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May 29, 2007 - Don't dimension it

 
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TS



Joined: 07 May 2006
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PostPosted: Wed May 30, 2007 4:53 am    Post subject: May 29, 2007 - Don't dimension it Reply with quote

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But HSV is the only model where hue/chroma has a single spectral value. All the other models-- RGB, CMYK, Lab-- arrive at chroma by intermingling "primary" components. Could it be that there are "primary pitches" which allow the generation of any of the others?

The reason why all the colour models use three primary colours is because the human eye has three kinds of sensing cells that each respond to a certain wavelength of light, but hearing doesn't work the same way.
Quote:
A complex tone already does have components that are other pitches. For example, here's a middle C that I just constructed. It's not a pure-tone 100% C; because of its overtones, this sound is 77% C, 16% G, and 7% E, but it does sound like a pitch and not a major triad.

The fundamental can be completely missing from a tone, but the tone still retains the character of a tone that has the fundamental. I don't think that a pitch is a single frequency, but that it's a collection of overtone frequencies, and whenever a tone's overtones match some of the frequencies in the collection, the tone is heard to be of that pitch.
Quote:
... and now just for comparison here's 5% C, 5% G, and 90% E, that no longer sounds like a middle C, but more like 100% E.

To me it still sounded like a C. I listened to the sound, then plucked the E-string on my guitar that was right next to me, but it didn't seem to match. Then I played a C on the guitar, and it matched. The 100% E matched the E-string, but I could barely hear it when it was mixed with the 5% C and 5% G, I only got a strong impression of the tone being C.
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aruffo
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PostPosted: Wed May 30, 2007 7:28 am    Post subject: Reply with quote

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The reason why all the colour models use three primary colours is because the human eye has three kinds of sensing cells that each respond to a certain wavelength of light, but hearing doesn't work the same way.

I was noticing that-- the articles which discussed the various color spaces pointed out that the primary components are due to biology. The biology of hearing, certainly, does not have the same kind of three-receptor structure, but I wonder about the research which seems to show that evaluation of pitch is a mathematical calculation and not just a pass-through to the tonotopic map. Perhaps 3-dimensional sound space does not operate on "primary pitches" but somehow involves the admixture of overtones in a way that's dependent on the partials of a starting pitch..? Or... bah. It seems to me that it should be possible to imagine a combination of sounds which could be mathematically altered to produce either A-flat or C-sharp or E or whatever as a calculated synthesis-- maybe I'm tackling a problem that's simply beyond my mathematical skills.

To put it another way, although visual and auditory biology do receive their sensory input differently, it seems that they nonetheless each perform a calculation upon the input components and generate a single synthesized sensory percept. Manipulating those components should theoretically make it possible to move along the Z-dimension; the heart of the problem, I believe, is answering what those components might be. On the other hand...

Quote:

whenever a tone's overtones match some of the frequencies in the collection, the tone is heard to be of that pitch.

Now that you mention it, perhaps there is a perceptual difference between the C-reinforcing overtonal E and the fundamental E. I am surprised that you hear the 90% E as a C-- I definitely hear it as an E first with some C "flavoring"-- but the presence of a C fundament and a G overtone, even weakly, would seem to strongly suggest to one's mind that the proper way to mentally complete the tone is by imagining it to be a C-pitch.

I don't know what factors are involved that allow you to hear it as a C and me to hear it as an E. When I recently played the C4-C4.5-C4 sequence for Rob Goldstone, even when I played it from the original experimenters' website (as opposed to my own constructions), he was unable to hear the difference between 4 and 4.5; to him they all sounded exactly the same. Is this a matter of expertise, bias, or expectation?
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boes



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PostPosted: Wed May 30, 2007 2:01 pm    Post subject: Reply with quote

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... and now just for comparison here's 5% C, 5% G, and 90% E, that no longer sounds like a middle C, but more like 100% E


To me it also sounds like a C!
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aruffo
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PostPosted: Wed May 30, 2007 3:07 pm    Post subject: Reply with quote

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To me it also sounds like a C!

