124edo: Difference between revisions

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VisualWikitext
Contribution (talk | contribs)
2,905 edits
Contribution (talk | contribs)
2,905 edits
Line 15: Line 15:
!Cents
!Cents
!Ratio
!Ratio
!JI Ratio Approximations
!JI Ratio Approximations
!JI Ratio Approximations
|-
|-
Line 21: Line 22:
|1.0
|1.0
|'''<big><u>1/1</u></big>'''
|'''<big><u>1/1</u></big>'''
|P1
|-
|-
|1
|1
Line 26: Line 28:
|1.0056
|1.0056
|
|
|^1
|-
|-
|2
|2
Line 31: Line 34:
|1.0112
|1.0112
|65/64
|65/64
|^^1
|-
|-
|3
|3
Line 36: Line 40:
|1.0169
|1.0169
|<big>65/64</big>
|<big>65/64</big>
|^^^1
|-
|-
|4
|4
Line 41: Line 46:
|1.0226
|1.0226
|<small>65/64</small>, <small>33/32</small>
|<small>65/64</small>, <small>33/32</small>
|^<sup>4</sup>1
|-
|-
|5
|5
Line 46: Line 52:
|1.0283
|1.0283
|33/32
|33/32
|vvvA1
|-
|-
|6
|6
Line 51: Line 58:
|1.0341
|1.0341
|33/32, <small>24/23</small>
|33/32, <small>24/23</small>
|vvA1, ^^d2
|-
|-
|7
|7
Line 56: Line 64:
|1.0399
|1.0399
|24/23, <small>23/22</small>, <small>67/64</small>, <small>22/21</small>, <small>33/32</small>
|24/23, <small>23/22</small>, <small>67/64</small>, <small>22/21</small>, <small>33/32</small>
|^^^d2
|-
|-
|8
|8
Line 61: Line 70:
|1.0457
|1.0457
|'''<big><u>23/22</u></big>''', '''<big>67/64</big>''', <big>22/21</big>, <big>24/23</big>, 21/20, <small>20/19</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>
|v<sup>4</sup>m2
|-
|-
|9
|9
Line 66: Line 76:
|1.0516
|1.0516
|'''<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>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>
|vvvm2
|-
|-
|10
|10
Line 71: Line 82:
|1.0575
|1.0575
|<big>18/17</big>, <big>19/18</big>, 20/19, <small>17/16</small>, <small>21/20</small>, <small>16/15</small>
|<big>18/17</big>, <big>19/18</big>, 20/19, <small>17/16</small>, <small>21/20</small>, <small>16/15</small>
|vvm2
|-
|-
|11
|11
Line 76: Line 88:
|1.0634
|1.0634
|'''<big>17/16</big>''', 16/15, 18/17, <small>19/18</small>, <small>15/14</small>
|'''<big>17/16</big>''', 16/15, 18/17, <small>19/18</small>, <small>15/14</small>
|vm2
|-
|-
|12
|12
Line 81: Line 94:
|1.0694
|1.0694
|<big>15/14</big>, 16/15, <small>17/16</small>, <small>14/13</small>, <small>69/64</small>
|<big>15/14</big>, 16/15, <small>17/16</small>, <small>14/13</small>, <small>69/64</small>
|m2
|-
|-
|13
|13
Line 86: Line 100:
|1.0754
|1.0754
|<big>14/13</big>, 69/64, 15/14, <small>13/12</small>, <small>16/15</small>
|<big>14/13</big>, 69/64, 15/14, <small>13/12</small>, <small>16/15</small>
|^m2
|-
|-
|14
|14
Line 91: Line 106:
|1.0814
|1.0814
|<big>13/12</big>, 69/64, 14/13, <small>25/23</small>, <small>12/11</small>
|<big>13/12</big>, 69/64, 14/13, <small>25/23</small>, <small>12/11</small>
|^^m2
|-
|-
|15
|15
Line 96: Line 112:
|1.0875
|1.0875
|'''<big><u>25/23</u></big>''', 12/11, 13/12, <small>35/32</small>, <small>23/21</small>, <small>69/64</small>
|'''<big><u>25/23</u></big>''', 12/11, 13/12, <small>35/32</small>, <small>23/21</small>, <small>69/64</small>
|^^^m2
|-
|-
|16
|16
Line 101: Line 118:
|1.0936
|1.0936
|'''<big><u>35/32</u></big>''', <big>23/21</big>, 12/11, <small>11/10</small>, <small>25/23</small>
|'''<big><u>35/32</u></big>''', <big>23/21</big>, 12/11, <small>11/10</small>, <small>25/23</small>
|~2
|-
|-
|17
|17
Line 106: Line 124:
|1.0997
|1.0997
|'''<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>11/10</u></big>''', 23/21, <small>21/19</small>, <small>35/32</small>, <small>12/11</small>, <small>71/64</small>
|vvvM2
|-
|-
|18
|18
Line 111: Line 130:
|1.1059
|1.1059
|'''<big><u>21/19</u></big>''', 71/64, <small>10/9</small>, <small>11/10</small>
|'''<big><u>21/19</u></big>''', 71/64, <small>10/9</small>, <small>11/10</small>
|vvM2
|-
|-
|19
|19
Line 116: Line 136:
|1.1121
|1.1121
|'''<big>10/9</big>''', 71/64, <small>19/17</small>, <small>21/19</small>
|'''<big>10/9</big>''', 71/64, <small>19/17</small>, <small>21/19</small>
|vM2
|-
|-
|20
|20
Line 121: Line 142:
|1.1183
|1.1183
|'''<big><u>19/17</u></big>''', <small>9/8</small>, <small>10/9</small>, <small>71/64</small>
|'''<big><u>19/17</u></big>''', <small>9/8</small>, <small>10/9</small>, <small>71/64</small>
|M2
|-
|-
|21
|21
Line 126: Line 148:
|1.1246
|1.1246
|'''<big><u>9/8</u></big>''', <small>26/23</small>, <small>19/17</small>, <small>17/15</small>
|'''<big><u>9/8</u></big>''', <small>26/23</small>, <small>19/17</small>, <small>17/15</small>
|^M2
|-
|-
|22
|22
Line 131: Line 154:
|1.1309
|1.1309
|'''<big><u>26/23</u></big>''', <big>17/15</big>, <small>25/22</small>, <small>9/8</small>, <small>73/64</small>
|'''<big><u>26/23</u></big>''', <big>17/15</big>, <small>25/22</small>, <small>9/8</small>, <small>73/64</small>
