The Frequency Response Theory

Thoughts and responses regarding the research at
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The Frequency Response Theory

Post by koenig » Sun May 15, 2011 11:31 pm

There is an AP method out there, I forget the name of it, that claims that the human ear has a unique frequency response such that each note takes on a different quality. He attributes this to the balance of overtones we hear for each different pitch. IE, an F# will have more 5th harmonic than Eb does, making it seem brighter or something like that.

Personally I've spent a ton of time listening to harmonics just for enjoyment. I just find the sounds fascinating. However, none of that has ever been "useful" because the difference in overtone production in each instrument is massive, not to mention variation in intonation. I'd love to get a cross sample of instruments to see if I can indeed notice a similarity between the overtones created by different notes.

Anyone think this is worth exploring? Has it been debunked? Is overtone balance (is this what constitutes timbre?) different than chroma? Do they affect each other?

Even if the overtones are not related, I think maybe acknowledging them would be helpful in learning AP. It's just stripping away one more level of sound that we've learned to ignore over the years. In all the music lessons I've had, we've only focused on reading notes and instrumental technique. I've never had a teacher that just played a note and told me to listen.

By the way Chris, thanks again for the incredible work you've done. Really getting back into ETC lately, it's fantastic.

Edit: Just remembered the Method - it's Bryce Alexander

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Post by aruffo » Mon May 16, 2011 1:25 pm

It depends on what you mean by "debunked". It's still true that no matter what you do-- no matter what method you try-- after a few weeks or months, you'll be able to name two or three notes. Too many of us method-creators have, in good faith, misunderstood this phenomenon to mean that our own method will teach perfect pitch; too many salesmen have exploited this phenomenon as "proof" that their method teaches perfect pitch. This new fellow seems, fortunately, to be on the side of the angels... but it doesn't mean he's not mistaken.

His theory is that absolute pitch judgment is based on "quality". Music theory defines "quality" as timbre: as he puts it, "perfect pitch is about the perceived spectra of the harmonics of the notes." Therefore, he figures that if you can learn to hear differences in timbre, you will learn to hear differences in "quality", and thus learn to make absolute judgments of pitch.

My research fundamentally disagrees with his theory. As I understand it, absolute listeners make two distinct judgments of a tone: pitch and height. Pitch judgment is based on fundamental frequency. Height judgment is a separate judgment based on timbre. As I've explained at some length, the evidence strongly suggests that height is timbre-- and absolute listeners are actually worse at classifying height than us normies.

Now here's the interesting bit. We non-absolute listeners make ONE judgment of pitch instead of two. Absolute listeners classify tone AND height. We non-absoluters classify tone AS height. Therefore, it is probable that by learning to better comprehend the timbre ("quality") of a tone, we will be able to make a more precise estimation of its height...

...which will enable us to pinpoint its relative position on the scale.

And while this would, indeed, enable a person to identify pitches, the strategy they'd have learned would be a relative strategy, that is, based on the relative "height" of a pitch. By pursuing a system that focuses on timbre, a person would learn a strategy that is distinctly in opposition to that of a true absolute listener. They could not learn, from this strategy, to make judgments of pitch class as an absolute listener does.

From what I understand.

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Post by Lyle » Mon May 16, 2011 4:02 pm

For nearly a year, I've meant to write about this approach. I've always given up before I start because it would take a hundred pages to properly explain. On top of that, while my skills have greatly advanced, I'm far from having "perfect pitch" as I imagine it would be.

I saw Bryce's method about a year ago and gave a shot at hearing the overtones. I was instantly convinced there is something to this. Within about 8 weeks, I was able to identify the 12 pitches by the sound of their "aura" rather than any other observation -- height, timbre, relative pitch aren't part of this process. I could still hear all those other properties, and now there was an additional property I effortlessly heard that never before was apparent to me. On my piano "D" now sounded really different than "C" in an unmistakable way.

This personal "breakthrough" is after twenty years of continuous attempts (almost every day) at learning both perfect and relative pitch, by all methods I could find, and with little results that were useful.

So my first message is, if you've tried and failed to hear anything different about the notes, try listening to the differences in overtone patterns between the pitches -- it worked for me.

Specifically, you need to learn to effortlessly hear the first 7 overtones (up to the dominant 7th chord and the base note 3 octaves higher). The way I practiced at my piano was to play the C below middle C (C3), then play a higher key such as G4, then replay the C3 to listen for G4. It takes hours of practice, these overtones seem to disappear more easily than they appear. You want to get to the point that you hear all of them instantly, without having to "search" for them. In the first few weeks, I had to play the note, search for a target overtone, didn't hear it, played the corresponding high key on the piano, then listened again. Eventually they became very clear. Also, you'll quickly find how each pitch's overtone pattern differs from the others.

