360edo

← 359edo

360edo

361edo →

Prime factorization	23 × 32 × 5 (highly composite)
Step size	3.33333 ¢
Fifth	211\360 (703.333 ¢)
Semitones (A1:m2)	37:25 (123.3 ¢ : 83.33 ¢)
Dual sharp fifth	211\360 (703.333 ¢)
Dual flat fifth	210\360 (700 ¢) (→ 7\12)
Dual major 2nd	61\360 (203.333 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

360edo is consistent in the 7-limit. Its 5-limit patent val supports misty temperament, and in the 7-limit 360edo supports the trimisty (name proposed by Eliora) 63 & 99 temperament with the comma basis 10976/10935, 2097152/2083725, which is similar to the misty temperament but has a period of 1/9 rather than 1/3 octave. In addition, 360edo provides the optimal patent val for the 41 & 360 temperament with comma basis 10976/10935, 16384000000/16209796869, on which it has lower badness than any other 7-limit temperament for which 360edo gives the optimal patent val. It also supports 12 & 360 with the comma basis 390625/388962, 67108864/66430125. 360edo tempers out the linus comma, meaning 15/14 corresponds to 1/10th of the octave, 36 steps.

360edo provides the optimal patent val in the 11-limit, and otherwise a good tuning in the 13-limit for the degrees temperament, the 80&140 temperament with period 20.

As an interval size measure

360 is the 13th highly composite EDO, with many proper divisors: 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180. One step of 360edo is known as the Dröbisch angle, being first proposed by Moritz Dröbisch in the 19th century at first merely by the name "angle".

Odd harmonics

Approximation of odd harmonics in 360edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+1.38	+0.35	+1.17	-0.58	-1.32	-0.53	-1.60	-1.62	-0.85	-0.78	-1.61
	Relative (%)	+41.3	+10.6	+35.2	-17.3	-39.5	-15.8	-48.1	-48.7	-25.4	-23.4	-48.2
Steps (reduced)		571 (211)	836 (116)	1011 (291)	1141 (61)	1245 (165)	1332 (252)	1406 (326)	1471 (31)	1529 (89)	1581 (141)	1628 (188)

Table of intervals

Eliora proposes notating 360edo with calendar dates, Jan 1 being the tonic, Jan 2 being the next step, etc, and each month having even 30 days. The notation is convenient because 1 month in this scenario is equal to 1 semitone, and corresponds to 12edo.

Any other notation system involving the number 360 can also be used.

