The power of Repetitiveness

Talk about what you've discovered by using ETC-- and post your high ranks!
gavriel
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Postby gavriel » Sun Mar 30, 2008 12:10 pm

paulriley wrote:gavriel, surely you could draw the same lines when comparing c4 with g4. They would still share the same high and low point wouldn't they? because the c5 doesn't "change" the c4.

But of course it does!
If we would have only a C4 (without a C5 compounded into it), it would look like a simple symmetric sinus wave. Primitively speaking, within one C4 cycle as marked with green on the picture the wave line would go upwards for a quarter of the cycle, then downward for another quarter reaching the starting level, the downwards for another quarter period and up again to the starting level.

However, in the compound wave form we have a line which goes up for a SIXTH of the (C4) cycle period reaching the same hight a regular C4 would reach after one FOURTH of a cycle, then (in the second sixth cycle) it goes downwards reaching the starting level, then (in the third sixth cycle) UP AND DOWN reaching the starting point AGAIN, then UPWARD AND DOWNWARD reaching the starting level AGAIN and finally deep downwards and then upwards to the starting level.

Thus in the compound waveform we have also one big top and one big bottom but the top is "earlier" (at the end of the first sixth rather than at the end of the first quarter) and the bottom is later (at the end of the fifth sixth).
Also in a non-compound sounds of a C4 and C5 the second tops of C5 would be as high as the first ones.
No other sound than C4+C5 will give exactly such a picture.

The compounding created the little bumps in such a way as to give the common denominator 12 within one big "C3" cycle. Buttt the C3 is not there and the G4 is not there either (there is no big huge top in the middle of the C3 period and the C3 period is not divided into three as it does in the natural G4 wave).

Figuratively speaking, the compound line is making minor snake-like movements to meat the ratios of a G4 without actually creating a G4 and this forces us to listen to periods of a C3 cycles to get repetitive scenarios BUT the C3 is not there either!

djf
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Postby djf » Sun Mar 30, 2008 1:38 pm

Image
Here's another C4+C5 compared to a G4. Gavriel, you're looking at the wrong things. The shape of the waveform isn't as important as the frequency. The C4+C5 that Chris made and you used sounds exactly the same as the one I just made, but the one I made is symmetric and Chris's isn't. Again, the fact that the frequencies are in a simple ratio has nothing to do with the "fractional height" and everything to do with the fact that C4 and G4 are a perfect fifth away from each other. To put it another way, the frequency determines the pitch (or chroma) and the shape of the waveform determines the timbre. A cello and a trombone both on a C4 sound distinctly different because of their different waveforms, but they still clearly sound at the same pitch and the same height.

aruffo
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Postby aruffo » Mon Mar 31, 2008 9:56 am

they still clearly sound at the same pitch and the same height.

Regardless of our current confusion about how to mathematically (or visually) analyze the waveforms, and regardless of the ultimate definition and application of "fractional height", this literal statement is exactly the one that the Patterson (et al) research disagrees with.

Although it is undeniable that a C4 tone produced by any instrument contains the same "fundamental" frequency, and that a "fundamental" frequency is unquestionably the same height no matter what instrument produces it, a timbre-- defined as an overtone/undertone series-- changes the perceived height of any complex waveform.

This has been known since the 19th century, when it was observed that a tuning fork made of thinner metal could produce the same pitch but still sound "higher". This effect has often been explained away by assigning it to some other adjective, variously "brightness" or "density" or the like, but the 1934 paper demonstrates (in a way that convinces me, at least) that these adjectives are all drawn from the same perceptual input.

In other words, the phenomenon of what can be called "fractional height" exists and has been observed in various ways since the 1800s. Although the logic and mathematics of our trying to dissect the waveform may be completely off target, the conclusion we're trying to find an explanation for is itself valid and has been for years.

abminor
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Postby abminor » Mon Mar 31, 2008 12:34 pm

Just wondering. In case someone succeeded in changing its pitch perception to chroma perception. Does it mean it would be closer to have absolute pitch ?

Not sure of that. Still you have to memorize the different chromas aren't you?

