Hindu system (Re: Alison Monteith)

Alison Monteith wrote :

<< I just have a curious desire, probably as a result of
following the list discussions, to see if there are any
mathematical patterns to the Hindu system >>

In my opinion, Hindu Classical system is the historical system whose
mathematical patterns are the nearest of pure algebraic structure.

Taking a like-Partch matrix generated with (1 9 81 45 3 27 243) you have
the 22 srutis + 40/27 which is the reverse of srutis 27/20. All harmonic
and melodic contextual relations are depending of this shaped diamond.

( Few anomalies like absence of 40/27 are mathematically justified
in my French paper non completed but soon on-line )

http://www.aei.ca/~plamothe/india.htm

Text is abstruse but arrays and graphics can show to you clear mathematical
patterns.

Pierre Lamothe

--- In tuning@egroups.com, Pierre Lamothe <plamothe@a...> wrote:

http://www.egroups.com/message/tuning/13354

In his article on Indian music, Pierre Lamothe wrote:

L'existence de l'accord, comme tel, dans
la structure, ne dépend pas seulement du fait que
ses tons forment un sous-ensemble, mais que tous
les intervalles entres ses tons existent bien dans
cette structure. Microtonalement, si les tons sonnent
relativement bien ensemble, ça constitue un accord
relativement consonant, mais si des intervalles
entre ses tons n'appartiennent pas à la structure, ce
n'est plus un accord de cette structure, autrement dit
c'est une discordance.

In the above paragraph, Pierre Lamothe is describing just what Paul
and I have been talking about (I think). The existence of one
interval within a chord... sonic structure, which is dissonant, and
which creates a different overall dissonance for the entire
structure. I believe this ties in with the notion of the "odd" limit.

It seems from the entire article that Pierre is *ALREADY* VERY
involved with the concepts similar to Harmonic Entropy as they apply
to Indian music. So Pierre is *ALREADY* doing this... or at least
that is what I was gleaning from what I could read...

The french in this article:

http://www.aei.ca/~plamothe/india.htm

is not really all that difficult, since there are many "shared"
technical terms between the languages...

The best part is the graphic at the very end! Even if you don't want
to read the French, go over to see that graphic! You'll be glad you
did...
__________ ___ __ __ _
Joseph Pehrson

--- In tuning@egroups.com, Pierre Lamothe <
plamothe@a...> wrote:
>
> Alison Monteith wrote :
>
> << I just have a curious desire, probably as a result of
> following the list discussions, to see if there are any
> mathematical patterns to the Hindu system >>
>
> Taking a like-Partch matrix generated with (1 9 81 45 3 27 243) you
have
> the 22 srutis + 40/27 which is the reverse of srutis 27/20. All
harmonic
> and melodic contextual relations are depending of this shaped
diamond.

I find this highly arbitrary -- where does the 45 come
from? Partch diamonds arise from consonance against
a monophonic tonic -- what kind of consonance do
these numbers capture? Joe Monzo and I have a more
"reasonable" explanation, found on Monz's page. And
Pierre, what harmonic and melodic contextual relations
are you speaking of? I thought you said you were
unaware of how the tones were actually used in Hindu
music.

--- In tuning@egroups.com, "Joseph Pehrson" wrote:
> http://www.egroups.com/message/tuning/13355
>
> In the above paragraph, Pierre Lamothe is describing just what
> Paul and I have been talking about (I think). The existence of
> one interval within a chord... sonic structure, which is
> dissonant, and which creates a different overall dissonance
> for the entire structure.

Isn't this precisely what Keenan Pepper defined as 'crunchiness'?

(Or am I getting confused again?)

>
> It seems from the entire article that Pierre is *ALREADY* VERY
> involved with the concepts similar to Harmonic Entropy as they
> apply to Indian music. So Pierre is *ALREADY* doing this... or
> at least that is what I was gleaning from what I could read...

I got this impression too.

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

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
> --- In tuning@egroups.com, "Joseph Pehrson" wrote:
> > http://www.egroups.com/message/tuning/13355
> >
>> The existence of
> > one interval within a chord... sonic structure, which is
> > dissonant, and which creates a different overall dissonance
> > for the entire structure.
>
>
> Isn't this precisely what Keenan Pepper defined as 'crunchiness'?
>
Yeah -- to Keenan Pepper, the 8:10:12:15 is a crunchy
chord within the 5-limit, since it contains five intervals
that are consonant within the 5-odd-limit, and one that
is dissonant (the 8:15).