Gallery of just intervals: Difference between revisions

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| 43.408335
| 43.408335
| Lzyy1, lazoyoyo comma
| Lzyy1, lazoyoyo comma
| A1<sup>575</sup>
| A1<sup>175</sup>
| Avicenna's enharmonic diesis, avicennma ({{Monzo|-9, 1, 2, 1}})
| Avicenna's enharmonic diesis, avicennma ({{Monzo|-9, 1, 2, 1}})
|-
|-
Line 364: Line 364:
| 186.333871
| 186.333871
| 1uzz3, luzozo 3rd
| 1uzz3, luzozo 3rd
|
|m3<sup>49</sup><sub>11</sub>
| werckismic minor second
| werckismic minor second
|-
|-
Line 376: Line 376:
| 192.557607
| 192.557607
| 19o17u2, nosu 2nd
| 19o17u2, nosu 2nd
|
|M2<sup>19</sup><sub>17</sub>
| quasi-meantone
|quasi-meantone
|-
|-
| [[28/25]]
|[[28/25]]
| 196.198479
|196.198479
| zgg3, zogugu 3rd
| zgg3, zogugu 3rd
|
|d3<sup>7</sup><sub>25</sub>
| middle major second
|middle major second
|-
|-
| [[55/49]]
|[[55/49]]
| 199.979843
|199.979843
| 1orry1, loruruyo unison
| 1orry1, loruruyo unison
|
|A1<sup>55</sup><sub>49</sub>
| werckismic tone
|werckismic tone
|-
|-
| [[64/57]]
|[[64/57]]
| 200.531983
|200.531983
| 19u2, inu 2nd
|19u2, inu 2nd
|
|M2<sub>19</sub>
| quasi-tempered whole tone, octave-reduced 57th subharmonic
|quasi-tempered whole tone, octave-reduced 57th subharmonic
|-
|-
| [[9/8]]
|[[9/8]]
| 203.910002
|203.910002
| w2, wa 2nd
|w2, wa 2nd
| M2
|M2
| Pythagorean (whole) tone, major (whole) tone, octave-reduced 9th harmonic
|Pythagorean (whole) tone, major (whole) tone, octave-reduced 9th harmonic
|-
|-
| [[17/15]]
|[[17/15]]
| 216.686695
|216.686695
| 17og3, sogu 3rd
|17og3, sogu 3rd
|
|d3<sup>17</sup><sub>5</sub>
| septendecimal whole tone, septendecimal eventone
|septendecimal whole tone, septendecimal eventone
|-
|-
| [[8/7]]
|[[8/7]]
| 231.174094
|231.174094
| r2, ru 2nd
|r2, ru 2nd
| M2<sub>7</sub>
| M2<sub>7</sub>
| supermajor second, septimal whole tone, octave-reduced 7th subharmonic
| supermajor second, septimal whole tone, octave-reduced 7th subharmonic
|-
|-
| [[63/55]]
|[[63/55]]
| 235.104252
|235.104252
| 1uzg3, luzogu 3rd
|1uzg3, luzogu 3rd
|
|m3<sup>7</sup><sub>55</sub>
| werckismic supermajor second
|werckismic supermajor second
|-
|-
| [[55/48]]
|[[55/48]]
| 235.676655
|235.676655
| 1oy2, loyo 2nd
|1oy2, loyo 2nd
|
|M2<sup>55</sup>
| keenanismic supermajor second
|keenanismic supermajor second
|-
|-
| [[15/13]]
|[[15/13]]
| 247.741053
|247.741053
| 3uy2, thuyo 2nd
|3uy2, thuyo 2nd
| A2<sup>5</sup><sub>13</sub>
|A2<sup>5</sup><sub>13</sub>
| tridecimal semifourth, tridecimal ultramajor second, tridecimal inframinor third
|tridecimal semifourth, tridecimal ultramajor second, tridecimal inframinor third
|-
|-
| 97/84
| 97/84
| 249.114503
|249.114503
| 97or2, ninety-soru 2nd
|97or2, ninety-soru 2nd
| M2<sup>97</sup><sub>7</sub>
|M2<sup>97</sup><sub>7</sub>
| homothetic semifourth
