Yahoo Tuning Groups Ultimate Backup tuning Reply to Jacky Ligon

P.S. Jacky -- have you tried _synthesizing_ the drum sound from your FFT
data? This is the true test of whether your FFT results are meaningful
(there are a lot of pitfalls in FFT analysis). If you can reproduce the
sound of the drum using your FFT data, that's a good sign you have a valid
analysis. I fear that in this case, since you just have integer overtones
(correct to an amazingly good precision), the sound you get will be nothing
like a drum. Even a plucked string has more inharmonicity than this.

🔗ligonj@northstate.net

Paul,

I'm not sure if I would have the capability of doing this, although
it would be something I'd like to test.

What are ways to insure accuracy with FFT? My FFT size can be set to
a maximum of 65536.

Thanks again,

Jacky

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> P.S. Jacky -- have you tried _synthesizing_ the drum sound from
your FFT
> data? This is the true test of whether your FFT results are
meaningful
> (there are a lot of pitfalls in FFT analysis). If you can reproduce
the
> sound of the drum using your FFT data, that's a good sign you have
a valid
> analysis. I fear that in this case, since you just have integer
overtones
> (correct to an amazingly good precision), the sound you get will be
nothing
> like a drum. Even a plucked string has more inharmonicity than this.

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗M. Edward Borasky <znmeb@teleport.com>

Fast Fourier Transform

--
M. Edward Borasky
mailto:znmeb@teleport.com
http://www.borasky-research.com

Cold leftover pizza: it's not just for breakfast any more!

> -----Original Message-----
> From: Joseph Pehrson [mailto:josephpehrson@compuserve.com]
> Sent: Monday, November 20, 2000 7:28 PM
> To: tuning@egroups.com
> Subject: [tuning] Re: Reply to Jacky Ligon
>
>
> --- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> http://www.egroups.com/message/tuning/15690
>
> I'm sorry... but what does "FFT" mean again?...
>
> _________ ___ __ _
> Joseph Pehrson
>
>
>
>
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🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

>> 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.

Well, the "fundamental" need not be the loudest partial -- but my question
is, in the results you posted, did you assume that the "fundamental" was
simple the leftmost spectral line from your FFT?

🔗ligonj@northstate.net

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
>
> Well, the "fundamental" need not be the loudest partial

I'm treating the cluster of pitches at C4 as the fundamental - the
piece is in C.

-- but my question
> is, in the results you posted, did you assume that
the "fundamental" was
> simple the leftmost spectral line from your FFT?

Please explain "the leftmost spectral line from your FFT". I'm not
sure how to answer that question.

Thanks,

Jacky Ligon

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

>Please explain "the leftmost spectral line from your FFT". I'm not
>sure how to answer that question.

Jacky, you yourself said:

>The selected FFT size directly affects the resolution of the
>resulting spectra. The number of spectral lines is always 1/2 of the
>selected FFT size. Thus a 1024 point FFT produces 512 output
>spectral lines.

>The frequency resolution of each spectral line is equal to the
>Sampling Rate divided by the FFT size. For instance, if the FFT size
>is 1024 and the Sampling Rate is 8192, the resolution of each
>spectral line will be:

> 8192 / 1024 = 8 Hz.

So what I'm asking is, did you assume that the fundamental was simply the
spectral line of lowest frequency?

🔗ligonj@northstate.net

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

> So what I'm asking is, did you assume that the fundamental was
simply the
> spectral line of lowest frequency?

No. Because I'm treating the frequency of highest amplitude as the
fundamental, but there are other frequency components of lower pitch
and amplitude in the sample.

Jacky

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

>No. Because I'm treating the frequency of highest amplitude as the
>fundamental, but there are other frequency components of lower pitch
>and amplitude in the sample.

Then what must be the case is that the fundamental you chose was exactly a
power of two times the lowest spectral line. Can you verify this, and tell
us which power of two it is? I'm putting my money on 16. Or just tell us
what the frequency of the lowest spectral line in your FFT is (this should
equal the frequency resolution of your FFT) and what the frequency of your
assumed fundamental is?

