124edo: Difference between revisions

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← 123edo

124edo

125edo →

Prime factorization

2² × 31

Step size

9.67742 ¢

Fifth

73\124 (706.452 ¢)

Semitones (A1:m2)

15:7 (145.2 ¢ : 67.74 ¢)

Dual sharp fifth

73\124 (706.452 ¢)

Dual flat fifth

72\124 (696.774 ¢) (→ 18\31)

Dual major 2nd

21\124 (203.226 ¢)

Consistency limit

5

Distinct consistency limit

5

124 equal divisions of the octave (abbreviated 124edo or 124ed2), also called 124-tone equal temperament (124tet) or 124 equal temperament (124et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 124 equal parts of about 9.68 ¢ each. Each step represents a frequency ratio of 2^1/124, or the 124th root of 2.

Theory

124edo is closely related to 31edo, but the patent vals differ on the mapping for 3. The equal temperament tempers out 2048/2025 (diaschisma) and [-6 -24 19⟩ 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. Note that although its sharp fifth is slightly closer to just, both fifths are about equally off in both directions, and its 9th harmonic is especially accurate as a result, so it can be considered a dual-fifth system, in which it performs very well in the 2.9.5.7.11.13.17.19.23.37 subgroup (the dual-fifth no-31's 37-limit), which is arguably the right way to analyze its approximations of JI. Also interesting is that one may want to double the number of notes to add a fifth closer to just, but this causes the relative errors of other primes to double leading to inconsistencies, so its most reasonable and capable conceptualization seems to be that of a dual-fifth system.

Odd harmonics

Approximation of odd harmonics in 124edo
Harmonic		3	5	7	9	11	13	15	17	19	21	23	25
Error	Absolute (¢)	+4.50	+0.78	-1.08	-0.68	+0.29	+1.41	-4.40	+1.50	+2.49	+3.41	+0.76	+1.57
Error	Relative (%)	+46.5	+8.1	-11.2	-7.1	+3.0	+14.5	-45.4	+15.5	+25.7	+35.3	+7.8	+16.2
Steps (reduced)		197 (73)	288 (40)	348 (100)	393 (21)	429 (57)	459 (87)	484 (112)	507 (11)	527 (31)	545 (49)	561 (65)	576 (80)

Approximation of odd harmonics in 124edo (continued)
Harmonic		27	29	31	33	35	37	39	41	43	45	47	49
Error	Absolute (¢)	+3.81	-3.77	-3.10	+4.79	-0.30	+0.27	-3.77	-3.26	+1.39	+0.10	+2.24	-2.17
Error	Relative (%)	+39.4	-39.0	-32.0	+49.5	-3.1	+2.8	-39.0	-33.6	+14.3	+1.0	+23.1	-22.4
Steps (reduced)		590 (94)	602 (106)	614 (118)	626 (6)	636 (16)	646 (26)	655 (35)	664 (44)	673 (53)	681 (61)	689 (69)	696 (76)

