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Old 7th December 2017, 02:45 AM   #41
calebprime
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The same simple structures and thinking, turned upside down, also illuminate polyrhythms. Just as notions of low-interval limits clear up some harmonic ideas, the same kind of notion clears up what are the limits of polyrhythmic intelligilibilty.

Suffice to say that some large part of middle-period Carter is both impossible to play accurately and not intelligible or hearable or even recognizable by savants.

That may not be a fatal criticism of the music, but it does give you some perspective on the spirit in which it was written. Being intelligible didn't matter.

It's the inversion of the low-interval limit. The upper bound on resultant rhythms in combination. If the resultant combination r's are faster than you can tap or sing or faster than 15 a second, they're not intelligible.

The static model of harmony would explain the simple Partch up-down generation system, or basic JI. Simple, but I've spoken with some old Boston microtonalists who didn't understand what Partch was doing! That's astounding ignorance in a specialist.
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Old 8th December 2017, 10:24 AM   #42
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Another way of saying the same thing.

First, an ideal sort of definition of consonance. What is pure consonance? It is anything that makes overtones of a fundamental frequency (whether the fund. is stated or not) that is in the auditory range.

I mean integer multiples. This is an extremely robust effect.


Ok, then, does that explain music as it's practiced? (Sophist's approach, etc.)
No, it couldn't and shouldn't.

You have to add, from your listening, all the variation over time.

While a JI model generating overtones from fundamentals all of which share a common overtone (the 1/1) is in a sense a static model, it too implies motion, because each "undertone" of which 1/1 is an overtone is separate from the others, to some degree or almost completely. That is there is a range from related fundamentals like /9 and /3 to fairly unrelated funds. like /13 vs. /12 or something.

So, while it is a model that is static (doesn't take time into account) it is not a model that means that anything goes, that any note in it is as closely related as any other. No, they are closer or more distant to each other.

In the 13-limit model I favor, there is implied motion -- you'd go from a chord on /13 to a chord on /3, which are thought of as separate regions, at least at first, for clarity, and for sonic clarity.

But in the more sophisticated view of the second half of the course, harmony in motion & practice, you could bring in all the effects of everything else, especially those things having to do with passing-tones, or directional tones, or tones in motion over time, in a rhythmic framework.
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Old 8th December 2017, 11:12 AM   #43
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Originally Posted by calebprime View Post
... What is pure consonance? It is anything that makes overtones of a fundamental frequency (whether the fund. is stated or not) that is in the auditory range.

I mean integer multiples. This is an extremely robust effect.


...
Q. Would something like only the 15th partial sounding with the 14th partial -- just those two notes -- be a consonance? You said anything.

A. Shut up, smartass.


Q. Why?

A. No, in that unusual example, you'd have the impression of dissonance until the rest were filled in. So I have to add other restrictions, which is no fun whatsoever, compared to a sweeping generalization. I going [sic!] to go home and drown my sorrows in hookers and blow. See what you've made your noble professor do?

Q. I'm...I'm sorry.

A Apology accepted. There's a book you can read. The psychology of the sensitive person.

Q. Is it right that you cover the entire work of Santana in the first half of the course? That you can't even mention Shostakovich until the second half?

A. Yes. It's fine. shut up.
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Old Yesterday, 05:12 AM   #44
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The difference between 40 hz. and 20 hz., etc

This is why I no longer teach.

Dani, here's a soundfile I just concocted by putting the sound of my son as a toddler babbling through an early version of Alchemy.

https://app.box.com/s/4u6k3hjxqholh37q1c0sr2da8huruabc

There's a lot that can be done with Alch. but right now you're hearing the sound slowed down and resonating through a comb filter.

The comb filter frequency starts at 40 hz. You can hear to what degree everything sounds like harmonics of one note.

Then you can hear the frequency move around as I move the dial -- the moves are obvious and not quite accurate, because it's hard to land on the exact right number.

I go up to 80 hz., back down to 40. I go down to 20, and you still have a strong sense of harmony, but you hear things shake, vibrate, flap, quiver, whatever you wish to call it. We're near the threshhold.

At around 16 hz, which I hit and sit on later, you hear the rhythm, but you still hear some of the Chord of I.

See if you can get a resonant comb filter and try this for yourself -- listen and decide where "harmony" starts to become "rhythm" -- somewhere gradually between 20 and 10 hz.
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Old Yesterday, 09:21 AM   #45
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Originally Posted by calebprime View Post
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.
I'm one of those people! For starters, I don't understand the notion that, because G2 is not a note in the bass register, it ceases to function as a bass. And... what is a note in the bass register? Is there a specific frequency where a bass ceases to be a bass? Isn't it context dependent? I can imagine a G2 being played by a bass player to determine the fundamental of a given chord. Is that wrong (objectively)?

I'm not talking about inversions played by a single instrument with a bass playing the root (which guitar players in particular tend to see as inversions).
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Old Yesterday, 09:32 AM   #46
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Just so we're clear, I mean G2 top space bass clef, or around 196 hz.

With ca. 19.6 hz as an easy-calc approximate root, this G2/196 hz. could be the 10th, 9th, 8, 7....1 of any fundamental.

So it's not "bass-ic" until it's maybe an octave lower.

Think about the voicing of the richest music you know -- bruckner, brahms, wagner. Still way above the low-interval limits, mostly. But I'm on shaky ground there, as I haven't been studying that lit for a while. (give this historical ass. an 90% true.)

