Yahoo Tuning Groups Ultimate Backup tuning 79 MOS out of 159tET Joint Meantone-Pythagorean System for Maqam Music

Here is the Sagittal Notation `sa79` for the meantone fifth taken as principal generator.

0: 1/1 C
1: 15.096 cents C/| D\Y/
2: 30.192 cents C|) DY/
3: 45.287 cents C/|\ DY)
4: 60.383 cents C||) D\!!!/
5: 75.479 cents C||\ D!!!)
6: 90.575 cents C/||\ D\!!!
7: 105.671 cents C/||| D\!!/
8: 120.766 cents C|||) D!!/
9: 135.862 cents C/|||\ D!!)
10: 150.958 cents CX) D\!/
11: 166.054 cents CX\ D!)
12: 181.150 cents C/X\ D\!
13: 196.245 cents D
14: 211.341 cents D/| E\Y/
15: 226.437 cents D|) EY/
16: 241.533 cents D/|\ EY)
17: 256.629 cents D||) E\!!!/
18: 271.725 cents D||\ E!!!)
19: 286.820 cents D/||\ E\!!!
20: 301.916 cents D/||| E\!!/
21: 317.012 cents D|||) E!!/
22: 332.108 cents D/|||\ E!!)
23: 347.204 cents DX) E\!/
24: 362.299 cents DX\ E!)
25: 377.395 cents D/X\ E\!
26: 392.491 cents E
27: 407.587 cents E/| F\!!/
28: 422.683 cents E|) F!!/
29: 437.778 cents E/|\ F!!)
30: 452.874 cents E||) F\!/
31: 467.970 cents E||\ F!)
32: 483.066 cents E/||\ F\!
33: 498.162 cents F
34: 513.257 cents F/| G\Y/
35: 528.353 cents F|) GY/
36: 543.449 cents F/|\ GY)
37: 558.545 cents F||) G\!!!/
38: 573.641 cents F||\ G!!!)
39: 588.736 cents F/||\ G\!!!
40: 603.832 cents F/||| G\!!/
41: 618.928 cents F|||) G!!/
42: 634.024 cents F/|||\ G!!)
43: 649.120 cents FX) G\!/
44: 664.215 cents FX\ G!)
45: 679.311 cents F/X\ G\!
46: 694.407 cents G
47: 709.503 cents G/| A\Y/
48: 724.599 cents G|) AY/
49: 739.695 cents G/|\ AY)
50: 754.790 cents G||) A\!!!/
51: 769.886 cents G||\ A!!!)
52: 784.982 cents G/||\ A\!!!
53: 800.078 cents G/||| A\!!/
54: 815.174 cents G|||) A!!/
55: 830.269 cents G/|||\ A!!)
56: 845.365 cents GX) A\!/
57: 860.461 cents GX\ A!)
58: 875.557 cents G/X\ A\!
59: 890.653 cents A
60: 905.748 cents A/| B\Y/
61: 920.844 cents A|) BY/
62: 935.940 cents A/|\ BY)
63: 951.036 cents A||) B\!!!/
64: 966.132 cents A||\ B!!!)
65: 981.227 cents A/||\ B\!!!
66: 996.323 cents A/||| B\!!/
67: 1011.419 cents A|||) B!!/
68: 1026.515 cents A/|||\ B!!)
69: 1041.611 cents AX) B\!/
70: 1056.706 cents AX\ B!)
71: 1071.802 cents A/X\ B\!
72: 1086.898 cents B
73: 1101.994 cents B/| C\!!/
74: 1117.090 cents B|) C!!/
75: 1132.185 cents B/|\ C!!)
76: 1147.281 cents B||) C\!/
77: 1162.377 cents B||\ C!)
78: 1177.473 cents B/||\ C\!
79: 2/1 C

It looks more beautiful than I expected! Try the Scala keyboard with SA79 mapping. That's the default for playing Maqam Music. However, I was expecting to see the Sagittal apotome sharp and flat. They are nowhere to be seen?

----- Original Message -----
From: George D. Secor
To: tuning@yahoogroups.com
Sent: 14 Haziran 2005 Salı 0:38
Subject: [tuning] Re: Meantone Maquams

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > For 79 you speak of a "wolf of 711 cents". The wide fifth of 79
is
> > almost 714 cents. I don't understand your requirements well
enough
> > to see why 79 appeals to you. While it is a sort of meantone
tuning,
> > its best 4:5 is not arrived at by a chain of 4 fifths.
>
> It's not 79, it's 159. 79 is a MOS.

If the generator is 92deg159, then your best 4:5 is -15 generators
along the chain, not +4. However, if you wanted to consider the
tones separated by 19 generators as simply subtle variations of the
same notated pitch, then a 19-ET notation (with no new microtonal
symbols) would suffice. (But I think Ozan needs more than 19
pitches/octave.)

> > You expressed an interest in 31-ET, and also in flexible
intonation
> > and ratios of 7 (as I infer from your "superpythagorean"
comment.
> > Since 31 represents both 4:5 and 4:7 extremely well, is 11-limit
> > consistent, and is also one of the very best meantones available,
> > would you be interested in some sort of adaptive JI based on 217-
ET,
> > a multiple of 31?
>
> That would work, but it's got more notes in it that 159.