Intervals

Table of intervals in 124edo
Step	Cents	Ratio	JI ratio approximations	Ups and downs notation val ⟨124 196] (124b)
0	0.0	1.0	1/1	P1
1	9.6774	1.0056		^1
2	19.3548	1.0112	65/64	^^1
3	29.0323	1.0169	65/64	^^^1
4	38.7097	1.0226	65/64, 33/32	^⁴1
5	48.3871	1.0283	33/32	vvvA1
6	58.0645	1.0341	33/32, 24/23	vvA1, ^^d2
7	67.7419	1.0399	24/23, 23/22, 67/64, 22/21, 33/32	^^^d2
8	77.4194	1.0457	23/22, 67/64, 22/21, 24/23, 21/20, 20/19	v⁴m2
9	87.0968	1.0516	20/19, 21/20, 19/18, 22/21, 67/64, 23/22, 18/17, 24/23	vvvm2
10	96.7742	1.0575	18/17, 19/18, 20/19, 17/16, 21/20, 16/15	vvm2
11	106.4516	1.0634	17/16, 16/15, 18/17, 19/18, 15/14	vm2
12	116.129	1.0694	15/14, 16/15, 17/16, 14/13, 69/64	m2
13	125.8065	1.0754	14/13, 69/64, 15/14, 13/12, 16/15	^m2
14	135.4839	1.0814	13/12, 69/64, 14/13, 25/23, 12/11	^^m2
15	145.1613	1.0875	25/23, 12/11, 13/12, 35/32, 23/21, 69/64	^^^m2
16	154.8387	1.0936	35/32, 23/21, 12/11, 11/10, 25/23	~2
17	164.5161	1.0997	11/10, 23/21, 21/19, 35/32, 12/11, 71/64	vvvM2
18	174.1935	1.1059	21/19, 71/64, 10/9, 11/10	vvM2
19	183.871	1.1121	10/9, 71/64, 19/17, 21/19	vM2
20	193.5484	1.1183	19/17, 9/8, 10/9, 71/64	M2
21	203.2258	1.1246	9/8, 26/23, 19/17, 17/15	^M2
22	212.9032	1.1309	26/23, 17/15, 25/22, 9/8, 73/64	^^M2
23	222.5806	1.1372	25/22, 73/64, 17/15, 8/7, 26/23	^^^M2
24	232.2581	1.1436	8/7, 73/64, 23/20, 25/22, 15/13, 17/15	^⁴M2
25	241.9355	1.15	23/20, 15/13, 37/32, 8/7, 22/19, 73/64	vvvA2
26	251.6129	1.1564	37/32, 22/19, 15/13, 23/20, 7/6	vvA2, ^^d3
27	261.2903	1.1629	7/6, 22/19, 37/32, 75/64, 15/13	^^^d3
28	270.9677	1.1694	75/64, 7/6, 27/23, 20/17	v⁴m3
29	280.6452	1.176	20/17, 27/23, 75/64, 13/11, 7/6	vvvm3
30	290.3226	1.1826	13/11, 19/16, 20/17, 25/21, 27/23, 75/64	vvm3
31	300.0	1.1892	25/21, 19/16, 13/11, 6/5	vm3
32	309.6774	1.1959	6/5, 25/21, 77/64, 19/16	m3
33	319.3548	1.2026	77/64, 6/5, 23/19	^m3
34	329.0323	1.2093	23/19, 17/14, 77/64, 28/23, 6/5, 39/32	^^m3
35	338.7097	1.2161	28/23, 17/14, 39/32, 23/19, 11/9, 27/22	^^^m3
36	348.3871	1.2229	11/9, 39/32, 27/22, 28/23, 16/13, 17/14	~3
37	358.0645	1.2298	16/13, 27/22, 79/64, 21/17, 11/9, 26/21, 39/32	vvvM3
38	367.7419	1.2367	21/17, 26/21, 79/64, 16/13, 27/22	vvM3
39	377.4194	1.2436	26/21, 5/4, 21/17, 79/64	vM3
40	387.0968	1.2506	5/4	M3
41	396.7742	1.2576	24/19, 5/4, 81/64, 19/15	^M3
42	406.4516	1.2646	81/64, 24/19, 19/15, 14/11	^^M3
43	416.129	1.2717	14/11, 19/15, 23/18, 81/64, 24/19, 41/32	^^^M3
44	425.8065	1.2788	23/18, 41/32, 14/11, 9/7	^⁴M3
45	435.4839	1.286	9/7, 41/32, 22/17, 23/18, 83/64	vvvA3
46	445.1613	1.2932	22/17, 83/64, 13/10, 9/7, 30/23	vvA3, ^^d4
47	454.8387	1.3005	13/10, 83/64, 30/23, 22/17, 17/13, 21/16	^^^d4
48	464.5161	1.3078	17/13, 30/23, 21/16, 13/10, 25/19, 83/64	v⁴4
49	474.1935	1.3151	25/19, 21/16, 17/13, 30/23	vvv4
50	483.871	1.3225	85/64, 25/19, 21/16, 4/3	vv4
51	493.5484	1.3299	85/64, 4/3	v4
52	503.2258	1.3373	4/3, 43/32, 85/64	P4
53	512.9032	1.3448	43/32, 27/20, 23/17, 4/3, 19/14	^4
54	522.5806	1.3524	23/17, 27/20, 19/14, 87/64, 43/32, 15/11	^^4
55	532.2581	1.3599	87/64, 19/14, 15/11, 23/17, 26/19, 27/20	^^^4
56	541.9355	1.3676	26/19, 15/11, 11/8, 87/64, 19/14	~4
57	551.6129	1.3752	11/8, 26/19, 18/13, 15/11	vvvA4
58	561.2903	1.3829	18/13, 25/18, 89/64, 11/8, 32/23	vvA4
59	570.9677	1.3907	89/64, 32/23, 25/18, 18/13, 7/5	vA4
60	580.6452	1.3985	7/5, 32/23, 45/32, 89/64, 25/18	A4
61	590.3226	1.4063	45/32, 24/17, 7/5, 17/12	^A4
62	600.0	1.4142	17/12, 24/17, 27/19, 91/64, 45/32	^^A4, vvd5
63	609.6774	1.4221	91/64, 27/19, 17/12, 10/7, 24/17, 33/23	vd5
64	619.3548	1.4301	10/7, 33/23, 23/16, 91/64, 27/19	d5
65	629.0323	1.4381	23/16, 33/23, 13/9, 10/7	^d5
66	638.7097	1.4462	13/9, 93/64, 16/11, 23/16, 33/23	^^d5
67	648.3871	1.4543	16/11, 93/64, 19/13, 13/9, 22/15	^^^d5
68	658.0645	1.4624	19/13, 22/15, 47/32, 16/11, 25/17, 93/64, 28/19	~5
69	667.7419	1.4706	25/17, 47/32, 28/19, 22/15, 34/23, 19/13	vvv5
70	677.4194	1.4789	34/23, 28/19, 95/64, 25/17, 47/32, 22/15	vv5
71	687.0968	1.4872	95/64, 34/23, 3/2, 28/19	v5
72	696.7742	1.4955	3/2, 95/64	P5
73	706.4516	1.5039	3/2, 97/64	^5
74	716.129	1.5123	97/64, 35/23, 32/21, 3/2	^^5
75	725.8065	1.5208	35/23, 32/21, 97/64, 26/17, 49/32, 23/15	^^^5
76	735.4839	1.5293	26/17, 49/32, 23/15, 32/21, 35/23, 20/13, 97/64	^⁴5
77	745.1613	1.5379	20/13, 23/15, 49/32, 17/11, 26/17, 99/64, 32/21	vvvA5
78	754.8387	1.5465	99/64, 17/11, 20/13, 14/9, 23/15	vvA5, ^^d6
79	764.5161	1.5552	14/9, 25/16, 99/64, 17/11, 36/23	^^^d6
80	774.1935	1.5639	36/23, 25/16, 11/7, 14/9, 101/64	v⁴m6
81	783.871	1.5727	11/7, 101/64, 30/19, 36/23, 25/16, 19/12	vvvm6
82	793.5484	1.5815	19/12, 30/19, 101/64, 27/17, 35/22, 11/7, 51/32	vvm6
83	803.2258	1.5904	35/22, 27/17, 51/32, 19/12, 8/5, 30/19, 101/64	vm6
84	812.9032	1.5993	8/5, 51/32, 35/22, 103/64, 27/17	m6
85	822.5806	1.6082	103/64, 21/13, 8/5, 34/21, 51/32	^m6
86	832.2581	1.6173	34/21, 21/13, 13/8, 103/64	^^m6
87	841.9355	1.6263	13/8, 34/21, 18/11, 21/13, 105/64	^^^m6
88	851.6129	1.6354	18/11, 105/64, 23/14, 13/8, 28/17, 33/20	~6
89	861.2903	1.6446	23/14, 28/17, 105/64, 33/20, 38/23, 18/11, 53/32	vvvM6
90	870.9677	1.6538	38/23, 53/32, 33/20, 28/17, 23/14, 5/3, 105/64	vvM6
91	880.6452	1.6631	5/3, 53/32, 107/64, 38/23, 33/20	vM6
92	890.3226	1.6724	107/64, 5/3, 32/19, 27/16	M6
93	900.0	1.6818	32/19, 27/16, 107/64, 22/13, 39/23, 5/3	^M6
94	909.6774	1.6912	22/13, 27/16, 39/23, 32/19, 17/10, 109/64	^^M6
95	919.3548	1.7007	17/10, 109/64, 39/23, 22/13, 27/16, 12/7	^^^M6
96	929.0323	1.7102	12/7, 109/64, 55/32, 17/10, 39/23	^⁴M6
97	938.7097	1.7198	55/32, 12/7, 19/11, 26/15, 111/64	vvvA6
98	948.3871	1.7295	19/11, 26/15, 111/64, 33/19, 40/23, 55/32, 12/7	vvA6, ^^d7
99	958.0645	1.7392	40/23, 33/19, 111/64, 26/15, 7/4, 19/11	^^^d7
100	967.7419	1.7489	7/4, 40/23, 33/19, 111/64, 26/15, 30/17	v⁴m7
