective tool to describe and
| compare, nothing else.
| zozbot234 wrote:
| > The whole idea of figured bass is chords.
|
| I think this might be missing the point a little bit -
| the bassline in figured bass has more primacy than any of
| the sonorities above it. The most relevant feature of
| "chord"-based approaches to music (as found historically,
| e.g. in performance methods for the Baroque guitar, and
| to a far lesser extent in repertoire for the lute) is
| that the vertical sonority (such as "Cmaj7") is all that
| matters; individual "voices" or "parts" are of secondary
| importance at best. This maps well enough to how lute- or
| guitar-like instruments might be played in an
| accompaniment role (since these instruments obscure the
| sense of a "melodic line" or a "part" the most, for a
| variety of reasons) but music includes a whole lot more
| than that.
| pclmulqdq wrote:
| It's interesting that you cite the Toccata and Fugue in D
| minor because some theorists believe that was actually
| written much later. The original theory was that
| Mendelssohn wrote it in the 19th century, but I believe
| there were some sources from the 1700s. It clearly has a
| very non-Bach character, including the octave doublings
| in the chords you mention.
|
| It's very clear that the man wrote chords. It's also very
| clear that harmony (ie vertical music theory) was not the
| tool used to write those chords. If you listen to BWV903,
| for example, there is a long section of arpeggiated
| chords that defy 18th and 19th century harmony.
|
| The OP's idea of a tritone substitution from Scarlatti
| does not have the same harmonic function as a tritone
| substitution in modern music. I would agree with you that
| if the function matches, you can certainly analyze things
| in the context of a later theory, but the function does
| not match.
|
| Finally, figured bass notates intervals, not chords. A
| crude realization can neglect voice leading in the upper
| voices, but more skilled realizers of figured bass will
| preserve voice leading between the intervals in the upper
| voices. The idea that figured bass is about chords sort
| of maps backwards the modern abuses of figured bass
| (which IMO should not be taught as a "basic music theory"
| subject - but that is for another day) onto the original
| method.
| jancsika wrote:
| That's a qualitatively different "tritone substitution" than
| what the author describes.
|
| author: spice up your jazz by simply replacing one dominant 7th
| chord with another a tritone away!
|
| Scarlatti: You thought I was aiming toward D-flat? Bitch, I'm
| surfing in G major! Your puny diatonic expectations cannot
| contain me.
|
| Put simply-- you can use regular expressions to try out the
| author's substitutions, but you'll need to build your own
| parser to try out Scarlatti's.
| elihu wrote:
| If you think of a dominant 7th chord as four notes in a 4:5:6:7
| resonance, then it seems the 7/5 interval is the "correct"
| tritone in this context. But a proper tritone substitution
| means turning the 7/5 into a 10/7 or a 10/7 into a 7/5, which
| means one or the other of the chords will be out of tune with
| itself.
|
| Alternatively, one could just hold one note fixed and move the
| other three, so you end up with both chords being self-
| consistent. That seems more mathematically satisfying at least.
|
| Ultimately, though, I suppose the only real standard of
| correctness in music is whatever you can get away with.
| neonscribe wrote:
| "Whatever you can get away with" is the entire basis of equal
| temperament.
| elihu wrote:
| It is, but in just intonation it's harder to get away with
| certain things when the math doesn't quite work out.
| zarzavat wrote:
| > A tritone is very dissonant
|
| I'm sure he didn't mean it literally, but to be pedantic a
| tritone is only moderately dissonant. A minor second is very
| dissonant.
| coldtea wrote:
| In some musical cultures it's also totally acceptable and
| featured all the time, without being considered dissonant.
| megmogandog wrote:
| Yes, this understanding would mean the 12-bar blues and blues
| music in general are an extremely dissonant form as they use
| the dominant seven chords as tonics.
|
| How many people consider the blues dissonant?
|
| It reminds me of my first counterpoint assignment. "Fourths
| aren't dissonant" I said, and it came back covered in red
| marks
| jmkr wrote:
| I assume most people would find a dominant dissonant. A V7
| is difficult to figure out. A V9 sounds better.
|
| To say blues doesnt sound dissonant sounds more like only
| adding the relative minor b5. Or British blues rock.
| coldtea wrote:
| V7 are bog standard in blues and rock, and nowhere near
| hard to figure out or sounding dissonant.
|
| And other cultures like tritones just fine, featuring
| them even more prominently.
|
| There's no inherent "tritones are dissonant" human
| universal, it's a common practice harmony prejudice.
| recursive wrote:
| I understand dissonance to be how big the numbers are when you
| express an interval as a reduced frequency ratio. By that
| metric it's pretty dissonant. How can it be considered
| moderately dissonant?
