[HN Gopher] What I Learned Writing an Album in Just Intonation
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What I Learned Writing an Album in Just Intonation
Author : pierrec
Score : 145 points
Date : 2024-08-13 18:55 UTC (3 days ago)
(HTM) web link (www.osar.fr)
(TXT) w3m dump (www.osar.fr)
| vunderba wrote:
| When I compose, I usually begin by sitting quietly and humming or
| singing out loud until I have a melody that I like. Because I was
| born and raised in the west, acoustically I'm naturally
| accustomed to a 12 tone equal temperament.
|
| Atonal music is more difficult for me to grok, and I kind of
| imagine that for you to be fluent and compose in these sort of
| microtonal scales you would need to be introduced to it at a
| young age - in much the same way that it's significantly easier
| to learn a second language if you grow up in a bilingual
| environment.
| eternauta3k wrote:
| I have no clue about this topic, but isn't Just Intonation what
| e.g. people sing when left to their own devices?
| handity wrote:
| Yes
| andybak wrote:
| I'm no expert but your use of "atonal" and "microtonal"
| interchangeably here seems way off the mark.
|
| "Atonal" usually refers to music composed without a fixed sense
| of key - and was originally used to describe music written
| using standard western 12TET.
|
| It's a property of the music's relationship to key signatures -
| not it's tuning system.
| pierrec wrote:
| I'd love to get some feedback on this, because I'm not sure I've
| hit the original goal of this article.
|
| For a long time, the topics of just intonation, harmonic
| lattices, and of their relationship with temperaments were
| difficult for me to understand, despite reading the theory on
| them. It's not until I applied the concepts that could say I
| understood them.
|
| I tried writing the "missing article" that would have given me
| this understanding right away, banking on the added value of
| interactive figures. Right now I suspect that I failed in the
| same way as my early readings did: this article might be hard to
| understand unless you're already familiar with the topic, which
| is a bit of a chicken-and-egg problem. I think I glossed over
| some concepts, and it sometimes looks like I'm pulling numbers
| out of thin air in some examples. Nonetheless I hope it will help
| some people understand these topics. Maybe what's needed is a
| slower-paced version of this as a longer series.
| thrtythreeforty wrote:
| The interactive harmonic lattice, with the commas clickable and
| audible, is first rate and is the best interactive illustration
| of JI problems I have yet seen.
|
| It is not quite clear from the explanation, that since the "3"
| direction is also dividing by 2 implicitly, the note
| confusingly labeled "3" is really just 3/2 - the perfect fifth.
| Similarly, the note labeled "5" is actually what we hear as the
| 12TET major third - clarifying a couple of examples on this
| lattice (or playing a chord) would be good.
|
| Then, the thing I think that might help is driving the point
| home a little more by creating a comma by hand - a "knight's
| move" to another tile 5 horizontal and 3 vertical, creates a
| ratio that _almost but not quite_ undoes itself. The (unwieldy)
| math is 1*3*3*3*3*5*5 /2/2/2/2/2/2/2/2/2/2/2 = 0.9887, _and
| this is what creates the commas in JI._ Hiding the octave
| transpositions, while making for a neat visualization of the
| lattice, confuses the underlying issue.
| pierrec wrote:
| I'm now realizing this and I totally agree that hiding the
| octave transpositions might make things confusing.
|
| Maybe this could be clarified by having a first lattice where
| this adjustment is not made, and everyone can observe how
| frequencies rapidly become extremely low or high, maybe to
| the point of being inaudible. Then we can ask "how can this
| problem be solved?" and introduce the concept of pitch class
| lattices where everything is transposed into one octave.
|
| Regarding intervals, I've always seen the irony and should
| probably mention it. Yes, the classical concept of fifth is
| related to the 3-ratio, while thirds are related to the
| 5-ratio. I'd argue this falls under the "empty your cup"
| category, but yes, leaving it untold probably doesn't help
| with understanding.
| thrtythreeforty wrote:
| To continue with an empty cup philosophy while still
| mentioning intervals, you can just posit "humans like how
| these 5- and 3-ratio intervals sound" and play chords using
| them to demonstrate. Then you don't need to handwave why
| this particular lattice was picked, and you can draw a
| comparison to 12TET's third and fifth.
| pyinstallwoes wrote:
| What are your thoughts on the fringe 432 theory, but the
| actual roots of it in relation to the geometric significance
| towards whole number ratios and then what is never discussed:
| the tuning associated with it?
| bongodongobob wrote:
| If you're talking about using 432 Hz vs 440 Hz it's
| nonsense. You could pick any frequency you want. The
| frequency you pick to tune an A to is arbitrary.
| pyinstallwoes wrote:
| Yeah but you don't have the same knowledge apparently.
| munchler wrote:
| In other words, 3 * 3 * 3 * 3 * 5 * 5 is 2025, which falls
| well short of 11 octaves (2^11 = 2048). No series of 3's and
| 5's can ever multiply to a power of 2.
| thrtythreeforty wrote:
| Oh, and one last point of feedback - it wasn't apparent to me
| that the "Aniron" progression was walking across the lattice.