101	977.4194	1.7587	30/17, 113/64, 7/4, 23/13, 39/22	vvvm7
102	987.0968	1.7686	23/13, 113/64, 30/17, 39/22, 16/9, 57/32	vvm7
103	996.7742	1.7785	16/9, 57/32, 39/22, 25/14, 23/13, 34/19, 113/64, 30/17	vm7
104	1006.4516	1.7884	34/19, 25/14, 57/32, 115/64, 16/9, 9/5, 39/22	m7
105	1016.129	1.7985	9/5, 115/64, 34/19, 38/21, 25/14, 29/16	^m7
106	1025.8065	1.8086	38/21, 29/16, 9/5, 20/11, 115/64	^^m7
107	1035.4839	1.8187	20/11, 29/16, 42/23, 38/21, 117/64, 11/6	^^^m7
108	1045.1613	1.8289	117/64, 42/23, 11/6, 20/11, 35/19, 59/32, 29/16	~7
109	1054.8387	1.8391	35/19, 59/32, 11/6, 24/13, 117/64, 42/23	vvvM7
110	1064.5161	1.8495	24/13, 59/32, 35/19, 13/7, 119/64, 11/6	vvM7
111	1074.1935	1.8598	119/64, 13/7, 28/15, 24/13, 15/8, 59/32	vM7
112	1083.871	1.8702	28/15, 15/8, 119/64, 32/17, 13/7	M7
113	1093.5484	1.8807	32/17, 15/8, 17/9, 121/64, 36/19, 28/15	^M7
114	1103.2258	1.8913	121/64, 17/9, 36/19, 19/10, 32/17, 40/21, 61/32, 15/8	^^M7
115	1112.9032	1.9019	19/10, 40/21, 61/32, 36/19, 21/11, 44/23, 121/64, 17/9, 23/12	^^^M7
116	1122.5806	1.9125	44/23, 21/11, 23/12, 61/32, 40/21, 123/64, 25/13, 19/10, 27/14	^⁴M7
117	1132.2581	1.9233	25/13, 123/64, 27/14, 23/12, 44/23, 31/16, 21/11, 61/32	vvvA7
118	1141.9355	1.934	31/16, 27/14, 33/17, 35/18, 25/13, 123/64, 39/20, 23/12	vvA7, ^^d1 +1 oct
119	1151.6129	1.9449	35/18, 33/17, 39/20, 31/16, 125/64, 45/23, 27/14	^^^d1 +1 oct
120	1161.2903	1.9558	45/23, 125/64, 39/20, 35/18, 63/32, 33/17	v⁴1 +1 oct
121	1170.9677	1.9667	63/32, 45/23, 125/64, 39/20, 127/64	vvv1 +1 oct
122	1180.6452	1.9778	127/64, 63/32	vv1 +1 oct
123	1190.3226	1.9889	127/64	v1 +1 oct
124	1200.0	2.0	2/1	P1 +1 oct
* 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: @@
 {{Infobox ET}}
-{{EDO intro|124}}
+{{ED intro}}
 == Theory ==
@@ Line 11: / Line 11: @@
 == Intervals ==
 {| class="wikitable mw-collapsible mw-collapsed center-5"
-|+124 EDO Table of Intervals
+|+ style="font-size: 105%; white-space: nowrap;" | Table of intervals in 124edo
-!Step
-!Cents
-!Ratio
-!JI Ratio Approximations
-!Ups and Downs Notation
-[[val]] <124 196] (124b)
 |-
-|0
+! Step
-|0.0
+! Cents
-|1.0
+! Ratio
-|'''<big><u>1/1</u></big>'''
+! JI ratio approximations
-|P1
+! Ups and downs notation<br />[[val]] {{val|124 196}} (124b)
 |-
-|1
+| 0
-|9.6774
+| 0.0
-|1.0056
+| 1.0
-|
+| '''<big><u>1/1</u></big>'''
-|^1
+| P1
 |-
-|2
+| 1
-|19.3548
+| 9.6774
-|1.0112
+| 1.0056
-|65/64
+|
-|^^1
+| ^1
 |-
-|3
+| 2
-|29.0323
+| 19.3548
-|1.0169
+| 1.0112
-|<big>65/64</big>
+| 65/64
-|^^^1
+| ^^1
 |-
-|4
+| 3
-|38.7097
+| 29.0323
-|1.0226
+| 1.0169
-|<small>65/64</small>, <small>33/32</small>
+| <big>65/64</big>
-|^<sup>4</sup>1
+| ^^^1
 |-
-|5
+| 4
-|48.3871
+| 38.7097
-|1.0283
+| 1.0226
-|33/32
+| <small>65/64</small>, <small>33/32</small>
-|vvvA1
+| ^<sup>4</sup>1
 |-
-|6
+| 5
-|58.0645
+| 48.3871
-|1.0341
+| 1.0283
-|33/32, <small>24/23</small>
+| 33/32
-|vvA1, ^^d2
+| vvvA1
 |-
-|7
+| 6
-|67.7419
+| 58.0645
-|1.0399
+| 1.0341
-|24/23, <small>23/22</small>, <small>67/64</small>, <small>22/21</small>, <small>33/32</small>
+| 33/32, <small>24/23</small>
-|^^^d2
+| vvA1, ^^d2
 |-
-|8
+| 7
-|77.4194
+| 67.7419
-|1.0457
+| 1.0399
-|'''<big><u>23/22</u></big>''', '''<big>67/64</big>''', <big>22/21</big>, <big>24/23</big>, 21/20, <small>20/19</small>
+| 24/23, <small>23/22</small>, <small>67/64</small>, <small>22/21</small>, <small>33/32</small>
-|v<sup>4</sup>m2
+| ^^^d2
 |-
-|9
+| 8
-|87.0968
+| 77.4194
-|1.0516
+| 1.0457
-|'''<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>
+| '''<big><u>23/22</u></big>''', '''<big>67/64</big>''', <big>22/21</big>, <big>24/23</big>, 21/20, <small>20/19</small>
-|vvvm2
+| v<sup>4</sup>m2
 |-
-|10
+| 9
-|96.7742
+| 87.0968
-|1.0575
+| 1.0516
-|<big>18/17</big>, <big>19/18</big>, 20/19, <small>17/16</small>, <small>21/20</small>, <small>16/15</small>
+| '''<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>
-|vvm2
+| vvvm2
 |-
-|11
+| 10
-|106.4516
+| 96.7742
-|1.0634
+| 1.0575
-|'''<big>17/16</big>''', 16/15, 18/17, <small>19/18</small>, <small>15/14</small>
+| <big>18/17</big>, <big>19/18</big>, 20/19, <small>17/16</small>, <small>21/20</small>, <small>16/15</small>
-|vm2
+| vvm2
 |-
-|12
+| 11
-|116.129
+| 106.4516
-|1.0694
+| 1.0634
-|<big>15/14</big>, 16/15, <small>17/16</small>, <small>14/13</small>, <small>69/64</small>
+| '''<big>17/16</big>''', 16/15, 18/17, <small>19/18</small>, <small>15/14</small>
-|m2
+| vm2
 |-
-|13
+| 12
-|125.8065
+| 116.129
-|1.0754
+| 1.0694
-|<big>14/13</big>, 69/64, 15/14, <small>13/12</small>, <small>16/15</small>
+| <big>15/14</big>, 16/15, <small>17/16</small>, <small>14/13</small>, <small>69/64</small>
-|^m2
+| m2
 |-
-|14
+| 13
-|135.4839
+| 125.8065
-|1.0814
+| 1.0754
-|<big>13/12</big>, 69/64, 14/13, <small>25/23</small>, <small>12/11</small>
+| <big>14/13</big>, 69/64, 15/14, <small>13/12</small>, <small>16/15</small>
-|^^m2
+| ^m2
 |-
-|15
+| 14
-|145.1613
+| 135.4839
-|1.0875
+| 1.0814
-|'''<big><u>25/23</u></big>''', 12/11, 13/12, <small>35/32</small>, <small>23/21</small>, <small>69/64</small>
+| <big>13/12</big>, 69/64, 14/13, <small>25/23</small>, <small>12/11</small>
-|^^^m2
+| ^^m2
 |-
-|16
+| 15
-|154.8387
+| 145.1613
-|1.0936
+| 1.0875
-|'''<big><u>35/32</u></big>''', <big>23/21</big>, 12/11, <small>11/10</small>, <small>25/23</small>
+| '''<big><u>25/23</u></big>''', 12/11, 13/12, <small>35/32</small>, <small>23/21</small>, <small>69/64</small>
-|~2
+| ^^^m2
 |-
-|17
+| 16
-|164.5161
+| 154.8387
-|1.0997
+| 1.0936
-|'''<big><u>11/10</u></big>''', 23/21, <small>21/19</small>, <small>35/32</small>, <small>12/11</small>, <small>71/64</small>
+| '''<big><u>35/32</u></big>''', <big>23/21</big>, 12/11, <small>11/10</small>, <small>25/23</small>
-|vvvM2
+| ~2
 |-
-|18
+| 17
-|174.1935
+| 164.5161