If I'm correct, the other "inharmonic spectra" you're getting with other
timbres with this kind of resolution would simply be otonal series with a
number that is not a power of two.

In any case, the moral of the story is, if you're trying to analyse an
inharmonic spectrum with an FFT in a meaningful way, you need a frequency
resolution many orders of magnitude finer than the fundamental frequency --
16 is an extremely small factor here.

By the way, your own post about the frequency resolution of an FFT should
tell you what accuracy to use in reporting the cents values of the partials
-- in other words, you should only report "significant digits". The point
goes even more strongly for ratios -- if I'm correct about the factor of 16,
there is absolutely no meaning to giving the ratios in any larger numbers
than 1/1, 17/16, 9/8, 19/16 . . .

🔗ligonj@northstate.net

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

I wrote,

> just tell us
> what the frequency of the lowest spectral line in your FFT is

Jacky wrote,

>86.1328

86HZ??? Surely you don't mean that? Because then, only multiples of 86Hz
will show up in your FFT. Surely you want a resolution finer than 86Hz??

🔗ligonj@northstate.net

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> I wrote,
>
> > just tell us
> > what the frequency of the lowest spectral line in your FFT is
>
> Jacky wrote,
>
> >86.1328
>
> 86HZ??? Surely you don't mean that? Because then, only multiples of
86Hz
> will show up in your FFT. Surely you want a resolution finer than
86Hz??

CHECKMATE! }: (

I just realized that this is the default setting of the program. What
would have been a better setting? 1 hz? This is as low as it goes.

Naive question: Wouldn't (or could it be possible) it all be
relative, even considering this resolution?

Jacky

🔗ligonj@northstate.net

--- In tuning@egroups.com, ligonj@n... wrote:
> --- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

Paul,

Upon re-reading the manual for my spectrum analyzer, the 86 hz is the
measured "Span", and is not refered to as resolution. Don't think
it's functioning as you thought. So really this is the frequency from
which the measurements begin. I retract my checkmate!

Jacky

P.S. I'll keep working with it and let you know the results.

🔗ligonj@northstate.net

--- In tuning@egroups.com, ligonj@n... wrote:
> --- In tuning@egroups.com, ligonj@n... wrote:
> > --- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

Paul,

The Spectral Line Resolution was set to .673 hz. This is what you
were asking. The frequency "Span" (where the measurement begins), and
the Spectral Line Resolution are two different things in this program.

Thanks,

Jacky

>
> Paul,
>
> Upon re-reading the manual for my spectrum analyzer, the 86 hz is
the
> measured "Span", and is not refered to as resolution. Don't think
> it's functioning as you thought. So really this is the frequency
from
> which the measurements begin. I retract my checkmate!
>
> Jacky
>
> P.S. I'll keep working with it and let you know the results.

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

>The Spectral Line Resolution was set to .673 hz. This is what you
>were asking.

So the lowest spectral line had a frequency of .673 Hz?

>The frequency "Span" (where the measurement begins), and
>the Spectral Line Resolution are two different things in this program.

Can you explain the "Span" then, please?

🔗ligonj@northstate.net

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> >The Spectral Line Resolution was set to .673 hz. This is what you
> >were asking.
>
> So the lowest spectral line had a frequency of .673 Hz?
>
> >The frequency "Span" (where the measurement begins), and
> >the Spectral Line Resolution are two different things in this
program.
>
> Can you explain the "Span" then, please?

Same as Frequency Range. This is configurable with a starting and
ending frequency, which determines the desired range of frequencies
measured. Had I realized that this was set to 86 hz, I would've
naturally lowered it, but I don't think it affected the reading,
since the samples "fundamental" was considerabley above this point.

Thanks,

Jacky

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

>Surely you want a resolution finer than
>86Hz??

>CHECKMATE! }: (

>I just realized that this is the default setting of the program.

Ouch! What was this program designed for -- analyzing electromagentic
spectra?