| bongodongobob wrote:
| For me, I don't think it's meaningful to think of two notes
| in a vacuum as anything. The logical part of me wants to
| think about it with math like you're suggesting, but 2 notes
| lack any context to give them meaning. Add another two to the
| chord or add other notes around it temporally, and now they
| don't sound bad at all. The idea of consonance and dissonance
| only makes sense to me within the framework of tension and
| release.
| recursive wrote:
| > now they don't sound bad at all
|
| I didn't mean to suggest that dissonance has any
| correlation with good/bad.
| zarzavat wrote:
| Yes, a tritone is dissonant because it isn't close to any
| simple ratio of frequencies. It has a spiciness that makes
| the music sound interesting without it being overly
| unpleasant.
|
| Avoiding dissonance entirely can also be unpleasant. e.g.
| barbershop harmony can sound saccharine because the human
| voice can hit those simple ratios much closer than 12TET can.
| 12TET gives us some dissonance for free, which people have
| learned to appreciate. Like spice tolerance, dissonance
| tolerance is learned not inate.
|
| A minor second is very dissonant, you can hear pronounced
| beating between the tones:
| https://en.wikipedia.org/wiki/Beat_(acoustics). This makes it
| stick out more than a tritone, so it has to be balanced more
| carefully.
| dcassett wrote:
| A tritone interval by itself (only 2 notes sounding) sounds
| quite dissonant to me.
|
| But in the context of the dominant 7th chord, the only note
| dissonant with the bass is the 7th. The tritone itself is not
| so prominent since it occurs between two non-bass notes.
| coldtea wrote:
| > _But never mind. What if we take my picture and rotate it 180
| degrees? Then we get a new chord! This trick is called a tritone
| substitution._
|
| I know tritone subtitution from music theory, and trying to grok
| this explanation. What does the "roation by 180 degrees"
| represent in this case?
| ksenzee wrote:
| He means turn the circle of fifths 180 degrees. In other words,
| move the chord up a tritone (six half-steps).
| dcassett wrote:
| The drawing looks like a circle of half steps, not a circle
| of fifths.
|
| It seems that the article would be clearer if the 180 degree
| rotation were to put F# at the top of the drawing.
| ksenzee wrote:
| Yes, good observation. Why would that help, though? No
| matter what's at the top, you're turning the whole thing
| halfway around.
| decasia wrote:
| I asked some classical music people once if there was a history
| of harmony. Someone retorted that the modern concept of harmony
| was an inadequate way of understanding counterpoint, and that the
| primary concept should be voice leading, not vertical harmony. I
| suppose it makes sense -- that our categories of musical analysis
| have histories, and it can be misleading to apply them out of
| context (as the rest of this thread is commenting).
|
| But I still wish someone would write a history about "what kinds
| of harmonies do people think sound good/melodious/interesting,
| and which do they consider bad/ugly/weird/useless at a given
| moment." Or if that history already exists, I wish I knew how to
| find it.
| wrs wrote:
| Leonard Bernstein's Harvard lectures have some of this.
|
| https://youtube.com/playlist?list=PLuQqHfLobLUIzDiIGrtE41KvQ...
| spacechild1 wrote:
| "Harmonielehre" by Dieter de la Motte is an excellent book that
| does exactly this. He explicitely points out that harmony must
| always be understood and analyzed in context. "Kontrapunkt",
| his book on counterpoint, follows the same principle and is
| just as good. I think/hope there are English translations.
| ofalkaed wrote:
| A great deal has been written on this but the vast bulk
| requires a solid understanding of theory, Cambridge's History
| of Western Music Theory gives a lifetimes worth of material to
| study on this topic.
| giraffe_lady wrote:
| You also need to locate such a project in place as well. There
| isn't just one music history, each culture has its own. They've
| only begun to somewhat converge in the last couple centuries,
| but there are at least dozens of distinct, independent musical
| traditions with at least a thousand years of continuous
| development.
| jdietrich wrote:
| From a jazz musician's perspective, classical theorists tend to
| confuse the map with the territory. Classical theory is (at
| least historically) often prescriptive rather than descriptive,
| which tends to cause some friction when applied to music
| outside of that idiom.
| dr_dshiv wrote:
| Music used to be treated like a science... the pythagoreans, for
| instance, conducted the first hypothesis driven scientific
| experiment on a musical question (whether whole number ratios
| affected chords with bronze chimes). Descartes' first book was
| all about music theory.
| ofalkaed wrote:
| Up until fairly recently the only people who treated music like
| a science were people who did not have much if anything to do
| with music beyond listening and thinking about it. When
| composers and musicians started treating music like a science
| (or math) people tended to complain about it and "reduce" it to
| academic wankery.
