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.
