The Frequency Response Theory

Thoughts and responses regarding the research at
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Post by steveAZ » Mon May 23, 2011 11:39 pm

I have worked on so many different types of ear training that I don't even care what method I use to get the correct answer anymore. I just use the mish mash of techniques living in my ear and that mish mash usually gives me an answer instantly. I don't question it. Melody triggers definitely helped to get me started (specifically Joshua Jobst's Pitch Paths).

One thing that I did to supplement my training was make every alert on my BlackBerry a different pitch (ex. B is for "new BBM message", "E is for new email", etc.) In addition to this I actually got an alarm app that I programmed to play a different pitch for every corresponding hour (ex. 12pm is C because it's home, 1pm is C# because it is 1 half step above C, 2pm is D, and so on until C at 12am). These alarms are in another octave so I don't confuse them with my message alerts.

I know this may sound extreme, but I wanted to create a situation where I HAVE to recognize pitches to perform different functions throughout my day. I'm finding it is working great and is really reinforcing my ear.

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Post by aruffo » Tue May 24, 2011 3:59 am

Ooh. That's brilliant... there's got to be functional meaning to each pitch. Nice.

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Post by steveAZ » Tue May 24, 2011 9:18 pm

Thanks Chris! That actually means a lot coming from you!

I realized that individual pitches for the alerts were becoming too easy, so I upped the ante and replaced them with thirds.....I plan on spending a week with these and moving onto different intervals/chords.

As for the Absolute Pitch Clock, I am keeping them as single pitches for now and testing another aspect of my ear/mind. Since each hour represents a different half step distance from the root, I can test my music theory knowledge in addition to AP (I'm finding that combining skills is not only challenging, but very practical). This exercise might be simple for people who studied theory for years, but I need to fill some gaps in my theory and knowing "A" is 9 half steps above C, meaning it's 9pm is very useful. I plan on spending a week with each key, naming the different pitches using AP and instantly knowing how the half step distances correspong to what time it is.

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Post by lorelei » Sat May 28, 2011 12:38 am

Great methods of reinforcing the ear, Steve. The idea is brilliant.
As for Bryce's method, I can say that even though I know what having AP is and what it's like to have it, I have nothing to compare my experiences to and therefore cannot truly say exactly how having it changes perception. However, I don't think using AP is about overtones, and yes I listened to Bryce's midi file that was supposedly an enhanced F#. To me, it just sounded like a weird F#, and it wasn't more f#-ish than a normal F#. Of course, I'm not completely sure, and if it works, it works.

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Post by Lyle » Wed Jun 08, 2011 8:49 pm

My thinking & my experience leads me to think that learning to consciously hear overtones is what "opens up" the ear's ability to identify pitches -- whatever ultimate process underlies perfect pitch. I imagine that identifying pitches directly by their overtones is probably too "slow" a brain process to explain perfect pitch, so instead, if overtones are relevant, they are an ingredient rather than a complete explanation. I.e., once you can clearly & consistently hear overtones, that unlocks the ability to hear "chroma," whatever chroma ultimately is. Once you hear that chroma, then the overtones aren't useful anymore and are consequently not listened to anymore. Again, I though I had been hearing "chroma" for more than 15 years, but after a few weeks of serious overtone listening, there is something I hear now that has nothing to do with what I thought "chroma" was. Maybe I still don't hear it. But whatever I am now hearing, I can automatically identify pitches on my piano, no effort or attention required.

Chris, I tried to google-search your research site, but couldn't zero in because the term "phase" is in the title of all your posts. Has anyone investigated the possibility that the 'phases' of a pitch's harmonic components is possibly relevant? I am thinking that for a single pitch, the overtones are phase-locked with respect to the fundamental -- but a chord of tones is very likely to not be so with respect to each other. So that, in hypothesis, the phase of the various overtone components could be used by the brain to identify the fundamental frequency through fixed phase relationships. It is so common to discard the phase of a Fourier transform that a great deal of people don't realize how much information is in it. Yet it seems like it'd be a trivial neural computation to detect a particular phase-locked relationship is present between multiple active frequencies. An alluring characteristic of this imagined process is that this is an inaudible property of pitch, thereby supporting all the mystery behind why we all hear the same pitch yet somehow we don't.

