FFT resolution

Recently, Dave Hill wrote:

>I used an autocorrelation technique to track frequency...
Then, using a frequency vs. time basis line... I added empirically
calibrated error correction modifications... If the results of my work
would be of significant value to a researcher or researchers in the
field, I would like to make my programs &c. available to them.

Perhaps even more useful than resurrecting your programs, could
you describe in a bit more detail the methods you used? I am
particularly interested in techniques for getting better resolution (in
terms of frequency) than the FFT can provide when using a "small"
window of data.

Thanks,

Bill Sethares

>So,the MR series resolution is good enough that one might, in all
>probability ,never wish for more ?

I'm inclined to guess that there's not a lot of economic incentive for
synth manufacturers to supply better than 0.1Hz resolution, but I certainly
don't know that for sure of course.

About getting the kind of resolution that Dave Hill and Charles Lucy
wrote about :
The 0.1 should be easy .

But this :
>Eventually we will get the required 1/196,608 units per octave
Maybe when they defrost us from those cryonic tanks,eh ?

But seriously folks, one way we can get this is in software synths.
As I mentioned before,the Max-MSP combo already does floating point
Hz accurate tuning.

Another way is using samplers. You can use a software synthesis system
like
Csound, CLM,etc.,etc. to synthesize a whole bunch of samples at any pitch
you
want, perfectly tuned. Then if you can figure out a way to get them into
a sampler ASAP with little pain and time ( and have the RAM for it),
you're done.
It would take mucho RAM, @ 100Kb for ea. mono sample @ one second long.
I don't think looping all those samples to conserve memory is a good way
to keep sane.
Besides, I think David First said something important about the nitty
gritty of the
looping process.
If you need to set up all 128 MIDI notes, that's 100Kb * 128 = @12.5MB per
"instrument",per layer (if you need velocity switching samples,etc).
It would take one of those 128MB samplers to pull it off.

-Drew

"I think the bees *suspect* something."- Winnie-the-Pooh