124edo: Difference between revisions

Revision as of 10:47, 24 April 2021

124edo is the equal division of the octave into 124 parts of 9.6774 cents each. It is closely related to 31edo, but the patent vals differ on the mapping for 3. It tempers out 2048/2025 (diaschisma) and 19073486328125/18075490334784 in the 5-limit. Using the patent val, it tempers out 3136/3125, 4000/3969, and 33614/32805 in the 7-limit; 385/384, 1232/1215, 1331/1323, and 3773/3750 in the 11-limit; 196/195, 364/363, 572/567, 625/624, and 1001/1000 in the 13-limit.

124 EDO Table of Intervals
Step	Cents	Ratio	JI Ratio Approximations
0	0.0	1.0	1/1
1	9.6774	1.0056
2	19.3548	1.0112
3	29.0323	1.0169	65/64
4	38.7097	1.0226	65/64
5	48.3871	1.0283	65/64, 33/32
6	58.0645	1.0341	33/32
7	67.7419	1.0399	33/32, 24/23
8	77.4194	1.0457	24/23, 23/22, 67/64, 22/21, 33/32
9	87.0968	1.0516	23/22, 67/64, 22/21, 24/23, 21/20, 20/19
10	96.7742	1.0575	20/19, 21/20, 19/18, 22/21, 67/64, 23/22, 18/17, 24/23
11	106.4516	1.0634	18/17, 19/18, 20/19, 17/16, 21/20, 16/15
12	116.129	1.0694	17/16, 16/15, 18/17, 19/18, 15/14
13	125.8065	1.0754	15/14, 16/15, 17/16, 14/13, 69/64
14	135.4839	1.0814	14/13, 69/64, 15/14, 13/12, 16/15
15	145.1613	1.0875	13/12, 69/64, 14/13, 25/23, 12/11
16	154.8387	1.0936	25/23, 12/11, 13/12, 35/32, 23/21, 69/64
17	164.5161	1.0997	35/32, 23/21, 12/11, 11/10, 25/23
18	174.1935	1.1059	11/10, 23/21, 21/19, 35/32, 12/11, 71/64
19	183.871	1.1121	21/19, 71/64, 10/9, 11/10
20	193.5484	1.1183	10/9, 71/64, 19/17, 21/19
21	203.2258	1.1246	19/17, 9/8, 10/9, 71/64
22	212.9032	1.1309	9/8, 26/23, 19/17, 17/15
23	222.5806	1.1372	26/23, 17/15, 25/22, 9/8, 73/64
24	232.2581	1.1436	25/22, 73/64, 17/15, 8/7, 26/23
25	241.9355	1.15	8/7, 73/64, 23/20, 25/22, 15/13, 17/15
26	251.6129	1.1564	23/20, 15/13, 37/32, 8/7, 22/19, 73/64
27	261.2903	1.1629	37/32, 22/19, 15/13, 23/20, 7/6
28	270.9677	1.1694	7/6, 22/19, 37/32, 75/64, 15/13
29	280.6452	1.176	75/64, 7/6, 27/23, 20/17
30	290.3226	1.1826	20/17, 27/23, 75/64, 13/11, 7/6
31	300.0	1.1892	13/11, 19/16, 20/17, 25/21, 27/23, 75/64
32	309.6774	1.1959	25/21, 19/16, 13/11, 6/5
33	319.3548	1.2026	6/5, 25/21, 77/64, 19/16
34	329.0323	1.2093	77/64, 6/5, 23/19
35	338.7097	1.2161	23/19, 17/14, 77/64, 28/23, 6/5, 39/32
36	348.3871	1.2229	28/23, 17/14, 39/32, 23/19, 11/9, 27/22
37	358.0645	1.2298	11/9, 39/32, 27/22, 28/23, 16/13, 17/14
38	367.7419	1.2367	16/13, 27/22, 79/64, 21/17, 11/9, 26/21, 39/32
39	377.4194	1.2436	21/17, 26/21, 79/64, 16/13, 27/22
40	387.0968	1.2506	26/21, 5/4, 21/17, 79/64
41	396.7742	1.2576	5/4
42	406.4516	1.2646	24/19, 5/4, 81/64, 19/15
43	416.129	1.2717	81/64, 24/19, 19/15, 14/11
44	425.8065	1.2788	14/11, 19/15, 23/18, 81/64, 24/19, 41/32