You can possibly convince yourself in 5 minutes that there is some value to be had for all the work. Use just C3 and E3. It may take some effort, but for C3, listen for an oscillating perfect fifth an octave higher -- C4 and G4. Then for E3, listen for an oscillating major sixth much higher, from B4 to G#5. These features stand out more in each respective tone, even if present in all tones.

This isn't dependent on the timbre. You'll hear it on everything, probably with a little more work, but in those first days I could hear the same C/E difference in piano, guitar, violin, cello, and flute with no extra effort. I don't have a definitive claim or answer to why this is so. Just seems to be part of the nature of the ear. Other pitches have their own overtone fingerprint, not all with motion.

I sum this up with the mantra to myself to "listen spectrally" -- listen to the entire frequency spectrum -- when you listen to a single tone, not just the fundamental pitch of the note. Most of us never have. Breaking the habit of not listening spectrally, and creating the habit of listening spectrally -- it's going to take some time.

I found it helpful, after learning to identify the pitches by their overtones, to practice melody triggers with them; this both solidified my perception by providing a second independent process, and sped up identification. I figure, the more independent routes you have to identify a pitch, the better you will generally be at identifying pitches.

But even expertly hearing & identifying by overtones, it's not enough to develop perfect pitch, not even close.

The first thing I noticed was that playing two notes in a row destroyed the identification. Working with a program I wrote, I started playing 2 notes melodically, slowly, and increased speed until that was no longer a problem. The point is, identifying 1 note is isolation is probably only 5% of the battle, there are more difficult obstacles after you've achieved that.

One of the most difficult tasks is hearing more than one tone at once. But, this is almost entirely a relative pitch problem. In fact, I suspect the entire reason perfect pitch remains useless to those who achieve some level of it, is because relative pitch is undeveloped yet the natural sounds of relative pitch dominate the subtleties of perfect pitch. The very nature of tonal music -- having a "key" and "scale" -- involves simultaneous pitches that aren't always present. But that harmonic character -- two or more at once -- also obscures the lighter sounds of pitch character. You have to learn to identify those "louder" characteristics so you can hear underneath them.

I'll throw out a surprising claim of my own, that I haven't heard anywhere: it isn't enough to learn to identify the 12 pitches, and it isn't enough to learn the 12 scale degrees, you need to instinctively, effortlessly, unconditionally, instantly know the sound of 144 pitch-degrees. I practice this by playing a random I-IV-V-I cadence followed by a random pitch, and saying it's "C-Do" "F-So" or "Eb-Re". I can't do that yet for all the keys (my current successful practice set is only half the keys right now but with all the pitches) but once I can, then it's time to work on 2 and 3 note melodies. What is obvious to me right now is that when I hear a pitch, sometimes the absolute pitch is clear to me ("it's an E") while the relative solfege is unknown, while other times it's the solfege that is obvious. They interfere with each other enough that it's no wonder that an untrained ear doesn't consistently identify notes. But once you can do this, it is quite a feeling -- without really paying attention to the cadence, I might realize first that not only is it a "B" playing but it also sounds like "Mi" and so (logical inference) this must be the key of G. It's like magic... useful, practical magic.

Getting to the more theoretical points, it appears to me that overtone-hearing is at once necessary for the existence of perfect pitch, but it is not sufficient. In fact, I think that those with well-developed pitch don't listen to the overtones at all even if they had to (unconsciously) at the start. In the beginning, with great effort, you may process pitch along the lines of "hear overtones -> associatively recall pitch name." After untold practice with many timbres, this process becomes "hear fundamental -> associatively recall overtones -> pitch name" and finally, it's just "fundamental frequency -> pitch name." Toss in an instinctive identification of scale degrees, and the magic of perfect pitch seems less magical.

I think that evolutionarily, the ear was developed to be insensitive to absolute frequencies and receptive to relative frequencies. It just makes sense that, though computationally more elaborate, it is far more conducive to survival to recognize sounds that are the same but higher or lower (big bear, little bear, Doppler-shifted running bear, doesn't matter!). The thing is, there's a loophole: the ear isn't linear in frequency response. And that loophole can be exploited, unknowingly by children, to develop perfect pitch.

One more thought, and that's that identification by overtone fingerprint is not the same as timbre identification -- it appears to me to be more like "anti-timbre." A picture would explain this better than words but that's for another time. If you picture a graph with frequency on the horizontal axis and amplitude on the vertical axis, then you can plot the single note C3 and all of its overtones by vertical bars, of generally decreasing height and always decreasing horizontal distance. Nothing unusual here. But now consider the ear's non-linear frequency response at these same frequencies. Picture this separate graph as not just positive but also negative bars -- when this second graph is added to the source tone's graph, some of the bars increase in height, but others *decrease*. That is why, I believe, you can have the sound of C-ness present even if you change timbres -- there is a predictable mangling of the input that your brain can use to consistently identify different tones.