|
| Pythagoras and Descartes had more to do with criticism and
| theory than anything anyone was listening to or composing,
| which was instrumental in the development of western theory. I
| don't think we have any music following the ideas of the
| Pythagoreans until the mid/late 20th century, anyone know of
| earlier examples?
| pclmulqdq wrote:
| There is pretty strong evidence that Bach, for example, was
| also very much into math and thought about music in a very
| mathematical way. Some other composers definitely did the
| same, but I agree with you that mathematical thinking was
| never a prerequisite for composers.
|
| I would suspect that many of the ones from the early periods
| were far more "mathematical" than 20th and 21st century
| composers, but there is very little writing either way.
| ofalkaed wrote:
| I don't think many early composers get as mathematical as
| someone like Xenakis or even Schoenberg. Or maybe its just
| the way in which the math manifests in composition, Xenakis
| was far more direct with it than Bach. I can't see how one
| could make a viable case for pre 20th century composers
| being more mathematical but the argument could be
| interesting and worthwhile.
| pclmulqdq wrote:
| I'm not sure how you're defining "mathematical." The
| definition really changes who is on the list. Schoenberg
| and the 12 tone crowd had some of the most obvious
| applications of math, but composers of the Baroque era
| treated music a lot more like a logic puzzle than
| anything the 20th century composers came close to. For
| example, I encourage you to do some research into canons
| and how they are written. That is what I meant by
| "mathematical," rather the idea of doing arithmetic on
| notes (which I happen to think is a crude excuse for
| creativity).
| ofalkaed wrote:
| >rather the idea of doing arithmetic on notes (which I
| happen to think is a crude excuse for creativity).
|
| That is a very crude view of the relation between math
| and music in 20th and 21st centuries. The puzzles Bach
| was working out had more to do with the theory than the
| math and we can support this, the math aspect is more
| interesting conjecture than something we can demonstrate,
| at least from what I have read on the subject which tends
| to be filled with assumptions and generalizations.
|
| Schoenberg and his ilk are more music influenced by math,
| set theory in music is not set theory in math. We don't
| really see math literal in music until the rise of
| computer music and they are often doing things more than
| just seeing what the math results in. The thing with much
| computer music is that it is deeply tied into how music
| works on a computer right down to the way sound is
| generated which requires us to throw away traditional
| ideas of orchestration and form to understand it as
| something other than just a musical representation of
| math. I lack the math to get much of this stuff but I
| find it very interesting and it certainly provides me
| with a good number of ideas.
|
| I define math as math.
| pclmulqdq wrote:
| I gather that you have defined math completely
| differently than me, or at least defined it in a way that
| gives computers primacy over every other form of math.
|
| > The puzzles Bach was working out had more to do with
| the theory than the math and we can support this, the
| math aspect is more interesting conjecture than something
| we can demonstrate, at least from what I have read on the
| subject which tends to be filled with assumptions and
| generalizations.
|
| This sentence structure is very much beyond me, but from
| what I gathered, you do not consider propositional logic
| as created by harmony/counterpoint to be "math" and you
| believe that those rules are arbitrary and not based on
| math at all. That is sort of a fringe view that is
| facially false. Around the world, rules of harmony have a
| lot to do with the harmonic series, scales, tunings, and
| other building blocks that are hugely based on math. A
| lot of that was actually up to the composers and
| producers of music in the 19th century and earlier
| (around the world).
|
| > We don't really see math literal in music until the
| rise of computer music and they are often doing things
| more than just seeing what the math results in.
|
| I see that you have defined "math as math" in terms of
| the totality of the math involved in the process of
| composition. Most 21st century composers and producers I
| know do absolutely no math (defined in any way) when
| writing music. I will also say that the producers of
| computer music absolutely _do not_ throw away
| "traditional ideas of orchestration and form" unless they
| are lazy or bad. Many of them very clearly understand
| that stuff and riff on it in ways that can only be done
| when you combine a deep artistic instinct (0 math) with a
| computer (that does all the math for you).
| viraptor wrote:
| > early periods were far more "mathematical" than 20th and
| 21st century composers
|
| We've got way more composers and variety today. But part of
| that variety is https://en.wikipedia.org/wiki/Math_rock
| jzemeocala wrote:
| well the Pythagorean comma and how to divide it amongst the
| octave was the central objective during the whole evolution
| of temperament (from meantone to modern day 12-tet). So that
| takes us back to at least the 15th/16th century
| ofalkaed wrote:
| That is more theory than practice unless you want to reduce
| Pythagoras down to a comma. I was referring more to people
| who decided to take Pythagoras and related writings as
| gospel.
| dr_dshiv wrote:
| Aristoxenus (Pythagorean student of Aristotle) seemed to
| have developed a proto-equal temperament system.