|^^M2
|-
|-
|23
|23
Line 136: Line 160:
|1.1372
|1.1372
|'''<big>25/22</big>''', 73/64, 17/15, <small>8/7</small>, <small>26/23</small>
|'''<big>25/22</big>''', 73/64, 17/15, <small>8/7</small>, <small>26/23</small>
|^^^M2
|-
|-
|24
|24
Line 141: Line 166:
|1.1436
|1.1436
|'''<big>8/7</big>''', 73/64, <small>23/20</small>, <small>25/22</small>, <small>15/13</small>, <small>17/15</small>
|'''<big>8/7</big>''', 73/64, <small>23/20</small>, <small>25/22</small>, <small>15/13</small>, <small>17/15</small>
|^<sup>4</sup>M2
|-
|-
|25
|25
Line 146: Line 172:
|1.15
|1.15
|'''<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><u>23/20</u></big>''', 15/13, <small>37/32</small>, <small>8/7</small>, <small>22/19</small>, <small>73/64</small>
|vvvA2
|-
|-
|26
|26
Line 151: Line 178:
|1.1564
|1.1564
|'''<big><u>37/32</u></big>''', <big>22/19</big>, <big>15/13</big>, <small>23/20</small>, <small>7/6</small>
|'''<big><u>37/32</u></big>''', <big>22/19</big>, <big>15/13</big>, <small>23/20</small>, <small>7/6</small>
|vvA2, ^^d3
|-
|-
|27
|27
Line 156: Line 184:
|1.1629
|1.1629
|7/6, 22/19, <small>37/32</small>, <small>75/64</small>, <small>15/13</small>
|7/6, 22/19, <small>37/32</small>, <small>75/64</small>, <small>15/13</small>
|^^^d3
|-
|-
|28
|28
Line 161: Line 190:
|1.1694
|1.1694
|<big>75/64</big>, 7/6, 27/23, <small>20/17</small>
|<big>75/64</big>, 7/6, 27/23, <small>20/17</small>
|v<sup>4</sup>m3
|-
|-
|29
|29
Line 166: Line 196:
|1.176
|1.176
|'''<big><u>20/17</u></big>''', <big>27/23</big>, 75/64, <small>13/11</small>, <small>7/6</small>
|'''<big><u>20/17</u></big>''', <big>27/23</big>, 75/64, <small>13/11</small>, <small>7/6</small>
|vvvm3
|-
|-
|30
|30
Line 171: Line 202:
|1.1826
|1.1826
|'''<big>13/11</big>''', 19/16, <small>20/17</small>, <small>25/21</small>, <small>27/23</small>, <small>75/64</small>
|'''<big>13/11</big>''', 19/16, <small>20/17</small>, <small>25/21</small>, <small>27/23</small>, <small>75/64</small>
|vvm3
|-
|-
|31
|31
Line 176: Line 208:
|1.1892
|1.1892
|'''<big>25/21</big>''', <big>19/16</big>, <small>13/11</small>, <small>6/5</small>
|'''<big>25/21</big>''', <big>19/16</big>, <small>13/11</small>, <small>6/5</small>
|vm3
|-
|-
|32
|32
Line 181: Line 214:
|1.1959
|1.1959
|6/5, 25/21, <small>77/64</small>, <small>19/16</small>
|6/5, 25/21, <small>77/64</small>, <small>19/16</small>
|m3
|-
|-
|33
|33
Line 186: Line 220:
|1.2026
|1.2026
|'''<big><u>77/64</u></big>''', <big>6/5</big>, <small>23/19</small>
|'''<big><u>77/64</u></big>''', <big>6/5</big>, <small>23/19</small>
|^m3
|-
|-
|34
|34
Line 191: Line 226:
|1.2093
|1.2093
|'''<big>23/19</big>''', 17/14, <small>77/64</small>, <small>28/23</small>, <small>6/5</small>, <small>39/32</small>
|'''<big>23/19</big>''', 17/14, <small>77/64</small>, <small>28/23</small>, <small>6/5</small>, <small>39/32</small>
|^^m3
|-
|-
|35
|35
Line 196: Line 232:
|1.2161
|1.2161
|'''<big>28/23</big>''', <big>17/14</big>, <big>39/32</big>, 23/19, <small>11/9</small>, <small>27/22</small>
|'''<big>28/23</big>''', <big>17/14</big>, <big>39/32</big>, 23/19, <small>11/9</small>, <small>27/22</small>
|^^^m3
|-
|-
|36
|36
Line 201: Line 238:
|1.2229
|1.2229
|'''<big><u>11/9</u></big>''', 39/32, 27/22, 28/23, <small>16/13</small>, <small>17/14</small>
|'''<big><u>11/9</u></big>''', 39/32, 27/22, 28/23, <small>16/13</small>, <small>17/14</small>
|~3
|-
|-
|37
|37
Line 206: Line 244:
|1.2298
|1.2298
|'''<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>16/13</big>''', <big>27/22</big>, 79/64, 21/17, <small>11/9</small>, <small>26/21</small>, <small>39/32</small>
|vvvM3
|-
|-
|38
|38
Line 211: Line 250:
|1.2367
|1.2367
|'''<big>21/17</big>''', <big>26/21</big>, <big>79/64</big>, <small>16/13</small>, <small>27/22</small>
|'''<big>21/17</big>''', <big>26/21</big>, <big>79/64</big>, <small>16/13</small>, <small>27/22</small>
|vvM3
|-
|-
|39
|39
Line 216: Line 256:
|1.2436
|1.2436
|26/21, <small>5/4</small>, <small>21/17</small>, <small>79/64</small>
|26/21, <small>5/4</small>, <small>21/17</small>, <small>79/64</small>
|vM3
|-
|-
|40
|40
Line 221: Line 262:
|1.2506
|1.2506
|'''<big><u>5/4</u></big>'''
|'''<big><u>5/4</u></big>'''
|M3
|-
|-
|41
|41
Line 226: Line 268:
|1.2576
|1.2576
|24/19, <small>5/4</small>, <small>81/64</small>, <small>19/15</small>
|24/19, <small>5/4</small>, <small>81/64</small>, <small>19/15</small>
|^M3
|-
|-
|42
|42
Line 231: Line 274:
|1.2646
|1.2646
|'''<big>81/64</big>''', <big>24/19</big>, <big>19/15</big>, <small>14/11</small>
|'''<big>81/64</big>''', <big>24/19</big>, <big>19/15</big>, <small>14/11</small>
|^^M3
|-
|-
|43
|43
Line 236: Line 280:
|1.2717
|1.2717