| You should make the projected versions semitransparent to show
| the main chord progression walking as it does in the JI
| lattice.
|
| Still, awesome diagrams.
| wonger_ wrote:
| I am very unfamiliar with the topic. Here's my takeaways from
| the article: - almost all music I've heard uses
| 12TET - JI is microtonal / an alternative tuning to 12TET
| - you're the author of the lovely ambient.garden, which uses JI
| - the audio widgets and visualizations were very helpful
| - JI has perfect harmonies, and 12TET approximates those enough
| to still sound good - JI opens up cool chord options
| - but there's extra pitfalls when making JI chords compared to
| 12TET - still not sure what consonant, continuous, or
| misleading chords are. I only know what dissonance sounds like
| - still haven't looked at numbers; all I know is that there's
| ratios in there somewhere
| lewispollard wrote:
| > still not sure what consonant, continuous, or misleading
| chords are. I only know what dissonance sounds like
|
| Consonance is the opposite of dissonance; so while a
| dissonant chord sounds jarring and unpleasant with beating, a
| consonant chord sounds harmonious, pleasant, smooth.
|
| I'm not sure about the other two either, I don't think
| they're commonly used terms.
|
| Maybe continuous refers to "continuo" in Baroque music, where
| the bassline and chords are separate but work together
| harmonically - in some tunings, perhaps this is harder.
|
| I think misleading refers to chords where their function
| harmonically is ambiguous until they resolve "home" at a
| later time - for example, not using the root note of a chord,
| instead using an inversion or modulation that feels like the
| chords could lead in several directions, creating a kind of
| uncertainty and tension in the piece that feels satisfying to
| resolve when the later chord indicates which of the paths
| through the harmony were the "correct" one.
| colanderman wrote:
| One definition of consonant intervals are those that share
| many overtones/partials in common [1]. This reduces the
| phenomenon of "beating" which is readily perceived as
| unpleasant dissonance. (Though small degrees of "beating" can
| be pleasant.)
|
| [1] https://en.wikipedia.org/wiki/Consonance_and_dissonance#A
| cou...
| jfengel wrote:
| The key to the article, and to all of Western music, is about
| a set of weird mathematical coincidences involving the
| twelfth root of two. In particular, that twelfth-root-of-two
| to the fourth power is almost exactly 4/3, and twelfth-root-
| of-two to the fifth power is is almost exactly 3/2. And, of
| course, twelfth-root-of-two to the 12th power is exactly 1.
|
| For some reason, not entirely well understood, when you play
| frequencies that are nice multiples together, they make
| pleasant patterns ("consonance"). They interfere and
| reinforce at regular intervals, and it sounds nice. When you
| don't get nice ratios, they make irregular interference
| patterns, and that sounds unpleasant ("dissonance").
|
| So... take a scale (one frequency to twice-that-frequency),
| divide it into 12 equal parts (geometrically), and you get of
| those nice patterns. Each successive note is the frequency of
| the previous note times the-twelfth-root-of-two. That's the
| "twelve tone equal temperament". It makes it easy to write
| pretty music just by following some mathematical rules.
|
| There's a Wikipedia article on the-twelfth-root-of-two:
|
| https://en.wikipedia.org/wiki/Twelfth_root_of_two
|
| EXCEPT... that those coincidences aren't perfect. They're
| very close, but tiny differences matter. Some intervals that
| should work, don't. Different scales take on different
| feelings, even though in theory they're just the same thing
| nudged up a few hertz.
|
| Anyway... that set of coincidences is the basis of all of the
| music you're familiar with. Other musical cultures also take
| advantage of it. But there's no fundamental reason why those
| particular coincidences should be the only interesting music,
| and so people look around (often, to yet more world musical
| cultures) for alternatives.
| cjbprime wrote:
| I think you're maybe missing the main motivation, which is
| that "correctly tuned" overtones are in nature, in physics,
| in all sounds -- they aren't a social construct, unlike
| everything else about music. I think the argument from JI
| advocates is that our body's perception knows very well
| what a justly-tuned chord sounds like, etc.
| bigstrat2003 wrote:
| I would say that this is way too technical for me, however, I
| also only have the slightest hint of music theory knowledge to
| begin with. It seems to me like that isn't a problem though,
| because this is a very technical topic by nature.
|
| Unrelated to the writing, but I was kind of disappointed that
| when listening to the examples, I cannot for the life of me
| hear a difference between just intonation and equal
| temperament. I know it's there, but I can't hear it _at all_.
| JohnKemeny wrote:
| Do you hear the differences when clicking the 275 vs the 277
| in the third player? If so, you can try to focus on those
| frequencies and see if they stand out to you.
| lewispollard wrote:
| I'm familiar with music theory and microtonal music and the
| first examples are just too close to really discern easily.
| The examples of "chord 1/2" in the section "The Far-Out
| Solution: Freestyle JI" are probably the first example that
| makes the difference clear, if you play the 12TET and the JI
| overlapping slightly. That's because subtle differences in
| tuning are much more perceptible in harmony (chords) than in
| melody (single notes), since notes playing together are
| perceived with noticeable effects introduced by our brains
| such as harmonic beating and feeling tone.
