Danny's maqams in pi ratio scales

The Saba maqam approximation is pretty good for my taste. What about Usshaq,
Huzzam, Karcighar and Kurdi?

Cordially,
Ozan

----- Original Message -----
From: "Danny Wier" <dawiertx@sbcglobal.net>
To: <tuning-math@yahoogroups.com>
Sent: 23 Nisan 2005 Cumartesi 23:41
Subject: Re: [tuning-math] more on e-pi ratios

>
> Ozan Yarman wrote (about my e/pi tuning):
>
> > I do, I do. Can we build maqams with these?
>
> Since it's close to 53-EDO, you can in the Turkish system. The octave is
> stretched by 7.42 cents, which might be a lot, unless you're tuning a
piano.
> The fifth is 4.34 cents sharp and the fourth is 3.08 cents sharp. This may
> create a problem when multiple octaves are piled on, unless you temper
down
> a 0.92-cent "schisma" every tone or something.
>
> Maqam as-Saba (the full minor tenth range) in Arabic tuning, treating the
E
> half-flat as two commas flat, could be tuned: 0.00 (Dugah/D/Re), 159.78,
> 295.95, 410.34, 683.60, 797.07, 1002.25, 1116.64, 1389.89, 1503.37.
>
>

Ozan Yarman wrote:

> The Saba maqam approximation is pretty good for my taste. What about > Usshaq,
> Huzzam, Karcighar and Kurdi?

I'm more familiar with Arabic terms than Turkish, so I'd have to look those up. I know what Kurd and Karjighar are, but Usshaq and Huzzam have different names in Arabic. But I'm sure they can all be accomodated.

But I make no spectacular claims of my scale being practical. What I found was an odd coincidence, which led me to favor 53-tone over everything else, as though it was some divine message. (Okay, I'm exaggerating.)

I still need to test tunings for prime-limits beyond 5, and naturally, I'll have to come up a notation system. Something a little like Bohlen-Pierce.

(For the Scalaphiles out there, the period or "octave" is 1981.795355 cents; the generator or "fifth" is 1731.234049 cents. After eight consecutive "fifths", the comma appears, about a 76th of the generator and an 87th of the period. I'm calculating the next smaller interval beyond the "schisma", which may involve dividing pi into thousands of quasi-equal steps.)

~Danny~

I wrote:

> (For the Scalaphiles out there, the period or "octave" is 1981.795355 > cents;
> the generator or "fifth" is 1731.234049 cents. After eight consecutive
> "fifths", the comma appears, about a 76th of the generator and an 87th of
> the period. I'm calculating the next smaller interval beyond the > "schisma",
> which may involve dividing pi into thousands of quasi-equal steps.)

As an afterthought, I prefer to use e/1 (~ 1731.234049 cents) as the period and pi/e (~ 250.561306 cents) as the generator. That makes an "octave" (I need a better name... "diapason"?) seven "tones" less a "comma".

Dear Danny,

Can we work on 29tET and make it an adaptive tuning so as to preserve the
thirds? This way, we may reach an optimal system where all maqams can be
expressed in any key with as little error as possible. Perhaps your
trancendental numbers may help us here.

Cordially,
Ozan

----- Original Message -----
From: "Danny Wier" <dawiertx@sbcglobal.net>
To: <tuning-math@yahoogroups.com>
Sent: 24 Nisan 2005 Pazar 2:48
Subject: Re: [tuning-math] Danny's maqams in pi ratio scales

>
> Ozan Yarman wrote:
>
> > The Saba maqam approximation is pretty good for my taste. What about
> > Usshaq,
> > Huzzam, Karcighar and Kurdi?
>
> I'm more familiar with Arabic terms than Turkish, so I'd have to look
those
> up. I know what Kurd and Karjighar are, but Usshaq and Huzzam have
different
> names in Arabic. But I'm sure they can all be accomodated.
>
> But I make no spectacular claims of my scale being practical. What I found
> was an odd coincidence, which led me to favor 53-tone over everything
else,
> as though it was some divine message. (Okay, I'm exaggerating.)
>
> I still need to test tunings for prime-limits beyond 5, and naturally,
I'll
> have to come up a notation system. Something a little like Bohlen-Pierce.
>
> (For the Scalaphiles out there, the period or "octave" is 1981.795355
cents;
> the generator or "fifth" is 1731.234049 cents. After eight consecutive
> "fifths", the comma appears, about a 76th of the generator and an 87th of
> the period. I'm calculating the next smaller interval beyond the
"schisma",
> which may involve dividing pi into thousands of quasi-equal steps.)
>
> ~Danny~
>
>