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Pajara (pronounced /pəˈd͡ʒɑːrə/, with the J as in "jar") is a temperament with a half-octave period that represents both 7/5 and 10/7, so 50/49 is tempered out and it is in the jubilismic clan. The generator is in the neighborhood of 105-110 cents, so that period + generator represents 3/2. Period minus 2 generators is 5/4, which, if you work it out, implies that 2048/2025 is tempered out, so pajara is also in the diaschismic family. Finally, two 4/3s (or a 2/1 minus two generators) represents 7/4 as well as 16/9, so 64/63 is tempered out and pajara is in the Archytas clan. Tempering out any two of these commas (among others) produces the unique temperament, pajara.

The 10-note MOS and LsssLsssss almost-MOS are called the symmetric and pentachordal decatonic scales and were independently invented/discovered by Paul Erlich and Gene Ward Smith. They are often thought of as subsets of 22edo, without much loss of generality and accuracy.

Interval chains

There are two different mappings of the 11 limit. One is just called "pajara" and is slightly more complex but suffers almost no loss of accuracy compared to the 7 limit. The other, called "pajarous" to avoid confusion, loses some accuracy and there's little reason to use it unless you're using 22edo, which is the intersection of both systems.

Basic 7-limit pajara

771.81
878.86
985.90
1092.95
0.
107.05
214.10
321.14
428.19
14/9
5/3
7/4~16/9

1/1

9/8~8/7
6/5
9/7
171.81
278.86
385.90
492.95
600.
707.05
814.10
921.14
1028.19
10/9
7/6
5/4
4/3
7/5~10/7
3/2
8/5
12/7
9/5

11-limit pajara

344.92
451.80
558.69
665.57
772.46
879.34
986.23
1093.11
0.
106.89
213.77
320.66
427.54
534.43
641.31
748.20
855.08
11/9

11/8

14/9~11/7
5/3
7/4~16/9

1/1

9/8~8/7
6/5
14/9~9/7

16/11

18/11
944.92
1051.80
1158.69
65.57
172.46
279.34
386.23
493.11
600.
706.89
813.77
920.66
1027.54
1134.43
41.31
148.20
255.08

11/6


11/10~10/9
7/6
5/4
4/3
7/5~10/7
3/2
8/5
12/7
9/5


12/11

Pajarous

432.96
542.54
652.11
761.69
871.27
980.85
1090.42
0.
109.58
219.15
328.73
438.31
547.89
657.46
767.04
14/11

16/11
14/9
18/11~5/3
7/4~16/9

1/1

9/8~8/7
6/5~11/9
9/7
11/8

11/7
1032.96
1142.54
52.11
161.69
271.27
380.85
490.42
600.
709.58
819.15
928.73
1038.31
1147.89
57.46
167.04
20/11


12/11~10/9
7/6
5/4
4/3
7/5~10/7
3/2
8/5
12/7
9/5~11/6


11/10

MOSes

10-note (proper)

See 2L 8s.
The true MOS is called the "symmetric" decatonic scale, because it repeats exactly at the half-octave, so the symmetric scale starting from 7/5~10/7 is the same as the symmetric scale starting from 1/1. The near-MOS, LsssLsssss, in which only the 5-step interval violates the "no more than 2 intervals per class" rule, is called the "pentachordal" decatonic, because it consists of two identical "pentachords" plus a split 9/8~8/7 whole tone to complete the octave.

12-note (proper)

See 10L 2s.

Spectrum of Pajara Tunings by Eigenmonzos

EDO degree
Eigenmonzo
Decatonic seventh
7\12

700.000

3/2
701.955
41\70

702.857
34\58

703.448
61\104

703.846
27\46

704.348

14/11
704.377

10/9
704.399
74\126

704.762
47\80

705.000
114\194

705.155

6/5
705.214 (5 and 15 limit minimax)
67\114

705.263
87\148

705.405
20\34

705.882
93\158

706.329
73\124

706.452
126\214

706.542

11/9
706.574
53\90

706.667
139\236

706.780

5/4
706.843 (7 and 11 limit POTT)
86\146

706.849
119\202

706.931
33\56

707.143

12/11
707.234
112\190

707.368

15/11
707.390
79\134

707.463
125\212

707.547
46\78

707.692
105\178

707.865
59\100

708.000

11/8
708.114
72\122

708.196

11/10
708.749 (11 limit minimax)

9/7
708.771
13\22

709.091
58\98

710.204
45\76

710.526
122\206

710.680
77\130

710.769
109\184

710.870

7/6
711.043 (7 limit minimax)
32\54

711.111

13/11
711.151 (13 limit minimax)
83\140

711.429
51\86

711.628

16/15
711.731
70\118

711.864
19\32

712.500
44\74

713.5135

13/10
713.553
25\42

714.286
31\52

715.385

8/7
715.587
6\10

720.000

References


Music

12-22hexachordal Dirge and
12-22hexachordal Sonatina both by Joel Grant Taylor, in the hexachordal dodecatonic MODMOS.
Smoke Filled Bar by Chris Vaisvil, also in 12-22h.
Chord Sequence in Paul Erlich's Decatonic Major by Jake Freivald