Steps	Cents	Approximate ratios	Ups and downs notation (Dual flat fifth 210\360)	Ups and downs notation (Dual sharp fifth 211\360)	Calendar notation
0	0	1/1	D	D	January 1
1	3.33		^D, ^E♭♭	^D, ^13E♭♭	January 2
2	6.67		^^D, ^^E♭♭	^^D, ^14E♭♭	January 3
3	10		^3D, ^3E♭♭	^3D, ^15E♭♭	January 4
4	13.33		^4D, ^4E♭♭	^4D, ^16E♭♭	January 5
5	16.67		^5D, ^5E♭♭	^5D, ^17E♭♭	January 6
6	20	86/85	^6D, ^6E♭♭	^6D, ^18E♭♭	January 7
7	23.33		^7D, ^7E♭♭	^7D, v18E♭	January 8
8	26.67	65/64, 66/65	^8D, ^8E♭♭	^8D, v17E♭	January 9
9	30	58/57	^9D, ^9E♭♭	^9D, v16E♭	January 10
10	33.33	52/51	^10D, ^10E♭♭	^10D, v15E♭	January 11
11	36.67	48/47	^11D, ^11E♭♭	^11D, v14E♭	January 12
12	40	44/43	^12D, ^12E♭♭	^12D, v13E♭	January 13
13	43.33	40/39	^13D, ^13E♭♭	^13D, v12E♭	January 14
14	46.67	38/37	^14D, ^14E♭♭	^14D, v11E♭	January 15
15	50		^15D, v15E♭	^15D, v10E♭	January 16
16	53.33	33/32	v14D♯, v14E♭	^16D, v9E♭	January 17
17	56.67	31/30, 94/91	v13D♯, v13E♭	^17D, v8E♭	January 18
18	60	88/85	v12D♯, v12E♭	^18D, v7E♭	January 19
19	63.33		v11D♯, v11E♭	v18D♯, v6E♭	January 20
20	66.67	80/77	v10D♯, v10E♭	v17D♯, v5E♭	January 21
21	70		v9D♯, v9E♭	v16D♯, v4E♭	January 22
22	73.33		v8D♯, v8E♭	v15D♯, v3E♭	January 23
23	76.67	23/22	v7D♯, v7E♭	v14D♯, vvE♭	January 24
24	80		v6D♯, v6E♭	v13D♯, vE♭	January 25
25	83.33		v5D♯, v5E♭	v12D♯, E♭	January 26
26	86.67	41/39	v4D♯, v4E♭	v11D♯, ^E♭	January 27
27	90	99/94	v3D♯, v3E♭	v10D♯, ^^E♭	January 28
28	93.33		vvD♯, vvE♭	v9D♯, ^3E♭	January 29
29	96.67	55/52	vD♯, vE♭	v8D♯, ^4E♭	January 30
30	100		D♯, E♭	v7D♯, ^5E♭	January 31
31	103.33	69/65	^D♯, ^E♭	v6D♯, ^6E♭	February 1
32	106.67	50/47	^^D♯, ^^E♭	v5D♯, ^7E♭	February 2
33	110		^3D♯, ^3E♭	v4D♯, ^8E♭	February 3
34	113.33		^4D♯, ^4E♭	v3D♯, ^9E♭	February 4
35	116.67	46/43	^5D♯, ^5E♭	vvD♯, ^10E♭	February 5
36	120	15/14	^6D♯, ^6E♭	vD♯, ^11E♭	February 6
37	123.33	102/95	^7D♯, ^7E♭	D♯, ^12E♭	February 7
38	126.67		^8D♯, ^8E♭	^D♯, ^13E♭	February 8
39	130	69/64	^9D♯, ^9E♭	^^D♯, ^14E♭	February 9
40	133.33		^10D♯, ^10E♭	^3D♯, ^15E♭	February 10
41	136.67	92/85	^11D♯, ^11E♭	^4D♯, ^16E♭	February 11
42	140		^12D♯, ^12E♭	^5D♯, ^17E♭	February 12
43	143.33		^13D♯, ^13E♭	^6D♯, ^18E♭	February 13
44	146.67	37/34	^14D♯, ^14E♭	^7D♯, v18E	February 14
45	150		^15D♯, v15E	^8D♯, v17E	February 15
46	153.33		v14D𝄪, v14E	^9D♯, v16E	February 16
47	156.67	104/95	v13D𝄪, v13E	^10D♯, v15E	February 17
48	160		v12D𝄪, v12E	^11D♯, v14E	February 18
49	163.33	100/91	v11D𝄪, v11E	^12D♯, v13E	February 19