>What
>would have been a better setting? 1 hz? This is as low as it goes.

That would be better, but would still not allow you to pin down values to
better than 4 cents at 440Hz. So you still wouldn't be justified in
specifying the last digit of your cents values _before_ the decimal point,
let alone any values _after_ the decimal point. For your purposes, that
doesn't seem too satisfactory.

>Naive question: Wouldn't (or could it be possible) it all be
>relative, even considering this resolution?

I don't understand the question . . .

🔗ligonj@northstate.net

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> >Fundamental: 261.625
>
> Suspiciously close to 3*86.1328. Perhaps some rounding error came
in here?

Paul,

I think you were right.

I re-ran the FFT with the frequency span 20-21830 hz, with an FFT
size of 66536 and line resolution of .673. Here are the first 35
frequencies sorted by amplitude:

267.819
268.492
66.618
46.431
47.104
65.945
67.291
267.146
45.758
269.165
65.273
47.777
67.964
64.600
266.473
102.956
48.450
103.629
45.085
102.283
63.927
269.838
38.356
68.637
63.254
37.683
62.581
104.302
49.123
43.739
271.857
39.029
557.172
557.845
35.664

And here are the cents values after reducing and sorting (267.819 hz
being treated as the 1/1):

0
4.345
8.673
8.679
13.002
25.901
25.908
42.96
68.237
70.327
109.344
204.873
235.519
265.632
462.881
515.353
541.005
566.282
591.196
615.756
639.972
663.855
733.57
744.924
756.203
767.41
1083.046
1101.564
1119.887
1138.017
1155.96
1173.692
1191.271
1191.277
1195.644

Obviously quite different results this time. I found also that the
default FFT Size was set much smaller with the first FFT results,
which is what I now believe gave me such wacky results. Just need to
tweak things a bit.

Well, I guess I'm going to have to change my liner notes now. What
was the limit of that scale I posted?

Thanks for the scrutiny,

Jacky

Do you play Chess? Almost afraid to get on the board with you Paul!!!

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

Jacky, I'm glad you got a reasonable spectrum now! Though octave-reducing
doesn't seem justified.

>Well, I guess I'm going to have to change my liner notes now. What
>was the limit of that scale I posted?

You had most of the identities of a 31-limit otonality there.

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗ligonj@northstate.net

That's funny! I kind of look like "The Kid from Deliverance", except
he is more handsome!!! Dueling microtonal guitars! If I can just
figure out how to wear mine in a holster! It's a double cutaway, and
I'm afraid I'll get injured. }: )

My main "Axe" is my noble Gibson SG Custom 12tET guitar. But I can
definately get some microtones (bends and such). I've really been
wanting to get a microtonal guitar, or else a GK2-A pickup for this
guitar, so that I can use it as a microtonal controller. The guitar
is my strongest musical voice. Ah, if money wasn't an object!

Thanks kindly for your help!

Jacky

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> >Do you play Chess? Almost afraid to get on the board with you
Paul!!!
>
> No -- but I'll take you up in a guitar duel anyday!

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

>My main "Axe" is my noble Gibson SG Custom 12tET guitar. But I can
>definately get some microtones (bends and such). I've really been
>wanting to get a microtonal guitar, or else a GK2-A pickup for this
>guitar, so that I can use it as a microtonal controller. The guitar
>is my strongest musical voice.

Glad to hear it! I'd definitely recommend a real, refretted microtonal
guitar if the guitar is your "voice". My 22-tET guitar is a very easily
navigable way of getting away from common-practice diatonicism and exploring
7- or 11-limit harmony (if you want to have 7- and 11-limit _and_ you're
into common-practice diatonicism, 31-tET is your best bet) -- though if
you're interested in 31-limit otonalities then equal temperament is not a
viable option and you'll need to get into bent frets and/or not having the
same notes on each string. (BTW, the simplest ET consistent in the 31-limit
is 311-tET, which is consistent all the way through the 41-limit!)