-|1.1059
+| 1.0997
-|'''<big><u>21/19</u></big>''', 71/64, <small>10/9</small>, <small>11/10</small>
+| '''<big><u>11/10</u></big>''', 23/21, <small>21/19</small>, <small>35/32</small>, <small>12/11</small>, <small>71/64</small>
-|vvM2
+| vvvM2
 |-
-|19
+| 18
-|183.871
+| 174.1935
-|1.1121
+| 1.1059
-|'''<big>10/9</big>''', 71/64, <small>19/17</small>, <small>21/19</small>
+| '''<big><u>21/19</u></big>''', 71/64, <small>10/9</small>, <small>11/10</small>
-|vM2
+| vvM2
 |-
-|20
+| 19
-|193.5484
+| 183.871
-|1.1183
+| 1.1121
-|'''<big><u>19/17</u></big>''', <small>9/8</small>, <small>10/9</small>, <small>71/64</small>
+| '''<big>10/9</big>''', 71/64, <small>19/17</small>, <small>21/19</small>
-|M2
+| vM2
 |-
-|21
+| 20
-|203.2258
+| 193.5484
-|1.1246
+| 1.1183
-|'''<big><u>9/8</u></big>''', <small>26/23</small>, <small>19/17</small>, <small>17/15</small>
+| '''<big><u>19/17</u></big>''', <small>9/8</small>, <small>10/9</small>, <small>71/64</small>
-|^M2
+| M2
 |-
-|22
+| 21
-|212.9032
+| 203.2258
-|1.1309
+| 1.1246
-|'''<big><u>26/23</u></big>''', <big>17/15</big>, <small>25/22</small>, <small>9/8</small>, <small>73/64</small>
+| '''<big><u>9/8</u></big>''', <small>26/23</small>, <small>19/17</small>, <small>17/15</small>
-|^^M2
+| ^M2
 |-
-|23
+| 22
-|222.5806
+| 212.9032
-|1.1372
+| 1.1309
-|'''<big>25/22</big>''', 73/64, 17/15, <small>8/7</small>, <small>26/23</small>
+| '''<big><u>26/23</u></big>''', <big>17/15</big>, <small>25/22</small>, <small>9/8</small>, <small>73/64</small>
-|^^^M2
+| ^^M2
 |-
-|24
+| 23
-|232.2581
+| 222.5806
-|1.1436
+| 1.1372
-|'''<big>8/7</big>''', 73/64, <small>23/20</small>, <small>25/22</small>, <small>15/13</small>, <small>17/15</small>
+| '''<big>25/22</big>''', 73/64, 17/15, <small>8/7</small>, <small>26/23</small>
-|^<sup>4</sup>M2
+| ^^^M2
 |-
-|25
+| 24
-|241.9355
+| 232.2581
-|1.15
+| 1.1436
-|'''<big><u>23/20</u></big>''', 15/13, <small>37/32</small>, <small>8/7</small>, <small>22/19</small>, <small>73/64</small>
+| '''<big>8/7</big>''', 73/64, <small>23/20</small>, <small>25/22</small>, <small>15/13</small>, <small>17/15</small>
-|vvvA2
+| ^<sup>4</sup>M2
 |-
-|26
+| 25
-|251.6129
+| 241.9355
-|1.1564
+| 1.15
-|'''<big><u>37/32</u></big>''', <big>22/19</big>, <big>15/13</big>, <small>23/20</small>, <small>7/6</small>
+| '''<big><u>23/20</u></big>''', 15/13, <small>37/32</small>, <small>8/7</small>, <small>22/19</small>, <small>73/64</small>
-|vvA2, ^^d3
+| vvvA2
 |-
-|27
+| 26
-|261.2903
+| 251.6129
-|1.1629
+| 1.1564
-|7/6, 22/19, <small>37/32</small>, <small>75/64</small>, <small>15/13</small>
+| '''<big><u>37/32</u></big>''', <big>22/19</big>, <big>15/13</big>, <small>23/20</small>, <small>7/6</small>
-|^^^d3
+| vvA2, ^^d3
 |-
-|28
+| 27
-|270.9677
+| 261.2903
-|1.1694
+| 1.1629
-|<big>75/64</big>, 7/6, 27/23, <small>20/17</small>
+| 7/6, 22/19, <small>37/32</small>, <small>75/64</small>, <small>15/13</small>
-|v<sup>4</sup>m3
+| ^^^d3
 |-
-|29
+| 28
-|280.6452
+| 270.9677
-|1.176
+| 1.1694
-|'''<big><u>20/17</u></big>''', <big>27/23</big>, 75/64, <small>13/11</small>, <small>7/6</small>
+| <big>75/64</big>, 7/6, 27/23, <small>20/17</small>
-|vvvm3
+| v<sup>4</sup>m3
 |-
-|30
+| 29
-|290.3226
+| 280.6452
-|1.1826
+| 1.176
-|'''<big>13/11</big>''', 19/16, <small>20/17</small>, <small>25/21</small>, <small>27/23</small>, <small>75/64</small>
+| '''<big><u>20/17</u></big>''', <big>27/23</big>, 75/64, <small>13/11</small>, <small>7/6</small>
-|vvm3
+| vvvm3
 |-
-|31
+| 30
-|300.0
+| 290.3226
-|1.1892
+| 1.1826
-|'''<big>25/21</big>''', <big>19/16</big>, <small>13/11</small>, <small>6/5</small>
+| '''<big>13/11</big>''', 19/16, <small>20/17</small>, <small>25/21</small>, <small>27/23</small>, <small>75/64</small>
-|vm3
+| vvm3
 |-
-|32
+| 31
-|309.6774
+| 300.0
-|1.1959
+| 1.1892
-|6/5, 25/21, <small>77/64</small>, <small>19/16</small>
+| '''<big>25/21</big>''', <big>19/16</big>, <small>13/11</small>, <small>6/5</small>
-|m3
+| vm3
 |-
-|33
+| 32
-|319.3548
+| 309.6774
-|1.2026
+| 1.1959
-|'''<big><u>77/64</u></big>''', <big>6/5</big>, <small>23/19</small>
+| 6/5, 25/21, <small>77/64</small>, <small>19/16</small>
-|^m3
+| m3
 |-
-|34
+| 33
-|329.0323
+| 319.3548
-|1.2093
+| 1.2026
-|'''<big>23/19</big>''', 17/14, <small>77/64</small>, <small>28/23</small>, <small>6/5</small>, <small>39/32</small>
+| '''<big><u>77/64</u></big>''', <big>6/5</big>, <small>23/19</small>
-|^^m3
+| ^m3
 |-
-|35
+| 34
-|338.7097
+| 329.0323
-|1.2161
+| 1.2093
-|'''<big>28/23</big>''', <big>17/14</big>, <big>39/32</big>, 23/19, <small>11/9</small>, <small>27/22</small>
+| '''<big>23/19</big>''', 17/14, <small>77/64</small>, <small>28/23</small>, <small>6/5</small>, <small>39/32</small>
-|^^^m3
+| ^^m3
 |-
-|36
+| 35
-|348.3871
+| 338.7097
-|1.2229
+| 1.2161
-|'''<big><u>11/9</u></big>''', 39/32, 27/22, 28/23, <small>16/13</small>, <small>17/14</small>
+| '''<big>28/23</big>''', <big>17/14</big>, <big>39/32</big>, 23/19, <small>11/9</small>, <small>27/22</small>
-|~3
+| ^^^m3
 |-
-|37
+| 36
-|358.0645
+| 348.3871
-|1.2298
+| 1.2229
-|'''<big>16/13</big>''', <big>27/22</big>, 79/64, 21/17, <small>11/9</small>, <small>26/21</small>, <small>39/32</small>
+| '''<big><u>11/9</u></big>''', 39/32, 27/22, 28/23, <small>16/13</small>, <small>17/14</small>
-|vvvM3
+| ~3
 |-
-|38
+| 37
-|367.7419
+| 358.0645
-|1.2367
+| 1.2298
-|'''<big>21/17</big>''', <big>26/21</big>, <big>79/64</big>, <small>16/13</small>, <small>27/22</small>
+| '''<big>16/13</big>''', <big>27/22</big>, 79/64, 21/17, <small>11/9</small>, <small>26/21</small>, <small>39/32</small>
-|vvM3
+| vvvM3
 |-
-|39
+| 38
-|377.4194
+| 367.7419
-|1.2436
+| 1.2367
-|26/21, <small>5/4</small>, <small>21/17</small>, <small>79/64</small>
