Notating 159 equal

If we had a Turkish notation scheme for 53, we could adapt it for
159 by adding a 1/3 comma symbol, which could be thought of as a
symbol for 225/224. However, Scala does not give anything about
Turkish notation for 53-et. Below is what it has for 159:

0: C
1: C>
2: C>>
3: C/
4: C7
5: C7>
6: C) Db(
7: C7/ DbL<
8: C77 DbL
9: C#( Db\
10: C#L< Db<<
11: C#L Db<
12: C#\ Db
13: C#<< Db>
14: C#< Db>>
15: C# Db/
16: C#> Db7
17: C#>> Db7>
18: C#/ Db)
19: C#7 DLL
20: C#7> DL\
21: C#) D(
22: DL<
23: DL
24: D\
25: D<<
26: D<
27: D
28: D>
29: D>>
30: D/
31: D7
32: D7>
33: D) Eb(
34: D7/ EbL<
35: D77 EbL
36: D#( Eb\
37: D#L< Eb<<
38: D#L Eb<
39: D#\ Eb
40: D#<< Eb>
41: D#< Eb>>
42: D# Eb/
43: D#> Eb7
44: D#>> Eb7>
45: D#/ Eb)
46: D#7 ELL
47: D#7> EL\
48: D#) E(
49: EL<
50: EL
51: E\
52: E<<
53: E<
54: E
55: E> Fb7
56: E>> Fb7>
57: E/ Fb)
58: E7 FLL
59: E7> FL\
60: E) F(
61: E7/ FL<
62: E77 FL
63: E#( F\
64: E#L< F<<
65: E#L F<
66: F
67: F>
68: F>>
69: F/
70: F7
71: F7>
72: F) Gb(
73: F7/ GbL<
74: F77 GbL
75: F#( Gb\
76: F#L< Gb<<
77: F#L Gb<
78: F#\ Gb
79: F#<< Gb>
80: F#< Gb>>
81: F# Gb/
82: F#> Gb7
83: F#>> Gb7>
84: F#/ Gb)
85: F#7 GLL
86: F#7> GL\
87: F#) G(
88: GL<
89: GL
90: G\
91: G<<
92: G<
93: G
94: G>
95: G>>
96: G/
97: G7
98: G7>
99: G) Ab(
100: G7/ AbL<
101: G77 AbL
102: G#( Ab\
103: G#L< Ab<<
104: G#L Ab<
105: G#\ Ab
106: G#<< Ab>
107: G#< Ab>>
108: G# Ab/
109: G#> Ab7
110: G#>> Ab7>
111: G#/ Ab)
112: G#7 ALL
113: G#7> AL\
114: G#) A(
115: AL<
116: AL
117: A\
118: A<<
119: A<
120: A
121: A>
122: A>>
123: A/
124: A7
125: A7>
126: A) Bb(
127: A7/ BbL<
128: A77 BbL
129: A#( Bb\
130: A#L< Bb<<
131: A#L Bb<
132: A#\ Bb
133: A#<< Bb>
134: A#< Bb>>
135: A# Bb/
136: A#> Bb7
137: A#>> Bb7>
138: A#/ Bb)
139: A#7 BLL
140: A#7> BL\
141: A#) B(
142: BL<
143: BL
144: B\
145: B<<
146: B<
147: B
148: B> Cb7
149: B>> Cb7>
150: B/ Cb)
151: B7 CLL
152: B7> CL\
153: B) C(
154: B7/ CL<
155: B77 CL
156: B#( C\
157: B#L< C<<
158: B#L C<
159: C

Gene, please, you don't want a Turkish notation scheme based on 53. The symbols suggested by Mildan Niyazi Ayomak are simply mind-boggling. Kemal Ilerici's approach of using numbers is equally unpleasant. And besides, it is fundamentally wrong in my sight to alter the limmas in order to acquire the desired pitches using the sharps and flats. What we need is a two-headed lion, a notation that can easily switch from meantone to pythagorean. Why don't you focus on the 79 MOS instead? Is it too horrible a manner of thinking to consider it as seperate from 159?

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 12 Haziran 2005 Pazar 1:25
Subject: [tuning] Notating 159 equal

If we had a Turkish notation scheme for 53, we could adapt it for
159 by adding a 1/3 comma symbol, which could be thought of as a
symbol for 225/224. However, Scala does not give anything about
Turkish notation for 53-et. Below is what it has for 159:

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

Why don't you focus on the 79 MOS instead? Is it too horrible a manner
of thinking to consider it as seperate from 159?

159 is conceptually simpler and no harder to measure, if measuring is
required for some reason I don't really get. I think you are simply
adding a needless layer of complexity; after all the maqams don't have
nearly as many notes as 79 or 159 either, and choosing a subset of one
or a subset of the other isn't much different. 159 is easier on the
brain; it's simpler.