Hypothesis, of course...

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Post by aruffo » Tue May 17, 2011 9:06 am

Hm... innnnteresting.

Although I can't entirely make sense of what you're saying, from what I can piece together I wonder if what you're describing is an increase of information.

What is the actual listening strategy? I don't mean the theory about the listening strategy... what do you literally do when you listen?

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Post by koenig » Tue May 17, 2011 10:20 am

Chris, I never realized that non-AP listeners are making only one judgement but now that you say it I know it to be true for myself. If I never noticed the overtones... maybe I never noticed the fundamental pitch either. Maybe I've just been lumping the entire sound into the idea of how high it is. What do you think?

Lyle, you mention specifically the differences between C3 and E3. Do you think that this would vary from person to person? Also, some day when you get a chance to write 100 pages, let it rip! I'd love to hear all about your experience.

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Post by Lyle » Tue May 17, 2011 11:44 am

An "increase of information" is exactly the way to think of it. There's more to the sound of a pitch than the fundamental frequency of the pitch, and we naturally do not listen to that extra information -- it's not part of what makes music "music," and it's certainly not part of anything naturally important in daily life. The ear requires training to not ignore those higher frequencies.

As for the listening strategy, it begins with a conscious effort to hear the strongest overtones when you play a single pitch. At first, I didn't hear them at all, and needed to practice to hear them; now, I don't listen for them specifically but try to hear "all" frequencies at once when I hear a pitch. In the beginning, I'd play a C3 and not hear the G4 overtone, so I'd consciously "search" for it, and it would appear; with more practice, upon playing a C3, the G4 overtone would just appear instantly without listening for it. The overtones come & go with a will of their own, it seemed. And the listening environment changes the sound just enough to be confusing -- listening live, listening through speakers, listening through headphones, even just moving your head one foot to the left, all of these at first make it really difficult to hear what you know is there. Practice, just more practice.

Today, it's still a somewhat conscious effort, but becoming less and less conscious -- more and more, the strongest overtones for a pitch just jump out, creating a unique sound above & around the pitch. On my piano, I don't have to think about it at all anymore, I just always know what the pitch is, whether it's played at random by my ear-training program or whether I'm playing it, eyes closed, just improvising. I have (much) more work to do before I will have really mastered the piano timbre; other timbres I can identify slowly, so that will require even more work to automate that identification. But it all began with listening to the overtone fingerprint of the tones in one octave on my primary instrument, comparing them to find what stood out the most about each. The first notes that I learned were C and E, precisely because the oscillation of the two different intervals jumped out in an obvious way, and I could (slowly) figure out which pitch was which by listening for those intervals; after a time and after practice hearing more overtones in an instant, a "richer" sound accompanied both tones, that made it unneccesary to listen for those oscillations. But today, when in doubt, I do listen for those kinds of motions/patterns, and it always works.

I used the term "aura" and that's because it seems like a good analogy to a visual aura -- like if you looked at a thermal image of a scene, different objects of different temperatures not only look different colorwise but also have a shimmering outline around them. You don't say that the thermal aura of a particular object "causes" that object to be a human, but because the object is a human, you know what it's aura will look like. Same thing aurally, you can infer the pitch from its aura, but the aura is not what makes the pitch a pitch.

I can't say that C3 and E3 are going to sound the same to everyone, but I bet most people are going to hear them similarly. That's part of the reason I suggest you try those first, right now, so you can provide us with some more data points. :-) My 10-year-old son says he hears these, in the same way I do, but there's just a tiny bit of population bias in that sample point...

I think it makes a huge difference to use your own instrument's higher pitches to point out the overtones. Early on, when I was learning C3, I'd alternately play the high perfect fifth and not play it, since that helps you focus your attention on what/where to listen. Knowing the various "ghost chords" for the different pitches, like the major sixth in E3, makes it so you can always play an overtone pattern to help you find it.

I want to emphasize again, though, that I am pretty sure that (1) in the beginning, you have to hear *something* different about the pitches, in order to have consistent "signpoints" to hang your note-name associations on, but (2) in the end, a master of perfect pitch is not using these overtones to necessarily make the identifications. (It will always be useful even if not necessary, as seems apparent from pianos being easier than sine waves for people with perfect pitch.) Our ears are engineered to *prevent* you from tagging individual frequencies, so you need an objective, recurring feature to begin creating "grooves" or "buckets" that tones will naturally fall into. Eventually, your ear has stripped away so many variations on each pitch's aura that you no longer identify a pitch by anything other than the fundamental frequency -- the bucket lights up instantly without any analysis baggage required.

