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Recommend some Atonal Music

Do you consider A Love Supreme atonal? I don't, except for during the solos maybe, and even then I hear* the tonal, thematic parts.

* Taking into account the temporal aspect -- tonality that "lingers" from earlier in the piece.
 
Do you consider A Love Supreme atonal? I don't, except for during the solos maybe, and even then I hear* the tonal, thematic parts.

* Taking into account the temporal aspect -- tonality that "lingers" from earlier in the piece.

Yeah, always tonal.

maybe I'll listen later today to see how out it gets...
 
Thanks Calebprime!

I didn't expect that you'd start a thread. Awesome! (listening to The Beatles...). :p
 
The Ur-piece of tonality is the drone bass.

Sorry. Ur-piece? But I'm guessing you're saying something like there's nothing more tonal than a drone bass.

I'm biased by western harmony, and tend to think of tonality in terms triads. I can't help it. In terms of gravity, a drone bass (modal?) is a bit of a black hole, whereas triadic based tonal music allows for little satellites here and there. Sorry, more silly analogies later.

As it moves up in register, though, a given drone bass becomes not a bass any more, and can be re-interpreted in more and more ways within strictly harmonic frameworks.
You mean, like Em can be interpreted as G6? Or you mean something different, and/or more complex?

A single tone then becomes not definitive, but ambiguous as it moves up. Indian music, with high-register drones.
So you're more or less equating bass stability with tonality (I'm not sure if I'm being precise), and if there isn't something we can call a bass, even if it's functioning as a drone, the whole harmonic structure is really perceived differently, and that leads, potentially, to atonality?


Western music to a large extent is about re-interpreting medium-to-high register drones so that their meaning or color changes.
You mean by way of parsimonious voice leading, for example?

A single sustained high tone is harmonically ambiguous. More tonally-strong than a single tone, then, is a series of tones that behaves according to (tonal) expectations.
This is getting interesting. I need time to digest it. I'm really interested in the theory.

Western music is also about harmony with independence of melodic voices, either in counterpoint or homophony, as in Bach chorales.

This principle of independence of voices is, in embryo, almost the principle of atonality waiting to happen: freedom, elaboration, independence, anarchy, argument. When you have voices moving in and out of a harmony via a passing-tone, you already have the seeds of atonality in that simple elaboration.
This is great. Thanks for your insights, Calebprime. They're intellectual food to me.

I think I get the idea that creating a 'civilization' of independent voices tends to 'moral flexibility' the more complex it gets, unlike, say, a drone, which is more akin to 'hunter-gathering'. Technology develops upon previous technology. There's always a spark that makes rapid changes start to happen. Yeah, no more silly analogies. You can relax from now on.

It's only when the referent becomes too elaborated that it begins to be obscured, that we're in my preferred zone here. Not fully simple, not fully obscure.

Atonality is very much like lack of perspective or weird perspective in painting, and like language without enough solid referents that you can understand what is being said.

There is a transition from See Dick Run, through the entire career of Joyce, ending in modernist overreach, if you will. The book that no-one read past page 60, Finnegans Wake, the atonal book.

Cubism is something like serialism -- codified lack of/altering of perspective.
The thing that bugs me... I tend to think of serialism as a very complex theory, but I'm not really sure it is, in contrast with the complexity developed around tonality. Say... the subdominant-dominant-tonic relation. It looks simple once you're exposed to it, but how long did it take for civilization to discover it?

Since I don't have a theoretical understanding of how atonality works aside from the intuitive 'make sure it doesn't sound tonal', I find it very difficult to understand what is it about a piece which makes it sound appealing. I know sometimes it depends on my state of mind, and of course you can play with rhythmic patterns to give a sense coherence to something atonal. I can reverse engineer the Beatles, some Zappa and some jazz because I have expectations based on my accumulated knowledge, but atonality? How did Pierre Boulez construct his pieces?