+| '''<big>21/17</big>''', <big>26/21</big>, <big>79/64</big>, <small>16/13</small>, <small>27/22</small>
-|vM3
+| vvM3
 |-
-|40
+| 39
-|387.0968
+| 377.4194
-|1.2506
+| 1.2436
-|'''<big><u>5/4</u></big>'''
+| 26/21, <small>5/4</small>, <small>21/17</small>, <small>79/64</small>
-|M3
+| vM3
 |-
-|41
+| 40
-|396.7742
+| 387.0968
-|1.2576
+| 1.2506
-|24/19, <small>5/4</small>, <small>81/64</small>, <small>19/15</small>
+| '''<big><u>5/4</u></big>'''
-|^M3
+| M3
 |-
-|42
+| 41
-|406.4516
+| 396.7742
-|1.2646
+| 1.2576
-|'''<big>81/64</big>''', <big>24/19</big>, <big>19/15</big>, <small>14/11</small>
+| 24/19, <small>5/4</small>, <small>81/64</small>, <small>19/15</small>
-|^^M3
+| ^M3
 |-
-|43
+| 42
-|416.129
+| 406.4516
-|1.2717
+| 1.2646
-|'''<big>14/11</big>''', 19/15, <small>23/18</small>, <small>81/64</small>, <small>24/19</small>, <small>41/32</small>
+| '''<big>81/64</big>''', <big>24/19</big>, <big>19/15</big>, <small>14/11</small>
-|^^^M3
+| ^^M3
 |-
-|44
+| 43
-|425.8065
+| 416.129
-|1.2788
+| 1.2717
-|'''<big>23/18</big>''', <big>41/32</big>, <small>14/11</small>, <small>9/7</small>
+| '''<big>14/11</big>''', 19/15, <small>23/18</small>, <small>81/64</small>, <small>24/19</small>, <small>41/32</small>
-|^<sup>4</sup>M3
+| ^^^M3
 |-
-|45
+| 44
-|435.4839
+| 425.8065
-|1.286
+| 1.2788
-|'''<big><u>9/7</u></big>''', 41/32, <small>22/17</small>, <small>23/18</small>, <small>83/64</small>
+| '''<big>23/18</big>''', <big>41/32</big>, <small>14/11</small>, <small>9/7</small>
-|vvvA3
+| ^<sup>4</sup>M3
 |-
-|46
+| 45
-|445.1613
+| 435.4839
-|1.2932
+| 1.286
-|'''<big>22/17</big>''', 83/64, <small>13/10</small>, <small>9/7</small>, <small>30/23</small>
+| '''<big><u>9/7</u></big>''', 41/32, <small>22/17</small>, <small>23/18</small>, <small>83/64</small>
-|vvA3, ^^d4
+| vvvA3
 |-
-|47
+| 46
-|454.8387
+| 445.1613
-|1.3005
+| 1.2932
-|'''<big><u>13/10</u></big>''', 83/64, 30/23, <small>22/17</small>, <small>17/13</small>, <small>21/16</small>
+| '''<big>22/17</big>''', 83/64, <small>13/10</small>, <small>9/7</small>, <small>30/23</small>
-|^^^d4
+| vvA3, ^^d4
 |-
-|48
+| 47
-|464.5161
+| 454.8387
-|1.3078
+| 1.3005
-|'''<big><u>17/13</u></big>''', 30/23, 21/16, <small>13/10</small>, <small>25/19</small>, <small>83/64</small>
+| '''<big><u>13/10</u></big>''', 83/64, 30/23, <small>22/17</small>, <small>17/13</small>, <small>21/16</small>
-|v<sup>4</sup>4
+| ^^^d4
 |-
-|49
+| 48
-|474.1935
+| 464.5161
-|1.3151
+| 1.3078
-|'''<big><u>25/19</u></big>''', <big>21/16</big>, <small>17/13</small>, <small>30/23</small>
+| '''<big><u>17/13</u></big>''', 30/23, 21/16, <small>13/10</small>, <small>25/19</small>, <small>83/64</small>
-|vvv4
+| v<sup>4</sup>4
 |-
-|50
+| 49
-|483.871
+| 474.1935
-|1.3225
+| 1.3151
-|85/64, <small>25/19</small>, <small>21/16</small>, <small>4/3</small>
+| '''<big><u>25/19</u></big>''', <big>21/16</big>, <small>17/13</small>, <small>30/23</small>
-|vv4
+| vvv4
 |-
-|51
+| 50
-|493.5484
+| 483.871
-|1.3299
+| 1.3225
-|<big>85/64</big>, 4/3
+| 85/64, <small>25/19</small>, <small>21/16</small>, <small>4/3</small>
-|v4
+| vv4
 |-
-|52
+| 51
-|503.2258
+| 493.5484
-|1.3373
+| 1.3299
-|4/3, <small>43/32</small>, <small>85/64</small>
+| <big>85/64</big>, 4/3
-|P4
+| v4
 |-
-|53
+| 52
-|512.9032
+| 503.2258
-|1.3448
+| 1.3373
-|'''<big>43/32</big>''', 27/20, <small>23/17</small>, <small>4/3</small>, <small>19/14</small>
+| 4/3, <small>43/32</small>, <small>85/64</small>
-|^4
+| P4
 |-
-|54
+| 53
-|522.5806
+| 512.9032
-|1.3524
+| 1.3448
-|'''<big><u>23/17</u></big>''', <big>27/20</big>, 19/14, <small>87/64</small>, <small>43/32</small>, <small>15/11</small>
+| '''<big>43/32</big>''', 27/20, <small>23/17</small>, <small>4/3</small>, <small>19/14</small>
-|^^4
+| ^4
 |-
-|55
+| 54
-|532.2581
+| 522.5806
-|1.3599
+| 1.3524
-|'''<big><u>87/64</u></big>''', <big>19/14</big>, 15/11, <small>23/17</small>, <small>26/19</small>, <small>27/20</small>
+| '''<big><u>23/17</u></big>''', <big>27/20</big>, 19/14, <small>87/64</small>, <small>43/32</small>, <small>15/11</small>
-|^^^4
+| ^^4
 |-
-|56
+| 55
-|541.9355
+| 532.2581
-|1.3676
+| 1.3599
-|'''<big>26/19</big>''', 15/11, <small>11/8</small>, <small>87/64</small>, <small>19/14</small>
+| '''<big><u>87/64</u></big>''', <big>19/14</big>, 15/11, <small>23/17</small>, <small>26/19</small>, <small>27/20</small>
-|~4
+| ^^^4
 |-
-|57
+| 56
-|551.6129
+| 541.9355
-|1.3752
+| 1.3676
-|'''<big><u>11/8</u></big>''', <small>26/19</small>, <small>18/13</small>, <small>15/11</small>
+| '''<big>26/19</big>''', 15/11, <small>11/8</small>, <small>87/64</small>, <small>19/14</small>
-|vvvA4
+| ~4
 |-
-|58
+| 57
-|561.2903
+| 551.6129
-|1.3829
+| 1.3752
-|<big>18/13</big>, 25/18, <small>89/64</small>, <small>11/8</small>, <small>32/23</small>
+| '''<big><u>11/8</u></big>''', <small>26/19</small>, <small>18/13</small>, <small>15/11</small>
-|vvA4
+| vvvA4
 |-
-|59
+| 58
-|570.9677
+| 561.2903
-|1.3907
+| 1.3829
-|'''<big><u>89/64</u></big>''', '''<big><u>32/23</u></big>''', <big>25/18</big>, 18/13, <small>7/5</small>
+| <big>18/13</big>, 25/18, <small>89/64</small>, <small>11/8</small>, <small>32/23</small>
-|vA4
+| vvA4
 |-
-|60
+| 59
-|580.6452
+| 570.9677
-|1.3985
+| 1.3907
-|'''<big>7/5</big>''', <small>32/23</small>, <small>45/32</small>, <small>89/64</small>, <small>25/18</small>
+| '''<big><u>89/64</u></big>''', '''<big><u>32/23</u></big>''', <big>25/18</big>, 18/13, <small>7/5</small>
-|A4
+| vA4
 |-
-|61
+| 60
-|590.3226
+| 580.6452
-|1.4063
+| 1.3985
-|'''<big><u>45/32</u></big>''', 24/17, 7/5, <small>17/12</small>
+| '''<big>7/5</big>''', <small>32/23</small>, <small>45/32</small>, <small>89/64</small>, <small>25/18</small>
-|^A4
+| A4
 |-
-|62
+| 61
-|600.0
+| 590.3226
-|1.4142
+| 1.4063