If true, that explains (to me) the conundrum and catch-22 of learning perfect pitch -- to learn the pitches, you have to hear something different about them, and someone "born with" it will say they sound different, but the fact they pitches sound different is not the process that makes true perfect pitch possible. As Chris pointed out years ago, hearing the chroma doesn't give you perfect pitch. Someone with perfect pitch will hear the chroma, and may introspectively think that explains why they can identify the notes, but that introspection turns out to be misleading for all of us because the identification happens at a much deeper level. Yet to get to that deeper level, you first have to have a way to segment the frequency spectrum -- and the non-linear frequency response of our physical ears seems to be what makes that possible.

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Post by Lyle » Tue May 17, 2011 12:26 pm

This may or may not help you get started, but since I already have them...

I am linking to a .zip file that contains C3 and E3 and 8 overtones of each. Each file plays the note with a peaking-eq applied to increase the volume of one overtone, followed by the non-eq'd note. The goal would be to try to hear the (very faint) overtone in the non-eq'd note. I can't tell you if this will work as well as picking the notes out on your instrument, or if it will even work at all to help you hear individual overtones, but it should give you an idea of what you're trying to hear.

These are Apple lossless files, so you will need iTunes to play them.

The goal is to get to the point that you hear the most important overtones instantly for each note, without effort -- that is not what this sequence of files will do, they will just point out each overtone. And they will only point out the overtone on *my* instrument, not yours, so your effort is better spent on your instrument -- even if your instrument is a piano, it's not my piano, and it's guaranteed they sound enough different to cause early learning difficulty. You will have to take your own instrument, one you are very familiar with, one you play every day because you just like to play music, and try the same thing with C3 and E3 until you hear it there. Once you've done that, there's no turning back, you won't be able to help but listen for that aura when you are playing your instrument...

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Post by aruffo » Wed May 18, 2011 8:17 am

Am I understanding this correctly..? It seems like you are describing how you recognize a C3 because you hear the interval it forms with a G4, or the "ghost chord" that is formed? If I'm misunderstanding that, I would appreciate clarification.. I have a couple questions yet otherwise.

This first question is a more minor point... I'm not sure what do you mean that the human ear is engineered to "prevent you from tagging individual frequencies". The human ear is designed as a Fourier analyzer; the ear is engineered to separate every incoming sound into its individual frequencies and deliver those frequencies to a "tonotopic map" in the brain-- an area where there are individual neurons that each respond to an individual frequency. This sounds like the opposite of what you're saying. Are you describing something else?

I was just reviewing Korpell's 1965 paper.. he tested absolute listneners by playing them fundamental frequencies that had the overtone structures of other tones. They consistently judged the tone based on its fundamental frequency and were not confused or misled by the mismatched overtones. This fits with your acknowledgement that "master of perfect pitch is not using these overtones"... but this leads to the most important question...

.. how is someone expected to stop using the overtones, and identify the pitch by its fundamental frequency alone, when the essential strategy used to identify them relies on their presence?

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Post by Lyle » Wed May 18, 2011 9:32 am

Close... I can recognize the C3 by listening for the oscillation between C4 and G4, not between C3 and G4; E3, by the oscillation of B4 and G#5. I think I heard these differences on my piano within the first hour of trying to hear overtones last year -- so it shouldn't take long to hear it for yourself, or not hear it if the case may be.

My statement about the ear's frequency tagging isn't about the sensory circuitry, where what you say is true -- rather that at the higher subconscious/conscious level, the signal has been processed intentionally to relate frequencies and omit individual frequencies. The final sound that is "presented" to our awareness doesn't favor one frequency over another, or otherwise allow us to latch on in a way to identify the absolute frequency.

An issue regarding overtone substitution that I have never had satisfactorily addressed -- particularly for an experiment 50 years ago -- is that introducing any new sine wave will necessarily produce harmonics of that sine wave. So removing the fundamental of a pitch, while leaving its recorded overtones, then adding a new different fundamental -- that new fundamental is now producing overtones of its own. The speaker naturally vibrates, the room vibrates, the ear drum vibrates...

And that brings me back to the fact that I can hear the same overtone fingerprints in a sine wave. Really, really faint: much harder to pick out than a piano or violin. That is Bryce's primary point -- that this happens inside the ear, not at the sound source. To demonstrate this another way, should you be able to hear the overtone pattern I describe in C3 and in E3, take a sampled instrument at C3 and pitch-shift the waveform to E3 -- the aura will have changed from C3 to E3.