|homothetic semifourth
|-
|-
| [[81/70]]
|[[81/70]]
| 252.268038
|252.268038
| rg2, rugu 2nd
|rg2, rugu 2nd
| M2<sub>35</sub>
|M2<sub>35</sub>
| septimal semi-augmented second, septimal ultramajor second
|septimal semi-augmented second, septimal ultramajor second
|-
|-
| [[22/19]]
|[[22/19]]
| 253.804926
|253.804926
| 19u1o2, nulo 2nd
|19u1o2, nulo 2nd
| M2<sup>11</sup><sub>19</sub>
|M2<sup>11</sup><sub>19</sub>
| undevicesimal semifourth, minimal minor third, godzilla semifourth
|undevicesimal semifourth, minimal minor third, godzilla semifourth
|-
|-
| [[64/55]]
|[[64/55]]
| 262.368344
|262.368344
| 1ug3, lugu 3rd
|1ug3, lugu 3rd
| m3<sub>55</sub>
|m3<sub>55</sub>
| keenanismic subminor third, octave-reduced 55th subharmonic
| keenanismic subminor third, octave-reduced 55th subharmonic
|-
|-
| [[7/6]]
|[[7/6]]
| 266.870906
|266.870906
| z3, zo 3rd
|z3, zo 3rd
| m3<sup>7</sup>
|m3<sup>7</sup>
| subminor third, septimal minor third
|subminor third, septimal minor third
|-
|-
| [[90/77]]
|[[90/77]]
| 270.079867
|270.079867
| 1ury2, luruyo 2nd
|1ury2, luruyo 2nd
|
|A2<sup>5</sup><sub>77</sub>
| swetismic subminor third
|swetismic subminor third
|-
|-
| [[62/53]]
|[[62/53]]
| 271.531027
|271.531027
| 53u31o2, fithu-thiwo 2nd
|53u31o2, fithu-thiwo 2nd
|
|M2<sup>31</sup><sub>53</sub>
| orwell subminor third
|orwell subminor third
|-
|-
| [[75/64]]
|[[75/64]]
| 274.582429
|274.582429
| yy2, yoyo 2nd
|yy2, yoyo 2nd
| A2<sup>25</sup>
|A2<sup>25</sup>
| classic augmented second
|classic augmented second
|-
|-
| [[20/17]]
|[[20/17]]
| 281.358304
|281.358304
| 17uy2, suyo 2nd
|17uy2, suyo 2nd
|
|A2<sup>5</sup><sub>17</sub>
| septendecimal augmented second, septendecimal minor third
|septendecimal augmented second, septendecimal minor third
|-
|-
| [[13/11]]
|[[13/11]]
| 289.209179
|289.209179
| 3o1u3, tholu 3rd
|3o1u3, tholu 3rd
| m3<sup>13</sup><sub>11</sub>
|m3<sup>13</sup><sub>11</sub>
| tridecimal minor third
| tridecimal minor third
|-
|-
| [[32/27]]
|[[32/27]]
| 294.134997
|294.134997
| w3, wa 3rd
|w3, wa 3rd
| m3
|m3
| Pythagorean minor third, octave-reduced 27th subharmonic
|Pythagorean minor third, octave-reduced 27th subharmonic
|-
|-
| [[19/16]]
|[[19/16]]
| 297.513016
|297.513016
| 19o3, ino 3rd
|19o3, ino 3rd
| m3<sup>19</sup>
|m3<sup>19</sup>
| otonal minor third, octave-reduced 19th harmonic
|otonal minor third, octave-reduced 19th harmonic
|-
|-
| [[25/21]]
|[[25/21]]
| 301.846520
|301.846520
| ryy2, ruyoyo 2nd
|ryy2, ruyoyo 2nd
| A2<sup>25</sup><sub>7</sub>
|A2<sup>25</sup><sub>7</sub>
| quasi-tempered minor third
|quasi-tempered minor third
|-
|-
| [[61/51]]
|[[61/51]]
| 309.974395
|309.974395
| 61o17u2, siwosu 2nd
|61o17u2, siwosu 2nd
|
|A2<sup>61</sup><sub>17</sub>
| myna third
|myna third
|-
|-
| [[6/5]]
|[[6/5]]
| 315.641287
|315.641287
