Yahoo Tuning Groups Ultimate Backup harmonic

>Query 1: Are Relative Harmonic Entropy, Sonance, and Cordance
equivalent?

The last two Words(?) were invented by Monzo. Sonance is not
equivalence to cordance, because sonance is dependent on musical
context and perhaps even conventions. Cordance does seem
qualitatively similar to harmonic entropy; although roughness seems
to be, in addition to harmonic entropy, a component of cordance.

>Query 2: We do not seem to have their units. If we do not have, we
should
>devise some measuring standard, however arbitrary, for study and
>comparison.

Though arbitrary, the vertical axis ranges from 4.29 to 6.08 in the
0.6% case. If you think it would be worth my while, I will repost the
graphs with tick marks and numbers to the left of the vertical axis,
and if you wish, a grid of parallel horizontal lines across the graph.

>Query 3: Now, I find myself intensely interested in the the RHE of
the
>following:

For the following, I will assume that by 'Relative' you mean relative
to the harmonic entropy of the unison, and that for the scales in
(i), (ii), and (iii), you mean to play a continuous drone at a pitch
of 0 cents. Fine means s=.006%, ordinary means s=.012%.

(i) 22-shruti gamut

I'm assuming a range from -550 to 1950 cents against the single drone
pitch at 0 cents.

cents fine HE ordinary HE
-498 1.4394 0.61959
-408 1.6526 0.67357
-386 1.5281 0.65559
-316 1.572 0.67198
-294 1.6476 0.6792
-204 1.6288 0.68845
-182 1.6314 0.69061
-112 1.6517 0.71196
-90 1.666 0.72601
0 0 0
90 1.666 0.72601
112 1.6517 0.71196
182 1.6314 0.69061
204 1.6288 0.68845
294 1.6476 0.6792
316 1.572 0.67198
386 1.5281 0.65559
408 1.6526 0.67357
498 1.4394 0.61959
520 1.6571 0.66059
590 1.6026 0.67538
612 1.6288 0.68461
702 1.2515 0.54437
792 1.6395 0.68719
814 1.5952 0.68118
884 1.4826 0.63804
906 1.6544 0.66726
996 1.6473 0.68036
1018 1.6004 0.67951
1088 1.6367 0.69541
1110 1.647 0.70642
1200 0.66624 0.29534
1290 1.6448 0.70453
1312 1.6367 0.69588
1382 1.6399 0.68105
1404 1.5879 0.67669
1494 1.6483 0.67859
1516 1.6131 0.68782
1586 1.4008 0.60633
1608 1.661 0.65414
1698 1.5469 0.66151
1720 1.6507 0.67775
1790 1.6309 0.69213
1812 1.6425 0.70003
1902 0.93502 0.41031

(ii) 22-teT scale

cents fine HE ordinary HE
-545.45 1.6362 0.693
-490.91 1.4982 0.62514
-436.36 1.6136 0.68818
-381.82 1.5434 0.65703
-327.27 1.6204 0.67687
-272.73 1.6069 0.67972
-218.18 1.6387 0.68654
-163.64 1.6351 0.6938
-109.09 1.6529 0.71348
-54.545 1.7098 0.75443
0 0 0
54.545 1.7098 0.75443
109.09 1.6529 0.71348
163.64 1.6351 0.6938
218.18 1.6387 0.68654
272.73 1.6069 0.67972
327.27 1.6204 0.67687
381.82 1.5434 0.65703
436.36 1.6136 0.68818
490.91 1.4982 0.62514
545.45 1.6362 0.693
600 1.639 0.67904
654.55 1.6533 0.70119
709.09 1.3601 0.55604
763.64 1.644 0.70204
818.18 1.6019 0.68205
872.73 1.5844 0.64978
927.27 1.632 0.69098
981.82 1.6223 0.67351
1036.4 1.6337 0.68101
1090.9 1.6377 0.69664
1145.5 1.6782 0.72976
1200 0.66624 0.29534
1254.5 1.6753 0.7276
1309.1 1.6382 0.69668
1363.6 1.6159 0.68484
1418.2 1.6344 0.68267
1472.7 1.5561 0.65817
1527.3 1.6298 0.69153
1581.8 1.4306 0.60928
1636.4 1.64 0.69406
1690.9 1.5752 0.6631
1745.5 1.6106 0.68387
1800 1.6361 0.69546
1854.5 1.6723 0.71355
1909.1 1.1255 0.43155
1963.6 1.6539 0.71382