| javier123454321 wrote:
| I thought this video was good at explaining and showing the
| difference audibly
| https://youtu.be/zJTBT5u9AwQ?si=M3csNlck4El_eluH
| black_knight wrote:
| I have limited pitch perception, but I could hear the 12TET
| chords "beating" while the just ones fade out much more
| smoothly.
|
| This beating occurs when two waves just a bit out of tune
| interfere, alternating between constructive and destructive
| interference.
| Levitz wrote:
| It's worth noting that part of the point is showing that the
| difference can be very small.
|
| The one at https://www.osar.fr/notes/justintonation/#compare
| is really tiny, the largest difference being 3hz, you can
| kind of compare side to side using
| https://www.szynalski.com/tone-generator/ and see for
| yourself.
|
| The difference is more perceptible below that, in the chord
| comparisons.
| sonorous_sub wrote:
| I think you could make the piece more interesting to the casual
| reader by grounding the subject in its history. It's been
| suggested by the book below that the dominance of equal
| temperament in western music is a relatively recent innovation,
| something like 120 years old, and is perhaps a consequence of
| the industrial revolution and the demand for mass manufacture
| of musical instruments having uniform qualities it produced.
|
| Further reading: How Equal Temperament Ruined Harmony (and Why
| You Should Care), by Ross W. Duffin (2008).
|
| My layman's takeaway from the book: Equal Temperament is a
| compromise tuning that allows a piano to access all major and
| minor modes, at the cost of the keys on the outer ring of the
| circle of fifths to be somewhat out of tune. An ET "C Major"
| "sounds best", and the further you move away from it in either
| direction, the worse the key sounds. Also, the fact that
| Beethoven and Mozart were aiming for just intonation and/or
| meantone in productions of their works seems to be sort of an
| inside secret among music maestros, with rigid adherence to
| equal temperament slyly pushed on competing rookies to keep
| them trapped in the lower ranks by virtue of their resulting
| weaker performances. But the subject is highly contentious in
| western music for sure.
| black_knight wrote:
| I disagree. I really liked that this post focused on the
| subject matter, rather than the history. History can be
| interesting in itself, but I find that when trying to
| actually learn something it is just a layer of distraction.
| Maybe "casual" reader would find it interesting to read about
| the history. But more technically inclined readers might then
| just bounce off the piece because they would have to weigh
| through history in order to get to the part which they
| actually found interesting.
| smrq wrote:
| I haven't read this book, but that takeaway doesn't sound
| right. In ET, all keys are equally out of tune--that's a
| natural consequence of it being equal. In contrast, it's just
| intonation in which chords become progressively further out
| of tune the further they get from the center.
|
| It's true that ET is a compromise in some ways, but it
| actually opens up the possibility for radical modulations
| into more distant keys without having to adjust intonation on
| the fly. In that sense, just intonation is also a compromise.
| olau wrote:
| If you have not read it, you might find the last part of the
| blog post most interesting. It covers shortcomings of just
| intonation.
| iainmerrick wrote:
| _Right now I suspect that I failed in the same way as my early
| readings did: this article might be hard to understand unless
| you 're already familiar with the topic_
|
| I really enjoyed this article (although I already knew the core
| concepts, so I may be confirming your suspicion, sorry!)
|
| The visualizations are terrific, especially the ones with the
| The Lord of the Rings chord progression. Despite knowing the
| concepts, I hadn't fully appreciated how TET forms a tiling;
| visualized that way, the "wrap around" the circle of fifths
| really hits home.
|
| Excellent work, thank you.
| eltoxo wrote:
| I think it is a really great article but I am a chef too
| already familiar with the ingredients and style of cooking.
|
| I think the main issue is getting people to try new dishes.
|
| Of course, the dishes have to be good and not just the chef
| fooling around. Sometimes this style seems like "hey try this
| new exotic dish! It is made from mixing organic ice cream,
| grass fed beef, fair trade coffee and sriracha. Oh you think it
| sucks? Well that is because your taste buds are use to standard
| western food!"
|
| I think of how no one needs an intellectual explanation as to
| why pad thai is good even if they only ever had pizza and
| burgers.
| klik99 wrote:
| I think you need some info in the start of the article about
| why 12tet was invented, what problems it was solving and how it
| fails. Like - In Bachs day you'd have to retune the instrument
| if you changed key signatures and you could only modulate a few
| steps away before the ratios sounded really bad. So 12TET opens
| up the possibilities to modulate far away from your original
| and requires less retuning, at the cost of adding various
| amounts of dissonance to intervals. I always find it
| interesting that each key signature in 12TET has a unique sound
| (Like CMaj vs EMaj) due to inconsistent ratios in perfect
| fifths, etc, and that "offness" is not necessarily a bad thing.
| You could also mention what most people think "microtonal" is
| (adding extra notes in between half steps) and why just
| intonation is different.
|
| IMO music is all about the balance of the harmonic/expected and
| dissonant/unexpected at various timescales. The experience of
| Just Intonation is interesting because at first it sounds wrong
| due to us expecting 12TET but once you recalibrate your
| expectations it sounds more pure and harmonic, like how choirs
| or string quartets slip into simpler ratios instead of sticking
| exactly to 12TET.