| g3, gu 3rd
|g3, gu 3rd
| m3<sub>5</sub>
|m3<sub>5</sub>
| classic minor third, just minor third
|classic minor third, just minor third
|-
|-
| [[77/64]]
|[[77/64]]
| 320.143849
|320.143849
| 1oz3, lozo 3rd
|1oz3, lozo 3rd
|
|m3<sup>77</sup>
| keenanismic minor third, octave-reduced 77th harmonic
|keenanismic minor third, octave-reduced 77th harmonic
|-
|-
| [[135/112]]
|[[135/112]]
| 323.352810
|323.352810
| ry2, ruyo 2nd
|ry2, ruyo 2nd
|
|A2<sup>5</sup><sub>7</sub>
| large septimal minor third, marvelous minor third ({{Monzo|-4, 3, 1, -1}})
| large septimal minor third, marvelous minor third ({{Monzo|-4, 3, 1, -1}})
|-
|-
| [[35/29]]
|[[35/29]]
| 325.562426
|325.562426
| 29uzy3, twenuzoyo 3rd
|29uzy3, twenuzoyo 3rd
|
|M3<sup>35</sup><sub>29</sub>
| doublewide minor third
| doublewide minor third
|-
|-
| [[23/19]]
|[[23/19]]
| 330.761331
|330.761331
| 23o19u3, twethonu 3rd
|23o19u3, twethonu 3rd
|
|A2<sup>23</sup><sub>19</sub>
| vicesimotertial supraminor third
|vicesimotertial supraminor third
|-
|-
| [[17/14]]
|[[17/14]]
| 336.129503
|336.129503
| 17or3, soru 3rd
|17or3, soru 3rd
|
|m3<sup>17</sup><sub>5</sub>
| septendecimal supraminor third
|septendecimal supraminor third
|-
|-
| [[73/60]]
|[[73/60]]
| 339.520756
|339.520756
| 73og3, seventy-thogu 3rd
|73og3, seventy-thogu 3rd
|
|m3<sup>73</sup><sub>5</sub>
| amity supraminor third
| amity supraminor third
|-
|-
| [[39/32]]
|[[39/32]]
| 342.482663
| 342.482663
| 3o3, tho 3rd
|3o3, tho 3rd
| m3<sup>13</sup>
|m3<sup>13</sup>
| lesser tridecimal neutral third, octave-reduced 39th harmonic
|lesser tridecimal neutral third, octave-reduced 39th harmonic
|-
|-
| [[625/512]]
|[[625/512]]
| 345.254855
|345.254855
| Ly<sup>4</sup>2, large quadyo 2nd
|Ly<sup>4</sup>2, large quadyo 2nd
| AA2<sup>625</sup>
| AA2<sup>625</sup>
| 5-limit neutral third ({{Monzo|-9, 0, 4}})
|5-limit neutral third ({{Monzo|-9, 0, 4}})
|-
|-
| [[11/9]]
|[[11/9]]
| 347.407941
| 347.407941
| 1o3, ilo 3rd
|1o3, ilo 3rd
| m3<sup>11</sup>
| m3<sup>11</sup>
| undecimal neutral third
|undecimal neutral third
|-
|-
| [[60/49]]
|[[60/49]]
| 350.616902
|350.616902
| rry2, ruruyo 2nd
|rry2, ruruyo 2nd
|
|A2<sup>5</sup><sub>49</sub>
| smaller septimal neutral third, (purple 3rd)
|smaller septimal neutral third, (purple 3rd)
|-
|-
| [[49/40]]
|[[49/40]]
| 351.338099
|351.338099
| zzg4, zozogu 4th
| zzg4, zozogu 4th
|
|d4<sup>49</sup><sub>5</sub>
| larger septimal neutral third, (purple 3rd)
|larger septimal neutral third, (purple 3rd)
|-
|-
| [[27/22]]
|[[27/22]]
| 354.547060
|354.547060
| 1u3, lu 3rd
|1u3, lu 3rd
| M3<sub>11</sub>
|M3<sub>11</sub>
| rastmic neutral third
|rastmic neutral third
|-
|-
| [[16/13]]
|[[16/13]]
| 359.472338
| 359.472338
| 3u3, thu 3rd
|3u3, thu 3rd
| M3<sub>13</sub>
|M3<sub>13</sub>
