115edo

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115edo

116edo →

Prime factorization	5 × 23
Step size	10.4348¢
Fifth	67\115 (699.13¢)
Semitones (A1:m2)	9:10 (93.91¢ : 104.3¢)
Consistency limit	7
Distinct consistency limit	7

115 equal divisions of the octave (abbreviated 115edo or 115ed2), also called 115-tone equal temperament (115tet) or 115 equal temperament (115et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 115 equal parts of about 10.4 ¢ each. Each step represents a frequency ratio of 2^1/115, or the 115th root of 2.

115edo tempers out 1594323/1562500 (unicorn comma) and 2109375/2097152 (semicomma) in the 5-limit, as well as 43046721/41943040 and 30958682112/30517578125 (trisedodge comma); 225/224, 1728/1715, and 9920232/9765625 in the 7-limit. 115edo supports the newspeak temperament, tempering out 441/440, 1375/1372, and 1944/1925 in the 11-limit. The wizardharry comma, 4000/3993 is also tempered out in 115edo.

Odd harmonics

Approximation of odd harmonics in 115edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	absolute (¢)	-2.82	-0.23	+1.61	+4.79	+1.73	+4.69	-3.05	-0.61	+5.10	-1.22	-2.19
	relative (%)	-27	-2	+15	+46	+17	+45	-29	-6	+49	-12	-21
Steps (reduced)		182 (67)	267 (37)	323 (93)	365 (20)	398 (53)	426 (81)	449 (104)	470 (10)	489 (29)	505 (45)	520 (60)