|
| I think with some more context/succinct summary at the
| beginning (which is REALLY HARD to write about for a general
| audience) the rest of the article would be more clear for
| people not steeped in music theory. A way I simplify it for
| others is by framing it all as simple ratios vs more
| complicated ratios, and how harmony is a kind of alchemy in
| mixing those ratios together in the right amounts.
| banana-lambda wrote:
| > each key signature in 12TET has a unique sound (Like CMaj
| vs EMaj) due to inconsistent ratios in perfect fifths
|
| I thought this wasn't true in 12TET, because in that case a
| perfect fifth interval is always a ratio of the twelfth root
| of two to power seven, or almost 3/2, no matter the starting
| point, C or E.
| klik99 wrote:
| Sorry, that was an incorrect thing I was taught and I never
| checked it... The ratio of a perfect fifth in 12TET is
| always 1.498307, not exactly 1.5, but it's close enough to
| 3/2. The deviation from "simple ratios" is more or less
| depending on the interval (P5(3/2): -0.001692923, M3(5/4):
| 0.00992105, m3(6/5): -0.010792885).
| jerf wrote:
| I really appreciate at the end how you explained some of _why_
| 12TET is so popular. There was a time when it was the new kid
| on the block, and there 's a reason it took over. Most articles
| of this type are so busy taking a dump on it that you can't get
| a clear answer to that question.
|
| I am a firm believer in the idea that if you want to know how
| to improve on something, you must clearly understand where you
| are coming from with current practice... and if your
| understanding of "current practice" is that it is entirely bad
| with no redeeming qualities, you don't understand current
| practice. We see that a lot in the programming space; there's a
| recurring set of ideas like "everything should be visually
| programmed everywhere!" that always come from people who spend
| a lot of time complaining about text without demonstrating any
| understand that it is there for a _reason_ , indeed, many
| reasons, and if you casually throw all those good reasons away
| in your attempt to be new and fresh, you are starting so far to
| the negative that you stand no hope of producing anything new
| and useful.
|
| Personally I really appreciate 12TET's ability to wrap the
| harmonies around as you show, and I've never thought about it
| that exact way, so I also appreciate the visualization. That
| doesn't mean it needs to be the only tuning used by anyone,
| though.
|
| On to the music itself. One thing that I have found when I
| listen to a lot of "microtonal" music is that for music that is
| nominally more "consonant", it ends up with things I would not
| call "dissonant" per se (at least, in the traditional ways that
| 12TET has dissonant intervals), but a whole bunch of intervals
| I'd just call _sour_. Now, I won 't deny that despite my
| general openness to alternate tuning pretty much everything I
| listen to is 12TET and I'm adjusted to that just like everyone
| else, but when I listen to Baroque-period music in pre-12TET
| tunings (as they were likely performed then), I hear the
| differences versus 12TET, but I don't hear that sourness in
| those pieces. It seems to me that if the goal is to seek
| greater consonance in tunings (and I acknowledge those who do
| not have that goal, this post is specifically about those who
| are seeking that) I would be hearing music that actually _is_
| generally more consonant. I would be more interested in
| alternate tunings if the resulting music was not so sour.
|
| I really appreciate that your "ambient garden" is both
| different from what I'm used to hearing, but also I find it
| quite approachable. Sure, a bit of adjustment is necessary, or
| at least helpful, but it seems like one could actually argue
| that there is indeed greater _consonances_ , and interesting
| contrast to conventional intervals, in that music, rather than
| just... sour intervals everywhere.
| Sesse__ wrote:
| My basic problem is that I'm really struggling to hear the
| difference between many of your samples :-) And I've already
| got a bit of experience with microtonality (DSP background,
| playing and have tuned multiple instruments, reasonable pitch
| perception). One of the big problems for me is that it's not so
| easy to hear them side-by-side; you have to stop one of them,
| then start the other (unless you want them both at the same
| time, which you probably don't), and both the start and stop
| buttons are pretty laggy. FWIW, most audio comparison tools
| I've seen (typically centered around compression or
| restoration) include some way of switching seamlessly between
| the two, without restarts.
| pclmulqdq wrote:
| If I may provide some constructive criticism as someone who
| also has a background in tuning and tuning theory: I believe
| the article is pretty cool and you clearly have a good
| background on modern microtonal music. However, it is also
| clear that you do not have a good background on historical
| tunings (there are some factual errors in this regard).
|
| Modern sources often implicitly assume that you understand
| tuning theory before teaching it, I agree. The understanding
| they often expect is this historical theory, though. I find
| that understanding historical tuning based on the idea of
| scales to be sort of tough to understand, while the circle of
| fifths is a lot more useful, and before 1900, pretty much
| nobody wrote about tuning in terms of scales since for all
| practical purposes it is very easy to hear frequency
| relationships in fifths and fourths rather than hearing them
| from steps.