50	166.67		v10D𝄪, v10E	^13D♯, v12E	February 20
51	170	32/29	v9D𝄪, v9E	^14D♯, v11E	February 21
52	173.33		v8D𝄪, v8E	^15D♯, v10E	February 22
53	176.67	31/28	v7D𝄪, v7E	^16D♯, v9E	February 23
54	180	91/82	v6D𝄪, v6E	^17D♯, v8E	February 24
55	183.33		v5D𝄪, v5E	^18D♯, v7E	February 25
56	186.67		v4D𝄪, v4E	v18D𝄪, v6E	February 26
57	190	77/69	v3D𝄪, v3E	v17D𝄪, v5E	February 27
58	193.33	85/76	vvD𝄪, vvE	v16D𝄪, v4E	February 28
59	196.67	28/25	vD𝄪, vE	v15D𝄪, v3E	March 1
60	200	64/57	E	v14D𝄪, vvE	March 2
61	203.33		^E, ^F♭	v13D𝄪, vE	March 3
62	206.67	98/87	^^E, ^^F♭	E	March 4
63	210	35/31	^3E, ^3F♭	^E, ^13F♭	March 5
64	213.33		^4E, ^4F♭	^^E, ^14F♭	March 6
65	216.67		^5E, ^5F♭	^3E, ^15F♭	March 7
66	220		^6E, ^6F♭	^4E, ^16F♭	March 8
67	223.33	33/29, 91/80	^7E, ^7F♭	^5E, ^17F♭	March 9
68	226.67	57/50	^8E, ^8F♭	^6E, ^18F♭	March 10
69	230		^9E, ^9F♭	^7E, v18F	March 11
70	233.33		^10E, ^10F♭	^8E, v17F	March 12
71	236.67	47/41	^11E, ^11F♭	^9E, v16F	March 13
72	240	85/74	^12E, ^12F♭	^10E, v15F	March 14
73	243.33		^13E, ^13F♭	^11E, v14F	March 15
74	246.67		^14E, ^14F♭	^12E, v13F	March 16
75	250		^15E, v15F	^13E, v12F	March 17
76	253.33	22/19	v14E♯, v14F	^14E, v11F	March 18
77	256.67	29/25	v13E♯, v13F	^15E, v10F	March 19
78	260	43/37	v12E♯, v12F	^16E, v9F	March 20
79	263.33		v11E♯, v11F	^17E, v8F	March 21
80	266.67	7/6	v10E♯, v10F	^18E, v7F	March 22
81	270		v9E♯, v9F	v18E♯, v6F	March 23
82	273.33	48/41	v8E♯, v8F	v17E♯, v5F	March 24
83	276.67		v7E♯, v7F	v16E♯, v4F	March 25
84	280		v6E♯, v6F	v15E♯, v3F	March 26
85	283.33		v5E♯, v5F	v14E♯, vvF	March 27
86	286.67		v4E♯, v4F	v13E♯, vF	March 28
87	290		v3E♯, v3F	F	March 29
88	293.33	77/65	vvE♯, vvF	^F, ^13G♭♭	March 30
89	296.67		vE♯, vF	^^F, ^14G♭♭	March 31
90	300	44/37	F	^3F, ^15G♭♭	April 1
91	303.33	56/47	^F, ^G♭♭	^4F, ^16G♭♭	April 2
92	306.67		^^F, ^^G♭♭	^5F, ^17G♭♭	April 3
93	310		^3F, ^3G♭♭	^6F, ^18G♭♭	April 4
94	313.33		^4F, ^4G♭♭	^7F, v18G♭	April 5
95	316.67		^5F, ^5G♭♭	^8F, v17G♭	April 6
96	320	77/64	^6F, ^6G♭♭	^9F, v16G♭	April 7
97	323.33	47/39	^7F, ^7G♭♭	^10F, v15G♭	April 8
98	326.67	99/82	^8F, ^8G♭♭	^11F, v14G♭	April 9
99	330	75/62	^9F, ^9G♭♭	^12F, v13G♭	April 10
100	333.33	40/33	^10F, ^10G♭♭	^13F, v12G♭	April 11
101	336.67		^11F, ^11G♭♭	^14F, v11G♭	April 12
102	340		^12F, ^12G♭♭	^15F, v10G♭	April 13
103	343.33	50/41	^13F, ^13G♭♭	^16F, v9G♭	April 14
104	346.67		^14F, ^14G♭♭	^17F, v8G♭	April 15
105	350		^15F, v15G♭	^18F, v7G♭	April 16
106	353.33		v14F♯, v14G♭	v18F♯, v6G♭	April 17