There seem to be a consensus that memorizing and recognizing chromas would be easier than doing the same thing with pitch heights (like recognizing the red color is easier than recognizing an absolute level of "geyness").

I just wondering what should prevent us from judging pitch in a relative way because we use chroma instead of height. Can't chromas be organized in a relative way too ? I think they can.

We are probably all doing that to some extent.

It seems to me that absolute pitch ability probably rely on a strong chroma perception however, I'm not sure it 's the only skill (or requirement if we consider a age limit exists) needed.

I think chris aruffo already wrote something on this subject somewhere.

djf
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Postby djf » Mon Mar 31, 2008 1:52 pm

aruffo wrote:This has been known since the 19th century, when it was observed that a tuning fork made of thinner metal could produce the same pitch but still sound "higher". This effect has often been explained away by assigning it to some other adjective, variously "brightness" or "density" or the like, but the 1934 paper demonstrates (in a way that convinces me, at least) that these adjectives are all drawn from the same perceptual input.

Right, I guess I didn't say exactly what I mean. Sorry for the confusion. What I meant was more or less the same thing I've been saying. I was just trying to find another way to put it that might make more sense, but I screwed up. However, I still hold that my "symmetric" C4+C5 sounds the same as your "in phase" C4+C5 because, as I think you mentioned on the front page a long time ago, when we hear a sound, our ears automatically deconstruct it into its component sounds, so the shape of the waveform matters less than the fact that it's made up of two tones whose frequencies differ by a factor of 2.

aruffo
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Postby aruffo » Mon Mar 31, 2008 2:58 pm

when we hear a sound, our ears automatically deconstruct it into its component sounds

Yes, that's true, and then our brain reconstructs the component sounds into whatever we think we're hearing. It's sort of automatic in that it doesn't happen consciously, but it's not automatic because it is highly (perhaps completely?) dependent on learning.

I think that the studies of "fractional" pitch height make a convincing case that our minds are recombining the frequencies of a complex sound into a mathematically averaged "height" that our brains can pinpoint and thus psychologically measure.

I took a look at a simplified, phase-matched waveform on the chance that the averaging which has been shown to exist could be obviously noted in the visual comparison-- that's how I discovered that the "missing fundamental illusion" isn't an illusion at all, because you can see that the supposedly-missing fundamental is physically created when the provided frequencies are (re)combined.

The visual image of the height-averaged waveform is too ambiguous to draw an obvious conclusion. I don't know what it means that the combined-C waveform crosses the zero-point with the frequency of the G-pitch, because only one out of its three cycles is a regular wave that resembles an G-cycle (an inverted one, at that).

Gavriel's come up with some examples that seem to be psychologically true, but we don't yet know how these can be physically explained except by abstractly mathematical averages.

gavriel
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Postby gavriel » Sun Apr 27, 2008 4:20 pm

Any progress on the fractional hearing issue and/or ETC 6??

Axeman
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Postby Axeman » Thu Oct 16, 2008 2:22 am

I think you're right about repetition. Long ago when I began thinking about perceptual differentiation, I considered that when you contemplate a fire truck, an apple, a stop sign, etc, you abstract out the quality of "red". At the time, the musical object I was thinking of was a single tone. A more complete musical object is, of course, a composition; there must be a way to make differential, functional judgments about compositions.

If you think about the function of pitch as a signifiers of particular dynamic events you get the same type of abstraction.

My boys play a PSII game called SlyII where a little critter (racoon I think) goes around pick pocketing from huge menacing looking thugs and smashing stuff to get rewarded with money.
I will come back to that.

I was thinking about AP acquisition in natural AP'ers - that it must be an incidental kind of learning for them. So as they learn about the world they somehow pick up the pitch recognition as an extra. If there is any truth in this statement -
I wonder if it's reasonable to distill that to the notion that color-coding indicates different static object-properties, while pitch-coding indicates different types of dynamic events.

-then as they are exposed to myriads of dynamic events each with its naturally associated pitch and ones that are closely pitched to each other and also closely contiguous. I think I am using that word in the right place...
Contiguity is a series of things in continuous connection, a grouping of parts in contiguous physical contact.[1] The concept was first set out in the Law of Contiguity, one of Aristotle's Laws of Association, which states that things which occur in proximity to each other in time or space are readily associated.