45	435.4839	1.286	23/18, 41/32, 14/11, 9/7
46	445.1613	1.2932	9/7, 41/32, 22/17, 23/18, 83/64
47	454.8387	1.3005	22/17, 83/64, 13/10, 9/7, 30/23
48	464.5161	1.3078	13/10, 83/64, 30/23, 22/17, 17/13, 21/16
49	474.1935	1.3151	17/13, 30/23, 21/16, 13/10, 25/19, 83/64
50	483.871	1.3225	25/19, 21/16, 17/13, 30/23
51	493.5484	1.3299	85/64, 25/19, 21/16, 4/3
52	503.2258	1.3373	85/64, 4/3
53	512.9032	1.3448	4/3, 43/32, 85/64
54	522.5806	1.3524	43/32, 27/20, 23/17, 4/3, 19/14
55	532.2581	1.3599	23/17, 27/20, 19/14, 87/64, 43/32, 15/11
56	541.9355	1.3676	87/64, 19/14, 15/11, 23/17, 26/19, 27/20
57	551.6129	1.3752	26/19, 15/11, 11/8, 87/64, 19/14
58	561.2903	1.3829	11/8, 26/19, 18/13, 15/11
59	570.9677	1.3907	18/13, 25/18, 89/64, 11/8, 32/23
60	580.6452	1.3985	89/64, 32/23, 25/18, 18/13, 7/5
61	590.3226	1.4063	7/5, 32/23, 45/32, 89/64, 25/18
62	600.0	1.4142	45/32, 24/17, 7/5, 17/12
63	609.6774	1.4221	17/12, 24/17, 27/19, 91/64, 45/32
64	619.3548	1.4301	91/64, 27/19, 17/12, 10/7, 24/17, 33/23
65	629.0323	1.4381	10/7, 33/23, 23/16, 91/64, 27/19
66	638.7097	1.4462	23/16, 33/23, 13/9, 10/7
67	648.3871	1.4543	13/9, 93/64, 16/11, 23/16, 33/23
68	658.0645	1.4624	16/11, 93/64, 19/13, 13/9, 22/15
69	667.7419	1.4706	19/13, 22/15, 47/32, 16/11, 25/17, 93/64, 28/19
70	677.4194	1.4789	25/17, 47/32, 28/19, 22/15, 34/23, 19/13
71	687.0968	1.4872	34/23, 28/19, 95/64, 25/17, 47/32, 22/15
72	696.7742	1.4955	95/64, 34/23, 3/2, 28/19
73	706.4516	1.5039	3/2, 95/64
74	716.129	1.5123	3/2, 97/64
75	725.8065	1.5208	97/64, 35/23, 32/21, 3/2
76	735.4839	1.5293	35/23, 32/21, 97/64, 26/17, 49/32, 23/15
77	745.1613	1.5379	26/17, 49/32, 23/15, 32/21, 35/23, 20/13, 97/64
78	754.8387	1.5465	20/13, 23/15, 49/32, 17/11, 26/17, 99/64, 32/21
79	764.5161	1.5552	99/64, 17/11, 20/13, 14/9, 23/15
80	774.1935	1.5639	14/9, 25/16, 99/64, 17/11, 36/23
81	783.871	1.5727	36/23, 25/16, 11/7, 14/9, 101/64
82	793.5484	1.5815	11/7, 101/64, 30/19, 36/23, 25/16, 19/12
83	803.2258	1.5904	19/12, 30/19, 101/64, 27/17, 35/22, 11/7, 51/32
84	812.9032	1.5993	35/22, 27/17, 51/32, 19/12, 8/5, 30/19, 101/64
85	822.5806	1.6082	8/5, 51/32, 35/22, 103/64, 27/17
86	832.2581	1.6173	103/64, 21/13, 8/5, 34/21, 51/32
87	841.9355	1.6263	34/21, 21/13, 13/8, 103/64
88	851.6129	1.6354	13/8, 34/21, 18/11, 21/13, 105/64
89	861.2903	1.6446	18/11, 105/64, 23/14, 13/8, 28/17, 33/20
90	870.9677	1.6538	23/14, 28/17, 105/64, 33/20, 38/23, 18/11, 53/32
91	880.6452	1.6631	38/23, 53/32, 33/20, 28/17, 23/14, 5/3, 105/64
92	890.3226	1.6724	5/3, 53/32, 107/64, 38/23, 33/20
93	900.0	1.6818	107/64, 5/3, 32/19, 27/16
94	909.6774	1.6912	32/19, 27/16, 107/64, 22/13, 39/23, 5/3
95	919.3548	1.7007	22/13, 27/16, 39/23, 32/19, 17/10, 109/64