How do you stop listening for overtones ultimately and start hearing just by fundamental frequency? Can't say I have a terrific answer to that. On the one hand, that might be something best accomplished as a child. On the other -- I have found simply with time & practice, my attention naturally no longer strains to pick out the overtone structure; it's just there, in exactly the same way that it's apparent that a timbre is a piano or a guitar, no thinking involved. Two, the ability to hear multiple tones simultaneously requires you to become less dependent on an overt harmonic aura, because the harmonic auras are now overlapping. Three, I expect this happens in the same way that any low-level associative learning occurs in the brain -- like your explanation for APA, there's a natural process that groups inputs by shared fundamental features. When you've instinctively identified a C for the millionth time on the thousandth timbre, your brain can't help but associate the loudest common factor between them, even if they share some higher (quieter) overtone pattern properties. In other words, your brain might have initially developed a really complicated circuit to identify a piano's C3; with some more circuitry added and some circuitry removed, it might now identify both the piano and the guitar; and so on, until the circuit has been pruned and streamlined to get rid of the excess, the unnecessary parts of what makes a C a C. That's the irony, I think, that you can't arrive at the final, simple, "correct" pitch-identification circuit, unless you've already built up a huge structure and torn it down over time. That huge structure seems to me to be the only way to get the pitches segmented, without which your ear can't anchor absolute associations.

In one way to look at it, we have several independent but co-occuring objects: the fundamental frequency of C, the overtone aura of C, and the name tag "C". Even if you start to learn pitch identification by the conscious association of the set {aura C, tag "C"}, there is 100% co-occurence of {fundamental of C, aura C}. That opens up the possibility of that becoming a circuit-level association. At first, the process might be: "aura C" activates "tag C". The conditions are then ripe for developing: "fundamental C" activates {"aura C", "tag C"}. At some level I know I am doing this, because when two tones are played at once, and I decide the bottom one is a C, suddenly the aura of C emerges from the aggregate aura when it was previously not apparent. Like many of the things you've brought up over the years -- none of which I specifically remember at the moment -- where activating one mental state causes something about the scene to jump out, but activating another mental state causes the same scene to promote a different characteristic.

Overall, I think of the overtone aura not as a strategy for learning perfect pitch -- it just is a feature present that can be used, that I've incorporated into my own "traditional" ear-training exercises. Good, effective learning strategies are more your department than mine. :-) It's crossed my mind that a potentially helpful step in APA might be to extend the 2-choice "C is present, C is not present" question to a 4-choice "C is present, D is present, C and D are present, neither C and D are present" once two notes have been practiced. That might be effective for focusing attention toward the final process, whatever it is.

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Post by aruffo » Wed May 18, 2011 4:43 pm

the signal has been processed intentionally to relate frequencies and omit individual frequencies

Ah yes.. to be sure. I suspect it's worth distinguishing that this is a function of the brain's processing, which can develop through learning, and not the ear, which is mechanically and biologically inalterable.

introducing any new sine wave will necessarily produce harmonics of that sine wave. So removing the fundamental of a pitch, while leaving its recorded overtones, then adding a new different fundamental

Before mentioning the study here, I looked very carefully at their method to make sure I understood what they were doing. Fifty years ago, the technology didn't exist for a researcher to remove or introduce a sine wave from a complex tone. What they did in this case was to alter the sound by changing the speed of the tape. Oh! I just realized I have the paper here.. let's see.. here is the graphic of the series.


If you want to see the entire paper, it's only three pages long. Anyway. The absolute listeners who heard these flute tones distinctly identified them as G. How does this result compare with the strategy you've been pursuing?

That's the irony, I think, that you can't arrive at the final, simple, "correct" pitch-identification circuit, unless you've already built up a huge structure and torn it down over time.

Here's an interesting question... can you think of anything, anything at all, that human beings learn from a process like this? It's easy to conceive of a transformative process like this-- shedding a cocoon immediately springs to mind-- but I can't [readily] think of any examples of anyone successfully learning anything through a process of learning something else. If you can think of one, then it might suggest a model of how this could work.

Otherwise it seems far too similar to

1. Collect underpants
2. ???
3. Profit!

I don't offer this rhetorically, as the joke intends. Rather, there is actually a way to fill in #2, if you understand how you're going to profit. Pulp the fibers and sell the recycled cloth? Open a fetish sex shop? Design new all-cotton fashions? Each one of these implies-- and, in its implication, explains-- what belongs as step #2.

Too many AP methods do the same thing.

1. [insert listening strategy here]
2. ???
3. Absolute pitch!

Again, in what I've researched, I am persuaded that this actually should be

1. Listening strategy to recognize chroma
2. Categorical perception of chroma
3. "Phonetic awareness" of pitch classes.

I've been completely hung up on #2 because categorical learning of a single dimension seems to be utterly unprecedented in adult human experience. Which is understandable, considering that there aren't that many unidimensional phenomena out there other than color and sound. Length, perhaps, but I don't think anyone ever learned to categorically distinguish inches or feet (or centimeters, for that matter).

