Yahoo Tuning Groups Ultimate Backup tuning RE: [tuning] locally concordant tetrads -- verifying Margo and Ge orge

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
>
> Anyway, the relevant harmonic entropy curve can be seen at
> http://www.egroups.com/files/tuning/perlich/harment.gif.
>
> Let me know if I can help clarify anything.

Paul writes in his article on harmonic entropy:

>One way of modeling this is with a Farey series and its mediants. The
>Farey series of order n is simply the set all the ratios of numbers
>not exceeding n, and the mediant between two consecutive fractions
in
>a Farey series is the sum of the numerators over the sum of the
>denominators (this definition has many mathematical and acoustical
>justifications).

I'm having a little trouble with the value "N" of the Farey series...
Is it kind of like a "resolution limit" of the ratios being
considered?? And, if so, how do you derive the "N number" limit from
the ratios?? Some easy, hopefully, examples might help...

I would post off-list, but I prefer to make my ignorance public.

___________ _____ ___ _ _
Joseph Pehrson

🔗Monz <MONZ@JUNO.COM>

> [Joseph Pehrson]
> http://www.egroups.com/message/tuning/11712
>
> I would post off-list, but I prefer to make my ignorance public.
>

Bravo, Joe! Making your ignorance public so that we can all
respond and watch the responses is precisely why I believe
that the information exchange provided by the internet is
one of the most important factors in our current evolution.

As we gradually become pieces of an ever more efficiently
connected collective mind, we must of necessity progress
to a higher stage as a lifeform, similar to the way that
millions of years ago bacteria grouped itself into symbiotic
relationships that evolved into more complex forms of life.

What's unfortunate is that so many chunks of the world are
still cut off from this process.

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

🔗Joseph Pehrson <pehrson@pubmedia.com>

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

Keenan wrote,

>I would be very interested in seeing a triad/tetrad total dyadic harmonic
>entropy graph based on an odd-limit (instead of a Farey series) that was
>octave-indifferent, as suggested here:

>"By the way, I intend to model Partch's "one-footed bride" with a sort of
>octave-equivalent harmonic entropy function; that is, rather than using a
>Farey series (or a series such as used by Mann where the sum of numerator
>and denominator does not exceed a certain limit), using instead the ratios
>up to a given Partch limit ("odd limit", that is, the largest odd factor of
>either the numerator or denominator does not exceed a certain limit)."

>This would tend to judge the entropy of the chord as a whole, not a
>particular voicing of the chord. This seemed to ba a problem in the local
>minima of the tetrad graph; some chords didn't make it or got bumped down
>simply beacause they didn't have a voicing open enough. Octave equivalence
>just makes sence.

As you may have noticed, I've been using an octave-equivalent harmonic
entropy formulation for this "scale" stuff. I will do the same for triads
and tetrads as soon as I get around to it (so much to do . . .). I can make
a color graph for triads just like I did before, but what would you like me
to do for tetrads?

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

I wrote,

>As you may have noticed, I've been using an octave-equivalent harmonic
entropy >formulation for this "scale" stuff. I will do the same for triads
and tetrads >as soon as I get around to it (so much to do . . .). I can make
a color graph >for triads just like I did before, but what would you like me
to do for >tetrads?

Here's the color graph for triads:

http://www.egroups.com/files/tuning/perlich/octeqtri.jpg

Note that this is not based on the odd-limit based harmonic entropy that
Keenan quoted, but simply uses a harmonic entropy curve that uses, for any
interval, the average of the harmonic entropy values for that interval and
for its inversion. It should be pretty close, though, I think . . .

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

Here are the results again, same as before but this time imposing octave
equivalence (by using, for each interval, the average of the entropies of
the smallest inversion (0-600¢) and the second-smallest inversion
(600-1200¢)):