Today I tried to improvise something on the piano (I'm calling it 'serial suicide'). First thing that came to mind: arpeggio of tritone with forth on top, similar motif a half step below... play chromatically... jump to another part of the octave, something similar... go down a fifth (trying to make it sound familar within its unfamilarity)... I tried to find melodic patterns... difficult within serial suicide. Rhythm is important, it's where I tend to find the tension and the fun. I don't know... after a while I thought that I would resolve it and connect it to a whole different tune, precisely because that would be unexpected, in an antiwagnerian antidramatic way.
 
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The Ur-piece of tonality is the drone bass.

As it moves up in register, though, a given drone bass becomes not a bass any more, and can be re-interpreted in more and more ways within strictly harmonic frameworks.

A single tone then becomes not definitive, but ambiguous as it moves up. Indian music, with high-register drones.

Western music to a large extent is about re-interpreting medium-to-high register drones so that their meaning or color changes.

A single sustained high tone is harmonically ambiguous. More tonally-strong than a single tone, then, is a series of tones that behaves according to (tonal) expectations.

Western music is also about harmony with independence of melodic voices, either in counterpoint or homophony, as in Bach chorales.

This principle of independence of voices is, in embryo, almost the principle of atonality waiting to happen: freedom, elaboration, independence, anarchy, argument. When you have voices moving in and out of a harmony via a passing-tone, you already have the seeds of atonality in that simple elaboration.

It's only when the referent becomes too elaborated that it begins to be obscured, that we're in my preferred zone here. Not fully simple, not fully obscure.

Atonality is very much like lack of perspective or weird perspective in painting, and like language without enough solid referents that you can understand what is being said.

There is a transition from See Dick Run, through the entire career of Joyce, ending in modernist overreach, if you will. The book that no-one read past page 60, Finnegans Wake, the atonal book.

Cubism is something like serialism -- codified lack of/altering of perspective.

Sorry. Ur-piece? But I'm guessing you're saying something like there's nothing more tonal than a drone bass.

I'm biased by western harmony, and tend to think of tonality in terms triads. I can't help it. In terms of gravity, a drone bass (modal?) is a bit of a black hole, whereas triadic based tonal music allows for little satellites here and there. Sorry, more silly analogies later.

You mean, like Em can be interpreted as G6? Or you mean something different, and/or more complex?

So you're more or less equating bass stability with tonality (I'm not sure if I'm being precise), and if there isn't something we can call a bass, even if it's functioning as a drone, the whole harmonic structure is really perceived differently, and that leads, potentially, to atonality?


You mean by way of parsimonious voice leading, for example?

This is getting interesting. I need time to digest it. I'm really interested in the theory.

This is great. Thanks for your insights, Calebprime. They're intellectual food to me.

I think I get the idea that creating a 'civilization' of independent voices tends to 'moral flexibility' the more complex it gets, unlike, say, a drone, which is more akin to 'hunter-gathering'. Technology develops upon previous technology. There's always a spark that makes rapid changes start to happen. Yeah, no more silly analogies. You can relax from now on.

The thing that bugs me... I tend to think of serialism as a very complex theory, but I'm not really sure it is, in contrast with the complexity developed around tonality. Say... the subdominant-dominant-tonic relation. It looks simple once you're exposed to it, but how long did it take for civilization to discover it?

Since I don't have a theoretical understanding of how atonality works aside from the intuitive 'make sure it doesn't sound tonal', I find it very difficult to understand what is it about a piece which makes it sound appealing. I know sometimes it depends on my state of mind, and of course you can play with rhythmic patterns to give a sense coherence to something atonal. I can reverse engineer the Beatles, some Zappa and some jazz because I have expectations based on my accumulated knowledge, but atonality? How did Pierre Boulez construct his pieces?