|'''<big>14/11</big>''', 19/15, <small>23/18</small>, <small>81/64</small>, <small>24/19</small>, <small>41/32</small>
|'''<big>14/11</big>''', 19/15, <small>23/18</small>, <small>81/64</small>, <small>24/19</small>, <small>41/32</small>
|^^^M3
|-
|-
|44
|44
Line 241: Line 286:
|1.2788
|1.2788
|'''<big>23/18</big>''', <big>41/32</big>, <small>14/11</small>, <small>9/7</small>
|'''<big>23/18</big>''', <big>41/32</big>, <small>14/11</small>, <small>9/7</small>
|^<sup>4</sup>M3
|-
|-
|45
|45
Line 246: Line 292:
|1.286
|1.286
|'''<big><u>9/7</u></big>''', 41/32, <small>22/17</small>, <small>23/18</small>, <small>83/64</small>
|'''<big><u>9/7</u></big>''', 41/32, <small>22/17</small>, <small>23/18</small>, <small>83/64</small>
|vvvA3
|-
|-
|46
|46
Line 251: Line 298:
|1.2932
|1.2932
|'''<big>22/17</big>''', 83/64, <small>13/10</small>, <small>9/7</small>, <small>30/23</small>
|'''<big>22/17</big>''', 83/64, <small>13/10</small>, <small>9/7</small>, <small>30/23</small>
|vvA3, ^^d4
|-
|-
|47
|47
Line 256: Line 304:
|1.3005
|1.3005
|'''<big><u>13/10</u></big>''', 83/64, 30/23, <small>22/17</small>, <small>17/13</small>, <small>21/16</small>
|'''<big><u>13/10</u></big>''', 83/64, 30/23, <small>22/17</small>, <small>17/13</small>, <small>21/16</small>
|^^^d4
|-
|-
|48
|48
Line 261: Line 310:
|1.3078
|1.3078
|'''<big><u>17/13</u></big>''', 30/23, 21/16, <small>13/10</small>, <small>25/19</small>, <small>83/64</small>
|'''<big><u>17/13</u></big>''', 30/23, 21/16, <small>13/10</small>, <small>25/19</small>, <small>83/64</small>
|v<sup>4</sup>4
|-
|-
|49
|49
Line 266: Line 316:
|1.3151
|1.3151
|'''<big><u>25/19</u></big>''', <big>21/16</big>, <small>17/13</small>, <small>30/23</small>
|'''<big><u>25/19</u></big>''', <big>21/16</big>, <small>17/13</small>, <small>30/23</small>
|vvv4
|-
|-
|50
|50
Line 271: Line 322:
|1.3225
|1.3225
|85/64, <small>25/19</small>, <small>21/16</small>, <small>4/3</small>
|85/64, <small>25/19</small>, <small>21/16</small>, <small>4/3</small>
|vv4
|-
|-
|51
|51
Line 276: Line 328:
|1.3299
|1.3299
|<big>85/64</big>, 4/3
|<big>85/64</big>, 4/3
|v4
|-
|-
|52
|52
Line 281: Line 334:
|1.3373
|1.3373
|4/3, <small>43/32</small>, <small>85/64</small>
|4/3, <small>43/32</small>, <small>85/64</small>
|P4
|-
|-
|53
|53
Line 286: Line 340:
|1.3448
|1.3448
|'''<big>43/32</big>''', 27/20, <small>23/17</small>, <small>4/3</small>, <small>19/14</small>
|'''<big>43/32</big>''', 27/20, <small>23/17</small>, <small>4/3</small>, <small>19/14</small>
|^4
|-
|-
|54
|54
Line 291: Line 346:
|1.3524
|1.3524
|'''<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><u>23/17</u></big>''', <big>27/20</big>, 19/14, <small>87/64</small>, <small>43/32</small>, <small>15/11</small>
|^^4
|-
|-
|55
|55
Line 296: Line 352:
|1.3599
|1.3599
|'''<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>87/64</u></big>''', <big>19/14</big>, 15/11, <small>23/17</small>, <small>26/19</small>, <small>27/20</small>
|^^^4
|-
|-
|56
|56
Line 301: Line 358:
|1.3676
|1.3676
|'''<big>26/19</big>''', 15/11, <small>11/8</small>, <small>87/64</small>, <small>19/14</small>
|'''<big>26/19</big>''', 15/11, <small>11/8</small>, <small>87/64</small>, <small>19/14</small>
|~4
|-
|-
|57
|57
Line 306: Line 364:
|1.3752
|1.3752
|'''<big><u>11/8</u></big>''', <small>26/19</small>, <small>18/13</small>, <small>15/11</small>
|'''<big><u>11/8</u></big>''', <small>26/19</small>, <small>18/13</small>, <small>15/11</small>
|vvvA4
|-
|-
|58
|58
Line 311: Line 370:
|1.3829
|1.3829
|<big>18/13</big>, 25/18, <small>89/64</small>, <small>11/8</small>, <small>32/23</small>
|<big>18/13</big>, 25/18, <small>89/64</small>, <small>11/8</small>, <small>32/23</small>
|vvA4
|-
|-
|59
|59
Line 316: Line 376:
|1.3907
|1.3907
|'''<big><u>89/64</u></big>''', '''<big><u>32/23</u></big>''', <big>25/18</big>, 18/13, <small>7/5</small>
|'''<big><u>89/64</u></big>''', '''<big><u>32/23</u></big>''', <big>25/18</big>, 18/13, <small>7/5</small>
|vA4
|-
|-
|60
|60
Line 321: Line 382:
|1.3985
|1.3985
|'''<big>7/5</big>''', <small>32/23</small>, <small>45/32</small>, <small>89/64</small>, <small>25/18</small>
|'''<big>7/5</big>''', <small>32/23</small>, <small>45/32</small>, <small>89/64</small>, <small>25/18</small>
|A4
|-
|-
|61
|61
Line 326: Line 388:
|1.4063
|1.4063
|'''<big><u>45/32</u></big>''', 24/17, 7/5, <small>17/12</small>
|'''<big><u>45/32</u></big>''', 24/17, 7/5, <small>17/12</small>
|^A4
|-
|-
|62
|62
Line 331: Line 394:
|1.4142
|1.4142
|<big>17/12</big>, <big>24/17</big>, <small>27/19</small>, <small>91/64</small>, <small>45/32</small>
|<big>17/12</big>, <big>24/17</big>, <small>27/19</small>, <small>91/64</small>, <small>45/32</small>
|^^A4, vvd5
|-
|-
|63
|63