Wikipedia. The 'readily associated' and '...proximity...' parts are what I'm trying to pick up on here.

Back to the PSII game. What if there was a game that simulated the above situation. For instance as the character goes about smashing stuff and picking pockets there was an accompanying sound (this already happens in the game). But integral to the design of the game is that the concept of contiguity is purposely used to advantage. The learning would be incidental and fun too I think. The sounds could be single notes or compositions of a particular key.
The cool thing about this too is that if it worked then the true learning inherent in the game would be almost subliminal. Not that I'm into subliminal stuff but I could imagine someone acquiring a better ear without even meaning to. The player is out there smashing and grabbing yet ends up hearing sound better.

Axeman
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Postby Axeman » Thu Oct 16, 2008 2:37 am

Whoops lost my train of thought. To finish
-then as they are exposed to myriads of dynamic events each with its naturally associated pitch and ones that are closely pitched to each other and also closely contiguous
they can't help but learn PP. This may also explain something about the low incidence of PP development because only those lucky enough to be brought up in environments with enough contiguous dynamic / pitch events acquire the ability. I think that the fact that the high incidence of PP in kids that learn music at an early age may be some proof of this. I don't know but maybe the repetition that is inherent in learning to play a musical instrument (practicing Fur Elise 200 times) may be significant enough dynamic events to act as triggers to other events of a more natural order.

SacumSuckum
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Gavriel's Stories

Postby SacumSuckum » Tue Apr 20, 2010 5:10 pm

Gavriel,

Does your father still have absolute pitch? Have you tried the method you mentioned in your first post yourself? Does your friend who played the organ still have absolute pitch? And are you a musician?

gavriel
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Postby gavriel » Tue Apr 20, 2010 5:53 pm

I am a musician, yes.
Full time. Since childhood.

No, as I later realized - they don't have a real real absolute pitch.
It is all nearby.
We all recognize pitches (if you practice 8 hours a day and a have a good relative pitch), but I don't hear music by pitches only by intervals.
I have to make a special effort to switch and even then - I guess it is memory what I hear - not a real absolute perception.

Seems that Chris is also a bit lost.

I am just waiting with patience.


Indeed, the only valid radical idea I remember coming up are the fractionals (fractional height).
But one needs a well done program to practice with this concept.

I was very excited when I read that C2+C3 can equal a G2 (with a C chroma) !

Why on earth aren't we working on THAT?

if a G2 can have a chroma of a G at time and at other times a chroma of a C, then the "difference" between these two cases is the ESSENCE of differentiating between the pitch chroma of a C and a G and ignoring/getting-fee-from pitch height per se.

One could easily create twelve 'G's comprising a chromatic "scale of chromas" from C to B. and feed APB or APA with these sounds.
You will hear sounds that all have the height of G but different chromas.

Hense chromas (only) recognition game.

Please can you HELP convince Chris to work on that idea?
The other ideas are all catch 22 and I am afraid a waste of time.

sinus C1+C2 = sounds like an octave of two 'C's to me with a strange feeling to it. I am very curious to know how a true born Absolute Listener would perceive such a sound as a normal C octave or as a C/G zombie-sound.
If the second case is the case the THAT IS WHAT WE SHOULD BE BUSY WITH!!

aruffo
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Postby aruffo » Tue Apr 20, 2010 8:50 pm

I've actually been doing a bit of experimentation with the mid-height stuff. Nothing official-- I still can't get support from the school for this-- but I was trying to figure out why, if height is perceived as a geometric mean of the spectral power, a C3.5 still sounds "lower" than a C#3.

Although I didn't save the wav files that I was putzing around with, so I can't post them here, I observed something first-hand which, once I heard it, made perfect sense-- a C tended to sound "lower" than a C# until its mean-height had been raised to close enough to the next higher C to make it "belong" to that higher octave. I tried similar efforts with a couple other pitches and achieved similar results-- but the results were slippery. They weren't at all consistent or definite.

