Revision as of 07:06, 19 October 2026 by Lucius Chiaraviglio(talk | contribs)(Create page, starting with the obligatory diatonic mapping and Bryan Deister's Leapweek mapping)
Due to the size of this tuning system, nearly half of the notes are missing in the standard diatonic mapping.
10
29
17
36
55
74
93
5
24
43
62
81
100
10
29
12
31
50
69
88
107
17
36
55
74
93
0
19
38
57
76
95
5
24
43
62
81
100
10
29
7
26
45
64
83
102
12
31
50
69
88
107
17
36
55
74
93
104
14
33
52
71
90
0
19
38
57
76
95
5
24
43
62
81
100
10
29
2
21
40
59
78
97
7
26
45
64
83
102
12
31
50
69
88
107
17
36
55
74
93
99
9
28
47
66
85
104
14
33
52
71
90
0
19
38
57
76
95
5
24
43
62
81
100
10
29
16
35
54
73
92
2
21
40
59
78
97
7
26
45
64
83
102
12
31
50
69
88
107
17
36
55
74
93
61
80
99
9
28
47
66
85
104
14
33
52
71
90
0
19
38
57
76
95
5
24
43
62
81
100
16
35
54
73
92
2
21
40
59
78
97
7
26
45
64
83
102
12
31
50
69
88
107
61
80
99
9
28
47
66
85
104
14
33
52
71
90
0
19
38
57
76
95
16
35
54
73
92
2
21
40
59
78
97
7
26
45
64
83
102
61
80
99
9
28
47
66
85
104
14
33
52
71
90
16
35
54
73
92
2
21
40
59
78
97
61
80
99
9
28
47
66
85
16
35
54
73
92
61
80
Leapweek + Pentacircle
It is possible to map 109edo by the stacking of fifths ~3/2 while getting all of the notes, but instead of the standard diatonic approach, it is necessary to make a mapping that spreads out the whole tone ~9/8 (19\109, made from stacking two fifths) to two keys right plus one key down-right, as demonstrated in Bryan Deister's 109edo improv (2026). Since the fifth of 109edo is mildly sharp, the quasi-Pythagorean major third (38\109) maps to a near-just undecimal (pentacircle) major third ~14/11, while the quasi-Pythagorean minor third (26\109) maps to a near-just (slightly flat) undecimal (pentacircle) minor third ~33/28, making 109edo a leapweek tuning, which also supports pentacircle clan (rank-3) and pentacircle (rank-4) temperaments since the pentacircle comma 896/891 is tempered out. The range is just over two octaves, with a few repeated notes to mitigate wrarpounds, and the octaves have a barely noticeable downward slant.