Line 336: Line 400:
|1.4221
|1.4221
|'''<big><u>91/64</u></big>''', '''<big>27/19</big>''', 17/12, 10/7, <small>24/17</small>, <small>33/23</small>
|'''<big><u>91/64</u></big>''', '''<big>27/19</big>''', 17/12, 10/7, <small>24/17</small>, <small>33/23</small>
|vd5
|-
|-
|64
|64
Line 341: Line 406:
|1.4301
|1.4301
|'''<big>10/7</big>''', 33/23, <small>23/16</small>, <small>91/64</small>, <small>27/19</small>
|'''<big>10/7</big>''', 33/23, <small>23/16</small>, <small>91/64</small>, <small>27/19</small>
|d5
|-
|-
|65
|65
Line 346: Line 412:
|1.4381
|1.4381
|'''<big><u>23/16</u></big>''', 33/23, 13/9, <small>10/7</small>
|'''<big><u>23/16</u></big>''', 33/23, 13/9, <small>10/7</small>
|^d5
|-
|-
|66
|66
Line 351: Line 418:
|1.4462
|1.4462
|<big>13/9</big>, <small>93/64</small>, <small>16/11</small>, <small>23/16</small>, <small>33/23</small>
|<big>13/9</big>, <small>93/64</small>, <small>16/11</small>, <small>23/16</small>, <small>33/23</small>
|^^d5
|-
|-
|67
|67
Line 356: Line 424:
|1.4543
|1.4543
|'''<big><u>16/11</u></big>''', '''<big>93/64</big>''', <small>19/13</small>, <small>13/9</small>, <small>22/15</small>
|'''<big><u>16/11</u></big>''', '''<big>93/64</big>''', <small>19/13</small>, <small>13/9</small>, <small>22/15</small>
|^^^d5
|-
|-
|68
|68
Line 361: Line 430:
|1.4624
|1.4624
|'''<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>19/13</big>''', 22/15, 47/32, <small>16/11</small>, <small>25/17</small>, <small>93/64</small>, <small>28/19</small>
|~5
|-
|-
|69
|69
Line 366: Line 436:
|1.4706
|1.4706
|'''<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><u>25/17</u></big>''', <big>47/32</big>, <big>28/19</big>, 22/15, <small>34/23</small>, <small>19/13</small>
|vvv5
|-
|-
|70
|70
Line 371: Line 442:
|1.4789
|1.4789
|'''<big><u>34/23</u></big>''', 28/19, 95/64, <small>25/17</small>, <small>47/32</small>, <small>22/15</small>
|'''<big><u>34/23</u></big>''', 28/19, 95/64, <small>25/17</small>, <small>47/32</small>, <small>22/15</small>
|vv5
|-
|-
|71
|71
Line 376: Line 448:
|1.4872
|1.4872
|<big>95/64</big>, <small>34/23</small>, <small>3/2</small>, <small>28/19</small>
|<big>95/64</big>, <small>34/23</small>, <small>3/2</small>, <small>28/19</small>
|v5
|-
|-
|72
|72
Line 381: Line 454:
|1.4955
|1.4955
|3/2, <small>95/64</small>
|3/2, <small>95/64</small>
|P5
|-
|-
|73
|73
Line 386: Line 460:
|1.5039
|1.5039
|3/2, <small>97/64</small>
|3/2, <small>97/64</small>
|^5
|-
|-
|74
|74
Line 391: Line 466:
|1.5123
|1.5123
|<big>97/64</big>, <small>35/23</small>, <small>32/21</small>, <small>3/2</small>
|<big>97/64</big>, <small>35/23</small>, <small>32/21</small>, <small>3/2</small>
|^^5
|-
|-
|75
|75
Line 396: Line 472:
|1.5208
|1.5208
|'''<big>35/23</big>''', <big>32/21</big>, 97/64, <small>26/17</small>, <small>49/32</small>, <small>23/15</small>
|'''<big>35/23</big>''', <big>32/21</big>, 97/64, <small>26/17</small>, <small>49/32</small>, <small>23/15</small>
|^^^5
|-
|-
|76
|76
Line 401: Line 478:
|1.5293
|1.5293
|'''<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><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>
|^<sup>4</sup>5
|-
|-
|77
|77
Line 406: Line 484:
|1.5379
|1.5379
|'''<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>20/13</u></big>''', 23/15, 49/32, <small>17/11</small>, <small>26/17</small>, <small>99/64</small>, <small>32/21</small>
|vvvA5
|-
|-
|78
|78
Line 411: Line 490:
|1.5465
|1.5465
|'''<big><u>99/64</u></big>''', '''<big>17/11</big>''', <small>20/13</small>, <small>14/9</small>, <small>23/15</small>
|'''<big><u>99/64</u></big>''', '''<big>17/11</big>''', <small>20/13</small>, <small>14/9</small>, <small>23/15</small>
|vvA5, ^^d6
|-
|-
|79
|79
Line 416: Line 496:
|1.5552
|1.5552
|'''<big><u>14/9</u></big>''', <small>25/16</small>, <small>99/64</small>, <small>17/11</small>, <small>36/23</small>
|'''<big><u>14/9</u></big>''', <small>25/16</small>, <small>99/64</small>, <small>17/11</small>, <small>36/23</small>
|^^^d6
|-
|-
|80
|80
Line 421: Line 502:
|1.5639
|1.5639
|'''<big>36/23</big>''', '''<big>25/16</big>''', <small>11/7</small>, <small>14/9</small>, <small>101/64</small>
|'''<big>36/23</big>''', '''<big>25/16</big>''', <small>11/7</small>, <small>14/9</small>, <small>101/64</small>
|v<sup>4</sup>m6
|-
|-
|81
|81
Line 426: Line 508:
|1.5727
|1.5727
|'''<big>11/7</big>''', 101/64, 30/19, <small>36/23</small>, <small>25/16</small>, <small>19/12</small>
|'''<big>11/7</big>''', 101/64, 30/19, <small>36/23</small>, <small>25/16</small>, <small>19/12</small>
|vvvm6
|-
|-
|82
|82
Line 431: Line 514:
|1.5815
|1.5815
|<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>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>
|vvm6
