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

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 (%)	-27.1	-2.2	+15.4	+45.9	+16.5	+44.9	-29.2	-5.8	+48.8	-11.7	-21.0
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	Approximate ratios	Ups and downs notation
0	0	1/1	D
1	10.4		^D, E♭♭
2	20.9		^^D, ^E♭♭
3	31.3		^3D, ^^E♭♭
4	41.7	40/39, 41/40, 42/41, 43/42, 44/43	^4D, ^3E♭♭
5	52.2	33/32, 34/33, 35/34	v4D♯, ^4E♭♭
6	62.6	29/28	v3D♯, v4E♭
7	73	24/23	vvD♯, v3E♭
8	83.5	21/20, 43/41	vD♯, vvE♭
9	93.9		D♯, vE♭
10	104.3	17/16	^D♯, E♭
11	114.8	31/29, 46/43, 47/44	^^D♯, ^E♭
12	125.2	43/40	^3D♯, ^^E♭
13	135.7	40/37	^4D♯, ^3E♭
14	146.1	25/23, 37/34	v4D𝄪, ^4E♭
15	156.5	23/21, 35/32	v3D𝄪, v4E
16	167	11/10, 43/39	vvD𝄪, v3E
17	177.4	31/28, 41/37	vD𝄪, vvE
18	187.8	29/26, 39/35	D𝄪, vE
19	198.3	28/25, 37/33, 46/41	E
20	208.7	35/31, 44/39	^E, F♭
21	219.1	42/37	^^E, ^F♭
22	229.6	8/7	^3E, ^^F♭
23	240	23/20	^4E, ^3F♭
24	250.4	37/32	v4E♯, ^4F♭
25	260.9	43/37	v3E♯, v4F
26	271.3	48/41	vvE♯, v3F
27	281.7	20/17	vE♯, vvF
28	292.2		E♯, vF
29	302.6	25/21, 31/26	F
30	313		^F, G♭♭
31	323.5	35/29, 41/34, 47/39	^^F, ^G♭♭
32	333.9	40/33	^3F, ^^G♭♭
33	344.3	39/32	^4F, ^3G♭♭
34	354.8	43/35	v4F♯, ^4G♭♭
35	365.2	21/17	v3F♯, v4G♭
36	375.7	41/33, 46/37	vvF♯, v3G♭
37	386.1	5/4	vF♯, vvG♭
38	396.5	39/31, 44/35	F♯, vG♭
39	407	43/34	^F♯, G♭
40	417.4	14/11	^^F♯, ^G♭
41	427.8	32/25, 41/32	^3F♯, ^^G♭
42	438.3		^4F♯, ^3G♭
43	448.7	48/37	v4F𝄪, ^4G♭
44	459.1	30/23, 43/33	v3F𝄪, v4G
45	469.6	21/16, 38/29	vvF𝄪, v3G
46	480	29/22, 33/25	vF𝄪, vvG
47	490.4		F𝄪, vG
48	500.9		G
49	511.3	39/29, 43/32, 47/35	^G, A♭♭
50	521.7	23/17	^^G, ^A♭♭
51	532.2	34/25	^3G, ^^A♭♭
52	542.6	26/19, 41/30	^4G, ^3A♭♭
53	553	11/8	v4G♯, ^4A♭♭
54	563.5		v3G♯, v4A♭
55	573.9	39/28, 46/33	vvG♯, v3A♭
56	584.3	7/5	vG♯, vvA♭
57	594.8	31/22	G♯, vA♭
58	605.2	44/31	^G♯, A♭
59	615.7	10/7	^^G♯, ^A♭
60	626.1	33/23	^3G♯, ^^A♭
61	636.5		^4G♯, ^3A♭
62	647	16/11	v4G𝄪, ^4A♭
63	657.4	19/13	v3G𝄪, v4A
64	667.8	25/17	vvG𝄪, v3A
65	678.3	34/23, 37/25	vG𝄪, vvA
66	688.7		G𝄪, vA
67	699.1		A
68	709.6		^A, B♭♭
69	720	44/29, 47/31	^^A, ^B♭♭
70	730.4	29/19, 32/21	^3A, ^^B♭♭
71	740.9	23/15, 43/28	^4A, ^3B♭♭
72	751.3	37/24	v4A♯, ^4B♭♭
73	761.7		v3A♯, v4B♭
74	772.2	25/16	vvA♯, v3B♭
75	782.6	11/7	vA♯, vvB♭
76	793		A♯, vB♭
77	803.5	35/22	^A♯, B♭
78	813.9	8/5	^^A♯, ^B♭
79	824.3	37/23	^3A♯, ^^B♭
80	834.8	34/21, 47/29	^4A♯, ^3B♭
81	845.2		v4A𝄪, ^4B♭
82	855.7	41/25	v3A𝄪, v4B
83	866.1	33/20	vvA𝄪, v3B
84	876.5		vA𝄪, vvB
85	887		A𝄪, vB
86	897.4	42/25, 47/28	B
87	907.8		^B, C♭
88	918.3	17/10	^^B, ^C♭
89	928.7	41/24	^3B, ^^C♭
90	939.1	43/25	^4B, ^3C♭
91	949.6		v4B♯, ^4C♭
92	960	40/23	v3B♯, v4C
93	970.4	7/4	vvB♯, v3C
94	980.9	37/21	vB♯, vvC
95	991.3	39/22	B♯, vC
96	1001.7	25/14, 41/23	C
97	1012.2		^C, D♭♭
98	1022.6		^^C, ^D♭♭
99	1033	20/11	^3C, ^^D♭♭
100	1043.5	42/23	^4C, ^3D♭♭
101	1053.9	46/25	v4C♯, ^4D♭♭
102	1064.3	37/20	v3C♯, v4D♭
103	1074.8		vvC♯, v3D♭
104	1085.2	43/23	vC♯, vvD♭
105	1095.7	32/17	C♯, vD♭
106	1106.1		^C♯, D♭
107	1116.5	40/21	^^C♯, ^D♭
108	1127	23/12	^3C♯, ^^D♭
109	1137.4		^4C♯, ^3D♭
110	1147.8	33/17	v4C𝄪, ^4D♭
111	1158.3	39/20, 41/21, 43/22	v3C𝄪, v4D
112	1168.7		vvC𝄪, v3D
113	1179.1		vC𝄪, vvD
114	1189.6		C𝄪, vD
115	1200	2/1	D