It depends on how you look at it. I was thinking that this is really
only 31 pitches/octave, with subtle variations in intonation that
could be indicated with little arrows that would guide students to
the desired pitch, but which Maqam masters would be free to
disregard, at their own discretion. You would never even come close
to using all 217 pitches, because you would only be modulating around
a circle of 31 (meantone) fifths.

> If you are
> going to take a multiple of a meantone system, the claims of 152 and
> 171 should be considered,

Yes, and as I pointed out, I don't expect that 19 pitches +
flexibility will be enough. Hmmm, now that I've said that, what
about two circles of 19? 38-ET would use the same Tartini
accidentals as 31-ET. All of the pitches of 152-ET can be arrived at
by increments up to +-2deg152, and there would be only 5 different
choices of pitch adjustment: down-large, down-small, none, up-small,
and up-large. Sagittal also has two small arrows for those, the
first two in the 152 row of Figure 9 of the Sagittal paper: the
smaller )|( is symmetrical, the larger )|~ assymetrical. The
Sagittal paper:
http://dkeenan.com/sagittal/Sagittal.pdf
also contains a footnote (#16 on page 20) suggesting that instruments
in 19, 31, or 38-ET could easily be used for JI, so this idea has
been around for at least a few years.

> but Ozan seems to find more interest in
> multiples of 53.

Okay, hold on a minute -- there's a connection to be made.

I believe you asked how Dave and I would notate 159. Scala will show
you if you enter "set nota sa159".

The first 7 symbols in the set:
159: |( ~|( /| |) (|( //| /|\ (|) )||( ~||( ||) ||\ (||
( /||) /||\
represent the best approximations of 5:7k (5103:5120), 17C
(4096:4131), 5C (80:81), 7C (63:64), 5:11S (44:45), 25C (6400:6561),
and 11M (32:33), respectively. The remaining symbols are their
apotome-complements.

But those are alterations to a chain of nominals generated by the
best fifth of 159. I think Ozan may want a notation that uses
nominals generated by a 159-meantone fifth (one degree smaller),
which would be something quite different. Gene, have you considered
looking at this as a chain of semi-159-meantone-fifths (46deg159)?
That's similar enough to 38-as-subset-of-152-ET that a chain of 38
tones could be notated with the Tartini symbols and fine-tuned as
increments +-2deg159.

--George

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--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Here is the Sagittal Notation `sa79` for the meantone fifth taken
as principal generator.
>
> 0: 1/1 C
> 1: 15.096 cents C/| D\Y/
> 2: 30.192 cents C|) DY/
> 3: 45.287 cents C/|\ DY)
> 4: 60.383 cents C||) D\!!!/
> 5: 75.479 cents C||\ D!!!)
> 6: 90.575 cents C/||\ D\!!!
> 7: 105.671 cents C/||| D\!!/
> 8: 120.766 cents C|||) D!!/
> 9: 135.862 cents C/|||\ D!!)
> 10: 150.958 cents CX) D\!/
> 11: 166.054 cents CX\ D!)
> 12: 181.150 cents C/X\ D\!
> 13: 196.245 cents D
> ...
>
> It looks more beautiful than I expected!

The sequence of accidentals is the same as for 72-ET, so you also
have semisharps and semiflats of 3 degrees.

> Try the Scala keyboard with SA79 mapping. That's the default for
playing Maqam Music. However, I was expecting to see the Sagittal
apotome sharp and flat. They are nowhere to be seen?

They're 6 degrees above and below the naturals:

0: 1/1 C
...
6: 90.575 cents C/||\
7: 105.671 cents D\!!/
...
13: 196.245 cents D

Ozan, you can experiment notating your MOS if you enter the pitches
in an .scl file and load that into Scala. (Or alternatively, you can
just enter "equal 159" and look for the MOS pitches.) You can then
enter:

set nota sa159 - to see how Sagittal notates your pitches with the
nominals in a chain of Pythagorean fifths
set nota sa19 - to see how many pitches (in a chain of meantone
fifths) can be distinguished using no microtonal accidentals
set nota sa38 - to see how many pitches (in a chain of meantone
fifths) can be distinguished using semi- and sesqui- (Tartini)
accidentals
set nota sa57n - to see how many pitches (in a chain of meantone
fifths) can be distinguished using the 1/3- and 2/3-sharp and -flat
accidentals (for which you could substitute the 43-tone symbol
sequence I have in the Tplus-53.gif file)

The "n" in sa57n is important, because if you leave it out, you won't
get a notation based on the native fifth of 57-ET;,instead it will be
notated as a subset of 171-ET.

For nominals based on a chain of 159-meantone fifths, I set the
notation to multiples of 19, because the 19-ET fifth is reasonably
close in size. You won't be able to go beyond 57, because "set nota
sa76" will notate the pitches as a subset of 152 (using its best
fifth); "set nota sa76n", although technically possible, isn't
implemented, because we judged a native-fifth 76-ET notation so
contorted as to be almost worthless.

Anyway, you should be able to see from the above that the meantone-
159 apotome is 8 degrees and that you'll need 7 symbols between the
natural and sharp to notate all of those (although your MOS may
require less). (This is not a lot, considering that 159-ET notation
based on its best fifth requires 14 symbols between the natural and
sharp.)

--George

79 MOS out of 159tET Joint Meantone-Pythagorean System for Maqam Music

🔗Ozan Yarman <ozanyarman@superonline.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗George D. Secor <gdsecor@yahoo.com>