|-
|-
|83
|83
Line 436: Line 520:
|1.5904
|1.5904
|'''<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><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>
|vm6
|-
|-
|84
|84
Line 441: Line 526:
|1.5993
|1.5993
|'''<big><u>8/5</u></big>''', 51/32, <small>35/22</small>, <small>103/64</small>, <small>27/17</small>
|'''<big><u>8/5</u></big>''', 51/32, <small>35/22</small>, <small>103/64</small>, <small>27/17</small>
|m6
|-
|-
|85
|85
Line 446: Line 532:
|1.6082
|1.6082
|'''<big>103/64</big>''', 21/13, <small>8/5</small>, <small>34/21</small>, <small>51/32</small>
|'''<big>103/64</big>''', 21/13, <small>8/5</small>, <small>34/21</small>, <small>51/32</small>
|^m6
|-
|-
|86
|86
Line 451: Line 538:
|1.6173
|1.6173
|'''<big>34/21</big>''', <big>21/13</big>, <small>13/8</small>, <small>103/64</small>
|'''<big>34/21</big>''', <big>21/13</big>, <small>13/8</small>, <small>103/64</small>
|^^m6
|-
|-
|87
|87
Line 456: Line 544:
|1.6263
|1.6263
|'''<big>13/8</big>''', 34/21, <small>18/11</small>, <small>21/13</small>, <small>105/64</small>
|'''<big>13/8</big>''', 34/21, <small>18/11</small>, <small>21/13</small>, <small>105/64</small>
|^^^m6
|-
|-
|88
|88
Line 461: Line 550:
|1.6354
|1.6354
|'''<big><u>18/11</u></big>''', 105/64, 23/14, <small>13/8</small>, <small>28/17</small>, <small>33/20</small>
|'''<big><u>18/11</u></big>''', 105/64, 23/14, <small>13/8</small>, <small>28/17</small>, <small>33/20</small>
|~6
|-
|-
|89
|89
Line 466: Line 556:
|1.6446
|1.6446
|'''<big>23/14</big>''', <big>28/17</big>, 105/64, 33/20, 38/23, <small>18/11</small>, <small>53/32</small>
|'''<big>23/14</big>''', <big>28/17</big>, 105/64, 33/20, 38/23, <small>18/11</small>, <small>53/32</small>
|vvvM6
|-
|-
|90
|90
Line 471: Line 562:
|1.6538
|1.6538
|'''<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>38/23</big>''', <big>53/32</big>, 33/20, 28/17, <small>23/14</small>, <small>5/3</small>, <small>105/64</small>
|vvM6
|-
|-
|91
|91
Line 476: Line 568:
|1.6631
|1.6631
|<big>5/3</big>, 53/32, <small>107/64</small>, <small>38/23</small>, <small>33/20</small>
|<big>5/3</big>, 53/32, <small>107/64</small>, <small>38/23</small>, <small>33/20</small>
|vM6
|-
|-
|92
|92
Line 481: Line 574:
|1.6724
|1.6724
|'''<big><u>107/64</u></big>''', 5/3, <small>32/19</small>, <small>27/16</small>
|'''<big><u>107/64</u></big>''', 5/3, <small>32/19</small>, <small>27/16</small>
|M6
|-
|-
|93
|93
Line 486: Line 580:
|1.6818
|1.6818
|<big>32/19</big>, 27/16, <small>107/64</small>, <small>22/13</small>, <small>39/23</small>, <small>5/3</small>
|<big>32/19</big>, 27/16, <small>107/64</small>, <small>22/13</small>, <small>39/23</small>, <small>5/3</small>
|^M6
|-
|-
|94
|94
Line 491: Line 586:
|1.6912
|1.6912
|'''<big>22/13</big>''', <big>27/16</big>, 39/23, 32/19, <small>17/10</small>, <small>109/64</small>
|'''<big>22/13</big>''', <big>27/16</big>, 39/23, 32/19, <small>17/10</small>, <small>109/64</small>
|^^M6
|-
|-
|95
|95
Line 496: Line 592:
|1.7007
|1.7007
|'''<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><u>17/10</u></big>''', <big>109/64</big>, 39/23, <small>22/13</small>, <small>27/16</small>, <small>12/7</small>
|^^^M6
|-
|-
|96
|96
Line 501: Line 598:
|1.7102
|1.7102
|12/7, 109/64, <small>55/32</small>, <small>17/10</small>, <small>39/23</small>
|12/7, 109/64, <small>55/32</small>, <small>17/10</small>, <small>39/23</small>
|^<sup>4</sup>M6
|-
|-
|97
|97
Line 506: Line 604:
|1.7198
|1.7198
|'''<big>55/32</big>''', 12/7, 19/11, <small>26/15</small>, <small>111/64</small>
|'''<big>55/32</big>''', 12/7, 19/11, <small>26/15</small>, <small>111/64</small>
|vvvA6
|-
|-
|98
|98
Line 511: Line 610:
|1.7295
|1.7295
|<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>19/11</big>, <big>26/15</big>, 111/64, 33/19, <small>40/23</small>, <small>55/32</small>, <small>12/7</small>
|vvA6, ^^d7
|-
|-
|99
|99
Line 516: Line 616:
|1.7392
|1.7392
|'''<big><u>40/23</u></big>''', <big>33/19</big>, 111/64, 26/15, <small>7/4</small>, <small>19/11</small>
|'''<big><u>40/23</u></big>''', <big>33/19</big>, 111/64, 26/15, <small>7/4</small>, <small>19/11</small>
|^^^d7
|-
|-
|100
|100
Line 521: Line 622:
|1.7489
|1.7489
|'''<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>7/4</big>''', <small>40/23</small>, <small>33/19</small>, <small>111/64</small>, <small>26/15</small>, <small>30/17</small>
|v<sup>4</sup>m7
|-
|-
|101
|101
Line 526: Line 628:
|1.7587
|1.7587
|30/17, 113/64, <small>7/4</small>, <small>23/13</small>, <small>39/22</small>
|30/17, 113/64, <small>7/4</small>, <small>23/13</small>, <small>39/22</small>
|vvvm7
|-
|-
|102
|102
Line 531: Line 634:
|1.7686
|1.7686