96	929.0323	1.7102	17/10, 109/64, 39/23, 22/13, 27/16, 12/7
97	938.7097	1.7198	12/7, 109/64, 55/32, 17/10, 39/23
98	948.3871	1.7295	55/32, 12/7, 19/11, 26/15, 111/64
99	958.0645	1.7392	19/11, 26/15, 111/64, 33/19, 40/23, 55/32, 12/7
100	967.7419	1.7489	40/23, 33/19, 111/64, 26/15, 7/4, 19/11
101	977.4194	1.7587	7/4, 40/23, 33/19, 111/64, 26/15, 30/17
102	987.0968	1.7686	30/17, 113/64, 7/4, 23/13, 39/22
103	996.7742	1.7785	23/13, 113/64, 30/17, 39/22, 16/9, 57/32
104	1006.4516	1.7884	16/9, 57/32, 39/22, 25/14, 23/13, 34/19, 113/64, 30/17
105	1016.129	1.7985	34/19, 25/14, 57/32, 115/64, 16/9, 9/5, 39/22
106	1025.8065	1.8086	9/5, 115/64, 34/19, 38/21, 25/14, 29/16
107	1035.4839	1.8187	38/21, 29/16, 9/5, 20/11, 115/64
108	1045.1613	1.8289	20/11, 29/16, 42/23, 38/21, 117/64, 11/6
109	1054.8387	1.8391	117/64, 42/23, 11/6, 20/11, 35/19, 59/32, 29/16
110	1064.5161	1.8495	35/19, 59/32, 11/6, 24/13, 117/64, 42/23
111	1074.1935	1.8598	24/13, 59/32, 35/19, 13/7, 119/64, 11/6
112	1083.871	1.8702	119/64, 13/7, 28/15, 24/13, 15/8, 59/32
113	1093.5484	1.8807	28/15, 15/8, 119/64, 32/17, 13/7
114	1103.2258	1.8913	32/17, 15/8, 17/9, 121/64, 36/19, 28/15
115	1112.9032	1.9019	121/64, 17/9, 36/19, 19/10, 32/17, 40/21, 61/32, 15/8
116	1122.5806	1.9125	19/10, 40/21, 61/32, 36/19, 21/11, 44/23, 121/64, 17/9, 23/12
117	1132.2581	1.9233	44/23, 21/11, 23/12, 61/32, 40/21, 123/64, 25/13, 19/10, 27/14
118	1141.9355	1.934	25/13, 123/64, 27/14, 23/12, 44/23, 31/16, 21/11, 61/32
119	1151.6129	1.9449	31/16, 27/14, 33/17, 35/18, 25/13, 123/64, 39/20, 23/12
120	1161.2903	1.9558	35/18, 33/17, 39/20, 31/16, 125/64, 45/23, 27/14
121	1170.9677	1.9667	45/23, 125/64, 39/20, 35/18, 63/32, 33/17
122	1180.6452	1.9778	63/32, 45/23, 125/64, 39/20, 127/64
123	1190.3226	1.9889	127/64, 63/32
124	1200.0	2.0	2/1
JI Ratio Approximations are comprised of 23 limit ratios and the odd harmonics up to 127. The JI Ratio Approximations are stylized as follows to indicate accuracy: Big Bold Underlined: absolute cent error < 1 cent. Big Bold: absolute cent error < 2 cents. Big: absolute cent error < 4 cents. Normal: absolute cent error < 8 cents. Small: absolute cent error < 16 cents.

@@ Line 1: / Line 1: @@
 '''124edo''' is the [[EDO|equal division of the octave]] into 124 parts of 9.6774 cents each. It is closely related to [[31edo]], but the patent vals differ on the mapping for 3. It tempers out 2048/2025 (diaschisma) and 19073486328125/18075490334784 in the 5-limit. Using the patent val, it tempers out 3136/3125, 4000/3969, and 33614/32805 in the 7-limit; 385/384, 1232/1215, 1331/1323, and 3773/3750 in the 11-limit; 196/195, 364/363, 572/567, 625/624, and 1001/1000 in the 13-limit.