498 702 1200 21.016
498 996 1200 21.522
204 702 1200 21.522
498 884 1200 21.572
316 702 1200 21.572
498 812 1200 21.654
388 702 1200 21.654
386 884 1200 21.981
316 814 1200 21.981
498 934 1200 22.029
266 702 1200 22.029
388 812 1200 22.649
440 760 1200 22.967
196 502 698 23.507
196 698 894 23.507
502 698 1004 23.507
306 502 1004 23.507
502 1004 1506 23.507
386 702 884 23.632
316 498 814 23.632
316 702 1018 23.632
182 498 884 23.632
498 884 1382 23.632
386 702 1088 23.788
498 814 1312 23.788
498 702 884 23.811
498 814 996 23.811
316 498 702 23.811
316 814 1018 23.811
204 386 702 23.811
204 702 1018 23.811
498 996 1382 23.811
182 386 884 23.811
182 498 996 23.811
386 884 1382 23.811
386 884 1088 23.885
498 996 1312 23.885
204 702 1088 23.885
316 814 1312 23.885
498 702 1086 24.03
384 588 1086 24.03
266 498 764 24.052
232 498 934 24.052
498 934 1432 24.052
436 702 934 24.052
266 702 968 24.052
498 702 932 24.058
498 766 996 24.058
498 996 1430 24.058
268 498 702 24.058
268 766 970 24.058
204 434 702 24.058
204 702 970 24.058
230 434 932 24.058
230 498 996 24.058
434 932 1430 24.058
314 702 886 24.119
388 572 886 24.119
184 498 812 24.119
388 702 1016 24.119
184 572 886 24.119
314 498 886 24.119
314 628 1016 24.119
314 628 812 24.119
312 810 1122 24.21
390 888 1278 24.21
264 498 884 24.238
264 580 966 24.238
386 620 884 24.238
386 702 966 24.238
234 620 936 24.238
316 580 814 24.238
316 702 936 24.238
234 498 814 24.238
498 810 1120 24.276
310 622 1120 24.276
386 774 1088 24.296
314 702 1088 24.296
498 886 1312 24.296
426 814 1312 24.296
188 576 1074 24.328
498 886 1074 24.328
498 814 1072 24.33
258 574 1072 24.33
498 884 1110 24.36
226 612 1110 24.36
314 812 1078 24.384
436 934 1322 24.384
388 886 1322 24.384
266 764 1078 24.384
270 702 884 24.385
432 702 1018 24.385
270 586 768 24.385
182 498 768 24.385
182 614 884 24.385
432 614 930 24.385
316 498 930 24.385
316 586 1018 24.385
498 766 1080 24.447
314 582 1080 24.447
384 812 1086 24.476
274 702 1086 24.476
498 926 1314 24.476
388 816 1314 24.476
312 626 886 24.523
260 574 886 24.523
314 574 888 24.523
314 626 940 24.523
264 436 700 24.617
264 764 1028 24.617
436 936 1372 24.617
172 436 936 24.617
500 764 936 24.617
246 568 814 24.776
246 632 878 24.776
386 632 954 24.776
322 568 954 24.776
230 388 618 24.785
232 620 812 24.79
388 580 968 24.79
388 620 1008 24.79
192 580 812 24.79
390 622 808 24.82
390 782 968 24.82
392 782 1014 24.82
232 622 1014 24.82
392 578 810 24.82
186 418 808 24.82
186 578 968 24.82
232 418 810 24.82
390 618 784 24.834
390 806 972 24.834
416 806 1034 24.834
166 394 784 24.834
228 394 810 24.834
228 618 1034 24.834
416 582 810 24.834
166 582 972 24.834
190 388 578 24.863
186 390 576 24.864
182 392 574 24.865
390 814 1006 24.872
424 616 810 24.872
424 814 1008 24.872
192 616 1006 24.872
390 584 776 24.872
192 386 776 24.872
194 386 810 24.872
194 584 1008 24.872
316 764 1080 24.877
436 884 1320 24.877
180 620 940 24.932
320 580 760 24.932
320 760 940 24.932
440 620 880 24.932
440 760 1020 24.932
180 440 760 24.932
260 440 880 24.932
260 580 1020 24.932
192 582 774 24.934
390 582 1008 24.934
192 618 810 24.934
426 618 1008 24.934
176 616 1056 24.964
440 880 1056 24.964

🔗Joseph Pehrson <pehrson@pubmedia.com>

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

http://www.egroups.com/message/tuning/11990

> Here are the results again, same as before but this time imposing
octave equivalence (by using, for each interval, the average of the
entropies of the smallest inversion (0-600¢) and the
second-smallest
inversion(600-1200¢)):
>
> 498 702 1200 21.016
> 498 996 1200 21.522
> 204 702 1200 21.522
> 498 884 1200 21.572

<snip>

I wonder how many of these tetrads we need for the Tuning Lab sound
files?? Do you think maybe 3 or 4 consecutive ones from one part of
the list, and then 3 or 4 from a couple of other consecutive
segments,
or what?? I'm thinking there should be about 12... it's a nice
number.
_______________ _____ __ __ _
Joseph Pehrson