Today I tried to improvise something on the piano (I'm calling it 'serial suicide'). First thing that came to mind: arpeggio of tritone with forth on top, similar motif a half step below... play chromatically... jump to another part of the octave, something similar... go down a fifth (trying to make it sound familar within its unfamilarity)... I tried to find melodic patterns... difficult within serial suicide. Rhythm is important, it's where I tend to find the tension and the fun. I don't know... after a while I thought that I would resolve it and connect it to a whole different tune, precisely because that would be unexpected, in an antiwagnerian antidramatic way.


Heh. Pardon the silly Ur-language. The land of Ur was the very first land, where the simplest people presumably went about their simple, drone-y ways.

A solid idea -- a hill I'd die fighting for, as JoeBentley (sp) would say -- is the low-interval limit which I'd like to try to link to a theoretical "lowest note" around 20 hz., [which has a nice relation to the 40-hz binding frequencies observed in the brain]. * The exact frequency is not important, the important thing is that around 20 or 16 hz, the sensation of a bass note gives way to a sensation of a rapid flapping, a rapid oscillation or rhythm.

I'd say that the lowest interval is approximately that interval's place in the overtone series based on that 20-hz. note.

Anything that violates this simple integer-over-lowest-bass is more and more dissonant based on precisely...

No, not precisely.

No, no exact important scales of dissonance are possible! There is only a general sense, and the sense that things either belong in the overtone series first, or not in a given sonority. Then the complex stuff happens, and we can throw that simple model out. Music happens.

Still, it's worth considering the radically naked overtone series, because some experimental and avant-garde, electronic musics are based on it, directly.




* This I'm making up and it doesn't matter. The important thing is the harmonic sensation of a real harmonic bass or not.
 
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One-note piece with drone in bass: In one sense, (if you went to Berklee they even said this explicitly) you can do anything over a drone, so it's not definitive of anything, but it really is: Everything you play over it becomes defined by it, becomes "magnetized", become part of its resonance, its expectations.

But as a drone moves up in register, it ceases to become only a fundamental, so it becomes possible within the lower-interval limit to define it in more and more harmonic overtone functions as it moves up.

I'm sure you've experienced what I call The Unbearable Lightness of One-Note (Or One-Chord) Music? That is, music that was intended to be so tonal, but surprisingly even when it gets displaced by a step or two, the effect might be jarring but not impossible, so a drone can go anywhere. Because it can go anywhere, it's unbearable, like a droning insect or like a droning leaf-blower. Undefined. No intelligence in one-note.

So What.

Impressions.

(Both examples of elaboration by-mode, and neighbor-motion of root of mode, causing maximum change of pitches)

But one-note changing in relation to any other note becomes meaningful.

A note is not meaningful, but an interval is.

An interval or set of notes that are elaborated -- gone next-door-to and returned to, as you rightly say, -- is a much stronger tonality than just one note.

But as soon as you add strengthening, interesting elaborating tones, you start to build in the seeds of potential atonal anarchy. Slippery slope of jaded addicted sophistication of fornicating evil tritone black male on feet.

Sorry for the purple prose. There actually was a guy who ran the music store in town who used to warn us kids to avoid the evil tritone.

I always cheerfully employed highly tonal rows, even super-trick rows that ensured harmonic results in several different ways at once.
 
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It seems that there are several ways that the word "atonal" is used when speaking of music. I think the most common use is probably to just describe music with lots of chromaticism (non-diatonic tones) or music that is sort of what is called "outside" in the jazz idiom. Or even music that discards the twelve equally tempered notes we generally employ in western music - stuff like Merzbow, maybe.

I was taking it to mean "atonal" in the more formal sense, where each of the twelve notes of the chormatic scale are given equal function, such that none of them can be rightfully called the tonic. Tone rows and all that.

Zappa does some great twelve tone stuff in parts of the tune The Adventures of Greggery Peccary. Or at least it sounds so - I haven't worked out the notes, but the sound immediately suggested a tone row to me.
 
Robert Simpson -- in the looser, not-really-atonal sense that I like.

listening as I type to Symph. 9.

I wouldn't be surprised if these were tone-rows carefully designed to resolve one after the other, even cycle-of-4ths.