(iii) the first 16 partials of a note (like C, for example)

cents fine HE ordinary HE
0 0 0
1200 0.66624 0.29534
1902 0.93501 0.41031
2400 1.0891 0.4771
2786.3 1.1808 0.51624
3102 1.2533 0.54603
3368.8 1.2999 0.56509
3600 1.338 0.5821
3803.9 1.3768 0.59527
3986.3 1.4 0.60457
4151.3 1.4267 0.61428
4302 1.4463 0.62798
4440.5 1.4536 0.62429
4568.8 1.4719 0.63412
4688.3 1.4777 0.63309
4800 1.4912 0.64149

(iv) The distance between each of the adjescent shruti-s

I wonder -- isn't it rare to hear adjacent shruti-s played at the
same time?

Anyhow,

cents fine HE ordinary HE
22 5.9783 6.2964
70 5.9782 6.6764
90 5.9596 6.6555

(v) The distance between each of the adjescent chromatic JI notes

They should all appear below (?)

(vi) The various intervals (there are so many of them)

That appear in the shruti scale?

cents fine HE ordinary HE
0 0 0
22 1.6846 0.36698
70 1.6845 0.74699
90 1.666 0.72601
92 1.6642 0.72439
112 1.6517 0.71196
114 1.651 0.71095
134 1.6468 0.70241
180 1.6315 0.69084
182 1.6314 0.69061
202 1.6279 0.68869
204 1.6288 0.68845
224 1.629 0.68581
226 1.6248 0.68557
272 1.6048 0.67963
274 1.6111 0.67991
294 1.6476 0.6792
296 1.6453 0.67843
316 1.572 0.67198
318 1.575 0.6723
338 1.6456 0.68499
364 1.6533 0.67784
384 1.5323 0.65602
386 1.5281 0.65559
406 1.6489 0.67127
408 1.6526 0.67357
428 1.6227 0.68669
430 1.6187 0.68712
476 1.6577 0.65939
478 1.6504 0.65437
498 1.4394 0.61959
500 1.4443 0.62007
520 1.6571 0.66059
522 1.6608 0.66562
568 1.6343 0.68082
588 1.5942 0.67499
590 1.6026 0.67538
610 1.6323 0.6837
612 1.6288 0.68461
632 1.6329 0.694
678 1.6786 0.63778
680 1.6688 0.6273
700 1.2608 0.54523
702 1.2515 0.54437
722 1.6532 0.6177
724 1.6698 0.62861
770 1.6394 0.69876
772 1.6376 0.69769
792 1.6395 0.68719
794 1.6404 0.6862
814 1.5952 0.68118
816 1.597 0.68151
836 1.6433 0.69012
862 1.6582 0.67092
882 1.4882 0.63867
884 1.4826 0.63804
904 1.6487 0.66334
906 1.6544 0.66726
926 1.6334 0.69072
928 1.6313 0.69107
974 1.5783 0.66976
976 1.5888 0.67049
996 1.6473 0.68036
998 1.6457 0.68077
1018 1.6004 0.67951
1020 1.6018 0.67939
1066 1.6323 0.68784
1086 1.636 0.69459
1088 1.6367 0.69541
1108 1.6457 0.70521
1110 1.647 0.70642
1130 1.6612 0.72165
1178 1.6837 0.51067
1200 0.66624 0.29534
1222 1.6839 0.51024
1270 1.6563 0.71918
1290 1.6448 0.70453
1292 1.6441 0.70345
1312 1.6367 0.69588
1314 1.6358 0.69537
1334 1.6314 0.69084
1380 1.6377 0.68167
1382 1.6399 0.68105
1402 1.5889 0.67645
1404 1.5879 0.67669
1424 1.6441 0.68544
1426 1.6449 0.68609
1472 1.5511 0.65781
1474 1.5658 0.65891
1494 1.6483 0.67859
1496 1.6459 0.68017
1516 1.6131 0.68782
1518 1.6141 0.68836
1538 1.6427 0.69465
1564 1.6655 0.65715
1584 1.4089 0.60714
1586 1.4008 0.60633
1606 1.6509 0.64784
1608 1.661 0.65414
1628 1.6481 0.69256
1630 1.6459 0.69348
1676 1.6467 0.67551
1678 1.6446 0.67367
1698 1.5469 0.66151
1700 1.5496 0.66188
1720 1.6507 0.67775
1722 1.6518 0.67937
1768 1.6409 0.68522
1788 1.6294 0.69148
1790 1.6309 0.69213
1810 1.641 0.69919
1812 1.6425 0.70003
1832 1.652 0.71138
1880 1.6771 0.56427
1902 0.93502 0.41031
1924 1.6795 0.56528
1972 1.6467 0.70842
1992 1.6372 0.69782
1994 1.6369 0.69709
2014 1.6351 0.69125
2016 1.6365 0.69072
2036 1.6195 0.68677
2084 1.5744 0.67276
2106 1.6483 0.68496
2128 1.6379 0.69247
2176 1.5187 0.63657
2196 1.6566 0.67557
2198 1.6546 0.67896
2218 1.6352 0.69064
2220 1.6369 0.68993
2288 1.6159 0.68522
2310 1.6362 0.6927
2400 1.0891 0.4771

