Yahoo Tuning Groups Ultimate Backup tuning Stearns 144-ET in ASCII

This is a good one.
--------------------------

144-ET Monzo ASCII adaptation of
Stearns 'crosshatch-Sims' notation

9 different symbols in addition to the letter-names:

+ > ^ #
- < v b
16&2/3� 33&1/3� 50� 100�
1/12 1/6 1/4 1/2 of a 'tone'

and ~
used in connection with all 8 as a 'mitigator'
of their actions, reduces the 'adjustment'
of the main symbol by 8&1/3� (= 1/24-tone)

DE- SEMI- /-------------- NOTATION ------------------\
GREE TONES

0 0.00 C
143 11.92 C-~
142 11.83 C-
141 11.75 C<~
140 11.67 C<
139 11.58 Cv~
138 11.50 Cv B^
137 11.42 B^~
136 11.33 B>
135 11.25 B>~
134 11.17 B+
133 11.08 B+~
132 11.00 B
131 10.92 B-~
130 10.83 B-
129 10.75 B<~
128 10.67 B<
127 10.58 Bv~
126 10.50 Bv (Bb^ A#^)
125 10.42 Bb^~ A#^~
124 10.33 Bb> A#>
123 10.25 Bb>~ A#>~
122 10.17 Bb+ A#+
121 10.08 Bb+~ A#+~
120 10.00 Bb A#
119 9.92 Bb-~ A#-~
118 9.83 Bb- A#-
117 9.75 Bb<~ A#<~
116 9.67 Bb< A#<
115 9.58 Bbv~ A#V~
114 9.50 (Bbv A#v) A^
113 9.42 A^~
112 9.33 A>
111 9.25 A>~
110 9.17 A+
109 9.08 A+~
108 9.00 A
107 8.92 A-~
106 8.83 A-
105 8.75 A<~
104 8.67 A<
103 8.58 Av~
102 8.50 Av (Ab^ G#^)
101 8.42 Ab^~ G#^~
100 8.33 Ab> G#>
99 8.25 Ab>~ G#>~
98 8.17 Ab+ G#+
97 8.08 Ab+~ G#+~
96 8.00 Ab G#
95 7.92 Ab-~ G#-~
94 7.83 Ab- G#-
93 7.75 Ab<~ G#<~
92 7.67 Ab< G#<
91 7.58 Abv~ G#v~
90 7.50 (Abv G#v) G^
89 7.42 G^~
88 7.33 G>
87 7.25 G>~
86 7.17 G+
85 7.08 G+~
84 7.00 G
83 6.92 G-~
82 6.83 G-
81 6.75 G<~
80 6.67 G<
79 6.58 Gv~
78 6.50 (F#^) Gv (Gb^)
77 6.42 F#^~ Gb^~
76 6.33 F#> Gb>
75 6.25 F#>~ Gb>~
74 6.17 F#+ Gb+
73 6.08 F#+~ Gb+~
72 6.00 F# Gb
71 5.92 F#-~ Gb-~
70 5.83 F#- Gb-
69 5.75 F#<~ Gb<~
68 5.67 F#< Gb<
67 5.58 F#v~ Gbv~
66 5.50 (F#v) F (Gbv)
65 5.42 F^~
64 5.33 F>
63 5.25 F>~
62 5.17 F+
61 5.08 F+~
60 5.00 F
59 4.92 F-~
58 4.83 F-
57 4.75 F<~
56 4.67 F<
55 4.58 Fv~
54 4.50 E^ Fv
53 4.42 E^~
52 4.33 E>
51 4.25 E>~
50 4.17 E+
49 4.08 E+~
48 4.00 E
47 3.92 E-~
46 3.83 E-
45 3.75 E<~
44 3.67 E<
43 3.58 Ev~
42 3.50 (D#^ Eb^) Ev
41 3.42 D#^~ Eb^~
40 3.33 D#> Eb>
39 3.25 D#>~ Eb>~
38 3.17 D#+ Eb+
37 3.08 D#+~ Eb+~
36 3.00 D# Eb
35 2.92 D#-~ Eb-~
34 2.83 D#- Eb-
33 2.75 D#<~ Eb<~
32 2.67 D#< Eb<
31 2.58 D#v~ Ebv~
30 2.50 D^ (D#v Ebv)
29 2.42 D^~
28 2.33 D>
27 2.25 D>~
26 2.17 D+
25 2.08 D+~
24 2.00 D
23 1.92 D-~
22 1.83 D-
21 1.75 D<~
20 1.67 D<
19 1.58 Dv~
18 1.50 (C#^ Db^) Dv
17 1.42 C#^~ Db^~
16 1.33 C#> Db>
15 1.25 C#>~ Db>~
14 1.17 C#+ Db+
13 1.08 C#+~ Dv+~
12 1.00 C# Db
11 0.92 C#-~ Db-~
10 0.83 C#- Db-
9 0.75 C#<~ Db<~
8 0.67 C#< Db<
7 0.58 C#v~ Dbv~
6 0.50 C^ (C#v Dbv)
5 0.42 C^~
4 0.33 C>
3 0.25 C>~
2 0.17 C+
1 0.08 C+~
0 0.00 C

-----------------------------------------------

index of enharmonicity = 1.395833...

= 201 different symbols
for 144 discrete pitches per 'octave'

using simplest possible notation for any degree
enharmonics only where necessary
- thus excluding those in ()

readily divided into smaller systems:

144-eq = (2^4)*(3^2) degrees

all possibilities of the matrix:

2^ 3^ # of degrees:

|1 0| = 2
|2 0| = 4
|3 0| = 8
|4 0| = 16

|0 1| = 3
|1 1| = 6
|2 1| = 12
|3 1| = 24
|4 1| = 48

|0 2| = 9
|1 2| = 18
|2 2| = 36
|3 2| = 72
|4 2| = 144

arranged in order of number of degrees:

|1 0| = 2 tritone
|0 1| = 3 augmented triad
|2 0| = 4 diminished 7th tetrad
|1 1| = 6 whole tones
|3 0| = 8
|0 2| = 9
|2 1| = 12 semitones
|4 0| = 16
|1 2| = 18 third-tones
|3 1| = 24 quarter-tones
|2 2| = 36 sixth-tones
|4 1| = 48 eighth-tones
|3 2| = 72 twelfth-tones
|4 2| = 144

144-eq contains all these divisions within it.

in addition, because 11 * 13 = 143,
144-eq approximates 11-eq and 13-eq extremely well:

11-eq:

2^( 1/11) = ~109.09�
2^(13/144) = ~108.33�

2^(1/11) / 2^(13/144) = ~0.76� = ~3/4� difference

13-eq:

2^( 1/13) = ~92.31� = ~92&1/3�
2^(11/144) = ~91.67� = ~91&2/3�

2^(1/13) / 2^(11/144) = ~0.64� = ~2/3� difference

13 smaller systems into which it divides exactly
2 into which it divides almost exactly

-monzo

Joseph L. Monzo....................monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html

|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |

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Stearns 144-ET in ASCII

🔗monz@xxxx.xxx

🔗Brett Barbaro <barbaro@xxxxxxxxx.xxxx>