RE: [tuning] Re: To Paul: FFT Results, (was) Graylessness and lim it (was: notation systems)

I wrote,

>> I may know what your problem is. What is the fundamental frequency,
>> according to your FFT? And according to your ear? Do they agree?
What I'm
>> guessing it that you're using a fundamental frequency corresponding
to the
>> period of your entire sample, which would of course be a subsonic
frequency,
>> and all the other frequencies are necessarily (by the design of
FFT) integer
>> multiples of that frequency. Could this be your error?

Jacky wrote,

>Paul,

>Hello.

>I'm not convinced that it is in error. The reason being is that the
>frequencies that I used to construct the scale were from 27-30 of the
>highest amplitude - and correct me if I'm wrong, these certainly
>*could* have been the found in such a sample as the prominent
>frequencies. It was the other 500 that I didn't use (of lesser
>amplitude), that we haven't (yet) considered.

It doesn't matter. You need to answer the question -- is your fundamental
frequency simply the lowest spectral line from your FFT? If it is, you will
only ever get an exact harmonic series as your spectrum, which is of course
useless if what you're trying to do is a Sethares-typ matching of tuning to
timbre.

>One other thing that makes me believe that it's either correct, or
>else, very close, is that the tuning *sounds* correct with the music.

You've got an otonal series as your tuning -- as Carl has discussed, this
will, in a way, "sound correct" with _any_ timbre with any fixed spectrum.
The reason is that the virtual pitch and combination tone processes will
yield psychologically far more coherent results when sets of partials can be
grouped into exact harmonic (i.e., otonal) series.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
>
> It doesn't matter. You need to answer the question -- is your
fundamental
> frequency simply the lowest spectral line from your FFT?

Paul,

Sorry for the delay, I had to get back to my studio to check the data.

There's a cluster of pitches of highest amplitude around C4, yet
there are other pitches lower than this in frequency, and of slightly
lower amplitude, so the answer is no - the fundamental is not the
lowest. In other words, there are frequencies lower in pitch than
those of the most prominent amplitude.

Thanks kindly,

Jacky Ligon