| greater tridecimal neutral third, octave reduced 13subharmonic
|greater tridecimal neutral third, octave reduced 13subharmonic
|-
|-
| [[21/17]]
|[[21/17]]
| 365.825498
|365.825498
| 17uz3, suzo 3rd
|17uz3, suzo 3rd
|
|M3<sup>7</sup><sub>17</sub>
| septendecimal submajor third
|septendecimal submajor third
|-
|-
| 51/41
|51/41
| 377.848005
|377.848005
| 41u17o4, fowuso 4th
|41u17o4, fowuso 4th
|
|d4<sup>17</sup><sub>41</sub>
| maja third
| maja third
|-
|-
| [[56/45]]
|[[56/45]]
| 378.602191
|378.602191
| zg4, zogu 4th
|zg4, zogu 4th
|
|d4<sup>7</sup><sub>5</sub>
| narrow perde segah, marvelous major third
|narrow perde segah, marvelous major third
|-
|-
| [[71/57]]
|[[71/57]]
| 380.228526
|380.228526
| 71o19u3, seventy-wonu 3rd
|71o19u3, seventy-wonu 3rd
|
|M3<sup>71</sup><sub>19</sub>
| witchcraft major third
| witchcraft major third
|-
|-
| [[76/61]]
|[[76/61]]
| 380.628211
|380.628211
| 61u19o4, siwuno 4th
|61u19o4, siwuno 4th
|
|d4<sup>19</sup><sub>61</sub>
| magic major third
|magic major third
|-
|-
| [[96/77]]
|[[96/77]]
| 381.811152
|381.811152
| 1ur3, luru 3rd
|1ur3, luru 3rd
|
|M3<sub>77</sub>
| undecimal perde segah, keenanismic major third
|undecimal perde segah, keenanismic major third
|-
|-
| [[5/4]]
|[[5/4]]
| 386.313714
|386.313714
| y3, yo 3rd
|y3, yo 3rd
| M3<sup>5</sup>
|M3<sup>5</sup>
| classic major third, just major third, octave-reduced 5th harmonic
|classic major third, just major third, octave-reduced 5th harmonic
|-
|-
| [[161/128]]
|[[161/128]]
| 397.100254
|397.100254
| 23oz4, twethozo 4th
|23oz4, twethozo 4th
| M3<sup>161</sup>
|M3<sup>161</sup>
| just/Pythagorean major third meantone, octave-reduced 161th harmonic
|just/Pythagorean major third meantone, octave-reduced 161th harmonic
|-
|-
| [[63/50]]
|[[63/50]]
| 400.108480
|400.108480
| zgg4, zogugu 4th
|zgg4, zogugu 4th
| d4<sup>7</sup><sub>25</sub>
|d4<sup>7</sup><sub>25</sub>
| quasi-tempered major third
|quasi-tempered major third
|-
|-
| [[81/64]]
|[[81/64]]
| 407.820003
|407.820003
| Lw3, large wa 3rd
|Lw3, large wa 3rd
| M3
|M3
| Pythagorean major third, octave-reduced 81st harmonic
|Pythagorean major third, octave-reduced 81st harmonic
|-
|-
| [[33/26]]
|[[33/26]]
| 412.745281
|412.745281
| 3u1o3, thulo 3rd
|3u1o3, thulo 3rd
| M3<sup>11</sup><sub>13</sub>
|M3<sup>11</sup><sub>13</sub>
| tridecimal major third
| tridecimal major third
|-
|-
| [[80/63]]
|[[80/63]]
| 413.577806
|413.577806
| ry3, ruyo 3rd
|ry3, ruyo 3rd
|
|M3<sup>5</sup><sub>7</sub>
| werckismic sharp major third
|werckismic sharp major third
|-
|-
| [[14/11]]
|[[14/11]]
| 417.507964
|417.507964
| 1uz4, luzo 4th
|1uz4, luzo 4th
| P4<sup>7</sup><sub>11</sub>
|P4<sup>7</sup><sub>11</sub>
| undecimal major third, undecimal diminished fourth
|undecimal major third, undecimal diminished fourth
|-
|-
| [[23/18]]
|[[23/18]]