This is spun carefully out of the same intervallic material over and over, in any case, with deliberate clashes against the pedals.
 
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Dani, I'm going to try to sort out some different areas of discussion, theory.
In no particular order:

-- What you're talking about with voice-leading is I think called Neo-Riemannian theory. There are whole huge dreary compendiums of the stuff. It is the going cottage industry for employing grad students and teaching assistants etc. in music theory. I just bought about five of these books, I may read them.

-- For a brief shining moment with serialism, it was as if composers could write books talking shop with other composers. Serialism made for good shop-talk. There was also a spirit of interdisciplinery research shown in the good books on music theory that were written by composer-theorists. Then that stopped, either because publishing changed, or the scene changed. I don't see books like that any more, even in serious music bookstores.

-- My approach with serialism is this: Generation of material is one thing, taste is another, hearing is another. A slightly augmented set of standard serial techniques is an excellent toolbox for generating pitch-material. It can be used to generate macro pitch sequences lasting the entire piece, or surface tunes that go by quickly. The virtue of the box of techniques is that everything is at least logically related. The composer can also insist if she wishes, that the musical results of such techniques are also always about being audibly related. I myself do insist. Others don't.

-- I've witnessed even fairly bright composers (I'm thinking of you, Daniel F.) who get bogged down in tedious and strict definitions of what serialism "must" be or ought to be "in essence". (It has to be about "interval fixing" or something.) No.

-- Instead, serialism to me as a composer is a generative technique, nothing more or less. It has to produce audibly related results. It also has to produce pleasing, musical results, which means I have to cherry-pick insanely to get the unlikely coincidences or tonal contrapuntal combinations.

-- To me, logical relations in composition are there to produce only the psychological result of hearing a resemblance. This sounds like this. It's like this, but different in this way, same in that way.

-- Therefore, mathematical invariance is less interesting than related variance.

-- Consider what happens, for example, when a melody changes from major to minor. It's an inexact transformation or resemblance when considered literally. At a higher level, I suppose it's perfectly systematic, but not from the pov of serialism.

-- Serialism was never a complete system in anyone's hands -- everyone was using some of the same techniques but making it up as they went along, too.
(Even Babbitt and Wuroninen)


-- What I'm talking about with harmony is best observed with synthesizers and computer-controlled tuning that can be set up quickly, as with Scala format.
If you (Dani or anyone else) take that path, it opens up a whole meaningful territory of harmony in 3D and living color, if you will.

-- Harmony with only 12 tone tuning is like 2D checkers. However, there are plenty of people who could and can do more with 3 notes than I can do with 60, so it's not a question of virtuosity or musicality.

-- It's only that 12-tone 2D thinking is a sort of theoretical limited Flatland. It can be a revelation to experience something more 3D.

-- Obviously for people whose musicianship exceeds their theory (most good musicians) the 2D aspect of 12 tones doesn't occur to them at all -- they're fully capable of transcending the limits of their own thinking in their music-making all the time.

-- JI theory (7-limit, 11, 13-limit) is something I sort of live with every day, but don't try to understand all that systematically. It means that intervals like 7/4, 11/4, 18/13, become real intervals, become real consonances, become meaningful.

-- I mention low interval limits because I've talked to musicians who don't seem to understand what bass is, what inversions are, what the overtone series is.

-- Heck, there was a kid at the MIT experimental studio before it became part of the media lab, this kid was from Juilliard. This kid, who had been at Juilliard for several years as a comp student, didn't know that an octave was a 2:1 ratio. This is the degree to which standard music theory as it's taught is sort of divorced from reality.



Well, top of head. See if any of this clears anything up.
 
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Atonal composers for today:

Stockhausen -- I like the early concrete pieces -- kontakte, gesang, hymnen, etc.

Donald Martino -- overrated in these parts in his time. He was at least a good atonal composer with a worked-out system and a beautiful pen. Probably neither his theoretical work nor his music will survive even the next 50. Had LPs with beautiful covers on Nonesuch back in the day.

