Yahoo Tuning Groups Ultimate Backup tuning 34 note circulating temperament with 15 pure major thirds

Aside from the pure thirds, it also has 18 -1 brats; this is the best
of brats if you are looking for synchronized beating. The pure major
thirds tend to be with fifths which aren't very sharp either, so this
temperament has a sweet range along the circle of minor thirds. If you
like 11/9 neutral thirds, or 14/11 thirds, these are also available.

! chan34.scl
34 note hanson based circulating scale with 15 pure major thirds and
18 -1 brats
34
!
254754959781491/249729352508160
30071722855/28903860244
38421792648/36129825305
6759548793775/6243233812704
1081527807004/975505283235
14412856352274025/12786142848417792
576514254090961/499458705016320
991798286653/843680244960
960013575180847/799133928026112
30614793048041/24972935250816
5/4
638254280871377/499458705016320
150358614275/115615440976
48114756568/36129825305
1459280021371/1076419622880
270381951751/195101056647
60205443660021679/42620476161392640
576514254090961/399566964013056
30663265517723/20810779375680
4800067875904235/3196535712104448
21305517838327/13873852917120
25/16
8/5
50840497270643/31216169063520
12028689142/7225965061
424031442260527/249729352508160
1351909758755/780404226588
1727914373344/975505283235
2882571270454805/1598267856052224
230425355849681/124864676254080
24000339379521175/12786142848417792
960013575180847/499458705016320
412730869507/210920061240
2

🔗Ozan Yarman <ozanyarman@superonline.com>

Fantastic Gene. This proposition covers almost 5/4 of the Maqamat if one sacrifices the correct notation with the cycle of fifths. Can you perhaps construct a proportional beating version of my 67 and 79 tone MOS scales?

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 09 Eylül 2005 Cuma 12:42
Subject: [tuning] 34 note circulating temperament with 15 pure major thirds

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> Fantastic Gene. This proposition covers almost 5/4 of the Maqamat if
one sacrifices the correct notation with the cycle of fifths. Can you
perhaps construct a proportional beating version of my 67 and 79 tone
MOS scales?

If I did, I might have to give it in terms of cents, and not exactly,
as the ratios are getting out of hand. I've been doing this by taking
a linear temperament as the basis for the tuning of the circulating
temperament, which may not help with your MOS, as the corresponding
temperament is kind of strange. One of my problems with trying to work
on this is that I'm still not clear what it is you really want to do.
However, it certainly would be possible to try for a 159 tone
circulating temperament based on your MOS, which because of its slight
irregulariy may do something useful. The brat for 159 are the same as
for 53, of course, so there should be a lot of pure fifths in any such
arrangement.

More straightforward would be a schismatic circulating temperament
based on 53, with again a lot of pure fifths. Somewhere in there you
may or may not find something useful--who knows?

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> More straightforward would be a schismatic circulating temperament
> based on 53, with again a lot of pure fifths. Somewhere in there you
> may or may not find something useful--who knows?

If you are willing to check and see if maqams can be found somewhere
or other inside of an irregular circulating temperament, another thing
it would be interesting to try is 103. I've mentioned before some
other talents it has, but from the point of view of beat rations, it
is interesting in that it has a brat near -1, which would allow the
construction of a circulating temperament with a lot of -1 brats. This
is the ultimate brat, and the synchronized beats would be relatively slow.

🔗Ozan Yarman <ozanyarman@superonline.com>

Forget the ratios, the cent values shall be quite fine.

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 10 Eylül 2005 Cumartesi 21:01
Subject: [tuning] Re: 34 note circulating temperament with 15 pure major thirds

Can you perhaps construct a proportional beating version of my 67 and 79 tone MOS scales?

My temperament solution is strange? That's a peculiar adjective to define it.

One of my problems with trying to work on this is that I'm still not clear what it is you really want to do.

I am trying to represent both the just diatonic major scale and the Pythagorean diatonic major scale in one system that can transpose these over all the 12 semitones per octave with minimal damage and the least number of notes while also approximating 11 and 13 limit intervals with minimum error. 79 MOS 159-tET is the integral solution to my problems as it is.

However, it certainly would be possible to try for a 159 tone circulating temperament based on your MOS, which because of its slight irregulariy may do something useful. The brat for 159 are the same as for 53, of course, so there should be a lot of pure fifths in any such arrangement.

But if I were then to take 79 out of 159, would that be ok?

More straightforward would be a schismatic circulating temperament
based on 53, with again a lot of pure fifths. Somewhere in there you may or may not find something useful--who knows?

53 is all wrong for my purposes because of the Pythagorean diatonic major scale being default.

Cordially,
Ozan

🔗Ozan Yarman <ozanyarman@superonline.com>

That is a fabulous temperament! I can't believe I skipped it rashly some months ago. Probably the unusual 699 cents fifth probably turned me off at first sight. 711 cent fifth is also perfect for super-Pythagorean!

Can you improve it Gene? It seems to be an excellent complete solution to all the Maqamat.

Cordially,
Ozan

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 11 Eylül 2005 Pazar 0:24
Subject: [tuning] Re: 34 note circulating temperament with 15 pure major thirds

If you are willing to check and see if maqams can be found somewhere or other inside of an irregular circulating temperament, another thing it would be interesting to try is 103. I've mentioned before some other talents it has, but from the point of view of beat rations, it is interesting in that it has a brat near -1, which would allow the construction of a circulating temperament with a lot of -1 brats. This is the ultimate brat, and the synchronized beats would be relatively slow.

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> That is a fabulous temperament! I can't believe I skipped it rashly
some months ago. Probably the unusual 699 cents fifth probably turned
me off at first sight. 711 cent fifth is also perfect for
super-Pythagorean!

I do think it is interesting as a utility scale; I believe I put you
off partly because I mentioned supporting miracle as one of its talents.

> Can you improve it Gene? It seems to be an excellent complete
solution to all the Maqamat.

I may be able to solve the simultaneous equations to get a scale with
a lot of -1 brats; that would also be less regular, and so might work
better for you. But I can't promise anything for a temperament of this
size.

🔗Ozan Yarman <ozanyarman@superonline.com>

Gene, have you obtained any results in this direction?

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 11 Eylül 2005 Pazar 6:42
Subject: [tuning] Re: 34 note circulating temperament with 15 pure major thirds

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> But if I were then to take 79 out of 159, would that be ok?

I'c creating circulating scales with this system, and experimenting
today, I think the number of simultaneous equations I need to solve is too large for 159 to work at all.

🔗Ozan Yarman <ozanyarman@superonline.com>

Gene,
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 11 Eylül 2005 Pazar 6:45
Subject: [tuning] Re: 34 note circulating temperament with 15 pure major thirds

I do think it is interesting as a utility scale; I believe I put you off partly because I mentioned supporting miracle as one of its talents.

Maybe.

> Can you improve it Gene? It seems to be an excellent complete
solution to all the Maqamat.

I may be able to solve the simultaneous equations to get a scale with a lot of -1 brats; that would also be less regular, and so might work better for you. But I can't promise anything for a temperament of this size.

I'm sure you can come up with something very interesting.

Cordially,
Ozan