|
| Written about by this guy (not peer reviewed, but has good
| presentation of the original Aristoxenus)
| https://siementerpstra.com/aristoxenus/
|
| http://terpstrakeyboard.com/about/
| trgn wrote:
| According to Vitruvius, Roman engineers had to learn music so
| they could tune the ropes of ballistic devices to the correct
| tension by listening to their pitch when striking them.
|
| Music was part of the quadrivium as well, on par with astronomy
| and math.
| neonscribe wrote:
| It's a shame to describe the tritone sub for G7 as C# F G# B,
| when the proper way to spell it is either Db F Ab Cb or C# E# G#
| B. Of course, then you'd have to explain about enharmonic
| equivalence and how chords are usually spelled with every other
| note.
| autarch wrote:
| I came here to pick this nit but you beat me to it. I think
| calling it Db7 is the best way to think of it, especially since
| in jazz it's often part of a descending sequence of II-V-I,
| where the tritone substitution turns it into II-bII-I. So in C
| major (where G is the dominant), it has to be Db.
| mkbosmans wrote:
| Why do you say a tritone substitution turns it in a II-bII-I?
| Can it be as easily said to be II-#I-I? In that case it would
| be C#.
| colanderman wrote:
| Enharmonic equivalents are usually chosen to match the
| direction of movement. So a descending passage will prefer
| to use flats.
| brudgers wrote:
| The root is the root.
|
| There can be only I.
| autarch wrote:
| I don't think this is correct. I think colanderman's
| answer is the right one, which is that when we're
| descending, we generally spell out the pitches with
| flats. If this were ascending, then we could have
| I-#I-II. But as I noted, in jazz this particular
| descending pattern is fairly common.
| brudgers wrote:
| _spell out the pitches_
|
| I, bII, etc. are chords not pitches. II-bII-I is a chord
| change. Pitches may go up or down and voices may go away
| or arrive. They may be part of those chords or not. And
| there may not even be a root pitch.
|
| Or if you want formal theory, chords are scales [1] and
| there ain't no such thing as a scale with a sharp I. If
| you sharp the one it's a different scale starting in a
| different place.
|
| The b in bII is not an accidental and bII is how to
| communicate the chord in passing. I/bII is also possible
| to communicate a modulation (as would be vii/II, etc. if
| the modulation is elsewhere).
|
| There are "enharmonics" for chords that aren"t the root
| of course, e.g. #IV and bV depending on intent,
| convention, or playability. But #I will be marked wrong
| on the entrance exam and only raise you standing among an
| avant guard that isnt accepting new members.
|
| [1] see Russell's _Lydian Chromatic Concept_.
| bonzini wrote:
| > If you sharp the one it's a different scale starting in
| a different place.
|
| It depends on what's the function. If you want to use the
| tritone-substituted G7 to modulate to the sharp fourth,
| you'd write it C#7 and resolve it to F# (or F#-).
| brudgers wrote:
| C#7 is the name of a chord not a pitch and not Roman
| Numeral Analysis. [0]
|
| The Roman Numeral analysis would be V7/#IV if you are
| _modulating_ in C. And something else if you aren 't in
| C. Roman Numeral Analysis is independent of key or tonal
| center. The Roman Numeral Analysis would be bII if you
| are not modulating because that's how Roman Numeral
| Analysis communicates.
|
| Thinking about Phrygian mode. The two is always a bII.
|
| {0} As an aside, in The Common Practice the bII is often
| notated N6 (for Neapolitan 6th) to set up a perfect
| cadence, i.e. I-N6-V-I.
| GlenTheEskimo wrote:
| Yeah, I've seen things spelled this way before in barbershop
| arrangements. Usually because it's less accidentals. I think it
| makes sense from a "what notes should I play" perspective, but
| seeing these chords spelled in a weird way gives you insight
| into how some composers actually think, and all that REALLY
| matters is what the music sounds like.
| coliveira wrote:
| The explanation is that a seventh chord is defined as a set of
| third intervals. So it cannot jump from C# to F, it needs to go
| from C# to E#. Even though these tones are the same, the C# to
| F doesn't make sense. The same can be said about F G#, it
| doesn't make sense because it is not a third.
| thaumasiotes wrote:
| I transcribed the music on the ghost ship in Monkey Island 1,
| which features a lot of chords in the background involving
| fourths, fifths, and whatever we want to call the half-step
| in between fa and so.
|
| Working with a MIDI file and without much grounding in music
| theory, I had and have no real way of determining whether to
| represent notes flat or sharp. I consulted several people and
| generally got a response of "Oh, interesting stuff! It's not
| clear how you should transcribe that."
|
| I'm still interested in opinions! If you want to check it
| out, the score is here:
| https://musescore.com/user/36584999/scores/7810499
| Kye wrote:
| My understanding is flat vs sharp is largely about intended
| use. Something about some instruments makes one way or the
| other better for playing.