This got me a-thinkin'-- if it still sounds more like a C to you, despite being only 5% C, then the idea of "primary pitches" is probably out the window. You're making me think that I shouldn't have dismissed the HSV pitch space so quickly, 'cos upon closer examination it seems to fit better. I'll write more about it on the main page shortly.

Anyone else hear C-not-E?

I was also noticing that there appears to be quite a volume of information about "pitch space" in the literature, but most of them seem to talk about "timbre brightness" without explicitly saying that this is equivalent to height; although some of them suggest that this may be a percept separate from fundamental frequency, they do not seem to think that this is a quality of the "pitch".
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etaxier



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PostPosted: Wed May 30, 2007 11:27 pm    Post subject: Reply with quote

I'm just responding to the 5%C...90%E question that Chris just posed. To me, the 5% C / 90% E sounded analogous to the "not quite C not quite G" example. In other words, it sounded like a C-E interval.

I think most people would at least hear the C as a root and the E as a "high loud background to the C."

5% isn't as low as you might think. Check out this article's bassoon graph which clearly shows that for some instruments, "the fundamental frequency produces far less than 10% of the total power" of a given note.

In further regards to the 5% C example, I think our minds are designed to seek out and construct notes that are closer to speech frequencies. E's pretty high up there in comparison, which is why I believe most people will automatically treat it as background to the C.
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aruffo
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PostPosted: Thu May 31, 2007 1:28 am    Post subject: Reply with quote

Ooh! Great link. Thanks f'r that.
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TS



Joined: 07 May 2006
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PostPosted: Sat Jun 02, 2007 3:32 pm    Post subject: Reply with quote

From the May 29, 2007 post:
Quote:
If the pitch cylinder were truly a two-dimensional model, then presumably it could be visually represented without requiring an implicit third dimension.
. . . .
But the helix model was created because a simple line could not represent octave equivalence; likewise, a two-dimensional plane cannot represent octave equivalence either.

Actually in the bottom graph in the latest "June 1, 2007 - Note soak"-post octave equivalence is represented with a single line on a two-dimensional plane, the line that's called "height". It only requires that the X-axis chroma scale repeats itself.

I don't know where this dimension thing is heading, perhaps it has something to do with the topic of how to rotate a tone, but my theory of chroma and height is this:
A tone's height is determined by where on the audio range the most powerful harmonics are.
Chroma is determined by the harmonics of a tone matching a mental collection of frequencies.

What this mental collection means is that there is an ideal model of chroma in the brain, that consists of a collection of frequencies. Whenever the person hears harmonics that fit this collection, the sound is heard as having the corresponding chroma. All the harmonics need not be heard, even the fundamental can be missing, and the chroma can still be identified, like a car that's coming from behind a house can be identified even when only a third of the car is visible.

For example the collection for the A-chroma has these frequencies:
55Hz, 110, 165, 220, 275, 330, 385, 440, 495, 550, 605, 660, 715, 770, 825, 880, 935, 990, 1045, 1100 and so on, adding 55 each step.
Now the tone A1 has the harmonics 55Hz, 110Hz, 165Hz and 220 Hz. These all fit the collection, so A1 is heard as having A-chroma. A2 has the harmonics 110, 220, 330, 440, and these also fit into the collection, so A2 also has A-chroma, and for A3, A4, A5, the same thing. If a sound has some extra harmonics that don't fit in this collection, then another chroma is heard along with the A.

This explains why octaves are equivalent, and why the fundamental harmonic can be missing and the tone still identified correctly. What it doesn't explain is why single sinewaves have chroma, and why for example A1(55Hz) and E3(165) are not equivalent, like A1 and A2, even though they have harmonics that fit the same collection.
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petew83



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PostPosted: Sat Jun 02, 2007 10:37 pm    Post subject: Reply with quote

Chris I love the new sound color wheel stuff. it's amazing how visual and sound color are turning out to have so many similarities.
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aruffo
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PostPosted: Sun Jun 03, 2007 8:36 am    Post subject: Reply with quote

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What this mental collection means is that there is an ideal model of chroma in the brain, that consists of a collection of frequencies. Whenever the person hears harmonics that fit this collection, the sound is heard as having the corresponding chroma.