|
| Just Intonation is built on top of the harmonic series (not the
| circle of fifths), and I would suggest that you introduce the
| concept of the harmonic series before thinking about scales and
| fixed temperaments (your "boring" solution). As someone who
| does understand Just Intonation pretty well, I found the idea
| of going straight to a concept of scales very confusing,
| personally. The scale for true just intoned tunings is built on
| top of the harmonic series relationships you showed later, and
| those don't all have nice intervalic ratios.
|
| Factually, the intervals were wrong for a typical Pythagorean
| scale: your fifth is 2^18/3^11 when the correct relationship
| for the typical notion of Pythagorean tuning is 3/2. Your scale
| stacks fourths based on 4/3 relationships, leaving the most
| important interval in the scale as the so-called "wolf" fifth.
| Most practical notions of Pythagorean tunings used fourths
| going one way and fifths going the other from the tonic,
| leaving the F#-C# relationship as the "wolf" (if the tonic is
| C), while all other fifths are pure. If you illustrate this
| with a circle of fifths rather than a graph showing scale
| degrees, it's a lot easier to understand. Pythagorean tuning
| also isn't really a type of just intonation since it doesn't
| use a harmonic series on a single note, but the exact
| definition of "just intonation" varies by source (some would
| say that even a temperament like Werckmeister is "just
| intonation").
|
| All that said:
|
| I would suggest you start with some ideas about tuning,
| introduce the harmonic series, introduce that "just intonation"
| is about preserving harmonic series relationships, and then go
| straight to your "freestyle" section. Eschew the notion that
| you need to understand the history of unequal temperaments to
| understand the present concept of the tension between the
| equal-tempered compromise scale and the just-intoned harmonic
| series.
|
| Since you're more interested in modern theory, and your
| innovation and interests are there, I think you can skip the
| history and just get straight to the math and the lattices.
| Whether you use circles of fifths if you do this is up to you
| (I'm guessing you shouldn't - they are not so useful for modern
| tuning ideas).
| pierrec wrote:
| Thanks for bringing in your understanding of historical
| tunings. Maybe a simpler correction would be to describe the
| example as "a Pythagorean tuning" rather than "THE
| Pythagorean tuning", which would be (according to some)
| technically correct despite not being historically
| representative. The goal of that example isn't to provide
| historical background, it's to provide one of the simplest
| possible derivations of 12 usable tones from just intervals.
| I believe that that the 3 being a multiplier or a divisor is
| a matter of perspective: if you start from the last tone in
| my example, the same scale is derived from reversed
| fractions. Starting from the middle might be closer to what
| you're describing, hopefully I'm getting that right.
|
| Grounding the whole thing in the harmonic series on would
| certainly make sense.
| pclmulqdq wrote:
| You are correct about the ratios not mattering that way,
| but it is jarring for someone who knows about this stuff to
| see 4/3 (the fourth) instead of 3/2 and to see the
| positioning of the wolf being the I-V relationship in the
| scale. I would suggest that if you want to keep it, you
| should be explicit that the frequency relationship on this
| fifth is far off, and I would suggest drawing a circle of
| fifths (which will be a lot more clear after seeing a fifth
| in the harmonic series). Instinctively, that section feels
| very wrong despite being (mostly) right. I would personally
| suggest dropping it entirely - you don't need the history.
|
| Edit: I was thinking about your existing diagram a bit
| more, and here is the rework I might suggest without doing
| anything too major:
|
| Do an up-a-fifth-down-a-fourth path through the chart, and
| that is easier to rationalize and understand than "mostly
| 4/3 with 2/3 ratios interspersed when we need to drop an
| octave":
|
| C * 3/2 -> G
|
| G * 2/3 -> D
|
| D * 3/2 -> A
|
| A * 2/3 -> E
|
| E * 3/2 -> B
|
| B * 2/3 -> F#
|
| There is only one break from the pattern right here with
| two descending perfect fourths in a row:
|
| F# * 2/3 -> C#
|
| C# * 3/2 -> G#
|
| ...
|
| You can also restart from C going down to F and Bb once you
| reach F# and that gives you the typical Pythagorean tuning,
| but then you will have to explain why that happens to
| readers who are unfamiliar with tuning.
| riemannzeta wrote:
| I will admit that I already had some familiarity with the
| topic, but I feel you did an amazing job at explaining
| specifically the constraints you're under as a composer, and in
| elucidating how having digital tools doesn't magically solve
| the problems you face in harmonizing in just intonation over
| the course of a piece. I had not really understood that before
| reading your article, and at least suspected that we might
| transition to hearing mostly Just Intonation eventually as
| digital tools became more widely used.
|
| Of course you could make it more accessible by starting from
| some even more basic principles and elaborating further on
| those foundations, but then you risk losing some of our
| audience that's already familiar with those. For me at least
| you struck a good balance. (No pun intended!)
| benwen wrote:
| " This also has the reputation of being terribly impractical,
| which is always a selling point for me."
|
| That was truly LOL. Thank you.
| an_aparallel wrote:
| posting related vinyl record collection comic:
| https://www.ratherrarerecords.com/wp-content/uploads/AlexGre...
| rob7cc wrote:
| What a marvelous article about intonation and temperament. It is
| one of those expositions that approach perfection in conveying
| the subject matter. I am no music theorist but rather an engineer
| with an appreciation for all things wave- or signal-oriented. I
| will want to read it multiple times to savor the explanations.