107	356.67		v13F♯, v13G♭	v17F♯, v5G♭	April 18
108	360	16/13	v12F♯, v12G♭	v16F♯, v4G♭	April 19
109	363.33	95/77	v11F♯, v11G♭	v15F♯, v3G♭	April 20
110	366.67		v10F♯, v10G♭	v14F♯, vvG♭	April 21
111	370		v9F♯, v9G♭	v13F♯, vG♭	April 22
112	373.33		v8F♯, v8G♭	v12F♯, G♭	April 23
113	376.67	46/37, 87/70	v7F♯, v7G♭	v11F♯, ^G♭	April 24
114	380		v6F♯, v6G♭	v10F♯, ^^G♭	April 25
115	383.33		v5F♯, v5G♭	v9F♯, ^3G♭	April 26
116	386.67	5/4	v4F♯, v4G♭	v8F♯, ^4G♭	April 27
117	390		v3F♯, v3G♭	v7F♯, ^5G♭	April 28
118	393.33	64/51	vvF♯, vvG♭	v6F♯, ^6G♭	April 29
119	396.67		vF♯, vG♭	v5F♯, ^7G♭	April 30
120	400		F♯, G♭	v4F♯, ^8G♭	May 1
121	403.33		^F♯, ^G♭	v3F♯, ^9G♭	May 2
122	406.67	43/34	^^F♯, ^^G♭	vvF♯, ^10G♭	May 3
123	410		^3F♯, ^3G♭	vF♯, ^11G♭	May 4
124	413.33		^4F♯, ^4G♭	F♯, ^12G♭	May 5
125	416.67		^5F♯, ^5G♭	^F♯, ^13G♭	May 6
126	420	65/51	^6F♯, ^6G♭	^^F♯, ^14G♭	May 7
127	423.33		^7F♯, ^7G♭	^3F♯, ^15G♭	May 8
128	426.67	55/43	^8F♯, ^8G♭	^4F♯, ^16G♭	May 9
129	430	50/39	^9F♯, ^9G♭	^5F♯, ^17G♭	May 10
130	433.33		^10F♯, ^10G♭	^6F♯, ^18G♭	May 11
131	436.67		^11F♯, ^11G♭	^7F♯, v18G	May 12
132	440		^12F♯, ^12G♭	^8F♯, v17G	May 13
133	443.33	31/24	^13F♯, ^13G♭	^9F♯, v16G	May 14
134	446.67	22/17	^14F♯, ^14G♭	^10F♯, v15G	May 15
135	450		^15F♯, v15G	^11F♯, v14G	May 16
136	453.33		v14F𝄪, v14G	^12F♯, v13G	May 17
137	456.67		v13F𝄪, v13G	^13F♯, v12G	May 18
138	460		v12F𝄪, v12G	^14F♯, v11G	May 19
139	463.33	98/75	v11F𝄪, v11G	^15F♯, v10G	May 20
140	466.67		v10F𝄪, v10G	^16F♯, v9G	May 21
141	470		v9F𝄪, v9G	^17F♯, v8G	May 22
142	473.33		v8F𝄪, v8G	^18F♯, v7G	May 23
143	476.67		v7F𝄪, v7G	v18F𝄪, v6G	May 24
144	480	62/47	v6F𝄪, v6G	v17F𝄪, v5G	May 25
145	483.33		v5F𝄪, v5G	v16F𝄪, v4G	May 26
146	486.67	102/77	v4F𝄪, v4G	v15F𝄪, v3G	May 27
147	490	69/52	v3F𝄪, v3G	v14F𝄪, vvG	May 28
148	493.33		vvF𝄪, vvG	v13F𝄪, vG	May 29
149	496.67		vF𝄪, vG	G	May 30
150	500		G	^G, ^13A♭♭	May 31
151	503.33		^G, ^A♭♭	^^G, ^14A♭♭	June 1
152	506.67		^^G, ^^A♭♭	^3G, ^15A♭♭	June 2
153	510	47/35	^3G, ^3A♭♭	^4G, ^16A♭♭	June 3
154	513.33	39/29, 74/55	^4G, ^4A♭♭	^5G, ^17A♭♭	June 4
155	516.67		^5G, ^5A♭♭	^6G, ^18A♭♭	June 5
156	520	104/77	^6G, ^6A♭♭	^7G, v18A♭	June 6
157	523.33	23/17	^7G, ^7A♭♭	^8G, v17A♭	June 7
158	526.67		^8G, ^8A♭♭	^9G, v16A♭	June 8
159	530		^9G, ^9A♭♭	^10G, v15A♭	June 9
160	533.33	49/36	^10G, ^10A♭♭	^11G, v14A♭	June 10
161	536.67		^11G, ^11A♭♭	^12G, v13A♭	June 11
162	540	56/41	^12G, ^12A♭♭	^13G, v12A♭	June 12
163	543.33	26/19	^13G, ^13A♭♭	^14G, v11A♭	June 13