I'd encourage you to read the "Separating chroma and height" papers that Patterson and his group have been putting out. They argue-- effectively, I think-- that chroma is also a mathematical synthesis. In this view, the collection you describe is not so much "fit" to a single pattern as "calculated" into a single result.

Quote:
I don't know where this dimension thing is heading

At this point I'm not exactly sure it's "heading" anywhere; it had been bothering me that the pitch helix was not two-dimensional, and then that it was not three-dimensional; now I'm satisfied that I at least have one three-dimensional model that would allow me to create plausible tones at any point within the cylinder, instead of just on a surface or on a line.
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TS



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PostPosted: Mon Jun 04, 2007 8:57 am    Post subject: Reply with quote

I don't really understand how the brain works well enough to say anything about that subject. I used the word "brain", but I really meant the unconscious mind, or whatever it is that processes sound.

What I meant was to propose a model for manipulating a tone while keeping the chroma of the tone constant, without really going into what happens in the brain. I think that chroma is a collection of harmonic frequencies, and any single frequency on its own doesn't matter, and can be removed, even the fundamental, and for example a tone with G-chroma doesn't need to actually have any harmonics that are the G-frequency, just as long as there are enough other frequencies present that fit the collection, which is a bit like the idea of primary pitches.

Initially you proposed that combining C, G and E pitches results in a tone that is still a C. Then you proposed that making the E louder than the other pitches would make the tone sound more like an E than a C, but to me it still sounded like a C, even though the C was almost nonexistent. What I'm saying is that you could remove the C altogether, and the tone would still sound like a C, because the G and E make it a C, so they are sort of like the primary pitches that together make another pitch. The loudness of the component pitches doesn't have much to do with it, more important are the positions of the component pitches in the spectrum. If the component pitches coincide with the overtones of the C, then they create a sensation of C-chroma, even when the C isn't there.
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petew83



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PostPosted: Mon Jun 04, 2007 9:08 am    Post subject: Reply with quote

'G and E make it a C'

I've read about this before. Crappy radios can't get the low notes but we still hear them because of this phenomenon. I guess there really is a way to mix 2 other pitches to get a third pitch. It really helps when u play the fundamental first, then play the major 6th above alone. Then u sense the C underneath even if you're not playing it, and the C feels like 'king'
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aruffo
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PostPosted: Mon Jun 04, 2007 11:00 am    Post subject: Reply with quote

Quote:
I think that chroma is a collection of harmonic frequencies, and any single frequency on its own doesn't matter, and can be removed, even the fundamental, and for example a tone with G-chroma doesn't need to actually have any harmonics that are the G-frequency

I'd both agree and disagree.

I'm adequately convinced that "chroma"-- the categorical classification and judgment of "pitch"-- is essentially drawn from the value of single vibratory frequencies. A single frequency on its own does matter because that's the essence of the chroma quality.

What I'm asserting is that any collection of harmonic frequencies is neurally and mathematically synthesized into a single numerical value, and this result is judged to be the "pitch" and classified into its chroma category. This is what the papers about separating chroma and height are showing to be the case, neurologically. They point out that even the noise sounds I've posted, which lack a fundamental frequency, seem to have a pitch value; try singing along with the noise and you will probably find yourself making a choice you feel comfortably matches its apparent pitch. The early papers (such as "the pitch of tonal masses") describe how a complex sound can be assigned a single pitch value even when the sound is perceptibly not a single tone.

I don't want to forget, either, that even before you get to the neurological part of it, the harmonics of a complex tone physically create the fundamental. The "missing fundamental" is not actually missing. Likewise, "combination tones" and similar phenomena may not be created by the source instrument but are nonetheless physically present due to the interaction of the waveforms which were deliberately generated.
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