|'''<big><u>23/13</u></big>''', <big>113/64</big>, <big>30/17</big>, 39/22, <small>16/9</small>, <small>57/32</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>
|vvm7
|-
|-
|103
|103
Line 536: Line 640:
|1.7785
|1.7785
|'''<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>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>
|vm7
|-
|-
|104
|104
Line 541: Line 646:
|1.7884
|1.7884
|'''<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>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
|-
|-
|105
|105
Line 546: Line 652:
|1.7985
|1.7985
|'''<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>9/5</big>''', '''<big>115/64</big>''', <small>34/19</small>, <small>38/21</small>, <small>25/14</small>, <small>29/16</small>
|^m7
|-
|-
|106
|106
Line 551: Line 658:
|1.8086
|1.8086
|'''<big><u>38/21</u></big>''', <big>29/16</big>, <small>9/5</small>, <small>20/11</small>, <small>115/64</small>
|'''<big><u>38/21</u></big>''', <big>29/16</big>, <small>9/5</small>, <small>20/11</small>, <small>115/64</small>
|^^m7
|-
|-
|107
|107
Line 556: Line 664:
|1.8187
|1.8187
|'''<big><u>20/11</u></big>''', 29/16, 42/23, <small>38/21</small>, <small>117/64</small>, <small>11/6</small>
|'''<big><u>20/11</u></big>''', 29/16, 42/23, <small>38/21</small>, <small>117/64</small>, <small>11/6</small>
|^^^m7
|-
|-
|108
|108
Line 561: Line 670:
|1.8289
|1.8289
|'''<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>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>
|~7
|-
|-
|109
|109
Line 566: Line 676:
|1.8391
|1.8391
|<big>35/19</big>, 59/32, 11/6, 24/13, <small>117/64</small>, <small>42/23</small>
|<big>35/19</big>, 59/32, 11/6, 24/13, <small>117/64</small>, <small>42/23</small>
|vvvM7
|-
|-
|110
|110
Line 571: Line 682:
|1.8495
|1.8495
|<big>24/13</big>, 59/32, 35/19, 13/7, <small>119/64</small>, <small>11/6</small>
|<big>24/13</big>, 59/32, 35/19, 13/7, <small>119/64</small>, <small>11/6</small>
|vvM7
|-
|-
|111
|111
Line 576: Line 688:
|1.8598
|1.8598
|'''<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><u>119/64</u></big>''', <big>13/7</big>, 28/15, <small>24/13</small>, <small>15/8</small>, <small>59/32</small>
|vM7
|-
|-
|112
|112
Line 581: Line 694:
|1.8702
|1.8702
|<big>28/15</big>, 15/8, <small>119/64</small>, <small>32/17</small>, <small>13/7</small>
|<big>28/15</big>, 15/8, <small>119/64</small>, <small>32/17</small>, <small>13/7</small>
|M7
|-
|-
|113
|113
Line 586: Line 700:
|1.8807
|1.8807
|'''<big>32/17</big>''', 15/8, 17/9, <small>121/64</small>, <small>36/19</small>, <small>28/15</small>
|'''<big>32/17</big>''', 15/8, 17/9, <small>121/64</small>, <small>36/19</small>, <small>28/15</small>
|^M7
|-
|-
|114
|114
Line 591: Line 706:
|1.8913
|1.8913
|'''<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><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
|-
|-
|115
|115
Line 596: Line 712:
|1.9019
|1.9019
|'''<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>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>
|^^^M7
|-
|-
|116
|116
Line 601: Line 718:
|1.9125
|1.9125
|'''<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><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>
|^<sup>4</sup>M7
|-
|-
|117
|117
Line 606: Line 724:
|1.9233
|1.9233
|'''<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>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>
|vvvA7
|-
|-
|118
|118
Line 611: Line 730:
|1.934
|1.934
|<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>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>
|vvA7, ^^d1 +1oct
|-
|-
|119
|119
Line 616: Line 736:
|1.9449
|1.9449
|'''<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><u>35/18</u></big>''', <big>33/17</big>, 39/20, 31/16, 125/64, <small>45/23</small>, <small>27/14</small>
|^^^d1 +1oct
|-
|-
|120
|120
Line 621: Line 742:
|1.9558
|1.9558
|'''<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>45/23</u></big>''', <big>125/64</big>, 39/20, <small>35/18</small>, <small>63/32</small>, <small>33/17</small>
|v<sup>4</sup>1 +1oct
|-
|-
|121
|121
Line 626: Line 748:
|1.9667
|1.9667
|'''<big>63/32</big>''', <small>45/23</small>, <small>125/64</small>, <small>39/20</small>, <small>127/64</small>
|'''<big>63/32</big>''', <small>45/23</small>, <small>125/64</small>, <small>39/20</small>, <small>127/64</small>
|vvv1 +1oct
|-
|-
|122
|122
Line 631: Line 754:
|1.9778
|1.9778
|127/64, 63/32
|127/64, 63/32
|vv1 +1oct
|-
|-
|123
|123
Line 636: Line 760:
|1.9889
|1.9889
|<big>127/64</big>
|<big>127/64</big>
|v1 +1oct
|-
|-
|124
|124
Line 641: Line 766:
|2.0
|2.0
|'''<big><u>2/1</u></big>'''
|'''<big><u>2/1</u></big>'''
|P1 +1oct
|-
|-
|colspan="4"|
|colspan="4"|
Line 650: Line 776:
* Normal: absolute cent error < 8 cents.