164	546.67	48/35	^14G, ^14A♭♭	^15G, v10A♭	June 14
165	550		^15G, v15A♭	^16G, v9A♭	June 15
166	553.33	95/69	v14G♯, v14A♭	^17G, v8A♭	June 16
167	556.67	40/29	v13G♯, v13A♭	^18G, v7A♭	June 17
168	560	76/55	v12G♯, v12A♭	v18G♯, v6A♭	June 18
169	563.33		v11G♯, v11A♭	v17G♯, v5A♭	June 19
170	566.67		v10G♯, v10A♭	v16G♯, v4A♭	June 20
171	570	57/41	v9G♯, v9A♭	v15G♯, v3A♭	June 21
172	573.33	39/28	v8G♯, v8A♭	v14G♯, vvA♭	June 22
173	576.67		v7G♯, v7A♭	v13G♯, vA♭	June 23
174	580		v6G♯, v6A♭	v12G♯, A♭	June 24
175	583.33		v5G♯, v5A♭	v11G♯, ^A♭	June 25
176	586.67	80/57, 87/62	v4G♯, v4A♭	v10G♯, ^^A♭	June 26
177	590		v3G♯, v3A♭	v9G♯, ^3A♭	June 27
178	593.33		vvG♯, vvA♭	v8G♯, ^4A♭	June 28
179	596.67		vG♯, vA♭	v7G♯, ^5A♭	June 29
180	600	41/29, 58/41, 99/70	G♯, A♭	v6G♯, ^6A♭	June 30
181	603.33		^G♯, ^A♭	v5G♯, ^7A♭	July 1
182	606.67		^^G♯, ^^A♭	v4G♯, ^8A♭	July 2
183	610		^3G♯, ^3A♭	v3G♯, ^9A♭	July 3
184	613.33	57/40	^4G♯, ^4A♭	vvG♯, ^10A♭	July 4
185	616.67		^5G♯, ^5A♭	vG♯, ^11A♭	July 5
186	620		^6G♯, ^6A♭	G♯, ^12A♭	July 6
187	623.33		^7G♯, ^7A♭	^G♯, ^13A♭	July 7
188	626.67	56/39	^8G♯, ^8A♭	^^G♯, ^14A♭	July 8
189	630	82/57, 95/66	^9G♯, ^9A♭	^3G♯, ^15A♭	July 9
190	633.33		^10G♯, ^10A♭	^4G♯, ^16A♭	July 10
191	636.67		^11G♯, ^11A♭	^5G♯, ^17A♭	July 11
192	640	55/38	^12G♯, ^12A♭	^6G♯, ^18A♭	July 12
193	643.33	29/20	^13G♯, ^13A♭	^7G♯, v18A	July 13
194	646.67		^14G♯, ^14A♭	^8G♯, v17A	July 14
195	650		^15G♯, v15A	^9G♯, v16A	July 15
196	653.33	35/24	v14G𝄪, v14A	^10G♯, v15A	July 16
197	656.67	19/13	v13G𝄪, v13A	^11G♯, v14A	July 17
198	660	41/28	v12G𝄪, v12A	^12G♯, v13A	July 18
199	663.33		v11G𝄪, v11A	^13G♯, v12A	July 19
200	666.67	72/49	v10G𝄪, v10A	^14G♯, v11A	July 20
201	670		v9G𝄪, v9A	^15G♯, v10A	July 21
202	673.33		v8G𝄪, v8A	^16G♯, v9A	July 22
203	676.67	34/23	v7G𝄪, v7A	^17G♯, v8A	July 23
204	680	77/52	v6G𝄪, v6A	^18G♯, v7A	July 24
205	683.33	95/64	v5G𝄪, v5A	v18G𝄪, v6A	July 25
206	686.67	55/37, 58/39	v4G𝄪, v4A	v17G𝄪, v5A	July 26
207	690	70/47	v3G𝄪, v3A	v16G𝄪, v4A	July 27
208	693.33		vvG𝄪, vvA	v15G𝄪, v3A	July 28
209	696.67		vG𝄪, vA	v14G𝄪, vvA	July 29
210	700		A	v13G𝄪, vA	July 30
211	703.33		^A, ^B♭♭	A	July 31
212	706.67		^^A, ^^B♭♭	^A, ^13B♭♭	August 1
213	710	104/69	^3A, ^3B♭♭	^^A, ^14B♭♭	August 2
214	713.33	77/51	^4A, ^4B♭♭	^3A, ^15B♭♭	August 3
215	716.67		^5A, ^5B♭♭	^4A, ^16B♭♭	August 4
216	720	47/31	^6A, ^6B♭♭	^5A, ^17B♭♭	August 5
217	723.33		^7A, ^7B♭♭	^6A, ^18B♭♭	August 6
218	726.67		^8A, ^8B♭♭	^7A, v18B♭	August 7
