360edo

From Xenharmonic Wiki
Revision as of 08:12, 3 August 2023 by CompactStar (talk | contribs)
Jump to navigation Jump to search
← 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

Template:EDO intro

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

References

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.

Retrieved from "https://en.xen.wiki/index.php?title=360edo&oldid=121510"