Or better yet, go fretless and devote your life to mastering the intonation
of 31-limit otonal chords . . .

🔗Monz <MONZ@JUNO.COM>

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

> http://www.egroups.com/message/tuning/15801
>
> > Fundamental: 261.625
>
> Suspiciously close to 3*86.1328. Perhaps some rounding error
> came in here?

Jacky and Paul:

261.625 is approximately the frequency of the 12-tET 'middle-C'
when 'A' = 440 Hz. In other words, the 'standard' middle-C that
comes with most synths.

Mathematically: 440 / (2^(9/12))

-monz
http://www.ixpres.com/interval/homepage.html

🔗ligonj@northstate.net

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
>
>
> 261.625 is approximately the frequency of the 12-tET 'middle-C'
> when 'A' = 440 Hz. In other words, the 'standard' middle-C that
> comes with most synths.
>
> Mathematically: 440 / (2^(9/12))
>
>
> -monz

Joe,

Yes, the sample was tuned to C 261.625 with a software application,
to bring it into concert pitch. The composition is in "C". This
sample was at another pitch before (higher). This little app
(usually) does a great job of detecting the prominently loud
frequencies in a sample, and then tuning them to a specified pitch
(you can enter a specific pitch such as C4, or specifying C, would
tune the sample to the closest C.) This is a crucial step in taming
inharmonic samples, such as gongs and the like, to be able to play
melodic music in the desired pitch center. Can't be without this for
the sampling sound design I do.

Thanks for the observation,

Jacky

🔗David Beardsley <xouoxno@virtulink.com>

"Paul H. Erlich" wrote:

> Or better yet, go fretless and devote your life to mastering the intonation
> of 31-limit otonal chords . . .

I finally got my fretless G'n'L/FreeNote S-500 earlier
this month. I feel that it's more liberating then my 62-just gtr.
I really like fretless!

--
* D a v i d B e a r d s l e y
* 49/32 R a d i o "all microtonal, all the time"
* http://www.virtulink.com/immp/lookhere.htm

🔗ligonj@northstate.net

--- In tuning@egroups.com, David Beardsley <xouoxno@v...> wrote:
>
> I finally got my fretless G'n'L/FreeNote S-500 earlier
> this month. I feel that it's more liberating then my 62-just gtr.
> I really like fretless!
>
> db
>
> --
> * D a v i d B e a r d s l e y
> * 49/32 R a d i o "all microtonal, all the time"
> * http://www.virtulink.com/immp/lookhere.htm

David,

Do you find that it's easy to orientate yourself on the neck? Are
there any markings?

How about the sustain of the instrument? How different is it from a
fretted instrument in this regard?

Thanks,

Jacky

🔗phv40@hotmail.com

--- In tuning@egroups.com, ligonj@n... wrote:
> My main "Axe" is my noble Gibson SG Custom 12tET guitar. But I can
> definately get some microtones (bends and such). I've really been
> wanting to get a microtonal guitar, or else a GK2-A pickup for this
> guitar, so that I can use it as a microtonal controller. The guitar
> is my strongest musical voice. Ah, if money wasn't an object!

Hi Jacky,

If you don't want to go the "have luthier rip out the frets on
old/cheap guitar route", Fretlessguitar.com sells fretless acoustics
for $450 and fretless electrics for about $650. The fretless
electrics include Sustainer circuits, which more than compensates for
the slightly shorter sustain in comparison to fretted guitars. A
glass fingerboard option, I was told, is to be offered next year and
would also be available as a retrofit to current fretless models. I
have a Fernandes Fretless Native Pro myself and the only thing I
would change is increase the gauge to .011s to improve the high
strings' natural sustain and responsiveness to the Sustainer. The
Sustainer takes longer to activate a .009 high E than the other
strings.

David B's fretless G&L is a very nice axe indeed. With the epoxy
coating, his high strings except for the high E have pretty good
natural sustain on the high notes. .009 E strings are just too thin
for fretless in my opinion.

Paolo