-|<big>17/12</big>, <big>24/17</big>, <small>27/19</small>, <small>91/64</small>, <small>45/32</small>
+| '''<big><u>45/32</u></big>''', 24/17, 7/5, <small>17/12</small>
-|^^A4, vvd5
+| ^A4
 |-
-|63
+| 62
-|609.6774
+| 600.0
-|1.4221
+| 1.4142
-|'''<big><u>91/64</u></big>''', '''<big>27/19</big>''', 17/12, 10/7, <small>24/17</small>, <small>33/23</small>
+| <big>17/12</big>, <big>24/17</big>, <small>27/19</small>, <small>91/64</small>, <small>45/32</small>
-|vd5
+| ^^A4, vvd5
 |-
-|64
+| 63
-|619.3548
+| 609.6774
-|1.4301
+| 1.4221
-|'''<big>10/7</big>''', 33/23, <small>23/16</small>, <small>91/64</small>, <small>27/19</small>
+| '''<big><u>91/64</u></big>''', '''<big>27/19</big>''', 17/12, 10/7, <small>24/17</small>, <small>33/23</small>
-|d5
+| vd5
 |-
-|65
+| 64
-|629.0323
+| 619.3548
-|1.4381
+| 1.4301
-|'''<big><u>23/16</u></big>''', 33/23, 13/9, <small>10/7</small>
+| '''<big>10/7</big>''', 33/23, <small>23/16</small>, <small>91/64</small>, <small>27/19</small>
-|^d5
+| d5
 |-
-|66
+| 65
-|638.7097
+| 629.0323
-|1.4462
+| 1.4381
-|<big>13/9</big>, <small>93/64</small>, <small>16/11</small>, <small>23/16</small>, <small>33/23</small>
+| '''<big><u>23/16</u></big>''', 33/23, 13/9, <small>10/7</small>
-|^^d5
+| ^d5
 |-
-|67
+| 66
-|648.3871
+| 638.7097
-|1.4543
+| 1.4462
-|'''<big><u>16/11</u></big>''', '''<big>93/64</big>''', <small>19/13</small>, <small>13/9</small>, <small>22/15</small>
+| <big>13/9</big>, <small>93/64</small>, <small>16/11</small>, <small>23/16</small>, <small>33/23</small>
-|^^^d5
+| ^^d5
 |-
-|68
+| 67
-|658.0645
+| 648.3871
-|1.4624
+| 1.4543
-|'''<big>19/13</big>''', 22/15, 47/32, <small>16/11</small>, <small>25/17</small>, <small>93/64</small>, <small>28/19</small>
+| '''<big><u>16/11</u></big>''', '''<big>93/64</big>''', <small>19/13</small>, <small>13/9</small>, <small>22/15</small>
-|~5
+| ^^^d5
 |-
-|69
+| 68
-|667.7419
+| 658.0645
-|1.4706
+| 1.4624
-|'''<big><u>25/17</u></big>''', <big>47/32</big>, <big>28/19</big>, 22/15, <small>34/23</small>, <small>19/13</small>
+| '''<big>19/13</big>''', 22/15, 47/32, <small>16/11</small>, <small>25/17</small>, <small>93/64</small>, <small>28/19</small>
-|vvv5
+| ~5
 |-
-|70
+| 69
-|677.4194
+| 667.7419
-|1.4789
+| 1.4706
-|'''<big><u>34/23</u></big>''', 28/19, 95/64, <small>25/17</small>, <small>47/32</small>, <small>22/15</small>
+| '''<big><u>25/17</u></big>''', <big>47/32</big>, <big>28/19</big>, 22/15, <small>34/23</small>, <small>19/13</small>
-|vv5
+| vvv5
 |-
-|71
+| 70
-|687.0968
+| 677.4194
-|1.4872
+| 1.4789
-|<big>95/64</big>, <small>34/23</small>, <small>3/2</small>, <small>28/19</small>
+| '''<big><u>34/23</u></big>''', 28/19, 95/64, <small>25/17</small>, <small>47/32</small>, <small>22/15</small>
-|v5
+| vv5
 |-
-|72
+| 71
-|696.7742
+| 687.0968
-|1.4955
+| 1.4872
-|3/2, <small>95/64</small>
+| <big>95/64</big>, <small>34/23</small>, <small>3/2</small>, <small>28/19</small>
-|P5
+| v5
 |-
-|73
+| 72
-|706.4516
+| 696.7742
-|1.5039
+| 1.4955
-|3/2, <small>97/64</small>
+| 3/2, <small>95/64</small>
-|^5
+| P5
 |-
-|74
+| 73
-|716.129
+| 706.4516
-|1.5123
+| 1.5039
-|<big>97/64</big>, <small>35/23</small>, <small>32/21</small>, <small>3/2</small>
+| 3/2, <small>97/64</small>
-|^^5
+| ^5
 |-
-|75
+| 74
-|725.8065
+| 716.129
-|1.5208
+| 1.5123
-|'''<big>35/23</big>''', <big>32/21</big>, 97/64, <small>26/17</small>, <small>49/32</small>, <small>23/15</small>
+| <big>97/64</big>, <small>35/23</small>, <small>32/21</small>, <small>3/2</small>
-|^^^5
+| ^^5
 |-
-|76
+| 75
-|735.4839
+| 725.8065
-|1.5293
+| 1.5208
-|'''<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>
+| '''<big>35/23</big>''', <big>32/21</big>, 97/64, <small>26/17</small>, <small>49/32</small>, <small>23/15</small>
-|^<sup>4</sup>5
+| ^^^5
 |-
-|77
+| 76
-|745.1613
+| 735.4839
-|1.5379
+| 1.5293
-|'''<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>
+| '''<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>
-|vvvA5
+| ^<sup>4</sup>5
 |-
-|78
+| 77
-|754.8387
+| 745.1613
-|1.5465
+| 1.5379
-|'''<big><u>99/64</u></big>''', '''<big>17/11</big>''', <small>20/13</small>, <small>14/9</small>, <small>23/15</small>
+| '''<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>
-|vvA5, ^^d6
+| vvvA5
 |-
-|79
+| 78
-|764.5161
+| 754.8387
-|1.5552
+| 1.5465
-|'''<big><u>14/9</u></big>''', <small>25/16</small>, <small>99/64</small>, <small>17/11</small>, <small>36/23</small>
+| '''<big><u>99/64</u></big>''', '''<big>17/11</big>''', <small>20/13</small>, <small>14/9</small>, <small>23/15</small>
-|^^^d6
+| vvA5, ^^d6
 |-
-|80
+| 79
-|774.1935
+| 764.5161
-|1.5639
+| 1.5552
-|'''<big>36/23</big>''', '''<big>25/16</big>''', <small>11/7</small>, <small>14/9</small>, <small>101/64</small>
+| '''<big><u>14/9</u></big>''', <small>25/16</small>, <small>99/64</small>, <small>17/11</small>, <small>36/23</small>
-|v<sup>4</sup>m6
+| ^^^d6
 |-
-|81
+| 80
-|783.871
+| 774.1935
-|1.5727
+| 1.5639
-|'''<big>11/7</big>''', 101/64, 30/19, <small>36/23</small>, <small>25/16</small>, <small>19/12</small>
+| '''<big>36/23</big>''', '''<big>25/16</big>''', <small>11/7</small>, <small>14/9</small>, <small>101/64</small>
-|vvvm6
+| v<sup>4</sup>m6
 |-
-|82
+| 81
-|793.5484
+| 783.871
-|1.5815
+| 1.5727
-|<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>
+| '''<big>11/7</big>''', 101/64, 30/19, <small>36/23</small>, <small>25/16</small>, <small>19/12</small>
-|vvm6
+| vvvm6
 |-
-|83
+| 82
-|803.2258
+| 793.5484
-|1.5904
+| 1.5815
-|'''<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>
+| <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>
-|vm6
+| vvm6
 |-
-|84
+| 83
-|812.9032
+| 803.2258
-|1.5993
+| 1.5904
-|'''<big><u>8/5</u></big>''', 51/32, <small>35/22</small>, <small>103/64</small>, <small>27/17</small>