+{| class="wikitable mw-collapsible mw-collapsed"
+|+124 EDO Table of Intervals
+!Step
+!Cents
+!Ratio
+!JI Ratio Approximations
+|-
+|0
+|0.0
+|1.0
+|'''<big><u>1/1</u></big>'''
+|-
+|1
+|9.6774
+|1.0056
+|
+|-
+|2
+|19.3548
+|1.0112
+|
+|-
+|3
+|29.0323
+|1.0169
+|65/64
+|-
+|4
+|38.7097
+|1.0226
+|<big>65/64</big>
+|-
+|5
+|48.3871
+|1.0283
+|<small>65/64</small>, <small>33/32</small>
+|-
+|6
+|58.0645
+|1.0341
+|33/32
+|-
+|7
+|67.7419
+|1.0399
+|33/32, <small>24/23</small>
+|-
+|8
+|77.4194
+|1.0457
+|24/23, <small>23/22</small>, <small>67/64</small>, <small>22/21</small>, <small>33/32</small>
+|-
+|9
+|87.0968
+|1.0516
+|'''<big><u>23/22</u></big>''', '''<big>67/64</big>''', <big>22/21</big>, <big>24/23</big>, 21/20, <small>20/19</small>
+|-
+|10
+|96.7742
+|1.0575
+|'''<big>20/19</big>''', <big>21/20</big>, 19/18, 22/21, 67/64, <small>23/22</small>, <small>18/17</small>, <small>24/23</small>
+|-
+|11
+|106.4516
+|1.0634
+|<big>18/17</big>, <big>19/18</big>, 20/19, <small>17/16</small>, <small>21/20</small>, <small>16/15</small>
+|-
+|12
+|116.129
+|1.0694
+|'''<big>17/16</big>''', 16/15, 18/17, <small>19/18</small>, <small>15/14</small>
+|-
+|13
+|125.8065
+|1.0754
+|<big>15/14</big>, 16/15, <small>17/16</small>, <small>14/13</small>, <small>69/64</small>
+|-
+|14
+|135.4839
+|1.0814
+|<big>14/13</big>, 69/64, 15/14, <small>13/12</small>, <small>16/15</small>
+|-
+|15
+|145.1613
+|1.0875
+|<big>13/12</big>, 69/64, 14/13, <small>25/23</small>, <small>12/11</small>
+|-
+|16
+|154.8387
+|1.0936
+|'''<big><u>25/23</u></big>''', 12/11, 13/12, <small>35/32</small>, <small>23/21</small>, <small>69/64</small>
+|-
+|17
+|164.5161
+|1.0997
+|'''<big><u>35/32</u></big>''', <big>23/21</big>, 12/11, <small>11/10</small>, <small>25/23</small>
+|-
+|18
+|174.1935
+|1.1059
+|'''<big><u>11/10</u></big>''', 23/21, <small>21/19</small>, <small>35/32</small>, <small>12/11</small>, <small>71/64</small>
+|-
+|19
+|183.871
+|1.1121
+|'''<big><u>21/19</u></big>''', 71/64, <small>10/9</small>, <small>11/10</small>
+|-
+|20
+|193.5484
+|1.1183
+|'''<big>10/9</big>''', 71/64, <small>19/17</small>, <small>21/19</small>
+|-
+|21
+|203.2258
+|1.1246
+|'''<big><u>19/17</u></big>''', <small>9/8</small>, <small>10/9</small>, <small>71/64</small>
+|-
+|22
+|212.9032
+|1.1309
+|'''<big><u>9/8</u></big>''', <small>26/23</small>, <small>19/17</small>, <small>17/15</small>
+|-
+|23
+|222.5806
+|1.1372
+|'''<big><u>26/23</u></big>''', <big>17/15</big>, <small>25/22</small>, <small>9/8</small>, <small>73/64</small>
+|-
+|24
+|232.2581
+|1.1436
+|'''<big>25/22</big>''', 73/64, 17/15, <small>8/7</small>, <small>26/23</small>
+|-
+|25
+|241.9355
+|1.15
+|'''<big>8/7</big>''', 73/64, <small>23/20</small>, <small>25/22</small>, <small>15/13</small>, <small>17/15</small>
+|-
+|26
+|251.6129
+|1.1564
+|'''<big><u>23/20</u></big>''', 15/13, <small>37/32</small>, <small>8/7</small>, <small>22/19</small>, <small>73/64</small>
+|-
+|27
+|261.2903
+|1.1629
+|'''<big><u>37/32</u></big>''', <big>22/19</big>, <big>15/13</big>, <small>23/20</small>, <small>7/6</small>
+|-
+|28
+|270.9677
+|1.1694
+|7/6, 22/19, <small>37/32</small>, <small>75/64</small>, <small>15/13</small>
+|-
+|29
+|280.6452
+|1.176
+|<big>75/64</big>, 7/6, 27/23, <small>20/17</small>
+|-
+|30
+|290.3226
