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Re: Mel scale, in general

Dick, Don, Leon, Pierre, Richard, Diana, and all,

I agree with Leon, that there are two aspects or types of pitch,
one associated with "place" and the other associated with 
periodicity. As long as we can identify the pitch chroma and
match the pitch on the piano, we are hearing periodicity pitch.
If we sense a general region of pitch, low vs. high, it's place
pitch, or tonal height.

A nice experiment is to synthesize several harmonics going from
k1 to k1 + k2 on a certain fundamental and gradually increase k1
while keeping k2 fixed at say 4 or 5. At what point do we switch
from hearing perodicity pitch to place pitch?

Another related experiment is start with a fundamental at say
1 KHz and again just have a group of harmonics k1 to k1 + k2.
Gradually lower the fundamental while raising k1. I find that
my aural receptor goes through some curious gyrations while
listening to this sound sequence.

I also think Steven's remarks in the book Dick referred us to
(Psycho-Physics) to be pretty interesting:

"Musicians are often surprised to be told that the apparent size of
a fifth expands to sound about seven times larger when it is moved
from a low-frequency interval, 64 to 96 hertz, to a higher-frequency
interval, 2048 to 3072 hertz. Those intervals both sound like 
musical fifths -- the frequencies are in the ratio 2 to 3 -- but as
Stumpf and other observant and psychologically oriented musicians
have noted, a fifth in an upper register seems perceptally larger
than a fifth in the lower register. ....
The musician's 'equal interval' generally means equal in frequency
ratio, and equal frequency ratios do not in general produce equal
intervals in subjective pitch."

To my ears, bass tones played at various frequencies do kind of 
compress in that way, but so do frequencies played above 4000 Hz, 
because it gets to be more difficult to associate a chroma pitch
to frequencies in these ranges.


Original message:
Date:         Thu, 30 Jul 2009 20:48:34 +0200
Reply-To: Leon van Noorden <leonvannoorden@xxxxxxx>
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From: Leon van Noorden <leonvannoorden@xxxxxxx>
Subject: Re: [AUDITORY] Mel scale, in general
Comments: To: "Richard F. Lyon" <DickLyon@xxxxxxx>
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Your formulation suggests that you identify pitch with chroma. My  
position is that pitch is a two dimensional entity, in which both  
chroma and tone height are involved.
In a musical context the chroma aspect plays a dominant role. In a  
speech context I have never noticed the appearance of the chroma  
aspect. Probably because we never talk with a limited set of fixed  
pitches. Or because our "vowel processor" is occupied with the meaning  
of the words and not with the names of the notes, which is certainly  
the case in the perception of possessors of absolute pitch, who are  
very chroma oriented.


On 30 Jul 2009, at 17:36, Richard F. Lyon wrote:

> Pierre,
> I think the resolution is in what Leon said, that the mel scale is  
> really more about "tone height" or "frequency" than about pitch or  
> melody.  So it's mis-named, at the least.  It's also not accurate,  
> as Don points out, and maybe a cochlear map is really the better  
> concept.
> But as you also know, it's used in speech primarily because it seems  
> to work well (at least a local optimum), which is mostly about not  
> resolving pitch harmonics but adequately resolving formants.  I  
> think you also agree with me in the feeling that it works well  
> largely because speech systems don't usually have a good model for  
> what to do with pitch information, so they're better off not  
> resolving it; and that this is a problem and an opportunity to find  
> a better way...
> Dick