(vii) The various "jumps" using which a raga is imporvised.

They should all appear above (?)

> Let me add
>here, that a raga is never developed linearly and randomly: It is
>elaborated by expanding the 'area' created by reaching one note to
>the
>next note non-sequentially. Like Sa to Ma, Pa to Re, Dha to Ga, etc.

>There is a definite number of factors which contribute to the mood
>of a
>raga. This mood can be empirically studied in terms of these known
>factors. The information on RHE of the above, I feel intuitionally,
>will
>be very significant.

>Your insight in these matters will be very valuable.

>Thank you for your time and input,
>Haresh.

Looking forward to more,
Paul

🔗vilaalbert@...

----- Original Message -----
From: wallyesterpaulrus
To: harmonic_entropy@yahoogroups.com
Sent: Tuesday, December 30, 2003 8:33 AM
Subject: [harmonic_entropy] Reply to Haresh

>Query 1: Are Relative Harmonic Entropy, Sonance, and Cordance
equivalent?

>Query 2: We do not seem to have their units. If we do not have, we
should
>devise some measuring standard, however arbitrary, for study and
>comparison.

>Query 3: Now, I find myself intensely interested in the the RHE of
the
>following:

(i) 22-shruti gamut

I'm assuming a range from -550 to 1950 cents against the single drone
pitch at 0 cents.

(ii) 22-teT scale

(iii) the first 16 partials of a note (like C, for example)

(iv) The distance between each of the adjescent shruti-s

I wonder -- isn't it rare to hear adjacent shruti-s played at the
same time?

Anyhow,

cents fine HE ordinary HE
22 5.9783 6.2964
70 5.9782 6.6764
90 5.9596 6.6555

(v) The distance between each of the adjescent chromatic JI notes

They should all appear below (?)

(vi) The various intervals (there are so many of them)

That appear in the shruti scale?

(vii) The various "jumps" using which a raga is imporvised.

They should all appear above (?)

>Your insight in these matters will be very valuable.

>Thank you for your time and input,
>Haresh.

Looking forward to more,
Paul

To unsubscribe from this group, send an email to:
harmonic_entropy-unsubscribe@egroups.com

Yahoo! Groups Sponsor
ADVERTISEMENT

------------------------------------------------------------------------------
Yahoo! Groups Links

a.. To visit your group on the web, go to:
/harmonic_entropy/

b.. To unsubscribe from this group, send an email to:
harmonic_entropy-unsubscribe@yahoogroups.com

c.. Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.