+|1.1826
+|'''<big><u>20/17</u></big>''', <big>27/23</big>, 75/64, <small>13/11</small>, <small>7/6</small>
+|-
+|31
+|300.0
+|1.1892
+|'''<big>13/11</big>''', 19/16, <small>20/17</small>, <small>25/21</small>, <small>27/23</small>, <small>75/64</small>
+|-
+|32
+|309.6774
+|1.1959
+|'''<big>25/21</big>''', <big>19/16</big>, <small>13/11</small>, <small>6/5</small>
+|-
+|33
+|319.3548
+|1.2026
+|6/5, 25/21, <small>77/64</small>, <small>19/16</small>
+|-
+|34
+|329.0323
+|1.2093
+|'''<big><u>77/64</u></big>''', <big>6/5</big>, <small>23/19</small>
+|-
+|35
+|338.7097
+|1.2161
+|'''<big>23/19</big>''', 17/14, <small>77/64</small>, <small>28/23</small>, <small>6/5</small>, <small>39/32</small>
+|-
+|36
+|348.3871
+|1.2229
+|'''<big>28/23</big>''', <big>17/14</big>, <big>39/32</big>, 23/19, <small>11/9</small>, <small>27/22</small>
+|-
+|37
+|358.0645
+|1.2298
+|'''<big><u>11/9</u></big>''', 39/32, 27/22, 28/23, <small>16/13</small>, <small>17/14</small>
+|-
+|38
+|367.7419
+|1.2367
+|'''<big>16/13</big>''', <big>27/22</big>, 79/64, 21/17, <small>11/9</small>, <small>26/21</small>, <small>39/32</small>
+|-
+|39
+|377.4194
+|1.2436
+|'''<big>21/17</big>''', <big>26/21</big>, <big>79/64</big>, <small>16/13</small>, <small>27/22</small>
+|-
+|40
+|387.0968
+|1.2506
+|26/21, <small>5/4</small>, <small>21/17</small>, <small>79/64</small>
+|-
+|41
+|396.7742
+|1.2576
+|'''<big><u>5/4</u></big>'''
+|-
+|42
+|406.4516
+|1.2646
+|24/19, <small>5/4</small>, <small>81/64</small>, <small>19/15</small>
+|-
+|43
+|416.129
+|1.2717
+|'''<big>81/64</big>''', <big>24/19</big>, <big>19/15</big>, <small>14/11</small>
+|-
+|44
+|425.8065
+|1.2788
+|'''<big>14/11</big>''', 19/15, <small>23/18</small>, <small>81/64</small>, <small>24/19</small>, <small>41/32</small>
+|-
+|45
+|435.4839
+|1.286
+|'''<big>23/18</big>''', <big>41/32</big>, <small>14/11</small>, <small>9/7</small>
+|-
+|46
+|445.1613
+|1.2932
+|'''<big><u>9/7</u></big>''', 41/32, <small>22/17</small>, <small>23/18</small>, <small>83/64</small>
+|-
+|47
+|454.8387
+|1.3005
+|'''<big>22/17</big>''', 83/64, <small>13/10</small>, <small>9/7</small>, <small>30/23</small>
+|-
+|48
+|464.5161
+|1.3078
+|'''<big><u>13/10</u></big>''', 83/64, 30/23, <small>22/17</small>, <small>17/13</small>, <small>21/16</small>
+|-
+|49
+|474.1935
+|1.3151
+|'''<big><u>17/13</u></big>''', 30/23, 21/16, <small>13/10</small>, <small>25/19</small>, <small>83/64</small>
+|-
+|50
+|483.871
+|1.3225
+|'''<big><u>25/19</u></big>''', <big>21/16</big>, <small>17/13</small>, <small>30/23</small>
+|-
+|51
+|493.5484
+|1.3299
+|85/64, <small>25/19</small>, <small>21/16</small>, <small>4/3</small>
+|-
+|52
+|503.2258
+|1.3373
+|<big>85/64</big>, 4/3
+|-
+|53
+|512.9032
+|1.3448
+|4/3, <small>43/32</small>, <small>85/64</small>
+|-
+|54
+|522.5806
+|1.3524
+|'''<big>43/32</big>''', 27/20, <small>23/17</small>, <small>4/3</small>, <small>19/14</small>
+|-
+|55
+|532.2581
+|1.3599
+|'''<big><u>23/17</u></big>''', <big>27/20</big>, 19/14, <small>87/64</small>, <small>43/32</small>, <small>15/11</small>
+|-
+|56
+|541.9355
+|1.3676
+|'''<big><u>87/64</u></big>''', <big>19/14</big>, 15/11, <small>23/17</small>, <small>26/19</small>, <small>27/20</small>
+|-
+|57
+|551.6129
+|1.3752
+|'''<big>26/19</big>''', 15/11, <small>11/8</small>, <small>87/64</small>, <small>19/14</small>