A trace of lyricism in these busy, detailed textures.
 
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The Kronos does a very good Berg string quartet. in the gray zone tonally.

They get it very in tune, fairly light on the vibrato, straight 12-tone tuning. Not so easy.
 
...I'm going to try to sort out some different areas of discussion, theory.

...

My thoughts always drift in the direction of JI theory, which can help inform your practice, if...

But that's only my project.

Two good books:

Tom Johnson __Other Harmony__ beyond tonal and atonal

and

Dave Liebman __A Chromatic Approach to Jazz Harmony and Melody__


with the reservation that these are grab-bags full of ideas and techniques, but without taste. You have to provide the taste.

Both are by composer/players for composer/players, one reason I like them.
 
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My taste for truly atonal music is limited, but some has great appeal, and I second the suggestion somewhere above of Berg's violin concerto.

Another composer I like who I think well worth further looks is Kurt Weill. Of course we all know Weill as a composer of some of the most hummable tunes around, but in his earlier incarnation he kept his melodic gift wrapped in an atonal package, and the result could be quite interesting. As time progressed he became less shy about being a lyrical composer as well as atonal, and the combination (or perhaps the struggle) can be quite striking. I think the violin concerto is quite intense and occasionally beautiful, and his second symphony, by which time he's getting quite melodic, is great.
 
I checked Berg's Violin Concerto and I liked it very much. I think I hear some quasi tonal qualities, like actual chord progresions that make sense. I hear some augmented chords too, not sure though. Which makes me think: their symmetric and regular nature (both the chords and the scale) and the augmented fifth are perfectly suited for atonality. Thinking of its use in movies right now.

Berg's Violin Concerto is beautiful. Oh, I see it premiered in El Palau de la Música, Barcelona! I began studing music there when I was I kid. I ended up hating it :D. Life is like a boomerang sometimes.

Heh. Pardon the silly Ur-language. The land of Ur was the very first land, where the simplest people presumably went about their simple, drone-y ways.

A solid idea -- a hill I'd die fighting for, as JoeBentley (sp) would say -- is the low-interval limit which I'd like to try to link to a theoretical "lowest note" around 20 hz., [which has a nice relation to the 40-hz binding frequencies observed in the brain]. * The exact frequency is not important, the important thing is that around 20 or 16 hz, the sensation of a bass note gives way to a sensation of a rapid flapping, a rapid oscillation or rhythm.

I'd say that the lowest interval is approximately that interval's place in the overtone series based on that 20-hz. note.

Anything that violates this simple integer-over-lowest-bass is more and more dissonant based on precisely...

No, not precisely.

No, no exact important scales of dissonance are possible! There is only a general sense, and the sense that things either belong in the overtone series first, or not in a given sonority. Then the complex stuff happens, and we can throw that simple model out. Music happens.

Still, it's worth considering the radically naked overtone series, because some experimental and avant-garde, electronic musics are based on it, directly.




* This I'm making up and it doesn't matter. The important thing is the harmonic sensation of a real harmonic bass or not.

One-note piece with drone in bass: In one sense, (if you went to Berklee they even said this explicitly) you can do anything over a drone, so it's not definitive of anything, but it really is: Everything you play over it becomes defined by it, becomes "magnetized", become part of its resonance, its expectations.

But as a drone moves up in register, it ceases to become only a fundamental, so it becomes possible within the lower-interval limit to define it in more and more harmonic overtone functions as it moves up.

I'm sure you've experienced what I call The Unbearable Lightness of One-Note (Or One-Chord) Music? That is, music that was intended to be so tonal, but surprisingly even when it gets displaced by a step or two, the effect might be jarring but not impossible, so a drone can go anywhere. Because it can go anywhere, it's unbearable, like a droning insect or like a droning leaf-blower. Undefined. No intelligence in one-note.

So What.

Impressions.