219	730		^9A, ^9B♭♭	^8A, v17B♭	August 8
220	733.33		^10A, ^10B♭♭	^9A, v16B♭	August 9
221	736.67	75/49	^11A, ^11B♭♭	^10A, v15B♭	August 10
222	740		^12A, ^12B♭♭	^11A, v14B♭	August 11
223	743.33		^13A, ^13B♭♭	^12A, v13B♭	August 12
224	746.67		^14A, ^14B♭♭	^13A, v12B♭	August 13
225	750		^15A, v15B♭	^14A, v11B♭	August 14
226	753.33	17/11	v14A♯, v14B♭	^15A, v10B♭	August 15
227	756.67	48/31	v13A♯, v13B♭	^16A, v9B♭	August 16
228	760		v12A♯, v12B♭	^17A, v8B♭	August 17
229	763.33		v11A♯, v11B♭	^18A, v7B♭	August 18
230	766.67		v10A♯, v10B♭	v18A♯, v6B♭	August 19
231	770	39/25	v9A♯, v9B♭	v17A♯, v5B♭	August 20
232	773.33	86/55	v8A♯, v8B♭	v16A♯, v4B♭	August 21
233	776.67		v7A♯, v7B♭	v15A♯, v3B♭	August 22
234	780	91/58, 102/65	v6A♯, v6B♭	v14A♯, vvB♭	August 23
235	783.33		v5A♯, v5B♭	v13A♯, vB♭	August 24
236	786.67		v4A♯, v4B♭	v12A♯, B♭	August 25
237	790		v3A♯, v3B♭	v11A♯, ^B♭	August 26
238	793.33	68/43	vvA♯, vvB♭	v10A♯, ^^B♭	August 27
239	796.67		vA♯, vB♭	v9A♯, ^3B♭	August 28
240	800		A♯, B♭	v8A♯, ^4B♭	August 29
241	803.33		^A♯, ^B♭	v7A♯, ^5B♭	August 30
242	806.67	51/32	^^A♯, ^^B♭	v6A♯, ^6B♭	August 31
243	810	91/57, 99/62	^3A♯, ^3B♭	v5A♯, ^7B♭	September 1
244	813.33	8/5	^4A♯, ^4B♭	v4A♯, ^8B♭	September 2
245	816.67		^5A♯, ^5B♭	v3A♯, ^9B♭	September 3
246	820		^6A♯, ^6B♭	vvA♯, ^10B♭	September 4
247	823.33	37/23	^7A♯, ^7B♭	vA♯, ^11B♭	September 5
248	826.67		^8A♯, ^8B♭	A♯, ^12B♭	September 6
249	830		^9A♯, ^9B♭	^A♯, ^13B♭	September 7
250	833.33		^10A♯, ^10B♭	^^A♯, ^14B♭	September 8
251	836.67		^11A♯, ^11B♭	^3A♯, ^15B♭	September 9
252	840	13/8	^12A♯, ^12B♭	^4A♯, ^16B♭	September 10
253	843.33		^13A♯, ^13B♭	^5A♯, ^17B♭	September 11
254	846.67		^14A♯, ^14B♭	^6A♯, ^18B♭	September 12
255	850		^15A♯, v15B	^7A♯, v18B	September 13
256	853.33		v14A𝄪, v14B	^8A♯, v17B	September 14
257	856.67	41/25	v13A𝄪, v13B	^9A♯, v16B	September 15
258	860		v12A𝄪, v12B	^10A♯, v15B	September 16
259	863.33		v11A𝄪, v11B	^11A♯, v14B	September 17
260	866.67	33/20	v10A𝄪, v10B	^12A♯, v13B	September 18
261	870		v9A𝄪, v9B	^13A♯, v12B	September 19
262	873.33		v8A𝄪, v8B	^14A♯, v11B	September 20
263	876.67	78/47	v7A𝄪, v7B	^15A♯, v10B	September 21
264	880		v6A𝄪, v6B	^16A♯, v9B	September 22
265	883.33		v5A𝄪, v5B	^17A♯, v8B	September 23
266	886.67		v4A𝄪, v4B	^18A♯, v7B	September 24
267	890		v3A𝄪, v3B	v18A𝄪, v6B	September 25
268	893.33		vvA𝄪, vvB	v17A𝄪, v5B	September 26
269	896.67	47/28	vA𝄪, vB	v16A𝄪, v4B	September 27
270	900	37/22	B	v15A𝄪, v3B	September 28
271	903.33		^B, ^C♭	v14A𝄪, vvB	September 29