🔗Haresh BAKSHI <hareshbakshi@...>

--- In harmonic_entropy@yahoogroups.com, <vilaalbert@h...> wrote:
>>>> .........
> Looking forward to more, >>>>

Indeed, there is more.

Hello ALL, I request Paul and other Group members to test the veracity of the eight audacious statements I am making below. Your remarks will be very valuable.

RHE and Raga-s
==============

A raga is a non-stochastic arrangement of notes. The improvisation of a raga is a process in which every future note to be performed depends not only on the present note being performed, but also on how this present note was arrived at.

Inferences from the above statements:

(1) the larger the number of notes in a raga, the greater is its Harmonic Entropy. Obviously, it follows that vivadi (omitted) notes lower the Harmonic Entropy.

(2) The greater the number of random ways in which we can combine the notes, the greater is the raga's Harmonic Entropy.

(3) The greater the distance of the notes from the Sa (tonic), the greater is the raga's Harmonic Entropy.

(4) The greater the specificity -- and consquent recognizability -- of a raga, the lower its Harmonic Entropy. This is because, one recognizes a raga from (i) the way and (ii) the order in which its constituent notes are ordered. This reduces randomness. This is where the "jumps" I referred to in the previous email, comes into play. These "jumps" lower the Harmonic Entropy of the raga.

(5) The longer one stays on a note, the lower the Harmonic Entropy gets. This happens all the time, because the vadi and samvadi notes are stayed on longer -- even some other notes are stayed longer on, too, depending upon the requirements of a raga. Similarly, vivadi (omitted) notes lower the Harmonic Entropy. At the end of every alap (phrase), we come back to Sa (tonic), resulting in minimum entropy.

(6) The greater the number of times a note is repeated, the lower the Harmonic Entropy gets. As an example, Ga-Ga has a lower Harmonic Entropy than Ga-Pa.

(7) The greater the use of embellishments [ornaments like gamaka, meend (glissando), murki etc.], the greater the Harmonic Entropy.

(8) The greater the use of vowels and consonants, the greater the Harmonic Entropy. The vowel normally used is singing is 'aa'. Variations are achieved by the use of 'ee', 'o', 'e' (as in "sEt"), and sometimes 'oo'. The use of consonants implies using the words of the composition used during singing.

(9) The greater the correctness of the notes (as JI frequencies), the lower the Harmonic Entropy.

As regards the math of Harmonic Entropy, I am acutely aware of my ignorance. But I have depended heavily on my experience and intuition, and on the fact that I can depend on the Harmonic Entropy pundits.

Regards, and thanks for your time,
Haresh.

🔗wallyesterpaulrus <wallyesterpaulrus@...>

Hi Haresh,

I'm afraid we are losing one another.

Before I attempt to address what you write below, perhaps you could
go back to message #698 and answer my questions there? Note that in
my answer to (iv) there I forgot the "relative" part, but all the
correct values can be found under my answer to (vi) anyway.