What this suggests to me is twofold. First: that C2+C3 doesn't actually equal G2. Like Deutsch's tritone paradox, the two tones will sound alternately higher or lower than each other depending on context. Second: that pitch and height are truly separate. You can't "increase" a C's height and get any pitch other than a C.

That applies to both perspectives. You can't "go up" from a C and get any pitch other than a C-- meaning both abstractly that C2.5 does not equal G2, and practically that there's no such thing as an "ascending" scale. There is a categorical-ordinal sequence, not a stepladder.

I wonder if these subtleties of height-interaction are an implicit consequence of using different instruments in the same pitch range.

gavriel
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Postby gavriel » Wed Apr 21, 2010 1:33 am

A relative listener (being a "height junky") might not be able to hear C2.5 as a G-ish C and jump between C2 and C3.

Did you try to test such a sound on a few absolute listeners??

irrespective of the above, if the ability to hear the compound height of a tonal mass can be developed artificially. It could be a synthetic intermediate stage on the way of developing absolute perception of sound eventually leading to absolute perception of height and chroma.

If height and chroma can be separated at all. that's a huge step and gives for the first time a possibility to train one of them in relation to a static point in the other.

The fact that a sinus C2+C3 combined generates a tone whose frequency is that of a G but wave SHAPE is that of a C. is a FACT.

I don't understand why you need the support of the school to feed APA with new sounds. This takes a day max to program.

It is as simple as generating the following sounds which all result with different chromas but equal frequency:

A4 = 440Hz
G#1+G#5 = 440Hz
G2+G5 = 440Hz
F#3+F#4+F#5 = 440Hz
F3+F5 = 440Hz
E1+E2+E3+E4+E5+E6 = 440Hz
D#1+D#3+D#4+D#6 = 440Hz
D4+D5 = 440Hz
C#2+C#3+C#4+C#5+C#6 = 440Hz
C2+C3+C5+C6 = 440Hz
B1+B3+B5 = 440Hz
A#2+A#3+A#4+A#5 = 440Hz

And letting us all train with these sounds.
Listening to only to different 440Hz sounds with different diatonically tuned chromas.

I would start with a
A4 = 440Hz

then introduce the chroma of the relative fifth E:
E1+E2+E3+E4+E5+E6 = 440Hz

then D with
D4+D5 = 440Hz

then F# with
F#3+F#4+F#5 = 440Hz

and so on.


The mind will be entertained differentiating the chromas of different 440Hz
which effectively means that we could be motivated to listen to 440Hz endlessly and dive ever deeper into that frequency braking it down to fine differences of the overtone make up.

just make sure that the pressure (volume/gain) of the wave is always totally equal. this can be easily measured. This is very important. After you have created the sounds measure their pressure and make it equal.


perceived loudness is a complex mater and a science in itself and can influence the perceive "color" fo a sound.
for example:
A#2+A#3+A#4+A#5 = 440Hz
is not at all 6 time louder than
A4 = 440Hz

You should create both sounds out of high quality sinuses and then measure the result. this can be done in a program like sequoia (I have it), or any other high end audio work-station.

Just imagine the melody word in APA being automatically played in chromas :-)

Please Chris.
the rest is a waste of time.
This is the only chance for a 3 dimensional operating with pitches.
Without a 3D scenario it is useless to hope develop an absolute perception of anything!!

How do you want to absolutely perceive the quality of a line in a 2D world where there is only up, down, right and left?
Fractionals give us depth, and therefore perspective, rotation, and even "front and back" of a sound.

Of course a natural absolute pitch listener does nto have to go through such a process, but that should not worry anybody.
To me it seems only natural to assume, that since we are already developed as relative pitch adults, we need to develop an extra hyper sensitivity first and then we could have the best of both worlds.

Again please Chris, can you do this?
or give us a sort of an "API" of your program and we will feed the sounds
in.. or let somebody send you these 12 sounds for a start for the chromatic 440Hz scale.

TS
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Postby TS » Wed Apr 21, 2010 11:18 am

gavriel wrote:The fact that a sinus C2+C3 combined generates a tone whose frequency is that of a G but wave SHAPE is that of a C. is a FACT.