272	906.67		^^B, ^^C♭	v13A𝄪, vB	September 30
273	910		^3B, ^3C♭	B	October 1
274	913.33		^4B, ^4C♭	^B, ^13C♭	October 2
275	916.67		^5B, ^5C♭	^^B, ^14C♭	October 3
276	920		^6B, ^6C♭	^3B, ^15C♭	October 4
277	923.33		^7B, ^7C♭	^4B, ^16C♭	October 5
278	926.67	41/24	^8B, ^8C♭	^5B, ^17C♭	October 6
279	930		^9B, ^9C♭	^6B, ^18C♭	October 7
280	933.33	12/7	^10B, ^10C♭	^7B, v18C	October 8
281	936.67		^11B, ^11C♭	^8B, v17C	October 9
282	940	74/43	^12B, ^12C♭	^9B, v16C	October 10
283	943.33	50/29	^13B, ^13C♭	^10B, v15C	October 11
284	946.67	19/11	^14B, ^14C♭	^11B, v14C	October 12
285	950		^15B, v15C	^12B, v13C	October 13
286	953.33		v14B♯, v14C	^13B, v12C	October 14
287	956.67		v13B♯, v13C	^14B, v11C	October 15
288	960		v12B♯, v12C	^15B, v10C	October 16
289	963.33	82/47	v11B♯, v11C	^16B, v9C	October 17
290	966.67		v10B♯, v10C	^17B, v8C	October 18
291	970		v9B♯, v9C	^18B, v7C	October 19
292	973.33	100/57	v8B♯, v8C	v18B♯, v6C	October 20
293	976.67	58/33	v7B♯, v7C	v17B♯, v5C	October 21
294	980		v6B♯, v6C	v16B♯, v4C	October 22
295	983.33		v5B♯, v5C	v15B♯, v3C	October 23
296	986.67	99/56	v4B♯, v4C	v14B♯, vvC	October 24
297	990	62/35	v3B♯, v3C	v13B♯, vC	October 25
298	993.33	87/49	vvB♯, vvC	C	October 26
299	996.67		vB♯, vC	^C, ^13D♭♭	October 27
300	1000	57/32	C	^^C, ^14D♭♭	October 28
301	1003.33	25/14	^C, ^D♭♭	^3C, ^15D♭♭	October 29
302	1006.67		^^C, ^^D♭♭	^4C, ^16D♭♭	October 30
303	1010		^3C, ^3D♭♭	^5C, ^17D♭♭	October 31
304	1013.33		^4C, ^4D♭♭	^6C, ^18D♭♭	November 1
305	1016.67		^5C, ^5D♭♭	^7C, v18D♭	November 2
306	1020		^6C, ^6D♭♭	^8C, v17D♭	November 3
307	1023.33	56/31	^7C, ^7D♭♭	^9C, v16D♭	November 4
308	1026.67		^8C, ^8D♭♭	^10C, v15D♭	November 5
309	1030	29/16	^9C, ^9D♭♭	^11C, v14D♭	November 6
310	1033.33		^10C, ^10D♭♭	^12C, v13D♭	November 7
311	1036.67	91/50	^11C, ^11D♭♭	^13C, v12D♭	November 8
312	1040		^12C, ^12D♭♭	^14C, v11D♭	November 9
313	1043.33	95/52	^13C, ^13D♭♭	^15C, v10D♭	November 10
314	1046.67		^14C, ^14D♭♭	^16C, v9D♭	November 11
315	1050		^15C, v15D♭	^17C, v8D♭	November 12
316	1053.33	68/37	v14C♯, v14D♭	^18C, v7D♭	November 13
317	1056.67		v13C♯, v13D♭	v18C♯, v6D♭	November 14
318	1060		v12C♯, v12D♭	v17C♯, v5D♭	November 15
319	1063.33	85/46	v11C♯, v11D♭	v16C♯, v4D♭	November 16
320	1066.67		v10C♯, v10D♭	v15C♯, v3D♭	November 17
321	1070		v9C♯, v9D♭	v14C♯, vvD♭	November 18
322	1073.33		v8C♯, v8D♭	v13C♯, vD♭	November 19
323	1076.67	95/51	v7C♯, v7D♭	v12C♯, D♭	November 20