| 424.364346
|424.364346
| 23o4, twetho 4th
|23o4, twetho 4th
|  
|M3<sup>23</sup>
| vicesimotertial diminished fourth
|vicesimotertial diminished fourth
|-
|-
| [[32/25]]
|[[32/25]]
| 427.372572
|427.372572
| gg4, gugu 4th
|gg4, gugu 4th
|
|d4<sub>25</sub>
| classic diminished fourth
|classic diminished fourth
|-
|-
| [[77/60]]
|[[77/60]]
| 431.875134
|431.875134
| 1ozg4, lozogu 4th
|1ozg4, lozogu 4th
|
|d4<sup>77</sup><sub>5</sub>
| swetismic supermajor third
|swetismic supermajor third
|-
|-
| [[9/7]]
|[[9/7]]
| 435.084095
|435.084095
| r3, ru 3rd
|r3, ru 3rd
| M3<sub>7</sub>
| M3<sub>7</sub>
| supermajor third, septimal major third
|supermajor third, septimal major third
|-
|-
| [[31/24]]
|[[31/24]]
| 443.080572
|443.080572
| 31o3, thiwo 3rd
|31o3, thiwo 3rd
|
|M3<sup>31</sup>
| sensi supermajor third
| sensi supermajor third
|-
|-
| [[22/17]]
|[[22/17]]
| 446.362533
|446.362533
| 17u1o3, sulo 3rd
|17u1o3, sulo 3rd
|
|M3<sup>11</sup><sub>17</sub>
| septendecimal supermajor third
|septendecimal supermajor third
|-
|-
| [[35/27]]
|[[35/27]]
| 449.274618
|449.274618
| zy4, zoyo 4th
|zy4, zoyo 4th
|
|P4<sup>35</sup>
| septimal semidiminished fourth
|septimal semidiminished fourth
|-
|-
| [[13/10]]
|[[13/10]]
| 454.213948
|454.213948
| 3og4, thogu 4th
|3og4, thogu 4th
| d4<sup>13</sup><sub>5</sub>
|d4<sup>13</sup><sub>5</sub>
| tridecimal semisixth, Barbados third, tridecimal 9/4 tone
|tridecimal semisixth, Barbados third, tridecimal 9/4 tone
|-
|-
| [[64/49]]
|[[64/49]]
| 462.348187
|462.348187
| rr3, ruru 3rd
|rr3, ruru 3rd
| M3<sub>49</sub>
|M3<sub>49</sub>
| septatonic major third
| septatonic major third
|-
|-
| [[17/13]]
|[[17/13]]
| 464.427748
|464.427748
| 17o3u4, sothu 4th
|17o3u4, sothu 4th
|
|P4<sup>17</sup><sub>13</sub>
| septendecimal sub-fourth
|septendecimal sub-fourth
|-
|-
| [[21/16]]
|[[21/16]]
| 470.780907
|470.780907
| z4, zo 4th
|z4, zo 4th
| P4<sup>7</sup>
|P4<sup>7</sup>
| sub-fourth, narrow fourth, 8ve-reduced 21st harmonic
|sub-fourth, narrow fourth, 8ve-reduced 21st harmonic
|-
|-
| [[33/25]]
|[[33/25]]
| 480.645516
|480.645516
| 1ogg4, logugu 4th
|1ogg4, logugu 4th
| d4<sup>11</sup><sub>25</sub>
|d4<sup>11</sup><sub>25</sub>
| "5-EDO"-esque fourth
|"5-EDO"-esque fourth
|-
|-
| [[117/88]]
|[[117/88]]
| 493.119721
|493.119721
| 3o1u4, tholu 4th
|3o1u4, tholu 4th
|
|P4<sup>13</sup><sub>11</sub>
| minthmic fourth ({{Monzo|-3, 2, 0, 0, -1, 1}})
|minthmic fourth ({{Monzo|-3, 2, 0, 0, -1, 1}})
|-
|-
| [[4/3]]
|[[4/3]]
| 498.044999
|498.044999
| w4, wa 4th
|w4, wa 4th
| P4
|P4
| just perfect fourth, octave-reduced 3rd subharmonic, diatessaron
|just perfect fourth, octave-reduced 3rd subharmonic, diatessaron
|-
|-
| [[75/56]]
|[[75/56]]
| 505.756522
|505.756522
| ryy3, ruyoyo 3rd
|ryy3, ruyoyo 3rd
|
|A3<sup>25</sup><sub>7</sub>