To me it seems that this simply is not true. What do you mean by frequency? To me frequency means "how often something repeats", and by this definition C2+C3 do not generate a tone whose frequency is G.

gavriel wrote:It is as simple as generating the following sounds which all result with different chromas but equal frequency:
A4 = 440Hz
G#1+G#5 = 440Hz
G2+G5 = 440Hz
F#3+F#4+F#5 = 440Hz
F3+F5 = 440Hz
E1+E2+E3+E4+E5+E6 = 440Hz
D#1+D#3+D#4+D#6 = 440Hz
D4+D5 = 440Hz
C#2+C#3+C#4+C#5+C#6 = 440Hz
C2+C3+C5+C6 = 440Hz
B1+B3+B5 = 440Hz
A#2+A#3+A#4+A#5 = 440Hz


Can you explain in more detail how you calculated all these combinations? I don't see how these combinations could have the same frequency 440Hz, or even the same height.

just make sure that the pressure (volume/gain) of the wave is always totally equal. this can be easily measured. This is very important. After you have created the sounds measure their pressure and make it equal.


Pressure (volume) is a difficult thing to keep constant. I think I have already mentioned somewhere that the volume level affects the bass/treble balance of a sound, and also that the type of speakers or headphones also changes overtone loudness balances. In addition to this, our earlobes form complicated filters that attenuate some frequencies and amplify others, and this effect is directional, so a sound coming from one direction has different overtone balance than a sound coming form another direction.

So even if you create perfect sound samples, get everyone to use identical perfect loudspeakers at identical volume levels, and surgically alter everyones earlobes to be perfect and identical, the overtone balances will still go off when the test subject tilts her head 5cm to one side. All in all, I don't think that height (timbre/overtone/etc.) listening can be made into a very precise exercise.

By the way, I watched a talk once on YouTube or some other video site, and the talker said that the height metaphor comes from the frequency response of human earlobes. If a sound originates from above eye level it has amplified treble content, and if it originates from below eye level it has diminished treble content, so a rising pitch seems to be moving higher because its treble content is getting louder.

I also just remembered a study that I heard about some time ago. Here's a link. I haven't read it, but it seems to be based on a height vs. chroma listening test, similar to what some german magazine had put online. Anyway, the study and the test indicate that people can be divided into two groups, chroma listeners and height listeners, so maybe these groups interpret pitch height differently. Maybe to some people C2.5 sounds higher than C#2, and to other people it doesn't.

gavriel
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Postby gavriel » Wed Apr 21, 2010 3:39 pm

All 'A' waves have their picks at multiples of 110 picks per second.
however when two 'A' are combined the smaller wave partly cancels and partly amplifies the big wave creating secondary (smaller) picks.
These secondary picks appear at their own frequency.

In the case of combining
the frequency of F3+F5
the main picks appear at the multiple of 174.61 Hz - hence at the frequency of an F.
BUT the secondary picks appear at 440 Hz !
generating a "phantom 'A'-ness"
...which I would love to learn to extract and recognize.
and which is definitely possible to learn (leaving aside for a second whether or not this is the way to Absolute Pitch) because it is second quality of Frequency - secondary picks / fractional height - that can be internally compared to the main frequency and therefore judged absolutely without an external reference.

When I edit a recording I often fight with a phasing cut. This si a cut that produces a whistling or low wind like sound.
This is cause by two takes which are similar at the point of the cut to cancel each other noticeable if they are in reverse phase.
When you move the cut (fade) on one of the takes a bit forward or backwards the phasing is gone.

Interestingly, often the whistling is lower than the original signals.
Meaning that the secondary picks that are phasing (or to put it differently the frequency at which a significant secondary pick appears during the phasing cut) is at a lower frequency than the original signals.

another example originates in the art of counterpoint of the 15th century.
paralel fifth and octaves were not allowed.
One fo the reasons is that in a church with a huge reverb, when a two voices sing an octave that is sliding upwards in paralel. The signal is phasing with the echo of the octave, generating a different hidden pitch, that was perceived as a disturbing dissonance.

Similarly, like a well phased F3+F5 hides an 'A' chroma in it's compound-ness. The Fs clash especially strongly 440 times per second. But the main picks are still at the F frequency.

You get my point??


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