mohajira approximations

wallyesterpaulrus a �crit :

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> > Does this mean it still refers to every *third* note of Blackjack.
> > Hope so, or I'll have to rewrite my notes... :)
> > J. pehrson
>
> that's right, and the great thing is that it happens no matter where
> you start, since every third note of 21 notes will always give you a
> 7-tone scale, and in the case of blackjack, always a mode of mohajira
> (in its 24-equal incarnation).

the mohajira series "justifies" "24-equal incarnation" as the simplest ET for
neutral thirds possible music, more than harmonic 3 "justifies" 12 ET.
(31 tet is slightly better, then 55 tet is specially very good, then 141 tet slightly better,
and perfection for a while is reached with 736).

--- In tuning@yahoogroups.com, jacques dudon <aeh@f...> wrote:
> wallyesterpaulrus a écrit :
>
> > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> > > Does this mean it still refers to every *third* note of
Blackjack.
> > > Hope so, or I'll have to rewrite my notes... :)
> > > J. pehrson
> >
> > that's right, and the great thing is that it happens no matter
where
> > you start, since every third note of 21 notes will always give
you a
> > 7-tone scale, and in the case of blackjack, always a mode of
mohajira
> > (in its 24-equal incarnation).
>
> the mohajira series "justifies" "24-equal incarnation" as the
simplest ET for
> neutral thirds possible music, more than harmonic 3 "justifies" 12
ET.
> (31 tet is slightly better, then 55 tet is specially very good,
then 141 tet slightly better,
> and perfection for a while is reached with 736).

what are your criteria?

wallyesterpaulrus wrote :

> --- In tuning@yahoogroups.com, jacques dudon <aeh@f...> wrote:
> > wallyesterpaulrus a �crit :
> >
> > > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> > > > Does this mean it still refers to every *third* note of
> Blackjack.
> > > > Hope so, or I'll have to rewrite my notes... :)
> > > > J. pehrson
> > >
> > > that's right, and the great thing is that it happens no matter
> where
> > > you start, since every third note of 21 notes will always give
> you a
> > > 7-tone scale, and in the case of blackjack, always a mode of
> mohajira
> > > (in its 24-equal incarnation).
> >
> > the mohajira series "justifies" "24-equal incarnation" as the
> simplest ET for
> > neutral thirds possible music, more than harmonic 3 "justifies" 12
> ET.
> > (31 tet is slightly better, then 55 tet is specially very good,
> then 141 tet slightly better,
> > and perfection for a while is reached with 736).
>
> what are your criteria?

Precision of the approximation of the generating interval for equal temperaments, or
% of chances to have a fully-differentially coherent scale for JI or unequal
temperaments.
I am not at all an advocate of 24 ET, but it is important to note that the consonance of
the neutral thirds (in regard of their differential coherence, which is highly musical,
as it applies to scales like Rast / Bayati and of course all modes of Mohajira)
justifies on its own 24 tones scales, independantly of the 3/2 consonance.
In other words, it means that the egyptians, using a lot 24 ET today, are not loosing
everything, fortunately.

--- In tuning@yahoogroups.com, jacques dudon <aeh@f...> wrote:
> wallyesterpaulrus wrote :
>
> > --- In tuning@yahoogroups.com, jacques dudon <aeh@f...> wrote:

> > > (31 tet is slightly better, then 55 tet is specially very good,
> > then 141 tet slightly better,
> > > and perfection for a while is reached with 736).
> >
> > what are your criteria?
>
> Precision of the approximation of the generating interval for equal
>temperaments,

ok . . .

> or
> % of chances to have a fully-differentially coherent scale for JI
>or unequal
> temperaments.

this you'll have to clarify. can you give some examples?
what "chances" are you referring to?

> I am not at all an advocate of 24 ET, but it is important to note
that the consonance of
> the neutral thirds (in regard of their differential coherence,
which is highly musical,
> as it applies to scales like Rast / Bayati and of course all modes
of Mohajira)
> justifies on its own 24 tones scales, independantly of the 3/2
consonance.
> In other words, it means that the egyptians, using a lot 24 ET
today, are not loosing
> everything, fortunately.

the egyptians make little to no use of the neutral thirds
*harmonically*, which is the only situation where combinational tones
can be heard. so i don't buy the relevance of "differential
coherence" to this music . . .

wallyesterpaulrus a �crit :

> --- In tuning@yahoogroups.com, jacques dudon <aeh@f...> wrote:
> > wallyesterpaulrus wrote :
> >
> > > --- In tuning@yahoogroups.com, jacques dudon <aeh@f...> wrote:
>
> > > > (31 tet is slightly better, then 55 tet is specially very good,
> > > then 141 tet slightly better,
> > > > and perfection for a while is reached with 736).
> > >
> > > what are your criteria?
> >
> > Precision of the approximation of the generating interval for equal
> >temperaments,
>
> ok . . .
>
> > or
> > % of chances to have a fully-differentially coherent scale for JI
> >or unequal
> > temperaments.
>
> this you'll have to clarify. can you give some examples?
> what "chances" are you referring to?

For what we were talking about, if you start with an equal division of the octave
that provides a good approximation of the interval you want to be -c, there will
be less to refine and you will be able to have at once a maximum of them.

> > I am not at all an advocate of 24 ET, but it is important to note
> that the consonance of
> > the neutral thirds (in regard of their differential coherence,
> which is highly musical,
> > as it applies to scales like Rast / Bayati and of course all modes
> of Mohajira)
> > justifies on its own 24 tones scales, independantly of the 3/2
> consonance.
> > In other words, it means that the egyptians, using a lot 24 ET
> today, are not loosing
> > everything, fortunately.
>
> the egyptians make little to no use of the neutral thirds
> *harmonically*, which is the only situation where combinational tones
> can be heard. so i don't buy the relevance of "differential
> coherence" to this music . . .

I don't try to spray any belief about the universal relevance of differential coherence.
What I found is that differential-coherent models for musical scales have sound
qualities also when difference tones are not heard, or even generated.
But I don't agree with you if you say that neutral thirds are not used harmonically
in arab or even persian music. Listen to q�n�n or santoor techniques, for example.
And if this was an argument, you should say you don't buy the relevance either for
spectral coherence in these music. At least, what can be said is that tuning is very
important, and precise, in the arabic and persian culture. What tunings they use,
the question is open.

--- In tuning@yahoogroups.com, jacques dudon <aeh@f...> wrote:
> wallyesterpaulrus a écrit :
>
> At least, what can be said is that tuning is very
> important, and precise, in the arabic and persian culture.

on this we can agree!

wallyesterpaulrus a �crit :

> --- In tuning@yahoogroups.com, jacques dudon <aeh@f...> wrote:
> > wallyesterpaulrus a �crit :
> > At least, what can be said is that tuning is very
> > important, and precise, in the arabic and persian culture.
>
> on this we can agree!

I have no doubt. Then differential coherence, melodic coherence, spectral coherence,
(any other ?) are good tools, and that converge sometimes, to help us to understand
tunings done mostly by ear, when not determinated by instrument makers, who have
different logics. Ambiguity between close intervals showing different "polarities" of the
same entity (especially such as the neutral third...) can also be considered as a good reason,
in some instruments, to use something in the middle, as we know. This does not means
that acoustics are always absent, nor that they are highly subjective. Reality is multiple.