| The author's album based on just intonation is linked in the
| article ("A Walk Through The Ambient Garden") and I highly
| recommend it: it is a mesmerizing composition.
| keybits wrote:
| To save people a few clicks, there's a wonderful visualisation
| of the generated music at https://ambient.garden/
| thomasahle wrote:
| This reminds me of when I stumpled into a music theory flame war
| by proposing the "scale": 1, 15/14, 15/13, ..., 15/8, 2.
| https://music.stackexchange.com/questions/66620/what-is-a-te...
|
| This set of 8 nodes (can be transposed to whichever base
| frequency) has _the lowest common denominator between any pair of
| nodes_ among all 8-node scales.
|
| I thought that might make it a good choice for a just intonation
| scale (which can really be any subset of frequencies you build
| you music from), but it turned out a sensitive subject.
| the_other wrote:
| Why is it a sensitive subject?
| pyinstallwoes wrote:
| Wait until you hear about A=432Hz
| the_other wrote:
| I've heard a little about this one. It's not that
| interesting, IMO. Some people think tuning even temperament
| down such that middle A becomes 432Hz (rather than 440Hz)
| is better for your health as well as the tone. I can get a
| little "woo" from time to time, but this one left me cold.
| colanderman wrote:
| Oh hey, I've experimented a bit recently with the similar scale
| 1, 24:23, 12:11, ... 24:13, 2. Essentially a 12-tone version of
| yours. I've been calling it the "utonal" scale as it is a
| utonal [1] series. Complements what I call the "otonal" scale
| of 1, 13:12, 7:6, etc.
|
| The trouble is, while intervals with the root are very
| consonant, arbitrary intervals don't sound great.
|
| I've noticed though, that a utonal scale is very similar to the
| scale of harmonics [2], which is traditionally used relative to
| a moveable root note. So I intend to experiment in that
| direction.
|
| [1] https://en.wikipedia.org/wiki/Otonality_and_utonality
|
| [2] https://en.wikipedia.org/wiki/Scale_of_harmonics
| muhrizqiardi wrote:
| Haven't read it fully (to be honest this topic is new to me), but
| it's funny that as I read this article, I also happen to listen
| to a microtonal music: Flying Microtonal Banana by King Gizzard &
| The Lizard Wizard.
|
| Both the name of the album and the name of the band sounds funny,
| trust me when I say this: It's one of the best microtonal album
| out there. They really mixed the sound element of turkish(?)
| music into the album. Highly recommended!
| lovegrenoble wrote:
| Avez-vous la version francaise, monsieur ?
| Sharlin wrote:
| Should be noted that any ensemble that consists only of
| continuous-pitch instruments (eg. strings, trombone, human voice,
| fretless guitar) is free from the shackles of 12TET and its
| harmonies naturally tune to as close to "pure" intervals as the
| performers' skills allow.
| kaapipo wrote:
| The guitar doesn't event need to be fretless; there is a lot of
| leeway (even towards flat) even with frets if you know the
| technique!
| cchi_co wrote:
| A richer and more authentic harmonic experience
| naltroc wrote:
| Yes, this should be noted.
|
| Naturally JI instruments include any instrument which has a
| continuous frequency domain, like trombone, fretless stringed
| instruments, and human voice.
|
| Instruments with keys or frets may be "bendable". However, the
| direction and quantity of bend varies with with each tone it is
| paired with, making this incredibly impractical.
| Levitz wrote:
| I never thought about this, does a choir left to its own
| devices naturally gravitate to JI rather than ET?
| PaulDavisThe1st wrote:
| It seems to depend a lot on their age and experience. Years
| of only single 12TET will tend to pull them away from the JI
| "sound". However, I know a few choral singers who've tried
| (in midlife) to single JI and once they got over the initial
| "hump" they found it quite natural.
|
| The "beating" that occurs in 12TET is inaudible to most
| western listeners because we've become so acculturated to it.
| You have to get some exposure to music where it doesn't
| happen before you even notice it (and thus seek out more
| consonant harmony).
| nonrandomstring wrote:
| Sometimes I like writing stuff in odd scales and intonations. The
| "Lucy" tuning is also very pleasant [0]. I once met a producer
| who had guitars fretted to this tuning. It doesn't lend itself
| well to DAWs that have an underlying MIDI note logic. Practically
| it's better to work in Pd/Max with raw oscillators and arithmetic
| than to try shifting MIDI note values around with bend. The
| ZynAddSub engine (also used in Yoshimi synth) has a nice scales
| filter.
|
| Probably worth mentioning Jacob Joaquin [1] who did this stuff in
| Csound back in the 90s. On one of his patches I based a
| generative music system for a game, it was the "Harmonic tree" -
| very similar to the system in the article - repeated
| multiplication by integer fractions at each branch.
|
| Using simple timbres (like flute/organ/sine) you can make big but
| crystal clear sounding chords, and then slowly changing one
| "note" at a time you get an ever evolving soundscape that blows
| anything "Eno" off the map. Its in a sweet creative area between
| composition and additive synthesis.