Thanks,
Paul

--- In harmonic_entropy@yahoogroups.com, "Haresh BAKSHI"
<hareshbakshi@h...> wrote:
> --- In harmonic_entropy@yahoogroups.com, <vilaalbert@h...> wrote:
> >>>> .........
> > Looking forward to more, >>>>
>
> Indeed, there is more.
>
> Hello ALL, I request Paul and other Group members to test the
veracity of the eight audacious statements I am making below. Your
remarks will be very valuable.
>
> RHE and Raga-s
> ==============
>
> A raga is a non-stochastic arrangement of notes. The improvisation
of a raga is a process in which every future note to be performed
depends not only on the present note being performed, but also on how
this present note was arrived at.
>
> Inferences from the above statements:
>
> (1) the larger the number of notes in a raga, the greater is its
Harmonic Entropy. Obviously, it follows that vivadi (omitted) notes
lower the Harmonic Entropy.
>
> (2) The greater the number of random ways in which we can combine
the notes, the greater is the raga's Harmonic Entropy.
>
> (3) The greater the distance of the notes from the Sa (tonic), the
greater is the raga's Harmonic Entropy.
>
> (4) The greater the specificity -- and consquent recognizability --
of a raga, the lower its Harmonic Entropy. This is because, one
recognizes a raga from (i) the way and (ii) the order in which its
constituent notes are ordered. This reduces randomness. This is where
the "jumps" I referred to in the previous email, comes into play.
These "jumps" lower the Harmonic Entropy of the raga.
>
> (5) The longer one stays on a note, the lower the Harmonic Entropy
gets. This happens all the time, because the vadi and samvadi notes
are stayed on longer -- even some other notes are stayed longer on,
too, depending upon the requirements of a raga. Similarly, vivadi
(omitted) notes lower the Harmonic Entropy. At the end of every alap
(phrase), we come back to Sa (tonic), resulting in minimum entropy.
>
> (6) The greater the number of times a note is repeated, the lower
the Harmonic Entropy gets. As an example, Ga-Ga has a lower Harmonic
Entropy than Ga-Pa.
>
> (7) The greater the use of embellishments [ornaments like gamaka,
meend (glissando), murki etc.], the greater the Harmonic Entropy.
>
> (8) The greater the use of vowels and consonants, the greater the
Harmonic Entropy. The vowel normally used is singing is 'aa'.
Variations are achieved by the use of 'ee', 'o', 'e' (as in "sEt"),
and sometimes 'oo'. The use of consonants implies using the words of
the composition used during singing.
>
> (9) The greater the correctness of the notes (as JI frequencies),
the lower the Harmonic Entropy.
>
> As regards the math of Harmonic Entropy, I am acutely aware of my
ignorance. But I have depended heavily on my experience and
intuition, and on the fact that I can depend on the Harmonic Entropy
pundits.
>
> Regards, and thanks for your time,
> Haresh.

🔗Haresh BAKSHI <hareshbakshi@...>

--- In harmonic_entropy@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

......................

Hi Paul, I re-read your reply carefully. The questions you have
raised arose, I believe, because *my* questions were not very clear.
You have answered those, making certain assumptions which made my
questions clear. Except the seventh:

>>>> (vii) The various "jumps" using which a raga is imporvised.
They should all appear above (?) >>>>

Perhaps those jumps I referred to do not appear above. As an example
of "jumps", let me take up the raga Kedar. It is highly non-linear,
and its alap typically goes like: [assuming C to be the Sa]
C4 F (E)G, G C5 A Bb A G, F C4 D C4.
1 2 3 4 5 6 7 8 9 10 11 12 13 (notes numbered for clarity)

Notice the jumps between each of 1 and 2, 4 and 5, 5 and 6, 10 and 11.
I am trying to know if such jumps lower the value of Harmonic Entropy.
Two reasons: (i) such jumps reduce the number of notes [in absence of
such jumps, like the jump 1 to 2 in the above example, the number of
notes would have gone up from two (C4 and F) to four (C4 D E F)];
(ii) such jumps usually, though not necessarily, reduce the magnitude
of Harmonic Entropy because they add consonance (C to F is 3:4).

In the case of (i) above, I have assumed that Harmonic Entropy
increases with increase in the number of notes. Why? Because, instead
of the consonance (C4-F) only, we now would have roughness added by
the added notes D and E (C4-D, C4-E).

Let me know if you want me to re-read message #698 for more/other reasons.

Regards,
Haresh.

