User:BudjarnLambeth/Some tunings for Japanese scales

In my personal subjective opinion

The best-sounding tunings for most Japanese scales are:

• Meantone temperament in 55edo
• 2/11-comma meantone
• Meantone temperament in 43edo
• 1/5-comma meantone

Other tunings that aren't quite as good as those, but still very good, for most Japanese scales are:

• Any meantone tuning with a fifth between 697 ¢ (5/22-comma) and 701 ¢ (1/20-comma) - this includes 74, 43, 55, 67, 79, 91 and 12edo
  • (See User:BudjarnLambeth/Table of n-comma meantone generators.)
• Any undecental tuning - instead of 5-limit, this maps the scales as highly accurate no-5s, 13-limit scales, with no wolf intervals
• Any leapday tuning close to 29edo - instead of 5-limit, this maps the scales as highly accurate no-5s, 13-limit scales, with no wolf intervals
• Over-2 primodality

Tunings that sound bad to me include:

• The most obvious 5-limit just intonation interpetations of the scales: these have too many wolf intervals-between-intervals
• Pythagorean and similar tunings (e.g. schismic, garibaldi, cassandra, andromeda, 65edo, 53edo, 41edo - these have the same wolf problems as the just interpretations
• Any meantone tuning with fifths flatter than 2/9-comma (e.g. 31edo, quarter-comma, 50edo, 1/3-comma) - these include some tritones which are a bit sharper than 10/7, and to my ears those just sound unbearably bitter
• Any leapday tuning close to 46edo - the 10/7 tritone gets too sharp which makes the whole scale too bitter, like in the flatter meantone tunings

For all these tunings, any note will work as the tonic but my favourite is D tuned to 140-150 Hz.

The remainder of this page will list various Japanese scales in various tunings that I consider "good" for these scales.

I list all of the scales (including rotations) for 12, 29, 43 and 55 edos and the JI tunings.

For all other edos I only list 3 of the scales, but you can derive the rest from rotating those 3.

Japanese scales in 12edo

Hirajoshi step pattern

Akebono II

1\12
5\12
7\12
8\12
12\12

Hirajoshi or Kata-Kumoi

2\12
3\12
7\12
8\12
12\12

Hirajoshi Mode III or Kumoi II

4\12
5\12
9\12
11\12
12\12

Hirajoshi Mode V or Kumoi IV

4\12
6\12
7\12
11\12
12\12

Iwato

1\12
5\12
6\12
10\12
12\12

Kokin-Joshi step pattern

Akebono I

2\12
3\12
7\12
9\12
12\12

Han-Kumoi

2\12
5\12
7\12
8\12
12\12

Kokin-Joshi

1\12
5\12
7\12
10\12
12\12

Minor pentatonic step pattern

Minor pentatonic or min'yo

3\12
5\12
7\12
10\12
12\12

Major pentatonic or ryosen

2\12
4\12
7\12
9\12
12\12

Ritusen

2\12
5\12
7\12
9\12
12\12

Japanese scales in meantone tunings

91edo (~1/7-comma)

The others can be derived by rotating these.

Hirajoshi or Kata-Kumoi

15\91
23\91
53\91
61\91
91\91

Akebono I

15\91
23\91
53\91
68\91
91\91

Minor pentatonic or min'yo

23\91
38\91
53\91
76\91
91\91

79edo

The others can be derived by rotating these.

Hirajoshi or Kata-Kumoi

13\79
20\79
46\79
53\79
79\79

Akebono I

13\79
20\79
46\79
59\79
79\79

Minor pentatonic or min'yo

20\79
33\79
46\79
66\79
79\79

67edo (~1/6-comma)

The others can be derived by rotating these.

Hirajoshi or Kata-Kumoi

11\67
17\67
39\67
45\67
67\67

Akebono I

11\67
17\67
39\67
50\67
67\67

Minor pentatonic or min'yo

17\67
28\67
39\67
56\67
67\67

55edo

Hirajoshi step pattern

Akebono II

5\55
23\55
32\55
37\55
55\55

Hirajoshi or Kata-Kumoi

9\55
14\55
32\55
37\55
55\55

Hirajoshi Mode III or Kumoi II

18\55
23\55
41\55
50\55
55\55

Hirajoshi Mode V or Kumoi IV

18\55
28\55
32\55
50\55
55\55

Iwato

5\55
23\55
28\55
46\55
55\55

Kokin-Joshi step pattern

Akebono I

9\55
14\55
32\55
41\55
55\55

Han-Kumoi

9\55
23\55
32\55
37\55
55\55

Kokin-Joshi

5\55
23\55
32\55
46\55
55\55

Major pentatonic step pattern

Major pentatonic or ryosen

9\55
18\55
32\55
41\55
55\55

Minor pentatonic or min'yo

14\55
23\55
32\55
46\55
55\55

Ritusen

9\55
23\55
32\55
41\55
55\55

43edo (~1/5-comma)

