--- 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.

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