🔗wallyesterpaulrus <wallyesterpaulrus@...>

--- In harmonic_entropy@yahoogroups.com, "Haresh BAKSHI"
<hareshbakshi@h...> wrote:
> --- In harmonic_entropy@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> ......................
>
> Hi Paul, I re-read your reply carefully. The questions you have
> raised arose, I believe, because *my* questions were not very clear.
> You have answered those, making certain assumptions which made my
> questions clear. Except the seventh:
>
> >>>> (vii) The various "jumps" using which a raga is imporvised.
> They should all appear above (?) >>>>
>
> Perhaps those jumps I referred to do not appear above. As an example
> of "jumps", let me take up the raga Kedar. It is highly non-linear,
> and its alap typically goes like: [assuming C to be the Sa]
> C4 F (E)G, G C5 A Bb A G, F C4 D C4.
> 1 2 3 4 5 6 7 8 9 10 11 12 13 (notes numbered for clarity)
>
> Notice the jumps between each of 1 and 2, 4 and 5, 5 and 6, 10 and
11.
> I am trying to know if such jumps lower the value of Harmonic
Entropy.

Well, from 4 to 5 for example, it seems you'd be lowering the
harmonic entropy against a drone note at C4, but at the same time
you'd be raising it against a drone note at G3. It's not completely
clear how harmonic entropy values add but I don't think that's the
thrust of your question anyway. Please let me know what I have left
to be desired.

> Two reasons: (i) such jumps reduce the number of notes [in absence
of
> such jumps, like the jump 1 to 2 in the above example, the number of
> notes would have gone up from two (C4 and F) to four (C4 D E F)];
> (ii) such jumps usually, though not necessarily, reduce the
magnitude
> of Harmonic Entropy because they add consonance (C to F is 3:4).
>
> In the case of (i) above, I have assumed that Harmonic Entropy
> increases with increase in the number of notes. Why? Because,
instead
> of the consonance (C4-F) only, we now would have roughness added by
> the added notes D and E (C4-D, C4-E).

OK. I will try to address your set of questions now . . .

🔗wallyesterpaulrus <wallyesterpaulrus@...>

One could of course concoct a 'raga' with fewer notes that had a
larger average-over-time harmonic entropy than a 'raga' with more
notes, but I'm not sure if these could ever both be true Indian ragas.
One would have to study a very wide range of examples to have some
degree of certainty.

> (2) The greater the number of random ways in which we can combine
>the notes, the greater is the raga's Harmonic Entropy.

Rather unclear to me and some examples would help.

> (3) The greater the distance of the notes from the Sa (tonic), the
>greater is the raga's Harmonic Entropy.

Are you speaking of linear pitch-distance? If so, this assertion
would appear to be incorrect, unless backed up by some rather
extraordinary evidence. On the face of it, I don't see how it could
be correct.

> (4) The greater the specificity -- and consquent recognizability --
>of a raga, the lower its Harmonic Entropy. This is because, one
>recognizes a raga from (i) the way and (ii) the order in which its
>constituent notes are ordered. This reduces randomness. This is
>where the "jumps" I referred to in the previous email, comes into
>play. These "jumps" lower the Harmonic Entropy of the raga.

I'm having trouble digesting the "recognizability" claim.

> (5) The longer one stays on a note, the lower the Harmonic Entropy
>gets. This happens all the time, because the vadi and samvadi notes
>are stayed on longer -- even some other notes are stayed longer on,
>too, depending upon the requirements of a raga.

But aren't these notes sometimes ones with *high* harmonic entropy
against the drone?

> (6) The greater the number of times a note is repeated, the lower
>the Harmonic Entropy gets. As an example, Ga-Ga has a lower Harmonic
>Entropy than Ga-Pa.

This seems false. Ga-Ga would have a higher time-averaged harmonic
entropy against the drone than Ga-Pa, since Pa has lower harmonic
entropy against the drone than Ga.

> (7) The greater the use of embellishments [ornaments like gamaka,
>meend (glissando), murki etc.], the greater the Harmonic Entropy.

Perhaps, though in rare cases I think I've heard ornaments that could
actually decrease the Harmonic Entropy, as they touch on intervals
such as 7/4 against the drone.

> (8) The greater the use of vowels and consonants, the greater the
>Harmonic Entropy.

greater . . . compared with what?

> (9) The greater the correctness of the notes (as JI frequencies),
>the lower the Harmonic Entropy.

In general yes, though there are exceptions when the JI frequency
does not lie at a local minumum of harmonic entropy -- as you can see
clearly from the graph.