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Post by koenig » Tue Jun 21, 2011 9:22 am

Hey Lyle, thanks for sharing your experiences. I don't have much free time lately but I have been listening as you recommended whenever I get a chance. I realized that what I theorized earlier is correct... not only was I not hearing the overtones clearly, I was not hearing the fundamental frequency clearly either. Instead, my ear was just lumping the whole group of sounds together and ignoring anything that may make the notes unique. It's bizarre. Anyways, thanks again, I'll post here again in a few months to let you know how it worked out for me.

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Post by Nightprowler » Thu Sep 15, 2011 7:44 pm

Lyle, I was wondering if you could write a list of all 12 tones and the way you hear their overtones.
That would be very helpful I guess. :wink:

I am now working with the demo of Bryce's APsimulator and I can hear some differences. Maybe your hints would help me speed up the process of sorting all of the pitches.

Thank you for your great explanations an for sharing your experiences.

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Post by Lyle » Fri Sep 16, 2011 3:10 pm


I’m going to suggest a different approach. Rather than focus on what makes the tones different, practice listening for a specific overtone until it jumps out at you. I’d say, start with the fifth harmonic (the fourth overtone), which is two octaves plus a third higher than your base pitch. Using the piano as an example, play a pitch with your left hand, somewhere around middle C; with your right hand, play the pitch closest to that fifth harmonic. Listen to that pitch. Now play the left hand tone and without playing the higher pitch, see if you can hear the overtone. Maybe you’ll hear it, probably you won’t. Repeat many times, day after day, until (1) you start to hear it easily, then keep practicing until (2) you don’t have to search for it, it just pops out. Use the same instrument, same environment every day -- don't keep changing instruments or loudspeakers or headphones, just pick one setup and stick with it.

Do this with other pitches, and with other overtones, order not important. When you start to hear overtones without searching for them, you'll start to hear that there are subtle differences between each pitch's overtone pattern.

I had two other exercises I did, as much out of fascination as for ear-training. Each of the pitches has a particular set of “louder” overtones (it’s up to you to hear it, doesn’t matter how many words I use to describe it if you don’t hear it for yourself). I divided the 12 pitches of an octave into 4 groups of 3. Playing one group of pitches in sequence made a 3 note “melody” from the prominent overtone of each pitch. By listening, you can invent your own overtone melodies; repetitive playing helps you focus on the overtones in a way you hadn’t before.

Finally, I noticed that playing a circle-of-fifths sequence of pitches (say, G3 C3 F3 Bb2) made apparent a chromatically descending overtone melody. You’ll hear the fifth harmonic of G3, then the seventh harmonic of C3, then the fifth harmonic of F3, etc. You can play the descending sequence with your right hand while you play the circle-of-fifths with your left hand, then play again without hitting the guide tones and just listen for the chromatic descent. I like this one.

Overall, my point is, don’t worry about what makes the pitches different, because you’ll hear the difference only after you start listening differently.

One more thing -- do a similar exercise with a plain old normal major triad. You'll need to learn to hear each of the 3 pitches as clearly as if they were played alone. Play the triad, listen for one of the pitches, play the target pitch, repeat until the target pitch is no longer obscured by the rest of the chord sound. This is purely a relative pitch exercise, at first. Until you can separate the pitches aurally, effortlessly, you'll find it impossible to hear pitch colors when more than one pitch is played.

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Post by Nightprowler » Fri Sep 16, 2011 6:24 pm


Thank you for the Guide-tone thing and the Chord exercise. I'm going to try that.

Today I listened A LOT with a good friend of mine. We both play guitar and we sat there, turned off most of the lights and listened to the overtones of different pitches on our guitars.

We were able to hear them up to the natural seventh. (depending on the pitch)

We noticed movements in some pitches. (f.i. movement from double octave to third in F#2)

It was a cool experience and we were able to identify some pitches in the end.

I'll give you some updates on our further experiences.

We'll definitely try the guidetone thing.

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Post by Space » Fri Mar 09, 2012 5:54 am

I love this whole thread you got goin, Lyle. You're the first person that has really stated word for word that one ultimately has 144 pitches to learn. 12 absolutes each in 12 possible tonal contexts. That's basically the path I'm on.

Also, though I haven't approached it in quite as a meticulous way as you have, I've been considering strongly the relationship between what I feel to be 'pitch color' and timbre. It seems that my perception of pitch 'color' is similar to my perception of timbre, the way each pitch sounds to me as a whole. It creates a kind of 3 dimensional shape in my mind in a similar manner that the experience of various timbres does.

And though I haven't used the perception of overtones consciously to work on AP development (probably should try some!) I trained myself to hear overtones reasonably well years ago and even tuned a piano I owned once (took 3 weeks, though!).


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