* Normal: absolute cent error < 8 cents.
* <small>Small:</small> absolute cent error < 16 cents.
* <small>Small:</small> absolute cent error < 16 cents.
|
|}
|}


Revision as of 15:34, 10 August 2024

← 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

Template:EDO intro

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
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
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

124 EDO Table of Intervals
Step Cents Ratio JI Ratio Approximations JI Ratio Approximations
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 +1oct
119 1151.6129 1.9449 35/18, 33/17, 39/20, 31/16, 125/64, 45/23, 27/14 ^^^d1 +1oct
120 1161.2903 1.9558 45/23, 125/64, 39/20, 35/18, 63/32, 33/17 v41 +1oct
121 1170.9677 1.9667 63/32, 45/23, 125/64, 39/20, 127/64 vvv1 +1oct
122 1180.6452 1.9778 127/64, 63/32 vv1 +1oct
123 1190.3226 1.9889 127/64 v1 +1oct
124 1200.0 2.0 2/1 P1 +1oct

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.


Intervals

124 EDO Table of Intervals
Step Cents Ratio JI Ratio Approximations Step
0 0.000 P1 0
1 9.677 ^1 1
2 19.355 ^^1 2
3 29.032 ^^^1 3
4 38.710 ^41 4
5 48.387 vvvA1 5
6 58.065 32/31, 31/30, 30/29, 29/28 vvA1, ^^d2 6
7 67.742 28/27, 27/26, 26/25, 25/24 ^^^d2 7
8 77.419 24/23, 23/22, 22/21 v4m2 8
9 87.097 21/20, 20/19 vvvm2 9
10 96.774 19/18, 18/17 vvm2 10
11 106.452 17/16 vm2 11
12 116.129 16/15, 31/29, 15/14 m2 12
13 125.806 29/27, 14/13 ^m2 13
14 135.484 27/25, 13/12 ^^m2 14
15 145.161 25/23 ^^^m2 15
16 154.839 12/11, 23/21 ~2 16
17 164.516 11/10 vvvM2 17
18 174.194 32/29, 21/19, 31/28 vvM2 18
19 183.871 10/9 vM2 19
20 193.548 29/26, 19/17, 28/25 M2 20
21 203.226 9/8 ^M2 21
22 212.903 26/23, 17/15 ^^M2 22
23 222.581 25/22 ^^^M2 23
24 232.258 8/7 ^4M2 24
25 241.935 31/27, 23/20 vvvA2 25
26 251.613 15/13, 22/19 vvA2, ^^d3 26
27 261.290 29/25 ^^^d3 27
28 270.968 7/6 v4m3 28
29 280.645 27/23, 20/17 vvvm3 29
30 290.323 13/11, 32/27 vvm3 30
31 300.000 19/16, 25/21, 31/26 vm3 31
32 309.677 m3 32
33 319.355 6/5 ^m3 33
34 329.032 29/24, 23/19 ^^m3 34
35 338.710 17/14, 28/23 ^^^m3 35
36 348.387 11/9 ~3 36
37 358.065 27/22, 16/13 vvvM3 37
38 367.742 21/17, 26/21, 31/25 vvM3 38
39 377.419 vM3 39
40 387.097 5/4 M3 40
41 396.774 29/23 ^M3 41
42 406.452 24/19, 19/15 ^^M3 42
43 416.129 14/11 ^^^M3 43
44 425.806 23/18, 32/25 ^4M3 44
45 435.484 9/7 vvvA3 45
46 445.161 31/24, 22/17 vvA3, ^^d4 46
47 454.839 13/10 ^^^d4 47
48 464.516 30/23, 17/13 v44 48
49 474.194 21/16, 25/19, 29/22 vvv4 49
50 483.871 vv4 50
51 493.548 4/3 v4 51
52 503.226 P4 52
53 512.903 31/23 ^4 53
54 522.581 27/20, 23/17 ^^4 54
55 532.258 19/14, 15/11 ^^^4 55
56 541.935 26/19 ~4 56
57 551.613 11/8 vvvA4 57
58 561.290 29/21, 18/13 vvA4 58
59 570.968 25/18, 32/23 vA4 59
60 580.645 7/5 A4 60
61 590.323 31/22 ^A4 61
62 600.000 24/17, 17/12 ^^A4, vvd5 62
63 609.677 27/19 vd5 63
64 619.355 10/7 d5 64
65 629.032 23/16 ^d5 65
66 638.710 13/9, 29/20 ^^d5 66
67 648.387 16/11 ^^^d5 67
68 658.065 19/13 ~5 68
69 667.742 22/15, 25/17, 28/19 vvv5 69
70 677.419 31/21 vv5 70
71 687.097 v5 71
72 696.774 P5 72
73 706.452 3/2 ^5 73
74 716.129 ^^5 74
75 725.806 32/21 ^^^5 75
76 735.484 29/19, 26/17, 23/15 ^45 76
77 745.161 20/13 vvvA5 77
78 754.839 17/11, 31/20 vvA5, ^^d6 78
79 764.516 14/9 ^^^d6 79
80 774.194 25/16 v4m6 80
81 783.871 11/7 vvvm6 81
82 793.548 30/19, 19/12 vvm6 82
83 803.226 27/17 vm6 83
84 812.903 8/5 m6 84
85 822.581 29/18 ^m6 85
86 832.258 21/13 ^^m6 86
87 841.935 13/8 ^^^m6 87
88 851.613 31/19, 18/11 ~6 88
89 861.290 23/14, 28/17 vvvM6 89
90 870.968 vvM6 90
91 880.645 5/3 vM6 91
92 890.323 M6 92
93 900.000 32/19 ^M6 93