+|-
+|58
+|561.2903
+|1.3829
+|'''<big><u>11/8</u></big>''', <small>26/19</small>, <small>18/13</small>, <small>15/11</small>
+|-
+|59
+|570.9677
+|1.3907
+|<big>18/13</big>, 25/18, <small>89/64</small>, <small>11/8</small>, <small>32/23</small>
+|-
+|60
+|580.6452
+|1.3985
+|'''<big><u>89/64</u></big>''', '''<big><u>32/23</u></big>''', <big>25/18</big>, 18/13, <small>7/5</small>
+|-
+|61
+|590.3226
+|1.4063
+|'''<big>7/5</big>''', <small>32/23</small>, <small>45/32</small>, <small>89/64</small>, <small>25/18</small>
+|-
+|62
+|600.0
+|1.4142
+|'''<big><u>45/32</u></big>''', 24/17, 7/5, <small>17/12</small>
+|-
+|63
+|609.6774
+|1.4221
+|<big>17/12</big>, <big>24/17</big>, <small>27/19</small>, <small>91/64</small>, <small>45/32</small>
+|-
+|64
+|619.3548
+|1.4301
+|'''<big><u>91/64</u></big>''', '''<big>27/19</big>''', 17/12, 10/7, <small>24/17</small>, <small>33/23</small>
+|-
+|65
+|629.0323
+|1.4381
+|'''<big>10/7</big>''', 33/23, <small>23/16</small>, <small>91/64</small>, <small>27/19</small>
+|-
+|66
+|638.7097
+|1.4462
+|'''<big><u>23/16</u></big>''', 33/23, 13/9, <small>10/7</small>
+|-
+|67
+|648.3871
+|1.4543
+|<big>13/9</big>, <small>93/64</small>, <small>16/11</small>, <small>23/16</small>, <small>33/23</small>
+|-
+|68
+|658.0645
+|1.4624
+|'''<big><u>16/11</u></big>''', '''<big>93/64</big>''', <small>19/13</small>, <small>13/9</small>, <small>22/15</small>
+|-
+|69
+|667.7419
+|1.4706
+|'''<big>19/13</big>''', 22/15, 47/32, <small>16/11</small>, <small>25/17</small>, <small>93/64</small>, <small>28/19</small>
+|-
+|70
+|677.4194
+|1.4789
+|'''<big><u>25/17</u></big>''', <big>47/32</big>, <big>28/19</big>, 22/15, <small>34/23</small>, <small>19/13</small>
+|-
+|71
+|687.0968
+|1.4872
+|'''<big><u>34/23</u></big>''', 28/19, 95/64, <small>25/17</small>, <small>47/32</small>, <small>22/15</small>
+|-
+|72
+|696.7742
+|1.4955
+|<big>95/64</big>, <small>34/23</small>, <small>3/2</small>, <small>28/19</small>
+|-
+|73
+|706.4516
+|1.5039
+|3/2, <small>95/64</small>
+|-
+|74
+|716.129
+|1.5123
+|3/2, <small>97/64</small>
+|-
+|75
+|725.8065
+|1.5208
+|<big>97/64</big>, <small>35/23</small>, <small>32/21</small>, <small>3/2</small>
+|-
+|76
+|735.4839
+|1.5293
+|'''<big>35/23</big>''', <big>32/21</big>, 97/64, <small>26/17</small>, <small>49/32</small>, <small>23/15</small>
+|-
+|77
+|745.1613
+|1.5379
+|'''<big><u>26/17</u></big>''', <big>49/32</big>, 23/15, 32/21, <small>35/23</small>, <small>20/13</small>, <small>97/64</small>
+|-
+|78
+|754.8387
+|1.5465
+|'''<big><u>20/13</u></big>''', 23/15, 49/32, <small>17/11</small>, <small>26/17</small>, <small>99/64</small>, <small>32/21</small>
+|-
+|79
+|764.5161
+|1.5552
+|'''<big><u>99/64</u></big>''', '''<big>17/11</big>''', <small>20/13</small>, <small>14/9</small>, <small>23/15</small>
+|-
+|80
+|774.1935
+|1.5639
+|'''<big><u>14/9</u></big>''', <small>25/16</small>, <small>99/64</small>, <small>17/11</small>, <small>36/23</small>
+|-
+|81
+|783.871
+|1.5727
+|'''<big>36/23</big>''', '''<big>25/16</big>''', <small>11/7</small>, <small>14/9</small>, <small>101/64</small>
+|-
+|82
+|793.5484
+|1.5815
+|'''<big>11/7</big>''', 101/64, 30/19, <small>36/23</small>, <small>25/16</small>, <small>19/12</small>
+|-
+|83
+|803.2258