Short version, though. I agree that any "method" of musical listening which increases and enhances musical enjoyment must be worthwhile. And there are many, many ways to successfully learn to identify musical tones in isolation. But there are no methods-- not one, not even APA-- which progress beyond the listening strategy itself. All of them (except APA) promise that you'll learn to name some notes, and this is true. None of them explain how their listening strategy is supposed to lead to perfect pitch, because as far as they know (or care), once you've learned to name notes, you're already there (at #3). So they don't go any further.

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Post by koenig » Thu May 19, 2011 9:31 am

Hey Lyle, thanks for sharing the files, very interesting. The ones labeled "-10," are those highlighting the fundamental? It sounds lower than the fundamental pitch to me!

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Post by Lyle » Thu May 19, 2011 10:13 am

Thanks for posting the paper Chris, that makes the discussion easier. Their method and results are confirming what I'm saying -- this happens inside the ear, not at the signal source. There is no objective, measurable difference in the source signal apart from frequency scaling. Importantly, they didn't replace the fundamental, they pitch-shifted the entire waveform. I mentioned that you can do the same thing, once you are zeroed in on the C and E auras. This makes clear we need to emphasize there's a difference between physical *source* overtones, and *perceived* overtones. They aren't the same.

Reviewing a few facts -- it's a fact that the ear does not hear different frequencies at equal apparent loudness (; it's a fact that all sound sources and their physical environments will resonate at overtone frequencies. I don't think it's a stretch to claim that the ear hears the overtones of a waveform at different perceived loudness than a pitch-shifted or sped-up version of the same waveform. Yes? Then what remains is whether it's useful to consider this, whether it's learnable, and whether it enables perfect pitch. My experience says "yes" but I also expect to never attain the magical abilities of someone who has listened with perfect pitch from age 4. Convincing you or anyone that this was not all just a coincidence for me -- I'll try, but it's going to take more than 100 pages and I already know I'll give up before then. :-)

"can you think of anything, anything at all, that human beings learn from a process like this" At a very low level, on the order of neural circuitry, I'd say that pretty much anything we learn falls into this category. Neurons & their connections & support staff do not have any direct contact with our sensory reality. Everything that is learnable (not hard-wired) is born at first through co-occurence and association. Concept formation seems like the pinnacle of this exact process: find a group of things that have something in common, then tag them by the property-in-common and ignore everything different that's left over. The concept "circuit" you end up with is a structure that is different than its input associations yet couldn't have existed without them.

But let me try a couple of high-level examples. What about learning a foreign language? When I studied Spanish in school, the teacher said "hola" is functionally the same as "hello." I had to memorize it -- that is, produce it by association from the English word, so that when I saw someone and wanted to say "hello" I'd instead pause, remember "hola", and speak that instead. But after a period of time, that intermediate step was no longer necessary -- I didn't have to think in English before saying hi to someone. Nor did I any longer have to spell out the word in my head to figure out the Spanish pronunciation. "Fake it 'til you make it" as a physical principle of replacing associative processes with generative processes, perhaps?

What about learning a dance? A description of the dance in words is not "the" dance, nor is a sequence of illustrations, nor even is the dance entirely what you see someone else do. After you've translated the description into your mind, you start directing your muscles in a certain pattern. But we only say you "know" the dance when it's become mostly an unconscious procedure -- plenty of muscle memory, aural/visual timing helping to guide it. In the end, none of the inputs that taught you the dance are part of what makes it possible for you to perform the dance. Learning to play a song on an instrument is the same thing -- the notes you read on paper or hear from a recording are in an entirely different category than the muscle memory your fingers use to perform. Once you "know" it, you no longer need to mentally refer to the bulk of the information that was required to learn it.

"categorical learning of a single dimension" -- this is the heart of the matter: I don't agree with the premise that a pitch is one-dimensional, except that is how we use it *musically*. The ear is already fourier-transforming a signal into a large number of bins, and each bin is an independent dimension (phase/amplitude). The equivalent of how I'm hearing is that I am not just comparing the bin with the largest amplitude (the fundamental frequency) but also several of the non-zero bins of higher frequency. Take the bins of one signal, sliding the unchanged amplitudes over a few bins, transform back to the time domain, and you *won't* hear an identical-but-higher sound. Close, but not perfectly the same, because different bins have different equal-loudness levels.