I disagree entirely. 159 is not conceptually any simpler, and it has the wrong fifth as the default generator interval. For the correct mapping of Rast to the diatonical white keys, one certainly needs the meantone fifth (and its pure fifth complement) by default.

Also, jumping from C to G\ (in meantone notation) gives you Suz-i Dilara instead of Rast on the white keys. That's the biggest bonus of 79MOS, a possible switch between meantone to pythagorean in a snap. What's more, you don't require any accidentals for either scale if you place a notation indicator (such as M to P, etc...)
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 13 Haziran 2005 Pazartesi 13:11
Subject: [tuning] Re: Notating 159 equal

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

Why don't you focus on the 79 MOS instead? Is it too horrible a manner
of thinking to consider it as seperate from 159?

159 is conceptually simpler and no harder to measure, if measuring is
required for some reason I don't really get. I think you are simply
adding a needless layer of complexity; after all the maqams don't have
nearly as many notes as 79 or 159 either, and choosing a subset of one
or a subset of the other isn't much different. 159 is easier on the
brain; it's simpler.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> I disagree entirely. 159 is not conceptually any simpler, and it has
the wrong fifth as the default generator interval.

How can an equal temperament possibly not be simpler than a MOS, and
what does it matter if it has a good fifth and a meantone fifth? It
was chosen to have that.

> Also, jumping from C to G\ (in meantone notation) gives you Suz-i
Dilara instead of Rast on the white keys. That's the biggest bonus of
79MOS, a possible switch between meantone to pythagorean in a snap.

Anything you can do in the MOS you can do in 159, so I don't see the
point here. Isn't this a *theoretical* tuning? Am I missing the point
here? Anyway, the MOS is fine, but I don't think it makes things simpler.

So, should we abondon all hope when defining pentatonic systems, and stuff them all into a single diatonical package even when there is not a single reference to a diatonical gamut? Is that the conceptualization you suggest?

159 is not what I want, is not what I need, and I have nothing to do with it save to represent the correct pitches of the 79-tone system I proposed the ET way.

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 13 Haziran 2005 Pazartesi 22:13
Subject: [tuning] Re: Notating 159 equal

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> I disagree entirely. 159 is not conceptually any simpler, and it has
the wrong fifth as the default generator interval.

How can an equal temperament possibly not be simpler than a MOS, and
what does it matter if it has a good fifth and a meantone fifth? It
was chosen to have that.

> Also, jumping from C to G\ (in meantone notation) gives you Suz-i
Dilara instead of Rast on the white keys. That's the biggest bonus of
79MOS, a possible switch between meantone to pythagorean in a snap.

Anything you can do in the MOS you can do in 159, so I don't see the
point here. Isn't this a *theoretical* tuning? Am I missing the point
here? Anyway, the MOS is fine, but I don't think it makes things simpler.

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

> So, should we abondon all hope when defining pentatonic systems, and
stuff them all into a single diatonical package even when there is not
a single reference to a diatonical gamut? Is that the
conceptualization you suggest?

I'm suggesting if you need two sizes of fifths you use a system which
allows you enough flexibility to put them to use, and enough
conceptual simplicity people might actually accept it.

> 159 is not what I want, is not what I need, and I have nothing to do
with it save to represent the correct pitches of the 79-tone system I
proposed the ET way.

You havn't made clear how tne 79 MOS works, if it does, and it really
seems it actually shouldn't. 159, however, clearly can give both a 7
note Pythagorean and a 7 note meantone diatonic scale.

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 14 Haziran 2005 Salı 7:36
Subject: [tuning] Re: Notating 159 equal

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

> So, should we abondon all hope when defining pentatonic systems, and
stuff them all into a single diatonical package even when there is not
a single reference to a diatonical gamut? Is that the
conceptualization you suggest?

I'm suggesting if you need two sizes of fifths you use a system which
allows you enough flexibility to put them to use, and enough
conceptual simplicity people might actually accept it.

Why do you think 79 Mos is not flexible enough? 702 cents complementary fifth ties meantone to pythagorean and vice versa.

> 159 is not what I want, is not what I need, and I have nothing to do
with it save to represent the correct pitches of the 79-tone system I
proposed the ET way.

You havn't made clear how tne 79 MOS works, if it does, and it really
seems it actually shouldn't. 159, however, clearly can give both a 7
note Pythagorean and a 7 note meantone diatonic scale.

So can 79 MOS. In fact, you can get as much diatonical major scales as can be achieved by 159tET. I am, of course assuming 7.5 cent equivalences.

It's not clear how this is supposed to work. If you go around a circle
of fifths, you get two alternating sizes of fifths. If M is a meantone
fifth and P is a Pythagorean fifth, you get scales like MPMPMPP. How
are these going to be useful for maqams?

In exactly the way you delineated. Meantone fifth gives an E closer to 5/4, Pythagorean, to 81/64, Super-Pythagorean to 14/11. A significant number of Maqams require this precision in most cases. In order to specify the principal generator interval I can write M, P and SP to the staff wherever they may be required.