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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|124}}
{{ED intro}}


== Theory ==
== Theory ==
Line 11: Line 11:
== Intervals ==
== Intervals ==
{| class="wikitable mw-collapsible mw-collapsed center-5"
{| 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.
|}
|}


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[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
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