+|1.5904
+|<big>19/12</big>, <big>30/19</big>, <big>101/64</big>, 27/17, <small>35/22</small>, <small>11/7</small>, <small>51/32</small>
+|-
+|84
+|812.9032
+|1.5993
+|'''<big><u>35/22</u></big>''', <big>27/17</big>, <big>51/32</big>, 19/12, <small>8/5</small>, <small>30/19</small>, <small>101/64</small>
+|-
+|85
+|822.5806
+|1.6082
+|'''<big><u>8/5</u></big>''', 51/32, <small>35/22</small>, <small>103/64</small>, <small>27/17</small>
+|-
+|86
+|832.2581
+|1.6173
+|'''<big>103/64</big>''', 21/13, <small>8/5</small>, <small>34/21</small>, <small>51/32</small>
+|-
+|87
+|841.9355
+|1.6263
+|'''<big>34/21</big>''', <big>21/13</big>, <small>13/8</small>, <small>103/64</small>
+|-
+|88
+|851.6129
+|1.6354
+|'''<big>13/8</big>''', 34/21, <small>18/11</small>, <small>21/13</small>, <small>105/64</small>
+|-
+|89
+|861.2903
+|1.6446
+|'''<big><u>18/11</u></big>''', 105/64, 23/14, <small>13/8</small>, <small>28/17</small>, <small>33/20</small>
+|-
+|90
+|870.9677
+|1.6538
+|'''<big>23/14</big>''', <big>28/17</big>, 105/64, 33/20, 38/23, <small>18/11</small>, <small>53/32</small>
+|-
+|91
+|880.6452
+|1.6631
+|'''<big>38/23</big>''', <big>53/32</big>, 33/20, 28/17, <small>23/14</small>, <small>5/3</small>, <small>105/64</small>
+|-
+|92
+|890.3226
+|1.6724
+|<big>5/3</big>, 53/32, <small>107/64</small>, <small>38/23</small>, <small>33/20</small>
+|-
+|93
+|900.0
+|1.6818
+|'''<big><u>107/64</u></big>''', 5/3, <small>32/19</small>, <small>27/16</small>
+|-
+|94
+|909.6774
+|1.6912
+|<big>32/19</big>, 27/16, <small>107/64</small>, <small>22/13</small>, <small>39/23</small>, <small>5/3</small>
+|-
+|95
+|919.3548
+|1.7007
+|'''<big>22/13</big>''', <big>27/16</big>, 39/23, 32/19, <small>17/10</small>, <small>109/64</small>
+|-
+|96
+|929.0323
+|1.7102
+|'''<big><u>17/10</u></big>''', <big>109/64</big>, 39/23, <small>22/13</small>, <small>27/16</small>, <small>12/7</small>
+|-
+|97
+|938.7097
+|1.7198
+|12/7, 109/64, <small>55/32</small>, <small>17/10</small>, <small>39/23</small>
+|-
+|98
+|948.3871
+|1.7295
+|'''<big>55/32</big>''', 12/7, 19/11, <small>26/15</small>, <small>111/64</small>
+|-
+|99
+|958.0645
+|1.7392
+|<big>19/11</big>, <big>26/15</big>, 111/64, 33/19, <small>40/23</small>, <small>55/32</small>, <small>12/7</small>
+|-
+|100
+|967.7419
+|1.7489
+|'''<big><u>40/23</u></big>''', <big>33/19</big>, 111/64, 26/15, <small>7/4</small>, <small>19/11</small>
+|-
+|101
+|977.4194
+|1.7587
+|'''<big>7/4</big>''', <small>40/23</small>, <small>33/19</small>, <small>111/64</small>, <small>26/15</small>, <small>30/17</small>
+|-
+|102
+|987.0968
+|1.7686
+|30/17, 113/64, <small>7/4</small>, <small>23/13</small>, <small>39/22</small>
+|-
+|103
+|996.7742
+|1.7785
+|'''<big><u>23/13</u></big>''', <big>113/64</big>, <big>30/17</big>, 39/22, <small>16/9</small>, <small>57/32</small>
+|-
+|104
+|1006.4516
+|1.7884
+|'''<big><u>16/9</u></big>''', <big>57/32</big>, 39/22, 25/14, <small>23/13</small>, <small>34/19</small>, <small>113/64</small>, <small>30/17</small>
+|-
+|105
+|1016.129
+|1.7985
+|'''<big><u>34/19</u></big>''', <big>25/14</big>, 57/32, <small>115/64</small>, <small>16/9</small>, <small>9/5</small>, <small>39/22</small>
+|-
+|106
+|1025.8065
+|1.8086
+|'''<big>9/5</big>''', '''<big>115/64</big>''', <small>34/19</small>, <small>38/21</small>, <small>25/14</small>, <small>29/16</small>