I am quite convinced that perfect pitch musical literacy is not achievable without relative pitch. And relative pitch, in my experience, is a ridiculously hard skill to attain despite everyone saying "oh forget perfect pitch, you just need to practice relative pitch." 20 years later and I still have lousy relative pitch. (I find it surreal that I frequently perceive that it's a B, for example, than to perceive it's the third degree of the G scale!) Consider an example of playing two random white keys on the piano, harmonically; ought to be trivially easy, right? Especially once you've established the scale & key center as C in your ear. Yet, I continued to have trouble with this for many, many months, even after I knew the keys in isolation by their unique sound apart from the scale. I don't think I'm alone in that difficulty, but I bet a huge population of musicians don't even realize they can't do it. Not only should you not need perfect pitch to do that, but perfect pitch isn't going to solve that problem for you. How many of us can hear/analyze/know what's going on in realtime in a majority of what Bach wrote? Supposedly that's possible with just relative pitch, right? I'm saying at once that perfect pitch can't and doesn't help with that huge knowledge gap in our hearing, and that everyone is both understimating the effort required to learn to hear with relative pitch and overestimating how perfect pitch can help. Once you *do* hear with relative pitch, though, you can make use of this extra "chroma" property, but it's mostly useless until that point. (I'm definitely talking about learning perfect pitch as an adult -- how young kids learn music is going to be different if their most prominent auditory property is chroma.)

Without any ability to offer proof, I think what I'm proposing is my equivalent to your three steps would look like this:

1. Listening strategy -- practice to hear the overtones, until no effort is needed to notice some of them

2. Category perception -- learn to distinguish the nuances of overtone variations. This is a natural consequence of step 1, or at least, it was for me -- I didn't do anything special to *make* the pitch auras sound different to me, I just had to hear the aura to begin with. Comically, upon hearing the different auras, it was obvious in retrospect that every time I ever thought I hear the chroma before in my previous 20 years, in fact I wasn't hearing chroma at all. Which is an important question to be always asking yourself, am I hearing chroma because I think I'm hearing chroma?

3. Phonetic awareness -- it's 99% relative pitch, 90% of which is key-center and scale-degree recognition. Once you already know all the sounds of relative pitch, they no longer obscure the perfect pitch sounds. And you only need to know the single pitch of the key center to automatically map all the sounds into note names; hearing which note is the key center is a cornerstone of (useful) relative pitch training.

Obviously my 3-step answer is quite different than yours, and I don't have any evidence to say either one of us is right or wrong, or worse: not wrong & not right.

Just thinking through some numbers, maybe in a strange way. Let's say you hear 2 random pitches out of an octave, played in sequence. You've got the "loud," overbearing sound of how the interval feels (12 up-intervals and 12 down-intervals); 144 possibilities of which pitch followed by another pitch; there's the almost-as-loud sound of how those two notes feel against a key center (another twelve); there's the implied sound of their harmonic relationship (12); and so on. Not including the timbre, or how these two notes "feel" as a function of the notes before and after them, or the speed/duration they were played at, and so on. To an ear that does not automatically identify each of these individual properties, there are thousands of distinct "sounds" (already half a million possibilities in the few numbers I tossed out) and this is a huge mass of conflicting perceptions that completely overwhelms the subtle sound of a pitch's chroma. You don't have a choice that you hear this busy-cloud-of-sound-properties, but you do have a choice of how you hear it. Once trained, you hear in terms of the few & finite input factors: this scale degree, or this interval. You've pulled out all the parts of the sound you can identify, and only then can you hear the quiet parts, like chroma.

My experience confirms that perfect pitch is not about naming notes. It is the recognition of external tones in terms of an internal representation. When you hear a C major chord, the true identification of it is not in the syllables "C Ma-jor" nor the visual symbols, but the mapping to one's internal combination of the three tones with accompanying instrumental visualization. When one recognizes a dog, it is not the word "dog" that one is trying to active, but an internal representation of what a dog is, with every visual, auditory, behaviorial, purposeful characteristic of dogs lumped into a simultaneous mass that is an impression of everything, unique to dog-ness; the word is a spontaneous association that emerges *after* the internal mapping is established. The name of a note is immediately irrelevant -- in my mind, when I hear a 'D' on my instrument, what I perceive is literally the 'D' from that instrument -- it is self-referential. The linguistic label is not part of this perception. I have a "visualization" of the note, which is not specifically visual -- with an extra step, I can recall the visual position of the key, or the letter name, or the finger position, etc, but this is not the primary sensation of 'D' and the primary recognition of 'D'. One can recognize a dog and all of the implications, without ever using the word "dog" internally or externally. This is "modeling" -- an internal model of the external subject is created, mapping one-to-one to each others' components.

So the ability to names notes, and the ability to *use* notes -- they are truly different processes, requiring different behavior to accomplish.

Here's an analogy of why perfect pitch is useful to me and why "naming notes" just plain isn't. Imagine a world without Legos. With an untrained ear, without perfect pitch and without relative pitch, one's ability to manipulate musical notes is akin to manipulating Lego bricks as drawings paper, never directly perceiving them, never holding them or rotating them or flipping them or connecting them, never being able to manipulate them into structures that one can hold up to see with your own eyes. If your only contact with the Lego world is by drawing pictures on paper and academic journals, you don't really "get" what Legos are and how they can be used. It's almost doable, with a Ph.D. in Lego Analysis and decades of relentless study at a premier university's Lego Research department... but it isn't easy. And you'd never "grok" Legos and how to use them like a five-year-old with a real set of plastic bricks. That's what I think perfect pitch really brings to the musical table -- an ability to use pitches as naturally as kids use Legos.

