Harmonic Entropy and the Raga

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 a 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 being tolerant and condescending.

Regards, and thanks for your time,
Haresh.

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>

/tuning/topicId_50672.html#50672

wrote:
> 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.
>

***Hello Haresh!

Well, I'm a little confused about this and I'm sure that Paul Erlich
will get to it after he's read 400 more posts :) but Harmonic Entropy
implies *harmony*, no?

So, I guess with raga this would mean a pitch against a drone?? I'm
not sure there is such a thing as *horizontal* Harmonic Entropy, or
Melodic Harmonic Entropy, but Paul can and should correct me if I'm
wrong...

Joseph Pehrson

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

>>>> So, I guess with raga this would mean a pitch against a drone?? I'm not sure there is such a thing as *horizontal* Harmonic Entropy, or
> Melodic. >>>>

Hello Joseph, Yes, as you say, it would mean a pitch against a drone note -- in fact, a series if pitches (that is what alap is).

Even I am not sure that there is anything like a horizontal Harmonic Entropy, but every time we sing a note against the background of the drone, I am sure we create the right event for Harmonic Entropy to come into play -- unless the latter requires that each pitch lasts a certain minimum duration which is longer than a note typically lasts during an alap. In any case, the alap is a series of various degrees of dissonances resolved into a series of various degrees of consonances. Perhaps all music is like that, in some way or the other, in the ultimate analysis.

Regards,
Haresh.

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> ***Hello Haresh!
>
> Well, I'm a little confused about this and I'm sure that Paul
Erlich
> will get to it after he's read 400 more posts :) but Harmonic
Entropy
> implies *harmony*, no?
>
> So, I guess with raga this would mean a pitch against a drone??
I'm
> not sure there is such a thing as *horizontal* Harmonic Entropy, or
> Melodic Harmonic Entropy, but Paul can and should correct me if I'm
> wrong...
>
> Joseph Pehrson

You're right, Joseph. That's why the Indian sruti harmonic entropy
graph that I posted has three curves in three different colors on it -
- one for each of the drone notes.

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
wrote:
> 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 a 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 being tolerant and condescending.
>
> Regards, and thanks for your time,
> Haresh.

Since you posted these questions also to the harmonic_entropy
yahoogroup, I attempted to answer them there.

Happy New Year,
Paul