+| '''<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>
-|m6
+| vm6
 |-
-|85
+| 84
-|822.5806
+| 812.9032
-|1.6082
+| 1.5993
-|'''<big>103/64</big>''', 21/13, <small>8/5</small>, <small>34/21</small>, <small>51/32</small>
+| '''<big><u>8/5</u></big>''', 51/32, <small>35/22</small>, <small>103/64</small>, <small>27/17</small>
-|^m6
+| m6
 |-
-|86
+| 85
-|832.2581
+| 822.5806
-|1.6173
+| 1.6082
-|'''<big>34/21</big>''', <big>21/13</big>, <small>13/8</small>, <small>103/64</small>
+| '''<big>103/64</big>''', 21/13, <small>8/5</small>, <small>34/21</small>, <small>51/32</small>
-|^^m6
+| ^m6
 |-
-|87
+| 86
-|841.9355
+| 832.2581
-|1.6263
+| 1.6173
-|'''<big>13/8</big>''', 34/21, <small>18/11</small>, <small>21/13</small>, <small>105/64</small>
+| '''<big>34/21</big>''', <big>21/13</big>, <small>13/8</small>, <small>103/64</small>
-|^^^m6
+| ^^m6
 |-
-|88
+| 87
-|851.6129
+| 841.9355
-|1.6354
+| 1.6263
-|'''<big><u>18/11</u></big>''', 105/64, 23/14, <small>13/8</small>, <small>28/17</small>, <small>33/20</small>
+| '''<big>13/8</big>''', 34/21, <small>18/11</small>, <small>21/13</small>, <small>105/64</small>
-|~6
+| ^^^m6
 |-
-|89
+| 88
-|861.2903
+| 851.6129
-|1.6446
+| 1.6354
-|'''<big>23/14</big>''', <big>28/17</big>, 105/64, 33/20, 38/23, <small>18/11</small>, <small>53/32</small>
+| '''<big><u>18/11</u></big>''', 105/64, 23/14, <small>13/8</small>, <small>28/17</small>, <small>33/20</small>
-|vvvM6
+| ~6
 |-
-|90
+| 89
-|870.9677
+| 861.2903
-|1.6538
+| 1.6446
-|'''<big>38/23</big>''', <big>53/32</big>, 33/20, 28/17, <small>23/14</small>, <small>5/3</small>, <small>105/64</small>
+| '''<big>23/14</big>''', <big>28/17</big>, 105/64, 33/20, 38/23, <small>18/11</small>, <small>53/32</small>
-|vvM6
+| vvvM6
 |-
-|91
+| 90
-|880.6452
+| 870.9677
-|1.6631
+| 1.6538
-|<big>5/3</big>, 53/32, <small>107/64</small>, <small>38/23</small>, <small>33/20</small>
+| '''<big>38/23</big>''', <big>53/32</big>, 33/20, 28/17, <small>23/14</small>, <small>5/3</small>, <small>105/64</small>
-|vM6
+| vvM6
 |-
-|92
+| 91
-|890.3226
+| 880.6452
-|1.6724
+| 1.6631
-|'''<big><u>107/64</u></big>''', 5/3, <small>32/19</small>, <small>27/16</small>
+| <big>5/3</big>, 53/32, <small>107/64</small>, <small>38/23</small>, <small>33/20</small>
-|M6
+| vM6
 |-
-|93
+| 92
-|900.0
+| 890.3226
-|1.6818
+| 1.6724
-|<big>32/19</big>, 27/16, <small>107/64</small>, <small>22/13</small>, <small>39/23</small>, <small>5/3</small>
+| '''<big><u>107/64</u></big>''', 5/3, <small>32/19</small>, <small>27/16</small>
-|^M6
+| M6
 |-
-|94
+| 93
-|909.6774
+| 900.0
-|1.6912
+| 1.6818
-|'''<big>22/13</big>''', <big>27/16</big>, 39/23, 32/19, <small>17/10</small>, <small>109/64</small>
+| <big>32/19</big>, 27/16, <small>107/64</small>, <small>22/13</small>, <small>39/23</small>, <small>5/3</small>
-|^^M6
+| ^M6
 |-
-|95
+| 94
-|919.3548
+| 909.6774
-|1.7007
+| 1.6912
-|'''<big><u>17/10</u></big>''', <big>109/64</big>, 39/23, <small>22/13</small>, <small>27/16</small>, <small>12/7</small>
+| '''<big>22/13</big>''', <big>27/16</big>, 39/23, 32/19, <small>17/10</small>, <small>109/64</small>
-|^^^M6
+| ^^M6
 |-
-|96
+| 95
-|929.0323
+| 919.3548
-|1.7102
+| 1.7007
-|12/7, 109/64, <small>55/32</small>, <small>17/10</small>, <small>39/23</small>
+| '''<big><u>17/10</u></big>''', <big>109/64</big>, 39/23, <small>22/13</small>, <small>27/16</small>, <small>12/7</small>
-|^<sup>4</sup>M6
+| ^^^M6
 |-
-|97
+| 96
-|938.7097
+| 929.0323
-|1.7198
+| 1.7102
-|'''<big>55/32</big>''', 12/7, 19/11, <small>26/15</small>, <small>111/64</small>
+| 12/7, 109/64, <small>55/32</small>, <small>17/10</small>, <small>39/23</small>
-|vvvA6
+| ^<sup>4</sup>M6
 |-
-|98
+| 97
-|948.3871
+| 938.7097
-|1.7295
+| 1.7198
-|<big>19/11</big>, <big>26/15</big>, 111/64, 33/19, <small>40/23</small>, <small>55/32</small>, <small>12/7</small>
+| '''<big>55/32</big>''', 12/7, 19/11, <small>26/15</small>, <small>111/64</small>
-|vvA6, ^^d7
+| vvvA6
 |-
-|99
+| 98
-|958.0645
+| 948.3871
-|1.7392
+| 1.7295
-|'''<big><u>40/23</u></big>''', <big>33/19</big>, 111/64, 26/15, <small>7/4</small>, <small>19/11</small>
+| <big>19/11</big>, <big>26/15</big>, 111/64, 33/19, <small>40/23</small>, <small>55/32</small>, <small>12/7</small>
-|^^^d7
+| vvA6, ^^d7
 |-
-|100
+| 99
-|967.7419
+| 958.0645
-|1.7489
+| 1.7392
-|'''<big>7/4</big>''', <small>40/23</small>, <small>33/19</small>, <small>111/64</small>, <small>26/15</small>, <small>30/17</small>
+| '''<big><u>40/23</u></big>''', <big>33/19</big>, 111/64, 26/15, <small>7/4</small>, <small>19/11</small>
-|v<sup>4</sup>m7
+| ^^^d7
 |-
-|101
+| 100
-|977.4194
+| 967.7419
-|1.7587
+| 1.7489
-|30/17, 113/64, <small>7/4</small>, <small>23/13</small>, <small>39/22</small>
+| '''<big>7/4</big>''', <small>40/23</small>, <small>33/19</small>, <small>111/64</small>, <small>26/15</small>, <small>30/17</small>
-|vvvm7
+| v<sup>4</sup>m7
 |-
-|102
+| 101
-|987.0968
+| 977.4194
-|1.7686
+| 1.7587
-|'''<big><u>23/13</u></big>''', <big>113/64</big>, <big>30/17</big>, 39/22, <small>16/9</small>, <small>57/32</small>
+| 30/17, 113/64, <small>7/4</small>, <small>23/13</small>, <small>39/22</small>
-|vvm7
+| vvvm7
 |-
-|103
+| 102
-|996.7742
+| 987.0968
-|1.7785
+| 1.7686
-|'''<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>
+| '''<big><u>23/13</u></big>''', <big>113/64</big>, <big>30/17</big>, 39/22, <small>16/9</small>, <small>57/32</small>
-|vm7
+| vvm7
 |-
-|104
+| 103
-|1006.4516
+| 996.7742
-|1.7884
+| 1.7785
-|'''<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>
+| '''<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>
-|m7
+| vm7
 |-
-|105
+| 104
-|1016.129
+| 1006.4516
-|1.7985
+| 1.7884
-|'''<big>9/5</big>''', '''<big>115/64</big>''', <small>34/19</small>, <small>38/21</small>, <small>25/14</small>, <small>29/16</small>