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Post by Lyle » Thu May 19, 2011 10:17 am

Yes, -10 are the ones boosting the fundamental, it really does make the sounds deeper/richer, something for the psycho-acoustically inclined to explain to us...

-20 is the second harmonic, or first overtone, which is one octave above the fundamental; -30 is the second overtone, which is one octave and one perfect fifth above, etc.

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Post by steveAZ » Thu May 19, 2011 5:30 pm

Hey guys,

I'm glad someone brought up Bryce's method. I bought it a few months ago and haven't used it that much (mostly because I couldn't get it working very smoothly), but if you're saying there is something there, then I'll reinvestigate. How do you train with Bryce's method? Did you go through his course?

I agree with Lyle that music recognition is BOTH perfect pitch and relative pitch. Even people with perfect pitch aren't using ONLY perfect pitch when lifting a song (even though they might think they are). Relative pitch is not only important, but necessary to accurately hear music.

If you have a skill that you developed as a child (even unconsciously) then chances are you can just do it without thinking about it and you won't know why or how it's happening. That's why most people who possess perfect pitch can't explain the experience. It's abstract to them. It's just.....there.

Although it would've been great to be "born with" perfect pitch, I like that I am consciously getting into each tone/chord/melody.....this way I can solidify the skill. To be honest, at the end of the day, I don't even care what skill I use to recognize a song. As long as I'm accurate. I know that it'll require both perfect pitch and relative pitch, but any percentage of each is fine with me!

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Post by Lyle » Mon May 23, 2011 1:56 pm

While I used Bryce's software in the beginning, once I discovered how easy & fast & natural it was to use higher keys on my piano to target my attention toward specific overtones, I started doing that exclusively.

I spent a lot of time just listening to notes, playing the higher keys when I couldn't hear what I wanted, which really helped focus my hearing.

Then I started doing the usual ear-training exercises.

I worked in just one octave at first, from C3 to C4 (C4 being middle C). On a piano timbre only. And always the same specific timbre, through the same speakers -- different piano timbres require additional practice! Just focus on one instrument sound at first, preferably the instrument you play every day.

I had my software play just one note, out of just several white notes. I'd ask it to repeat it many times, until I thought I heard what made the note unique, even if I already knew which pitch it was by relative pitch. Once I was correctly answering that subset of notes, using 20-in-a-row as a yardstick, I'd add in another note. Did the white notes first, then added black notes in. I *encouraged* myself to identify the note using scale degrees (do-ra-re-me-mi-fa-fi-so-le-la-te-ti-do) as well as listening for the pitch aura. I got used to naming the tone by the solfege name, which is convenient (simple & singable) but if you do that you need to be prepared to "re-learn" it as moveable-do later. I did it and it's doable but just expect some practice will be required down the road. Took me about 3 months after the first overtone experience, before I was getting all the notes right.

When I got to be able to do single tones in one octave in one timbre pretty well, I wasn't satisfied that I really knew it -- for one thing, two tones in a row were nearly impossible to recognize, so I knew something else had to be learned. At this point I decided to, in parallel with everything below, work on melody triggers for all 12 tones. This was quite helpful in solidifying the recognition. In some ways the "image" produced by the melody trigger began to function as the "name" of the note; this is interesting because the part of the brain that hears pitches is not the same part as the one that verbally speaks letter names, and I noticed that it was a lot easier to name the pitch in terms of this mental mish-mashed trigger identity than it was to quickly spit out a letter name. So it was worth doing, because even if I wasn't recognizing the note by means of the melody trigger, I was able to "name" the note quicker, mentally. Visualizing the key on the keyboard is part of this recognition. I spent about 3 months on this.

After getting all 12 (13) correct, I started listening to 2 melodic tones played slowly. I started with just minor seconds until I had that down, then minor + major seconds, and so on, until it was just randomly two melodic notes in that one octave. Then, progressively faster 2-note melodies, which took some time. Then work on 2-note harmonic tones -- again, quite difficult, and difficult enough that I still trip over myself on these. Then, I started working on more than one expansion at once -- adding in another octave, doing 3-note and 4-note melodies, basic triads, etc. And as mentioned, I'm working on playing a cadence in a random key followed by a tone, working toward naming both the absolute and the relative name; I was surprised that this was not as difficult as I would have expected.

I'm just past the year mark since first trying to "hear spectrally." I really think it's going to be at least another year before I've got my piano hearing to the level I want it to be. And easily another year or two after that until I have more timbres at the same level. So this isn't a quick fix to musical frustrations!

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