It wouldn't be wrong, it would miss the point that it doesn't matter what the inv. is if it's that high, it has no characteristic "inversion" effect anymore.

If asked on a test, what's the inversion? You are correct sir, it's a 6-4, second inversion, g in the "bass", no question.
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Old Yesterday, 09:39 AM   #47
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Characteristic "inversion effect" with real low bass:

--the effect of the overtones of the bass clashing with the other notes.

Without that clash, no real inversion effect.
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Old Yesterday, 09:41 AM   #48
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On Neo-Riemannian theory, I just read a brief introduction. It's really focused on voice-leading, regardless of tonality/atonality. That's interesting. Also, I just noticed that, given any series of transformations L (leading tone), R (relative) and P (parallel), its repetition leads to the original chord (or group of pitches, or klang). Still not sure if the order of the factors alters the product. I have to figure that out.

Also, I'm curious about how augmented, diminished, seventh and extended chords fit in this theory.
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Old Yesterday, 09:43 AM   #49
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I mean that True Bass™ is absolute, gradual, and a function of something like our neural "clock-rate". This is the rate at which we perceive the world, as opposed to the rate at which hummingbirds perceive it, or sloths.

Whatever G2 is, man it's tenor. Not bass.
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Old Yesterday, 10:01 AM   #50
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Originally Posted by calebprime View Post
Just so we're clear, I mean G2 top space bass clef, or around 196 hz.

With ca. 19.6 hz as an easy-calc approximate root, this G2/196 hz. could be the 10th, 9th, 8, 7....1 of any fundamental.

So it's not "bass-ic" until it's maybe an octave lower.

Think about the voicing of the richest music you know -- bruckner, brahms, wagner. Still way above the low-interval limits, mostly. But I'm on shaky ground there, as I haven't been studying that lit for a while. (give this historical ass. an 90% true.)

It wouldn't be wrong, it would miss the point that it doesn't matter what the inv. is if it's that high, it has no characteristic "inversion" effect anymore.

If asked on a test, what's the inversion? You are correct sir, it's a 6-4, second inversion, g in the "bass", no question.
Ok. 196 hz doesn't sound like a bass in any way, shape or form. Agreed. Some of the concepts you regularly use are fairly new to me, and I don't know by memory what a G2 is, for example. I looked that up and I saw it referred to as around 98 hz. That still sounds like a bass to me. But, yeah, 196 hz is way too high to be considered a bass.
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Old Yesterday, 10:05 AM   #51
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Yeah, there are at least two standards. I forget which one I mean.

Glad we agree about that G2.

I feel I may rest now. My work is done.

You have learned much, Dani.
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Old Yesterday, 10:12 AM   #52
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Just so we're clear about neo-R theory and me:

--It might well be that a composer or an improviser has benefited from it, but I don't know that. It seems to be "by and for" theorists.

--I don't know it.

--You are smart. You might be able to absorb it into your bag of tricks. Take it into account.

--I would learn it enough to converse with you, but only for that reason.

--It is definitely something you should know if you want to fit into contemp. academic music theory world.

Go for it!
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Old Yesterday, 10:35 AM   #53
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Funny anecdote:

Rehearsing with a blues-soul-worldmusic-pseudojazz-whatever quartet, we were playing an instrumental gospelly-soul piece, and there's this part where we play a typical A7alt resolving to Dm. I asked the guitar player, a friend of mine and a fine blues player, both melodically and rhythmically:

Me: What are you playing on the A7 chord?
Guitar player: I'm not playing an A7.
Me: (looking at the bass player) Well, whatever you're playing, it's some type of A7 chord.
Guitar player: I'm playing a Bbm.

He clearly understands that he is not painting the harmonic canvas alone, and understands the function of that Bbm over A (an implicit A7alt, even if there's no 7th), but there's something about non academic guitar players (I don't know, magazines, tutorials, inertia?) that tends to make them think in these terms, whereas no matter how clueless we are, piano players have at least two octaves to figure out what bass sounds like.
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Old Yesterday, 10:44 AM   #54
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(mentally puts little finger on C (on D string), then Db,F,Bb all on 6th fret for Bb minor 9 with no bass)

Yeah, A7 #9

(Which is a mis-nomer, because it's really Amin7b5 b4, but that would confuse everybody.)


love it.
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Old Yesterday, 11:18 AM   #55
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Thanks, Calebprime. There's tons of information already in this thread about... many things.

I feel like atonality is the end of a journey I'm just starting, which starts with tonality. I've never really been into classical music, but I'm starting to feel like I need to do a historical discovery on my own, as I did with 20th century popular music (and still do) earlier.

While one part of me is playing funky grooves, another part is absorbing lots of fascinating information, and much of that is thanks to you. That could be useful in the future in terms of understanding music with a greater perspective. I feel like I've been on shaky grounds all this time, and I'm experiencing the excitement of discovery. Things like why did medieval musicians used only fifths to harmonize a melody and why the next audacity consisted of adding the third now have a deeper meaning.

JI is interesting, but it will take some time. Same with microtonal stuff. There's so much to learn with 12 equally tempered tones only, starting from Bach.

Serialism? Very interesting. Right now all I can do is cerealism. I don't know if I'll end up there. Depends on how much I am absorbed by other things (including jazz).

Music is soul food. Music theory is intellectual food for soul food. This is a feedback loop that never ends.
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