| thaumasiotes wrote:
| I've seen a few theories in various places:
|
| - Match the type of accidentals used by the key
| signature.
|
| - Use sharps when the melody is moving up, and flats when
| it's moving down.
|
| - Use whatever accidentals give you a visually pleasing
| spacing of notes in "thirds" as represented on the staff.
| (As advocated here.)
|
| - Use the accidentals that are physically compatible with
| other notes in the chord. (Only a concern for certain
| instruments, but e.g. I understand that the pedals on a
| harp affect many strings at once, so playing a particular
| combination of notes may require a clever approach to the
| pedals, indicated by what might otherwise look like an
| unnatural set of accidentals. This wouldn't apply to a
| piano, where G# is just a separate key from G, not a
| modification of the G key.) I think this is what you're
| going for?
| skybrian wrote:
| Another example would be the bass side of an accordion
| where Db and C# imply different buttons (though not
| different sounds - there are duplicates) and they're
| quite far away from each other.
| coliveira wrote:
| The accident you use really depends on the context. If
| you're talking about chords, then you should follow the
| "stack of thirds" explanation that I gave above, it is
| how chord theory works. However, the other rules you
| mention also can be used depending on your situation. In
| a melody, you normally want to add accidents only when
| needed.
| kazinator wrote:
| The C# grates on my eyes, since the V7 tritone substitute is
| IIb7. However, preserving the F and the B notation emphasizes
| the tritone interval that is inverted and shared with the
| substitute.
| pizza wrote:
| Question for music theory experts who are also coders: does it
| feel like understanding a programming language, or something
| else? Admittedly I've never really made any serious independent
| effort to learn it, or to retain whatever I tried to learn, but
| it is very difficult for me to even grasp a mental model of how
| understanding it is supposed to work, or feel, in my head.
|
| I can read a piece of code and know how the bits affect one
| another. When I read basically anything on music theory it feels
| like a string of non-sequiturs basically. Maybe there's just some
| skill floor where that all starts to feel organized?
| dools wrote:
| A bit. Music is a bit like programming but I think there are 2
| distinct ways to practise music: performance and composition.
| Theory helps you with both. I think that there's less of a
| "performance" aspect to programming, it's more "composition-
| like". Chess is an area where you have a combination of theory
| and skill that, to me, is more music-like (because you can play
| chess in a "performance way" and also in a "composition way").
|
| If your goal is to be able to improvise then the purpose of
| theory is really ear training: it allows you to develop an
| instinct about what to do with your body to produce a desired
| result. Improvisation is a bit like "composition in the
| moment", like speed chess.
|
| There are contrived situations where people treat programming
| as a performance activity but it's not the way most programmers
| spend their time.
| epiccoleman wrote:
| This was my favorite reply to the question. Music theory is
| great, and it really can be helpful with composition. But
| I've also found that what I'm _really_ looking for when
| trying to _improvise_ , or perform, is having studied and
| worked on the theory - specifically on the ear training and
| the process of connecting that to my fingers - to the point
| where I don't have to think about it any more.
|
| The composition vs performance framing is very useful I
| think. Some musicians might just want to do composition, and
| can spend a little more time between the notes figuring out
| what ought to come next. (Although even in this case, it's
| easy to get bogged down in analysis and forget about what
| _feels_ right). But a lot of musicians want to be able to
| _improvise_ - and the difference is like being able to write
| down a compelling argument vs being able to make a compelling
| "speech" off the cuff.
|
| Yeah, in both cases, you're going to need a good
| understanding of grammar and vocabulary - but when you're
| trying to make that speech (or improvise a solo), you're just
| not going to have the time to think about "the sound I want
| to hear next is the sound of the 5th of the chord the band is
| implying." All our practice and theory homework is in service
| of the fingers just doing what's in our heads automatically -
| and sometimes, even surprising ourselves with what comes out.
| dools wrote:
| > But I've also found that what I'm really looking for when
| trying to improvise, or perform, is having studied and
| worked on the theory - specifically on the ear training and
| the process of connecting that to my fingers - to the point
| where I don't have to think about it any more
|
| "The purpose of all theory is ear training" is actually a
| Warne Marsh quote, although one that I can't verify. My dad
| (who is/was a jazz musician) read it in an interview in
| Coda Magazine in 1976 and while I can find references to
| the interview I can't find a copy of it online.
|
| My dad used the quote "The purpose of all theory is ear
| training" as the inscription on his self-published basic
| and advanced keyboard harmony books. It's certainly a quote
| I've heard him repeat many times over the years.
