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'''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.
'''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]]
[[Category:Equal divisions of the octave]]
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