Hirajoshi step pattern

Akebono II

4\43
18\43
25\43
29\43
43\43

Hirajoshi or Kata-Kumoi

7\43
11\43
25\43
29\43
43\43

Hirajoshi Mode III or Kumoi II

14\43
18\43
32\43
39\43
43\43

Hirajoshi Mode V or Kumoi IV

14\43
22\43
25\43
39\43
43\43

Iwato

4\43
18\43
22\43
36\43
43\43

Kokin-Joshi step pattern

Akebono I

7\43
11\43
25\43
32\43
43\43

Han-Kumoi

7\43
18\43
25\43
29\43
43\43

Kokin-Joshi

4\43
18\43
25\43
36\43
43\43

Major pentatonic step pattern

Major pentatonic or ryosen

7\43
14\43
25\43
32\43
43\43

Minor pentatonic or min'yo

11\43
18\43
25\43
36\43
43\43

Ritusen

7\43
18\43
25\43
32\43
43\43

74edo (~3/14-comma)

The others can be derived by rotating these.

Hirajoshi or Kata-Kumoi

12\74
19\74
43\74
50\74
74\74

Akebono I

12\74
19\74
43\74
55\74
74\74

Minor pentatonic or min'yo

19\74
31\74
43\74
62\74
74\74

105edo (~2/9-comma, ~meantone CTE tuning)

The others can be derived by rotating these.

Hirajoshi or Kata-Kumoi

17\105
27\105
61\105
71\105
105\105

Akebono I

17\105
27\105
61\105
78\105
105\105

Minor pentatonic or min'yo

27\105
44\105
61\105
88\105
105\105

Japanese scales in undecental or leapday tunings

70edo

The others can be derived by rotating these.

Hirajoshi or Kata-Kumoi

12\70
17\70
41\70
46\70
70\70

Akebono I

12\70
17\70
41\70
53\70
70\70

Minor pentatonic or min'yo

17\70
29\70
41\70
58\70
70\70

99edo

The others can be derived by rotating these.

Hirajoshi or Kata-Kumoi

17\99
24\99
58\99
65\99
99\99

Akebono I

17\99
24\99
58\99
75\99
99\99

Minor pentatonic or min'yo

24\99
41\99
58\99
82\99
99\99

29edo

Hirajoshi step pattern

Akebono II

2\29
12\29
17\29
19\29
29\29

Hirajoshi or Kata-Kumoi

5\29
7\29
17\29
19\29
29\29

Hirajoshi Mode III or Kumoi II

10\29
12\29
22\29
27\29
29\29

Hirajoshi Mode V or Kumoi IV

10\29
15\29
17\29
27\29
29\29

Iwato

2\29
12\29
14\29
24\29
29\29

Kokin-Joshi step pattern

Akebono I

5\29
7\29
17\29
22\29
29\29

Han-Kumoi

5\29
12\29
17\29
19\29
29\29

Kokin-Joshi

2\29
12\29
17\29
24\29
29\29

Minor pentatonic step pattern

Minor pentatonic or min'yo

7\29
12\29
17\29
24\29
29\29

Major pentatonic or ryosen

5\29
10\29
17\29
22\29
29\29

Ritusen

5\29
12\29
17\29
22\29
29\29

104edo

The others can be derived by rotating these.

Hirajoshi or Kata-Kumoi

18\104
25\104
61\104
68\104
104\104

Akebono I

18\104
25\104
61\104
79\104
104\104

Minor pentatonic or min'yo

25\104
43\104
61\104
86\104
104\104

75edo

The others can be derived by rotating these.

Hirajoshi or Kata-Kumoi

13\75
18\75
44\75
49\75
75\75

Akebono I

13\75
18\75
44\75
57\75
75\75

Minor pentatonic or min'yo

18\75
31\75
44\75
62\75
75\75

Japanese scales in primodal JI

Over-2

Hirajoshi step pattern

Akebono II

34/32
43/32
48/32
51/32
64/32

Hirajoshi or Kata-Kumoi

36/32
38/32
48/32
51/32
64/32

Hirajoshi Mode III or Kumoi II

40/32
43/32
54/32
60/32
64/32

Hirajoshi Mode V or Kumoi IV

40/32
45/32
48/32
60/32
64/32

Iwato

68/64
86/64
91/64
114/64
128/64

Kokin-Joshi step pattern

Akebono I

36/32
38/32
48/32
54/32
64/32

Han-Kumoi

36/32
43/32
48/32
51/32
64/32

Kokin-Joshi

34/32
43/32
48/32
57/32
64/32

Major pentatonic step pattern

Major pentatonic or ryosen

36/32
40/32
48/32
54/32
64/32

Minor pentatonic or min'yo

38/32
43/32
48/32
57/32
64/32

Ritusen

36/32
43/32
48/32
54/32
64/32

To-do

Tunings that I have yet to try properly and plan to try in future:

• Over-3, -5, -7, -11, -13, -17, -19 & -23 primodality
  • Semiprime modes of the above
• Compton in 84edo & 96edo
• Narrowed compton tunings
• Augmented tunings
• Diminished tunings
• Pajara tunings
• Diaschismic tunings