94 909.677 27/16, 22/13 ^^M6 94
95 919.355 17/10 ^^^M6 95
96 929.032 29/17, 12/7 ^4M6 96
97 938.710 31/18 vvvA6 97
98 948.387 19/11, 26/15 vvA6, ^^d7 98
99 958.065 ^^^d7 99
100 967.742 7/4 v4m7 100
101 977.419 vvvm7 101
102 987.097 30/17, 23/13 vvm7 102
103 996.774 16/9 vm7 103
104 1006.452 25/14 m7 104
105 1016.129 9/5 ^m7 105
106 1025.806 29/16 ^^m7 106
107 1035.484 20/11, 31/17 ^^^m7 107
108 1045.161 11/6 ~7 108
109 1054.839 vvvM7 109
110 1064.516 24/13 vvM7 110
111 1074.194 13/7 vM7 111
112 1083.871 28/15, 15/8 M7 112
113 1093.548 32/17 ^M7 113
114 1103.226 17/9 ^^M7 114
115 1112.903 19/10 ^^^M7 115
116 1122.581 21/11, 23/12 ^4M7 116
117 1132.258 25/13, 27/14 vvvA7 117
118 1141.935 29/15, 31/16 vvA7, ^^d1 +1oct 118
119 1151.613 ^^^d1 +1oct 119
120 1161.290 v41 +1oct 120
121 1170.968 vvv1 +1oct 121
122 1180.645 vv1 +1oct 122
123 1190.323 v1 +1oct 123
124 1200.000 2/1 P1 +1oct 124
125 1209.677 ^1 +1oct 125
126 1219.355 ^^1 +1oct 126
127 1229.032 ^^^1 +1oct 127
128 1238.710 ^41 +1oct 128
129 1248.387 vvvA1 +1oct 129
130 1258.065 31/15, 29/14 vvA1 +1oct, ^^d2 +1oct 130
131 1267.742 27/13, 25/12 ^^^d2 +1oct 131
132 1277.419 23/11 v4m2 +1oct 132
133 1287.097 21/10 vvvm2 +1oct 133
134 1296.774 19/9 vvm2 +1oct 134
135 1306.452 17/8 vm2 +1oct 135
136 1316.129 32/15, 15/7 m2 +1oct 136
137 1325.806 28/13 ^m2 +1oct 137
138 1335.484 13/6 ^^m2 +1oct 138
139 1345.161 ^^^m2 +1oct 139
140 1354.839 24/11 ~2 +1oct 140
141 1364.516 11/5 vvvM2 +1oct 141
142 1374.194 31/14 vvM2 +1oct 142
143 1383.871 20/9 vM2 +1oct 143
144 1393.548 29/13 M2 +1oct 144
145 1403.226 9/4 ^M2 +1oct 145
146 1412.903 ^^M2 +1oct 146
147 1422.581 25/11 ^^^M2 +1oct 147
148 1432.258 16/7 ^4M2 +1oct 148
149 1441.935 23/10 vvvA2 +1oct 149
150 1451.613 30/13 vvA2 +1oct, ^^d3 +1oct 150
151 1461.290 ^^^d3 +1oct 151
152 1470.968 7/3 v4m3 +1oct 152
153 1480.645 vvvm3 +1oct 153
154 1490.323 26/11 vvm3 +1oct 154
155 1500.000 19/8, 31/13 vm3 +1oct 155
156 1509.677 m3 +1oct 156
157 1519.355 12/5 ^m3 +1oct 157
158 1529.032 29/12 ^^m3 +1oct 158
159 1538.710 17/7 ^^^m3 +1oct 159
160 1548.387 22/9 ~3 +1oct 160
161 1558.065 27/11, 32/13 vvvM3 +1oct 161
162 1567.742 vvM3 +1oct 162
163 1577.419 vM3 +1oct 163
164 1587.097 5/2 M3 +1oct 164
165 1596.774 ^M3 +1oct 165
166 1606.452 ^^M3 +1oct 166
167 1616.129 28/11 ^^^M3 +1oct 167
168 1625.806 23/9 ^4M3 +1oct 168
169 1635.484 18/7 vvvA3 +1oct 169
170 1645.161 31/12 vvA3 +1oct, ^^d4 +1oct 170
171 1654.839 13/5 ^^^d4 +1oct 171
172 1664.516 v44 +1oct 172
173 1674.194 21/8, 29/11 vvv4 +1oct 173
174 1683.871 vv4 +1oct 174
175 1693.548 8/3 v4 +1oct 175
176 1703.226 P4 +1oct 176
177 1712.903 ^4 +1oct 177
178 1722.581 27/10 ^^4 +1oct 178
179 1732.258 19/7, 30/11 ^^^4 +1oct 179
180 1741.935 ~4 +1oct 180
181 1751.613 11/4 vvvA4 +1oct 181
182 1761.290 vvA4 +1oct 182
183 1770.968 25/9 vA4 +1oct 183
184 1780.645 14/5 A4 +1oct 184
185 1790.323 31/11 ^A4 +1oct 185
186 1800.000 17/6 ^^A4 +1oct, vvd5 +1oct 186
187 1809.677 vd5 +1oct 187
188 1819.355 20/7 d5 +1oct 188
189 1829.032 23/8 ^d5 +1oct 189
190 1838.710 26/9, 29/10 ^^d5 +1oct 190
191 1848.387 32/11 ^^^d5 +1oct 191
192 1858.065 ~5 +1oct 192
193 1867.742 vvv5 +1oct 193
194 1877.419 vv5 +1oct 194
195 1887.097 v5 +1oct 195
196 1896.774 P5 +1oct 196
197 1906.452 3/1 ^5 +1oct 197
198 1916.129 ^^5 +1oct 198
199 1925.806 ^^^5 +1oct 199
200 1935.484 ^45 +1oct 200
201 1945.161 vvvA5 +1oct 201
202 1954.839 31/10 vvA5 +1oct, ^^d6 +1oct 202
203 1964.516 28/9 ^^^d6 +1oct 203
204 1974.194 25/8 v4m6 +1oct 204
205 1983.871 22/7 vvvm6 +1oct 205
206 1993.548 19/6 vvm6 +1oct 206
207 2003.226 vm6 +1oct 207
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