+| '''<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>
-|^m7
+| m7
 |-
-|106
+| 105
-|1025.8065
+| 1016.129
-|1.8086
+| 1.7985
-|'''<big><u>38/21</u></big>''', <big>29/16</big>, <small>9/5</small>, <small>20/11</small>, <small>115/64</small>
+| '''<big>9/5</big>''', '''<big>115/64</big>''', <small>34/19</small>, <small>38/21</small>, <small>25/14</small>, <small>29/16</small>
-|^^m7
+| ^m7
 |-
-|107
+| 106
-|1035.4839
+| 1025.8065
-|1.8187
+| 1.8086
-|'''<big><u>20/11</u></big>''', 29/16, 42/23, <small>38/21</small>, <small>117/64</small>, <small>11/6</small>
+| '''<big><u>38/21</u></big>''', <big>29/16</big>, <small>9/5</small>, <small>20/11</small>, <small>115/64</small>
-|^^^m7
+| ^^m7
 |-
-|108
+| 107
-|1045.1613
+| 1035.4839
-|1.8289
+| 1.8187
-|'''<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>
+| '''<big><u>20/11</u></big>''', 29/16, 42/23, <small>38/21</small>, <small>117/64</small>, <small>11/6</small>
-|~7
+| ^^^m7
 |-
-|109
+| 108
-|1054.8387
+| 1045.1613
-|1.8391
+| 1.8289
-|<big>35/19</big>, 59/32, 11/6, 24/13, <small>117/64</small>, <small>42/23</small>
+| '''<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>
-|vvvM7
+| ~7
 |-
-|110
+| 109
-|1064.5161
+| 1054.8387
-|1.8495
+| 1.8391
-|<big>24/13</big>, 59/32, 35/19, 13/7, <small>119/64</small>, <small>11/6</small>
+| <big>35/19</big>, 59/32, 11/6, 24/13, <small>117/64</small>, <small>42/23</small>
-|vvM7
+| vvvM7
 |-
-|111
+| 110
-|1074.1935
+| 1064.5161
-|1.8598
+| 1.8495
-|'''<big><u>119/64</u></big>''', <big>13/7</big>, 28/15, <small>24/13</small>, <small>15/8</small>, <small>59/32</small>
+| <big>24/13</big>, 59/32, 35/19, 13/7, <small>119/64</small>, <small>11/6</small>
-|vM7
+| vvM7
 |-
-|112
+| 111
-|1083.871
+| 1074.1935
-|1.8702
+| 1.8598
-|<big>28/15</big>, 15/8, <small>119/64</small>, <small>32/17</small>, <small>13/7</small>
+| '''<big><u>119/64</u></big>''', <big>13/7</big>, 28/15, <small>24/13</small>, <small>15/8</small>, <small>59/32</small>
-|M7
+| vM7
 |-
-|113
+| 112
-|1093.5484
+| 1083.871
-|1.8807
+| 1.8702
-|'''<big>32/17</big>''', 15/8, 17/9, <small>121/64</small>, <small>36/19</small>, <small>28/15</small>
+| <big>28/15</big>, 15/8, <small>119/64</small>, <small>32/17</small>, <small>13/7</small>
-|^M7
+| M7
 |-
-|114
+| 113
-|1103.2258
+| 1093.5484
-|1.8913
+| 1.8807
-|'''<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>
+| '''<big>32/17</big>''', 15/8, 17/9, <small>121/64</small>, <small>36/19</small>, <small>28/15</small>
-|^^M7
+| ^M7
 |-
-|115
+| 114
-|1112.9032
+| 1103.2258
-|1.9019
+| 1.8913
-|'''<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>
+| '''<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>
-|^^^M7
+| ^^M7
 |-
-|116
+| 115
-|1122.5806
+| 1112.9032
-|1.9125
+| 1.9019
-|'''<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>
+| '''<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>
-|^<sup>4</sup>M7
+| ^^^M7
 |-
-|117
+| 116
-|1132.2581
+| 1122.5806
-|1.9233
+| 1.9125
-|'''<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>
+| '''<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>
-|vvvA7
+| ^<sup>4</sup>M7
 |-
-|118
+| 117
-|1141.9355
+| 1132.2581
-|1.934
+| 1.9233
-|<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>
+| '''<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>
-|vvA7, ^^d1 +1 oct
+| vvvA7
 |-
-|119
+| 118
-|1151.6129
+| 1141.9355
-|1.9449
+| 1.934
-|'''<big><u>35/18</u></big>''', <big>33/17</big>, 39/20, 31/16, 125/64, <small>45/23</small>, <small>27/14</small>
+| <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>
-|^^^d1 +1 oct
+| vvA7, ^^d1 +1 oct
 |-
-|120
+| 119
-|1161.2903
+| 1151.6129
-|1.9558
+| 1.9449
-|'''<big><u>45/23</u></big>''', <big>125/64</big>, 39/20, <small>35/18</small>, <small>63/32</small>, <small>33/17</small>
+| '''<big><u>35/18</u></big>''', <big>33/17</big>, 39/20, 31/16, 125/64, <small>45/23</small>, <small>27/14</small>
-|v<sup>4</sup>1 +1 oct
+| ^^^d1 +1 oct
 |-
-|121
+| 120
-|1170.9677
+| 1161.2903
-|1.9667
+| 1.9558
-|'''<big>63/32</big>''', <small>45/23</small>, <small>125/64</small>, <small>39/20</small>, <small>127/64</small>
+| '''<big><u>45/23</u></big>''', <big>125/64</big>, 39/20, <small>35/18</small>, <small>63/32</small>, <small>33/17</small>
-|vvv1 +1 oct
+| v<sup>4</sup>1 +1 oct
 |-
-|122
+| 121
-|1180.6452
+| 1170.9677
-|1.9778
+| 1.9667
-|127/64, 63/32
+| '''<big>63/32</big>''', <small>45/23</small>, <small>125/64</small>, <small>39/20</small>, <small>127/64</small>
-|vv1 +1 oct
+| vvv1 +1 oct
 |-
-|123
+| 122
-|1190.3226
+| 1180.6452
-|1.9889
+| 1.9778
-|<big>127/64</big>
+| 127/64, 63/32
-|v1 +1 oct
+| vv1 +1 oct
 |-
-|124
+| 123
-|1200.0
+| 1190.3226
-|2.0
+| 1.9889
-|'''<big><u>2/1</u></big>'''
+| <big>127/64</big>
-|P1 +1 oct
+| v1 +1 oct
 |-
-|colspan="4"|
+| 124
-JI Ratio Approximations are comprised of 23 limit ratios and the odd harmonics up to 127.<br>
+| 1200.0
-The JI Ratio Approximations are stylized as follows to indicate accuracy:
+| 2.0
-* '''<big><u>Big Bold Underlined:</u></big>''' absolute cent error < 1 cent.
+| '''<big><u>2/1</u></big>'''
-* <big>'''Big Bold:'''</big> absolute cent error < 2 cents.
+| P1 +1 oct
-* <big>Big:</big> absolute cent error < 4 cents.
+|-
-* Normal: absolute cent error < 8 cents.
+| colspan="5" style="padding-left: 1em;" | <nowiki />* JI ratio approximations are comprised of 23 limit ratios and the odd harmonics up to 127.<br />
-* <small>Small:</small> absolute cent error < 16 cents.
+: 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|###]] <!-- 3-digit number -->

124edo: Difference between revisions

Revision as of 19:22, 20 February 2025

Theory

Odd harmonics

Intervals

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