|
| [0] http://www.harmonics.com/lucy/lsd/colors.html
|
| [1] https://github.com/jacobjoaquin
| colanderman wrote:
| You can use the same construction as the Lucy scale with the
| periods of planets to produce true "music of the spheres"!
| Though the pitches tend to be clumpy, it does sound quite
| otherworldly.
| carterschonwald wrote:
| This is interesting, but the harpsichord based samples really
| made me not wanna listen. But that's probably just me disliking
| harpsichord
| cchi_co wrote:
| They have a unique sound that not everyone enjoys.
| naltroc wrote:
| Would it be more appealing if we relabeled "harpsichord" as
| "pluck triangle synth"? :P
| pierrec wrote:
| The choice of instrument is not entirely innocent. Harpsichords
| are rich in harmonics, and those harmonics are almost exactly
| multiples of the fundamental. This is perfect for revealing
| natural ratios in chords. Pianos have "bent" harmonics which
| would slightly obscure this. This is inharmonicity:
| https://en.wikipedia.org/wiki/Inharmonicity
| cchi_co wrote:
| It's interesting to see how just intonation can offer a richer
| harmonic
| naltroc wrote:
| Here are three additional references on applied Just Intonation.
|
| The first book is abstracted away from composition and provides a
| more general description of tuning systems.
|
| The next two are composition focused, explaining how tuning
| system is an option for musical works.
|
| 1) The book "How Equal Temperament Ruined Harmony" provides
| excellent historical context on why ET was a great solution and
| how we kind of got stuck with it.
|
| While it could be read by anybody, having a bit of musical
| knowledge OR physics of acoustics knowledge may benefit you.
|
| https://www.amazon.com/Equal-Temperament-Ruined-Harmony-Shou...
|
| There are also two composers who recognize ET as a constraint (as
| opposed to the "the only option").
|
| 2) Harry Partch built many of his own instruments to circumvent
| issues from 12ET and composed music just for them. He describes
| his conceptualizations of JI in "Genesis Of A Music":
|
| https://www.amazon.com/Genesis-Music-Account-Creative-Fulfil...
|
| 3) Paul Hindemtith also has some opinions on the matter, though
| both Partch and I disagree with his points of view. Nonetheless
| he has some at-the-time innovating ideas, some of which are valid
| and others of which may not have aged well. You can read about
| them in "The Craft of Musical Composition"
|
| https://www.amazon.com/Craft-Musical-Composition-Theoretical...
| elevation wrote:
| For practical performance of alternate intonations, you can tune
| a guitar so that a particular chord shape presents perfect roots
| and 5ths, while arranging for a single string to be a perfect
| third (e.g, a few cents "flat" compared to equal temperament.)
|
| When playing this same chord shape (or an appropriate derivative)
| up the neck, the relative intervals is maintained for other
| chords, allowing perfect intonation not just of the root chord
| but of other chords in the key family.
|
| For chord shapes where a flatted string cannot be used as a 2nd
| or 3rd, it will sound objectionably flat, but for many chord
| shapes it's possible to fret the flat string with additional
| pressure to bring it back into tolerance.
|
| Mastering this technique makes the guitar sound much more in tune
| with itself which is a wonderful sensation as a player.
| cscheid wrote:
| (In case you didn't know, it's fun that) Jacob Collier plays a
| 5-string guitar in a tuning that takes advantage of this trick
| exactly. IIRC, from lowest to highest he tunes them a fifth, a
| fifth, a fourth and a fourth apart. By flatting the middle
| string a dozen cents or so, you can get a root-fifth-perfect
| tenth voicing of a major chord. Neat trick.
| wrs wrote:
| Speaking of Jacob Collier, this is a good time to mention the
| song where he "hacks" equal temperament to modulate to
| G-half-sharp without anyone noticing.
|
| https://www.youtube.com/watch?v=Xd54l8gfi7M&t=3m17s
| cjbprime wrote:
| One more Jacob Collier mention: also generally releases
| albums using just intonation, I think, and especially does
| hand-tuning of thirds etc. I like his description of having
| to "monkey swing" when an e.g. flattened third needs to
| become a new root note.
| bwanab wrote:
| Aren't you still fighting the fact that the frets themselves
| are tuned as 12TET?
| elevation wrote:
| The fight increases the faster/further you jump around the
| circle of 5ths. The 12TET fret spacing aligns octaves and
| 5ths with JI, so if you tune for a JI `I` chord, your other
| chords will be internally JI but only your `V` chord will be
| spaced perfectly from the `I` chord. The other chords will be
| closer to perfect JI the closer they are to `I` on the circle
| of fifths.
|
| This microtuning isn't perfect in theory, but it's a
| favorable compromise for a lot of western music, especially
| for legato strumming where the inter-string intervals are
| heard more often than the inter-fret intervals.
| kazinator wrote:
| Most guitars are not properly in equal temperament intonation,
| because that requires compensation at the nut.