| ess3 wrote:
| A quote from a jazz theory book comes to mind. Goes something
| like this:
|
| Jazz is 99% theory 1% magic. The difference between the
| greats is that they've forgotten all the theory
| bonzini wrote:
| That makes no sense. They've internalized the theory so
| much that they can focus on the magic, and each of them has
| their own kind of magic, but they absolutely know the
| theory.
| rectang wrote:
| Haha this is the second time my degree has come in handy after
| getting me a job in a record store after college.
|
| I'd say "music theory" as a general concept is closer to
| understanding computer science principles like managing
| complexity or the memory hierarchy. Individual disciplines,
| such as orchestrating for a specific kind of ensemble (string
| quartet, big band...) or writing in specific forms (fugue, AABA
| popular song...) are closer to mastering practical programming
| tasks like working fluently in a given programming language.
| kleinsch wrote:
| There's a bunch of theory that goes into understanding why a
| tritone sub works for a Dom7 for the 5 chord, but it's not
| something you think about when you're using it. You learn how
| it sounds and you start using it instinctively.
|
| Other people can probably figure out better analogies, but I'd
| say it's something like the difference reading an article about
| generics or monads vs actually using them every day. To an
| outsider these seem like a ton to think about, but when you use
| them every day they're just part of your toolbox.
| cousin_it wrote:
| I think the only "universal" part of music theory is the
| integer resonance stuff, "a perfect fifth is a 2:3 frequency
| ratio", because integer resonances do seem to have biological
| significance for us. The rest is culturally dependent: it's not
| describing some uniquely necessary mathematical object, but
| more like describing the spoken language of a certain region
| and time period. The best way to understand it is to play music
| from that period, notice some common "moves" (like the move
| from dominant to tonic), and realize "hey, music theory has a
| name for that".
|
| You wouldn't use music theory to write music, same as you
| wouldn't use a grammar book to write a novel. You write music
| by intuiting the sequence of moves you want to make, guided by
| your ear and listening experience, and maybe even coming up
| with some new ones. Then if you're successful, theorists will
| make theories about it.
| Kye wrote:
| The canonical video on the subject:
| https://www.youtube.com/watch?v=Kr3quGh7pJA
|
| Some people will naively say "All music has pentatonic!
| Universal!" but ignore vital cultural context. One example in
| the video is ragas: they can look a lot like Western scales
| and modes, but they have a time and context.
|
| Western music _also_ has a time and context, but it doesn 't
| stand out as much to us unless someone goes full ham breaking
| that context like with the Imperial March in a Major mode:
| https://www.youtube.com/watch?v=B9MShtCg4fk
|
| It changes the mood from "this is the bad guys!" to something
| more positive and triumphant.
| PaulDavisThe1st wrote:
| There are also several traditions that have scales/modes
| where certain note sequences (typical pairs) are only
| "allowed" in one direction (i.e you can play #3 after #1 if
| you're ascending from #1 to #3, but not the other way
| around).
|
| This adds additional confusion to comparing scales/modes
| between cultures.
|
| We do have at least one such mode/scale in the western
| european classical tradition, but it is not widely used.
| crdrost wrote:
| So it's not biological significance... You are born loving
| the sound "shush," white noise. This is also the great irony
| of people complaining about distortion and thick bassy kick
| beats, we actually like it because it's warm and "takes us
| back": indeed even to the noisy slushy womb and the heartbeat
| there.
|
| Rather it's that things that hit one tone either also tickle
| the hairs in your organ of Corti at 2x, 3x, 4x, 5x the
| frequency (strings) or at 3x, 5x, 7x, 9x the frequency (half-
| open acoustic resonators--guitar bodies, panflutes), and your
| brain feels comfortable when those tickle together as they
| are familiar.
| hyperadvanced wrote:
| I fit the bill. There are obviously similarities: music
| notation is a formal language like programming languages. When
| you read notation, you can pretty quickly grasp certain
| relationships and substructures within the piece. With jazz
| notation especially you can quickly figure out what the general
| strategy of the piece is and once you've got an ear for how it
| works, you can theorize or write little melodies or
| complementary bits just from sight alone.
|
| I would also say that the obvious impact of the ear and/or the
| tools you're using to play music make it very different than
| programming. Without the knowing how you would actually play a
| piece of music, it can be difficult to visualize or interpret
| notation, whereas code is pretty straightforward in how it's
| made or what it actually does. The "feel" is really abstract
| and interacting with the piece is more akin to observing a
| running system than it is to touching code.
| memset wrote:
| Yes - well, almost. As coders, theory scratches the itch of
| understanding what's happening "under the hood." We might say
| that "Bach's music is brilliant", but why? Theory helps make
| the music, and the things that make it sound interesting,
| explainable.
|
| That said, making music is not merely a technical exercise -
| there could be multiple theoretical ways to describe a harmony.