Best,
Paul

🔗Haresh BAKSHI <hareshbakshi@...>

--- In harmonic_entropy@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:
..............

Hello Paul, thank you very much for your considered views on so many questions. While I mull over your responses, I have the following to add:

>>>> (1) the larger the number of notes in a raga, the greater is its
> >Harmonic Entropy. Obviously, it follows that vivadi (omitted) notes
> >lower the Harmonic Entropy.
>>
> One could of course concoct a 'raga' with fewer notes that had a
> larger average-over-time harmonic entropy than a 'raga' with more
> notes, but I'm not sure if these could ever both be true Indian
> ragas.
> One would have to study a very wide range of examples to have some
> degree of certainty. >>>>

Does not the statement (i) account for the pentatonic raga-s, for example, being so powerfully stable and dominant from "times immemorial", in all kinds of music?

>>>> (3) The greater the distance of the notes from the Sa (tonic), the greater is the raga's Harmonic Entropy.
>>
> Are you speaking of linear pitch-distance? If so, this assertion
> would appear to be incorrect, unless backed up by some rather
> extraordinary evidence. On the face of it, I don't see how it could
> be correct. >>>>

If I read the graph correctly, for example, the Pa closer to Sa has much lower Harmonic Entropy than the Pa of the higher octave, farther away and right.

>>>> (8) The greater the use of vowels and consonants, the greater the
> >Harmonic Entropy.
>>
> greater . . . compared with what? >>>>

greater than it would be if the alap was rendered only in "aa...", without the use of other vowels and consonants.

Regards,
Haresh.

🔗wallyesterpaulrus <wallyesterpaulrus@...>

--- In harmonic_entropy@yahoogroups.com, "Haresh BAKSHI"
<hareshbakshi@h...> wrote:
> --- In harmonic_entropy@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> ..............
>
> Hello Paul, thank you very much for your considered views on so
many questions. While I mull over your responses, I have the
following to add:
>
> >>>> (1) the larger the number of notes in a raga, the greater is
its
> > >Harmonic Entropy. Obviously, it follows that vivadi (omitted)
notes
> > >lower the Harmonic Entropy.
> >>
> > One could of course concoct a 'raga' with fewer notes that had a
> > larger average-over-time harmonic entropy than a 'raga' with more
> > notes, but I'm not sure if these could ever both be true Indian
> > ragas.
> > One would have to study a very wide range of examples to have
some
> > degree of certainty. >>>>
>
> Does not the statement (i) account for the pentatonic raga-s, for
>example, being so powerfully stable and dominant from "times
>immemorial", in all kinds of music?

I remember reading that none of the pentatonic raga-s correspond to
the usual major and minor pentatonic scales, even when everything is
approximated to 12-equal. Of course, some of the pentatonic raga-s
that are used may have even lower harmonic entropy than the usual
pentatonic scale no matter how the latter is oriented against the
drone . . .

>> >>>> (3) The greater the distance of the notes from the Sa
(tonic), the greater is the raga's Harmonic Entropy.
>> >>
>> > Are you speaking of linear pitch-distance? If so, this assertion
>> > would appear to be incorrect, unless backed up by some rather
>> > extraordinary evidence. On the face of it, I don't see how it
>could
>> > be correct. >>>>
>
>> If I read the graph correctly, for example, the Pa closer to Sa
>has much lower Harmonic Entropy than the Pa of the higher octave,
>farther away and right.

Pa appears in three different registers on the graph -- on the far
left, in the exact center, and on the far right. Either way, I have
difficulty seeing how you would arrive at this statement above, much
less the assertion (3) above . . .

> >>>> (8) The greater the use of vowels and consonants, the greater
the
> > >Harmonic Entropy.
> >>
> > greater . . . compared with what? >>>>
>
> greater than it would be if the alap was rendered only in "aa...",
> without the use of other vowels and consonants.

I don't see why that would be the case . . . probably "oo..."
or "u..." would be closer to a sine wave if that's what you had in
mind . . .

Trying,
Paul