(Both examples of elaboration by-mode, and neighbor-motion of root of mode, causing maximum change of pitches)

But one-note changing in relation to any other note becomes meaningful.

A note is not meaningful, but an interval is.

An interval or set of notes that are elaborated -- gone next-door-to and returned to, as you rightly say, -- is a much stronger tonality than just one note.

But as soon as you add strengthening, interesting elaborating tones, you start to build in the seeds of potential atonal anarchy. Slippery slope of jaded addicted sophistication of fornicating evil tritone black male on feet.

Sorry for the purple prose. There actually was a guy who ran the music store in town who used to warn us kids to avoid the evil tritone.

I always cheerfully employed highly tonal rows, even super-trick rows that ensured harmonic results in several different ways at once.

Dani, I'm going to try to sort out some different areas of discussion, theory.
In no particular order:

-- What you're talking about with voice-leading is I think called Neo-Riemannian theory. There are whole huge dreary compendiums of the stuff. It is the going cottage industry for employing grad students and teaching assistants etc. in music theory. I just bought about five of these books, I may read them.

-- For a brief shining moment with serialism, it was as if composers could write books talking shop with other composers. Serialism made for good shop-talk. There was also a spirit of interdisciplinery research shown in the good books on music theory that were written by composer-theorists. Then that stopped, either because publishing changed, or the scene changed. I don't see books like that any more, even in serious music bookstores.

-- My approach with serialism is this: Generation of material is one thing, taste is another, hearing is another. A slightly augmented set of standard serial techniques is an excellent toolbox for generating pitch-material. It can be used to generate macro pitch sequences lasting the entire piece, or surface tunes that go by quickly. The virtue of the box of techniques is that everything is at least logically related. The composer can also insist if she wishes, that the musical results of such techniques are also always about being audibly related. I myself do insist. Others don't.

-- I've witnessed even fairly bright composers (I'm thinking of you, Daniel F.) who get bogged down in tedious and strict definitions of what serialism "must" be or ought to be "in essence". (It has to be about "interval fixing" or something.) No.

-- Instead, serialism to me as a composer is a generative technique, nothing more or less. It has to produce audibly related results. It also has to produce pleasing, musical results, which means I have to cherry-pick insanely to get the unlikely coincidences or tonal contrapuntal combinations.

-- To me, logical relations in composition are there to produce only the psychological result of hearing a resemblance. This sounds like this. It's like this, but different in this way, same in that way.

-- Therefore, mathematical invariance is less interesting than related variance.

-- Consider what happens, for example, when a melody changes from major to minor. It's an inexact transformation or resemblance when considered literally. At a higher level, I suppose it's perfectly systematic, but not from the pov of serialism.

-- Serialism was never a complete system in anyone's hands -- everyone was using some of the same techniques but making it up as they went along, too.
(Even Babbitt and Wuroninen)


-- What I'm talking about with harmony is best observed with synthesizers and computer-controlled tuning that can be set up quickly, as with Scala format.
If you (Dani or anyone else) take that path, it opens up a whole meaningful territory of harmony in 3D and living color, if you will.

-- Harmony with only 12 tone tuning is like 2D checkers. However, there are plenty of people who could and can do more with 3 notes than I can do with 60, so it's not a question of virtuosity or musicality.

-- It's only that 12-tone 2D thinking is a sort of theoretical limited Flatland. It can be a revelation to experience something more 3D.

-- Obviously for people whose musicianship exceeds their theory (most good musicians) the 2D aspect of 12 tones doesn't occur to them at all -- they're fully capable of transcending the limits of their own thinking in their music-making all the time.

-- JI theory (7-limit, 11, 13-limit) is something I sort of live with every day, but don't try to understand all that systematically. It means that intervals like 7/4, 11/4, 18/13, become real intervals, become real consonances, become meaningful.

-- I mention low interval limits because I've talked to musicians who don't seem to understand what bass is, what inversions are, what the overtone series is.