324	1080	28/15	v6C♯, v6D♭	v11C♯, ^D♭	November 21
325	1083.33	43/23	v5C♯, v5D♭	v10C♯, ^^D♭	November 22
326	1086.67		v4C♯, v4D♭	v9C♯, ^3D♭	November 23
327	1090		v3C♯, v3D♭	v8C♯, ^4D♭	November 24
328	1093.33	47/25	vvC♯, vvD♭	v7C♯, ^5D♭	November 25
329	1096.67		vC♯, vD♭	v6C♯, ^6D♭	November 26
330	1100		C♯, D♭	v5C♯, ^7D♭	November 27
331	1103.33	104/55	^C♯, ^D♭	v4C♯, ^8D♭	November 28
332	1106.67		^^C♯, ^^D♭	v3C♯, ^9D♭	November 29
333	1110		^3C♯, ^3D♭	vvC♯, ^10D♭	November 30
334	1113.33	78/41	^4C♯, ^4D♭	vC♯, ^11D♭	December 1
335	1116.67		^5C♯, ^5D♭	C♯, ^12D♭	December 2
336	1120		^6C♯, ^6D♭	^C♯, ^13D♭	December 3
337	1123.33	44/23	^7C♯, ^7D♭	^^C♯, ^14D♭	December 4
338	1126.67		^8C♯, ^8D♭	^3C♯, ^15D♭	December 5
339	1130		^9C♯, ^9D♭	^4C♯, ^16D♭	December 6
340	1133.33	77/40	^10C♯, ^10D♭	^5C♯, ^17D♭	December 7
341	1136.67		^11C♯, ^11D♭	^6C♯, ^18D♭	December 8
342	1140	85/44	^12C♯, ^12D♭	^7C♯, v18D	December 9
343	1143.33	60/31, 91/47	^13C♯, ^13D♭	^8C♯, v17D	December 10
344	1146.67	64/33	^14C♯, ^14D♭	^9C♯, v16D	December 11
345	1150		^15C♯, v15D	^10C♯, v15D	December 12
346	1153.33	37/19	v14C𝄪, v14D	^11C♯, v14D	December 13
347	1156.67	39/20	v13C𝄪, v13D	^12C♯, v13D	December 14
348	1160	43/22	v12C𝄪, v12D	^13C♯, v12D	December 15
349	1163.33	47/24	v11C𝄪, v11D	^14C♯, v11D	December 16
350	1166.67	51/26	v10C𝄪, v10D	^15C♯, v10D	December 17
351	1170	57/29	v9C𝄪, v9D	^16C♯, v9D	December 18
352	1173.33	65/33	v8C𝄪, v8D	^17C♯, v8D	December 19
353	1176.67		v7C𝄪, v7D	^18C♯, v7D	December 20
354	1180	85/43	v6C𝄪, v6D	v18C𝄪, v6D	December 21
355	1183.33		v5C𝄪, v5D	v17C𝄪, v5D	December 22
356	1186.67		v4C𝄪, v4D	v16C𝄪, v4D	December 23
357	1190		v3C𝄪, v3D	v15C𝄪, v3D	December 24
358	1193.33		vvC𝄪, vvD	v14C𝄪, vvD	December 25
359	1196.67		vC𝄪, vD	v13C𝄪, vD	December 26
360	1200	2/1	D	D	December 27

Regular temperament properties

Rank-2 temperaments

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	119\360	396.67	44/35	Squarschmidt
2	53\360	176.67	448/405	Quatracot
3	211\360 (91\360)	703.33 (303.33)	3/2	Misty
4	23\360	76.67	4302592/4100625	Reenactment
9	211\360 (11\360)	703.33 (36.67)	3/2	Trimisty
20	211\360 (13\360)	703.33 (43.33)	3/2 (45/44)	Degrees

Music

• Idyllic Tribe by Eliora

References

• Logarithmic size measures

Application as a logarithmic scale outside of music

360edo is used in the eyeborg, which maps its scale degrees onto color hues, thus converting color into sound waves. The device was originally intended to help colorblind individuals.