Intervals

Steps	Cents	Ups and downs notation	Approximate ratios
0	0	D	1/1
1	10.4348	↑D, E♭♭
2	20.8696	↑↑D, ↓8E♭	78/77
3	31.3043	↑3D, ↓7E♭	50/49, 56/55, 64/63
4	41.7391	↑4D, ↓6E♭	40/39
5	52.1739	↑5D, ↓5E♭	33/32
6	62.6087	↑6D, ↓4E♭	80/77
7	73.0435	↑7D, ↓3E♭	25/24
8	83.4783	↑8D, ↓↓E♭	21/20, 22/21
9	93.913	D♯, ↓E♭	55/52
10	104.348	↑D♯, E♭	35/33, 52/49
11	114.783	↑↑D♯, ↓8E	16/15
12	125.217	↑3D♯, ↓7E	14/13
13	135.652	↑4D♯, ↓6E
14	146.087	↑5D♯, ↓5E
15	156.522	↑6D♯, ↓4E	35/32
16	166.957	↑7D♯, ↓3E	11/10
17	177.391	↑8D♯, ↓↓E
18	187.826	D𝄪, ↓E	39/35, 49/44
19	198.261	E	28/25, 55/49
20	208.696	↑E, F♭	44/39
21	219.13	↑↑E, ↓8F	25/22
22	229.565	↑3E, ↓7F	8/7
23	240	↑4E, ↓6F
24	250.435	↑5E, ↓5F
25	260.87	↑6E, ↓4F	64/55, 65/56
26	271.304	↑7E, ↓3F	75/64
27	281.739	↑8E, ↓↓F	33/28
28	292.174	E♯, ↓F	13/11, 77/65
29	302.609	F	25/21
30	313.043	↑F, G♭♭	6/5
31	323.478	↑↑F, ↓8G♭	77/64
32	333.913	↑3F, ↓7G♭	40/33
33	344.348	↑4F, ↓6G♭	39/32
34	354.783	↑5F, ↓5G♭	49/40
35	365.217	↑6F, ↓4G♭
36	375.652	↑7F, ↓3G♭
37	386.087	↑8F, ↓↓G♭	5/4
38	396.522	F♯, ↓G♭	44/35, 49/39, 63/50
39	406.957	↑F♯, G♭
40	417.391	↑↑F♯, ↓8G	14/11, 80/63
41	427.826	↑3F♯, ↓7G	32/25, 50/39
42	438.261	↑4F♯, ↓6G
43	448.696	↑5F♯, ↓5G
44	459.13	↑6F♯, ↓4G	64/49
45	469.565	↑7F♯, ↓3G	21/16, 55/42
46	480	↑8F♯, ↓↓G	33/25
47	490.435	F𝄪, ↓G	65/49
48	500.87	G	4/3
49	511.304	↑G, A♭♭	35/26
50	521.739	↑↑G, ↓8A♭
51	532.174	↑3G, ↓7A♭
52	542.609	↑4G, ↓6A♭
53	553.043	↑5G, ↓5A♭	11/8
54	563.478	↑6G, ↓4A♭
55	573.913	↑7G, ↓3A♭	39/28
56	584.348	↑8G, ↓↓A♭	7/5
57	594.783	G♯, ↓A♭	55/39
58	605.217	↑G♯, A♭	78/55
59	615.652	↑↑G♯, ↓8A	10/7
60	626.087	↑3G♯, ↓7A	56/39
61	636.522	↑4G♯, ↓6A
62	646.957	↑5G♯, ↓5A	16/11
63	657.391	↑6G♯, ↓4A
64	667.826	↑7G♯, ↓3A
65	678.261	↑8G♯, ↓↓A	65/44, 77/52
66	688.696	G𝄪, ↓A	52/35
67	699.13	A	3/2
68	709.565	↑A, B♭♭
69	720	↑↑A, ↓8B♭	50/33
70	730.435	↑3A, ↓7B♭	32/21
71	740.87	↑4A, ↓6B♭	49/32
72	751.304	↑5A, ↓5B♭	77/50
73	761.739	↑6A, ↓4B♭
74	772.174	↑7A, ↓3B♭	25/16, 39/25
75	782.609	↑8A, ↓↓B♭	11/7, 63/40
76	793.043	A♯, ↓B♭
77	803.478	↑A♯, B♭	35/22, 78/49
78	813.913	↑↑A♯, ↓8B	8/5
79	824.348	↑3A♯, ↓7B
80	834.783	↑4A♯, ↓6B
81	845.217	↑5A♯, ↓5B	80/49
82	855.652	↑6A♯, ↓4B	64/39
83	866.087	↑7A♯, ↓3B	33/20
84	876.522	↑8A♯, ↓↓B
85	886.957	A𝄪, ↓B	5/3
86	897.391	B	42/25
87	907.826	↑B, C♭	22/13
88	918.261	↑↑B, ↓8C	56/33
89	928.696	↑3B, ↓7C
90	939.13	↑4B, ↓6C	55/32
91	949.565	↑5B, ↓5C
92	960	↑6B, ↓4C
93	970.435	↑7B, ↓3C	7/4
94	980.87	↑8B, ↓↓C	44/25
95	991.304	B♯, ↓C	39/22
96	1001.74	C	25/14
97	1012.17	↑C, D♭♭	70/39
98	1022.61	↑↑C, ↓8D♭
99	1033.04	↑3C, ↓7D♭	20/11
100	1043.48	↑4C, ↓6D♭	64/35
101	1053.91	↑5C, ↓5D♭
102	1064.35	↑6C, ↓4D♭
103	1074.78	↑7C, ↓3D♭	13/7
104	1085.22	↑8C, ↓↓D♭	15/8
105	1095.65	C♯, ↓D♭	49/26, 66/35
106	1106.09	↑C♯, D♭
107	1116.52	↑↑C♯, ↓8D	21/11, 40/21
108	1126.96	↑3C♯, ↓7D	48/25
109	1137.39	↑4C♯, ↓6D	77/40
110	1147.83	↑5C♯, ↓5D	64/33
111	1158.26	↑6C♯, ↓4D	39/20
112	1168.7	↑7C♯, ↓3D	49/25, 55/28, 63/32
113	1179.13	↑8C♯, ↓↓D	77/39
114	1189.57	C𝄪, ↓D
115	1200	D	2/1