| marvelous fourth
|marvelous fourth
|-
|-
| [[980/729]]
|[[980/729]]
| 512.235522
|512.235522
| zzy5, zozoyo 5th
|zzy5, zozoyo 5th
| d5<sup>245</sup>
|d5<sup>245</sup>
| sensamagic fourth, septimal sesquidiminished grave fifth
| sensamagic fourth, septimal sesquidiminished grave fifth
|-
|-
| [[27/20]]
|[[27/20]]
| 519.551289
|519.551289
| g4, gu 4th
|g4, gu 4th
| P4<sub>5</sub>
|P4<sub>5</sub>
| acute fourth
|acute fourth
|-
|-
| [[19/14]]
|[[19/14]]
| 528.687110
|528.687110
| 19or4, noru 4th
| 19or4, noru 4th
|
|P4<sup>19</sup><sub>7</sub>
| hendrix fourth
|hendrix fourth
|-
|-
| [[49/36]]
|[[49/36]]
| 533.741811
|533.741811
| zz5, zozo 5th
|zz5, zozo 5th
| d5<sup>49</sup>
|d5<sup>49</sup>
| Arabic lute acute fourth
|Arabic lute acute fourth
|-
|-
| [[15/11]]
|[[15/11]]
| 536.950772
|536.950772
| 1uy4, luyo 4th
|1uy4, luyo 4th
| A4<sup>5</sup><sub>11</sub>
|A4<sup>5</sup><sub>11</sub>
| undecimal augmented fourth, subaugmented fourth
| undecimal augmented fourth, subaugmented fourth
|-
|-
| [[48/35]]
|[[48/35]]
| 546.815381
|546.815381
| rg4, rugu 4th
|rg4, rugu 4th
|
|P4<sub>35</sub>
| septimal super-fourth
|septimal super-fourth
|-
|-
| [[11/8]]
|[[11/8]]
| 551.317942
| 551.317942
| 1o4, ilo 4th
|1o4, ilo 4th
| P4<sup>11</sup>
|P4<sup>11</sup>
| super-fourth, undecimal semi-augmented fourth, octave-reduced 11th harmonic or harmonic 11th, Alphorn-Fa
|super-fourth, undecimal semi-augmented fourth, octave-reduced 11th harmonic or harmonic 11th, Alphorn-Fa
|-
|-
| [[18/13]]
|[[18/13]]
| 563.382340
| 563.382340
| 3u4, thu 4th
|3u4, thu 4th
| A4<sup>13</sup>
|A4<sub>13</sub>
| tridecimal augmented fourth
|tridecimal augmented fourth
|-
|-
| [[25/18]]
|[[25/18]]
| 568.717426
|568.717426
| yy4, yoyo 4th
|yy4, yoyo 4th
| A4<sup>25</sup>
|A4<sup>25</sup>
| classic augmented fourth, pental augmented fourth ({{Monzo|-1 -2 2}})
|classic augmented fourth, pental augmented fourth ({{Monzo|-1 -2 2}})
|-
|-
| [[88/63]]
|[[88/63]]
| 578.582034
|578.582034
| 1or4, loru 4th
|1or4, loru 4th
|
|P4<sup>11</sup><sub>7</sub>
| werckismic augmented fourth
|werckismic augmented fourth
|-
|-
| [[7/5]]
| [[7/5]]
| 582.512193
|582.512193
| zg5, zogu 5th
|zg5, zogu 5th
| d5<sup>7</sup><sub>5</sub>
|d5<sup>7</sup><sub>5</sub>
| augmented fourth, septimal tritone, Huygen's tritone
|augmented fourth, septimal tritone, Huygen's tritone
|-
|-
| [[45/32]]
|[[45/32]]
| 590.223716
|590.223716
| y4, yo 4th
|y4, yo 4th
| A4<sup>5</sup>
|A4<sup>5</sup>
| smaller pental tritone, diatonic tritone ({{Monzo|-5 2 1}})
|smaller pental tritone, diatonic tritone ({{Monzo|-5 2 1}})
|-
|-
| [[108/77]]
|[[108/77]]
| 585.721154
|585.721154
| 1ur4, luru 4th
|1ur4, luru 4th
|
|A4<sub>77</sub>
| swetismic augmented fourth ({{Monzo|2, 3, 0, -1, -1}})
|swetismic augmented fourth ({{Monzo|2, 3, 0, -1, -1}})
|-