| You still have to listen to it and ask, "what makes the most
| sense? Is this functioning as a resolution to some tension?"
| It's easy in a classroom to lose sight of the fact that the
| theory was invented after the fact.
| phlakaton wrote:
| Not in my experience.
|
| Sure, music theory involves learning the "syntax" of music
| notation, the "semantics" of e.g. key and genre, and the
| "programming pearls" of common musical idioms like tritone
| substitutions. There are analogs.
|
| But what distinguishes music theory is:
|
| 1. The language and notation is hundreds of years old. It's
| been with us in one form or another 200 times longer than COBOL
| has. Maybe longer.
|
| 2. You don't have the peculiar challenge of having to speak it
| in the very precise form that a computer requires of a
| programming language. The terminology and communication between
| musicians is much fuzzier than that, much more like a human
| language.
| phlakaton wrote:
| (More like 20 times. But what's an order of magnitude to a
| musician accustomed to dB anyway.)
| shermantanktop wrote:
| As someone who has come back to jazz improvisation after many
| years, and being a coder, the performance aspect is a little
| like playing a video game.
|
| But this game has 1) very short levels (1-2 seconds), 2)
| repeated patterns in the levels and sequence of levels, 3)
| strong incentives to solve levels in novel and interesting
| ways, but 4) there are hidden mines everywhere which can damage
| you, but 5) you get points for hitting the mines in the right
| way so that you avoid damage. The mines are "wrong notes."
|
| Music theory gives you power ups to see the mines, quickly plot
| paths, and treat sequences of levels as part of a meta-level.
| But you have to be FAST.
|
| (I have been known to stretch an analogy too far..)
| asimpletune wrote:
| Learning music theory is more about expanding your taste
| vocabulary and giving names to each new thing.
| brudgers wrote:
| [I am not a music theory expert but just finished two semesters
| of music theory at community college and have several decades
| of experience as an adult]
|
| Functional harmony is usually what people mean by music theory.
|
| Functional is the key to my understanding. Functional Harmony
| is what has been done harmonically and melodically in styles of
| music derived from The Period of Common Practice. Functional
| Harmony describes what some people did. Using it makes music
| that sounds like what those people did.
|
| From the street where I live, I see cultural institutions that
| ascribe moral value to the conventions of The Period of Common
| Practice. There's an industry built up around The Period of
| Common Practice and the flow of money means there are jobs for
| those of jobbing age and careers for those of careering age.
|
| It is a disjointed mess like any jobs program.
| UncleMeat wrote:
| They have totally different goals.
|
| Music theory is descriptive, not prescriptive. Oodles of people
| make music without knowing a lick of it, and people who learn
| it in academic environments still typically make music starting
| from other concepts. "Listen to records and vibe with what they
| are doing" is typically a much more effective way of learning
| to improvise seriously than "learn the theory rules", for
| example.
|
| "Music Theory" also typically is very tightly bound to harmonic
| analysis modes that are focused on about two centuries of
| western european music. This is necessarily going to limit its
| effectiveness when applied in other spaces (even here, when
| applied to jazz).
| 613style wrote:
| This is exactly what I got wrong when I started learning jazz
| piano as an adult. My wife is a lifelong musician and I got
| to the annoying point where I'd be playing and she'd walk by
| and go "that third chord sounds wrong." I'd ask why and she'd
| be unable to elaborate until she sat down and played the
| better version intuitively. Then she'd retroactively analyze
| what she did to explain it to me. I understood the theory,
| she understood the sounds. It was always humbling and helped
| me understand that intellectualizing comes second.
| dhosek wrote:
| One of the things I think is cool is that a standard chord
| sequence in Jazz is the ii7-V7-IM7 (e.g., Dm7-G7-CM7) which, if
| you do the tritone substitution turns into ii7-II7-IM7 so you get
| this nice little chromatic descending sequence happening in the
| bassline.
|
| It's also worth noting that when comping, the most important
| notes to be sure to hit are the 3rd (which expresses whether
| we're major or minor) and the 7th (which gives the flavor of the
| chord), since the root is likely covered by the bass player and
| the fifth is implied by the 3rd (if you're at a piano, try you
| can see this by, e.g., playing C-E-G-B in the right hand and C in
| the left, and comparing that to E-B in the right hand and C in
| the left. A jazz pianist soloing will likely do their melody line
| in the right hand and hit 3-7 with the left), so the tritone
| substitution will be made/implied by whatever the bass player
| does against that.
|
| The other fun thing is to just vamp on a II7-V7 sequence. Some
| notable places you'll encounter this in music you've heard
| include the Simpsons theme and the Beatles' "I Am the Walrus."