+|-
+|107
+|1035.4839
+|1.8187
+|'''<big><u>38/21</u></big>''', <big>29/16</big>, <small>9/5</small>, <small>20/11</small>, <small>115/64</small>
+|-
+|108
+|1045.1613
+|1.8289
+|'''<big><u>20/11</u></big>''', 29/16, 42/23, <small>38/21</small>, <small>117/64</small>, <small>11/6</small>
+|-
+|109
+|1054.8387
+|1.8391
+|'''<big><u>117/64</u></big>''', <big>42/23</big>, 11/6, <small>20/11</small>, <small>35/19</small>, <small>59/32</small>, <small>29/16</small>
+|-
+|110
+|1064.5161
+|1.8495
+|<big>35/19</big>, 59/32, 11/6, 24/13, <small>117/64</small>, <small>42/23</small>
+|-
+|111
+|1074.1935
+|1.8598
+|<big>24/13</big>, 59/32, 35/19, 13/7, <small>119/64</small>, <small>11/6</small>
+|-
+|112
+|1083.871
+|1.8702
+|'''<big><u>119/64</u></big>''', <big>13/7</big>, 28/15, <small>24/13</small>, <small>15/8</small>, <small>59/32</small>
+|-
+|113
+|1093.5484
+|1.8807
+|<big>28/15</big>, 15/8, <small>119/64</small>, <small>32/17</small>, <small>13/7</small>
+|-
+|114
+|1103.2258
+|1.8913
+|'''<big>32/17</big>''', 15/8, 17/9, <small>121/64</small>, <small>36/19</small>, <small>28/15</small>
+|-
+|115
+|1112.9032
+|1.9019
+|'''<big><u>121/64</u></big>''', <big>17/9</big>, <big>36/19</big>, 19/10, <small>32/17</small>, <small>40/21</small>, <small>61/32</small>, <small>15/8</small>
+|-
+|116
+|1122.5806
+|1.9125
+|'''<big>19/10</big>''', <big>40/21</big>, <big>61/32</big>, 36/19, 21/11, <small>44/23</small>, <small>121/64</small>, <small>17/9</small>, <small>23/12</small>
+|-
+|117
+|1132.2581
+|1.9233
+|'''<big><u>44/23</u></big>''', <big>21/11</big>, <big>23/12</big>, 61/32, 40/21, <small>123/64</small>, <small>25/13</small>, <small>19/10</small>, <small>27/14</small>
+|-
+|118
+|1141.9355
+|1.934
+|'''<big><u>25/13</u></big>''', '''<big>123/64</big>''', 27/14, 23/12, <small>44/23</small>, <small>31/16</small>, <small>21/11</small>, <small>61/32</small>
+|-
+|119
+|1151.6129
+|1.9449
+|<big>31/16</big>, 27/14, 33/17, <small>35/18</small>, <small>25/13</small>, <small>123/64</small>, <small>39/20</small>, <small>23/12</small>
+|-
+|120
+|1161.2903
+|1.9558
+|'''<big><u>35/18</u></big>''', <big>33/17</big>, 39/20, 31/16, 125/64, <small>45/23</small>, <small>27/14</small>
+|-
+|121
+|1170.9677
+|1.9667
+|'''<big><u>45/23</u></big>''', <big>125/64</big>, 39/20, <small>35/18</small>, <small>63/32</small>, <small>33/17</small>
+|-
+|122
+|1180.6452
+|1.9778
+|'''<big>63/32</big>''', <small>45/23</small>, <small>125/64</small>, <small>39/20</small>, <small>127/64</small>
+|-
+|123
+|1190.3226
+|1.9889
+|127/64, 63/32
+|-
+|124
+|1200.0
+|2.0
+|'''<big><u>2/1</u></big>'''
+|-
+|colspan="4"|
+JI Ratio Approximations are comprised of 23 limit ratios and the odd harmonics up to 127.<br>
+The JI Ratio Approximations are stylized as follows to indicate accuracy:
+* '''<big><u>Big Bold Underlined:</u></big>''' absolute cent error < 1 cent.
+* <big>'''Big Bold:'''</big> absolute cent error < 2 cents.
+* <big>Big:</big> absolute cent error < 4 cents.
+* Normal: absolute cent error < 8 cents.
+* <small>Small:</small> absolute cent error < 16 cents.
+|}
 [[Category:Equal divisions of the octave]]

124edo: Difference between revisions

Revision as of 10:47, 24 April 2021

Navigation menu

Search