|-
| [[24/17]]
|[[24/17]]
| 596.999591
| 596.999591
| 17u4, su 4th
|17u4, su 4th
| A4<sub>17</sub>
|A4<sub>17</sub>
| smaller septendecimal tritone
|smaller septendecimal tritone
|-
|-
| 99/70
| 99/70
| 600.088324
|600.088324
| 1org4, lorugu 4th
|1org4, lorugu 4th
| P4<sup>11</sup><sub>35</sub>
|P4<sup>11</sup><sub>35</sub>
| homothetic quasi-tempered tritone
|homothetic quasi-tempered tritone
|-
|-
| [[17/12]]
|[[17/12]]
| 603.000409
|603.000409
| 17o5, iso 5th
|17o5, iso 5th
| d5<sup>17</sup>
|d5<sup>17</sup>
| larger septendecimal tritone
|larger septendecimal tritone
|-
|-
| [[64/45]]
|[[64/45]]
| 609.776284
|609.776284
| g5, gu 5th
|g5, gu 5th
| d5<sub>5</sub>
|d5<sub>5</sub>
| larger pental tritone, diatonic tritone ({{Monzo|6 -2 -1}})
|larger pental tritone, diatonic tritone ({{Monzo|6 -2 -1}})
|-
|-
| [[10/7]]
|[[10/7]]
| 617.487807
|617.487807
| ry4, ruyo 4th
|ry4, ruyo 4th
| A4<sup>5</sup><sub>7</sub>
|A4<sup>5</sup><sub>7</sub>
| diminished fifth, Euler's tritone, superaugmented fourth
|diminished fifth, Euler's tritone, superaugmented fourth
|-
|-
| [[23/16]]
|[[23/16]]
| 628.274347
|628.274347
| 23o5, twetho 5th
|23o5, twetho 5th
| A4<sup>23</sup>
|A4<sup>23</sup>
| vicesimotertial superaugmented fourth, octave-reduced 23rd harmonic
|vicesimotertial superaugmented fourth, octave-reduced 23rd harmonic
|-
|-
| [[36/25]]
|[[36/25]]
| 631.282574
|631.282574
| gg5, gugu 5th
|gg5, gugu 5th
| d5<sub>25</sub>
|d5<sub>25</sub>
| pental diminished fifth, classic diminshed fifth ({{Monzo|2 2 -2}})
|pental diminished fifth, classic diminshed fifth ({{Monzo|2 2 -2}})
|-
|-
| [[13/9]]
|[[13/9]]
| 636.617660
| 636.617660
| 3o5, tho 5th
|3o5, tho 5th
| d5<sub>13</sub>
|d5<sup>13</sup>
| tridecimal diminished fifth
|tridecimal diminished fifth
|-
|-
| [[16/11]]
|[[16/11]]
| 648.682058
|648.682058
| 1u5, lu 5th
|1u5, lu 5th
| P5<sub>11</sub>
|P5<sub>11</sub>
| sub-fifth, octave-reduced 11th subharmonic
|sub-fifth, octave-reduced 11th subharmonic
|-
|-
| [[35/24]]
|[[35/24]]
| 653.184619
|653.184619
| zy5, zoyo 5th
|zy5, zoyo 5th
|
|P5<sup>35</sup>
| septimal sub-fifth
|septimal sub-fifth
|-
|-
| [[22/15]]
|[[22/15]]
| 663.049228
|663.049228
| 1og5, logu 5th
|1og5, logu 5th
| d5<sup>11</sup><sub>5</sub>
|d5<sup>11</sup><sub>5</sub>
| undecimal diminished fifth, semidiminished fifth
| undecimal diminished fifth, semidiminished fifth
|-
|-
| [[72/49]]
|[[72/49]]
| 666.258889
|666.258889
| rr4, ruru 4th
|rr4, ruru 4th
|
|A4<sub>49</sub>
| septimal catafifth
|septimal catafifth
|-
|-
| [[81/55]]
|[[81/55]]
| 670.188347
|670.188347
| 1ug5, lugu 5th
|1ug5, lugu 5th
|
|P5<sub>55</sub>
| undecimal catafifth
|undecimal catafifth
|-
|-
| [[28/19]]
|[[28/19]]
| 671.312890
|671.312890
| 19uz5, nuzo 5th
| 19uz5, nuzo 5th
|
|P5<sup>7</sup><sub>19</sub>
| hendrix fifth