| zefhous wrote:
| Like Sting said, "it's not a chord until the bass player
| decides what the root is."
| recursive wrote:
| There's even a name for the 3rd and 7th. Collectively, they're
| known as the "guide tones".
| brudgers wrote:
| _you get this nice little chromatic descending sequence
| happening in the bassline_
|
| If and only if the chords all stay in the same inversion and
| the bass line doesn't make leaps. That might be what you want
| and it is idiomatic in some genres/styles. But it might not be
| what you want or even what you get from the notation depending
| on how the musicians interpret the notation.
| ilayn wrote:
| "Music theorists tend to bombard their audience with more
| information than nonexperts can swallow in one sitting." groaned
| the mathematician, in cognitive dissonance.
| odyssey7 wrote:
| "A tritone is very dissonant, so the dominant seventh chord
| really wants to 'resolve' to something more sweet."
|
| "I see you _shiver_ with antici----"
|
| It's not dissonance that makes you want to hear the completion of
| the sentence, rather, it's grammar. If you play a tritone out of
| context, there is no need for it to resolve, but you can cast
| context around it by adding a resolution to a tonic just after.
| The tritone has a culturally-learned grammatical role in western
| music; and that role is not a universal law of aesthetics.
|
| "----pation."
| anon291 wrote:
| Interesting. John Baez is the brother of Joan Baez, the famous
| singer. Didn't know he was into music too.
|
| That being said, Tritone substitutions sound good in some
| circumstances, but seem over the top in others. Use with care, as
| always. They'll always seem more appropriate in jazz genres
| taejo wrote:
| According to Wikipedia they are first cousins, not siblings
| bonzini wrote:
| Toxic by Britney Spears is basically built on secondary
| dominants and tritone substitutions (i-VI7-II7-V7 becomes
| i-IIIb7-II7-IIb7), so they definitely have their place in pop
| music too. Whether the composers thought about it that way, we
| can't know, but in any case what matters is whether the bass
| line sounds good.
| SoftTalker wrote:
| Does one normally learn any theory as part of learning to play an
| instrument?
|
| I played in middle and high school concert band and took private
| lessons in addition to that for a few of those years.
|
| I never learned a lick of theory from any of my instructors.
| Maybe because as a horn player you can't play chords. All I
| learned was to read notes and play my part. After a year of high
| school band I came to the conclusion that this was just work and
| gave me no enjoyment at all so I quit. Everyone seemed surprised.
| Nifty3929 wrote:
| Yes, and yes. The reason you weren't taught much theory is
| because on a horn you're only playing one note. But I think
| that's really a shame, because you were deprived of the
| understand of what you were playing and why, in the context of
| the notes and chords that the rest of the band was playing. And
| even when playing a horn solo piece, there is always an
| understandable, chord-based structure to the piece.
|
| Edit: Also it really doesn't take much effort or theory to
| understand most of what would be interesting. Like many
| subjects, the 80% of what's helpful can be written on just a
| few pages and learned in a few hours - but whole college
| curriculums can be made of the details and nuances. Go read up
| on 7th chords, cadences, and simple chord progressions if
| interested.
| ghostpepper wrote:
| This is an oversimplification imho. Many of the greatest jazz
| musicians like Miles Davis and John Coltrane played
| instruments that could only play one note at a time, and they
| still manage to convey harmonic concepts.
|
| I don't have an answer for why most music teachers don't
| teach theory (and improv) other than it's more challenging
| and they might not know it themselves, and it's easier to
| teach rote memorization.
|
| There are plenty of people who learn piano (which obviously
| doesn't suffer from the single-note "limitation") and also
| learn almost no theory.
| brudgers wrote:
| In the US, theory is typically part of post-secondary musical
| education. Some high schools might have it, but in a lot of
| high schools filling out the marching and symphonic bands with
| warm bodies will drive a lot of a music program.
|
| Typically, piano is part of post-secondary music program
| requirements and keyboards make it practical to apply music
| theory to make sounds...arpeggiation will get your ear so far.
| Polyphony gives a much clearer picture of what music theory is
| describing.
|
| If you're interested in learning music theory, a polyphonic
| keyboard that makes sounds without a computer (maybe one with
| speakers, but at least with a headphone jack) is my
| recommendation. Maybe it's better if it is small and portable.
| A MIDI controller with a phone or tablet might be ok, but
| phones and tablets have email and the internet and those can
| interrupt what you set out to do.
|
| Anyway, theory usually comes later in the US system. There are
| exceptions of course.
| pohl wrote:
| Horn players can always outline chords, perhaps with outright
| arpeggios or by choosing chord tones on downbeats. That said,
| even if your teacher had armed you with theory its still just
| comes down to an assload of work. But maybe that might have
| helped you connect with a feeling of reward.
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