-- Heck, there was a kid at the MIT experimental studio before it became part of the media lab, this kid was from Juilliard. This kid, who had been at Juilliard for several years as a comp student, didn't know that an octave was a 2:1 ratio. This is the degree to which standard music theory as it's taught is sort of divorced from reality.



Well, top of head. See if any of this clears anything up.

My thoughts always drift in the direction of JI theory, which can help inform your practice, if...

But that's only my project.

Two good books:

Tom Johnson __Other Harmony__ beyond tonal and atonal

and

Dave Liebman __A Chromatic Approach to Jazz Harmony and Melody__


with the reservation that these are grab-bags full of ideas and techniques, but without taste. You have to provide the taste.

Both are by composer/players for composer/players, one reason I like them.

Oh, now I understand what you were saying about drones (the modal jazz examples helped).

I checked superficially what the Neo-Riemannian theory was about before because you mentioned it here some time ago, in a Beatles thread. Seems interesting. I read about the three basic transformations. Well, nothing too surprising, but it's good to systematize stuff that makes sense. I have too many things to learn, but I'll look into it sooner or later.

I didn't know about ratios and the mathematical and physical aspect of music until recently. It's fascinating. What does 7/4 sound like? Some type of sixth with some added spare change?

What do you mean when you say:

"I'd say that the lowest interval is approximately that interval's place in the overtone series based on that 20-hz. note."

Are you saying that a 20hz->40hz is the lowest frequency interval that makes sense to human ears?
 
I mean that in this construct, the lowest allowed harmonic octave 2:1 is ca. 40 hz. to 20 hz.

the lowest harmonic fifth 3:2 is ca. 60 hz. to 40 hz.

The lowest fourth 4:3 is ca. 80 to 60 hz.

The lowest major third is ca. 100 hz. to 80 hz.

The lowest minor third 6:5 is ca. 120 hz. to 100 hz.



-----

What is it to be lower? It is to be muddy, unintelligible, dissonant.


Intervals above this 20 hz root. (give or take) in the overtone series as described are perfectly consonant.

The other intervals don't get a wrist-band and don't get through the door.
They are excluded. Contaminated. Spicy. Wrong. Other. Bad. Dirty. Unclean. Hideous. My Mother Said No, caleb don't touch that.
Wash your hands afterward.

Dani. I have no idea at the moment whether that 20 hz. basis as lowest sounds right. I'll check it, or I hope you do.

What I'm describing, though, is quite a robust effect of muddiness as you get too low. And: important consequence: microtuning the intervals exactly changes how pure, clean, acceptable they can seem. Perfect JI intonation is least muddy, usually.
 
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Crap. Hate new computer. Lost post again.

Anyway, the notion of low-interval limits would be a piece of Static Harmony, which would -- in an ideal music theory -- cover just intonation, scales, ratios, intervals, triads.

This would be half of the course. The other half would be Applied Harmony, or Harmony in Motion. This introduces all the complexities that come with practice, with motion, elaboration, tension & release, passing-tones, counterpoint, melody, contours.

Static Harmony includes the lattice, which in a sense already implies moving beyond the limits of a static, unchanging view, because it is endless.

https://www.google.com/search?q=mus...uiyvfXAhXp5YMKHRcBBTUQsAQIOA&biw=1280&bih=664
 
Without being clear about basic grounding of harmonic concepts, students make absurd mistakes about what they say about harmony, and how they analyze the lit.

For example, the person who thought it was significant that a particular C major triad was in "6 4 position" (second inversion, or G in the lowest position) when the lowest note was a G2 -- that is, not a note in the bass register. No, the chord simply had no functional bass. It wasn't relevant to say it was "in .[].. position."

Without theory and practice actually helping each other, as they rarely do with most musicians, it's easy to take a cynical view of theory as just some idle philosophy. Musicians who take this view never innovate in fundamental musical ways, however innovative they may be in extra-musical ways, or however good they are.
 
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