|
| In particular, an unwound G string can be off. I got sick of
| three decades of listening to that out of my main guitar, and
| earlier this year finally did something out of it with
| satisfactory results:
|
| https://mstdn.ca/@Kazinator/112332540341043265
|
| Without this string, I cannot get these G and D power chords to
| be in tune simultaneously:
|
| G: E |---|---|-*-| B |---|---|-*-|
| G o|---|---|---| D o|---|---|---|
|
| D: E x|---|---|---| B |---|---|-*-|
| G |---|-*-|---| D o|---|---|---|
|
| If you tune the latter D, then the open G is too flat in the
| former G. If you sharpen the open G, the latter D is out of
| tune.
|
| The problem is that when we fret the A note on the G string
| near the nut, it stretches; the string goes sharp. So the
| interval between the nut and that fret is wider than a tone,
| without the compensation that shrinks it.
|
| The other strings have the problem, but the unwound G has it
| worse due to lower tension relative to mass. I'm so happy with
| the G compensation on that guitar, that it needs nothing else.
|
| Anyways, there are videos out there which do A/B comparisons
| between ordinary guitars and just intonation. They feature
| uncompensated guitars, so they perpetrate a fallacy.
|
| The guitarist must experience a properly intonated guitar with
| nut compensation first, then decide whether going to exotic
| intonations is worth it.
| sporkl wrote:
| Overall a good intro on the subject. I feel like at the start it
| might benefit from being a bit more explicit about pitches being
| frequencies and ratios being intervals; probably just worth a
| reminder for people who aren't as familiar
|
| Might be interesting to talk about how the usual ratios come from
| the harmonic series. For sounds that don't produce a harmonic
| series, other potentially non-integer ratios can actually sound
| more consonant. The youtube channel New Tonality[0] has a bunch
| of great videos about this
|
| Also wanted to mention that I've been working on a piece of
| commercial software[1] for working with freestyle/adaptive just
| intonation, if anyone's interested
|
| [0]: https://www.youtube.com/@new_tonality [1]:
| https://www.dmitrivolkov.com/projects/pivotuner/
| pierrec wrote:
| Thanks for posting this. The approach of keeping the
| traditional 12 notes while changing the tuning on-the-fly is
| really interesting and maybe the right tradeoff. This is so
| spot-on because adaptive JI is mentioned as a possible solution
| at the end of the article. It's the classic HN move where a
| weird topic is being discussed and someone says "why yes, I've
| made tools that happen to exactly match the niche topic being
| discussed!"
|
| In fact, it's probably not my business, but this topic is so
| profoundly niche (and likely to remain so for a while) that I
| personally wouldn't make this commercial. My reasoning (and the
| reason I open-sourced some projects) is that it will limit
| adoption while changing almost nothing about my income.
| Obviously I hope I'm wrong, maybe these techniques will pick up
| in popularity. It's also possible that I think this way simply
| because I'm bad at marketing.
| sporkl wrote:
| yeah, in general I do want to open source it, but for the
| time being I'm a student and every little bit counts
| flobosg wrote:
| For more pieces in just intonation, check out
| https://en.wikipedia.org/wiki/List_of_compositions_in_just_i...
| hypertexthero wrote:
| One of the linked music examples, "occultation" by Pure Code, is
| beautiful ambient music.
| crtasm wrote:
| If the author is here, the audio clips don't play for me. Firefox
| console has: Uncaught (in promise) TypeError:
| document.querySelector(...).contentDocument is null
| pierrec wrote:
| Sure, I also use Firefox but I don't have this error, so that's
| not really enough detail for me to look into it.
| riemannzeta wrote:
| I feel like I can hear beat frequencies in the 12TET chords that
| I don't hear in the JI chord examples.
|
| Anybody else hearing that? Or is that my imagination?
| naltroc wrote:
| Yes!
|
| We don't even have to listen to the audio examples to know that
| yes, ET chords produce beat frequencies. This is an artifact of
| the non-integer relationships created in ET chords that don't
| exist in the JI examples.
|
| A piano will produce similar beat frequencies when playing a
| perfect fifth. Some ears are more sensitive to hearing it than
| others.
| riemannzeta wrote:
| Thank you! I'm so glad to have that confirmed. I feel like I
| do hear them, and actually have come around to liking them.
| They feel quite different from what you get with a pure
| harmony in Just Intonation -- maybe the ephemerality of the
| flow of energy back and forth between different subharmonics
| adds to the excitement somehow.
|
| It's hard for me not to think of the electric guitar in this
| context. I love the purity of an acoustic played in a
| plangent tone like Django. But the incredibly rich spectrum
| introduced when an amplifier saturates and tons of additional
| harmonics and subharmonics that aren't supposed to be there
| gets introduced -- that's it own kind of excitement. Like
| falling into an abyss aurally.
| riemannzeta wrote:
| Readers who enjoyed this essay might also enjoy this one, which
| goes into further depth on the mathematics of musical intervals,
| the connection between the "blue note" in Equal Tempered jazz
| music, and more:
|
| https://iopscience.iop.org/article/10.1088/0034-4885/72/7/07...
|
| As an added bonus, the author draws an extended analogy between
| musical intervals and energy levels in quantum mechanics toward
| the end of the article, and indeed the study of the patterns in
| intervals between and among energy levels in the simple harmonic
| osciallator remains an active area of reasearch!
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