|hendrix fifth
|-
|-
| [[40/27]]
|[[40/27]]
| 680.448711
|680.448711
| y5, yo 5th
|y5, yo 5th
| P5<sup>5</sup>
|P5<sup>5</sup>
| grave fifth
|grave fifth
|-
|-
| [[729/490]]
|[[729/490]]
| 687.764478
|687.764478
| rrg5, rurugu 4th
|rrg5, rurugu 4th
| A4<sub>245</sub>
|A4<sub>245</sub>
| sensamagic fifth, septimal sesquiaugmented acute fourth
|sensamagic fifth, septimal sesquiaugmented acute fourth
|-
|-
| [[112/75]]
|[[112/75]]
| 694.243478
|694.243478
| zgg6, zogugu 6th
|zgg6, zogugu 6th
|
|d6<sup>7</sup><sub>25</sub>
| marvelous fifth
|marvelous fifth
|-
|-
| 16384/10935
|16384/10935
| 700.001280
|700.001280
| sg6, sagu 6th
|sg6, sagu 6th
| d6<sub>5</sub>
|d6<sub>5</sub>
| Kirnberger's fifth ("[[12edo|12-EDO]]"-esque fifth)
|Kirnberger's fifth ("[[12edo|12-EDO]]"-esque fifth)
|-
|-
| [[3/2]]
|[[3/2]]
| 701.955001
|701.955001
| w5, wa 5th
|w5, wa 5th
| P5
|P5
| [[just perfect fifth]], octave-reduced 3rd harmonic, diapente
|[[just perfect fifth]], octave-reduced 3rd harmonic, diapente
|-
|-
| [[182/121]]
|[[182/121]]
| 706.717684
|706.717684
| 3o1uuz6, tholuluzo 6th
|3o1uuz6, tholuluzo 6th
|
|m6<sup>91</sup><sub>121</sub>
| tridecimal gentle fifth ({{Monzo|1, 0, 0, 1, -2, 1}})
|tridecimal gentle fifth ({{Monzo|1, 0, 0, 1, -2, 1}})
|-
|-
| [[176/117]]
|[[176/117]]
| 706.880279
|706.880279
| 3u1o5, thulo 5th
|3u1o5, thulo 5th
|
|P5<sup>11</sup><sub>13</sub>
| minthmic fifth ({{Monzo|4, -2, 0, 0, 1, -1}})
|minthmic fifth ({{Monzo|4, -2, 0, 0, 1, -1}})
|-
|-
| [[50/33]]
|[[50/33]]
| 719.354484
|719.354484
| 1uyy5, luyoyo 5th
|1uyy5, luyoyo 5th
|
|A5<sup>25</sup><sub>11</sub>
| "[[5edo|5-EDO]]"-esque fifth
|"[[5edo|5-EDO]]"-esque fifth
|-
|-
| [[32/21]]
|[[32/21]]
| 729.219093
|729.219093
| r5, ru 5th
|r5, ru 5th
| P5<sub>7</sub>
|P5<sub>7</sub>
| super-fifth, wide fifth, octave-reduced 21st subharmonic
|super-fifth, wide fifth, octave-reduced 21st subharmonic
|-
|-
| [[26/17]]
|[[26/17]]
| 735.572252
|735.572252
| 17u3o5, sutho 5th
|17u3o5, sutho 5th
|
|P5<sup>13</sup><sub>17</sub>
| septendecimal super-fifth
|septendecimal super-fifth
|-
|-
| [[49/32]]
|[[49/32]]
| 737.651813
|737.651813
| zz6, zozo 6th
|zz6, zozo 6th
| m6<sup>49</sup>
|m6<sup>49</sup>
| superduper fifth, octave-reduced 49th harmonic
|superduper fifth, octave-reduced 49th harmonic
|-
|-
| [[20/13]]
|[[20/13]]
| 745.786052
|745.786052
| 3uy5, thuyo 5th
|3uy5, thuyo 5th
| A5<sup>5</sup><sub>13</sub>
|A5<sup>5</sup><sub>13</sub>
| tridecimal semitenth, Barbados sixth, ratwolf wolf fifth
|tridecimal semitenth, Barbados sixth, ratwolf wolf fifth
|-
|-
| [[17/11]]
|[[17/11]]
| 753.637467
|753.637467
| 17o1u6, solu 6th
|17o1u6, solu 6th
|
|m6<sup>17</sup><sub>11</sub>
| septendecimal subminor sixth
|septendecimal subminor sixth
|-
|-
| [[14/9]]
| [[14/9]]
| 764.915905
|764.915905
| z6, zo 6th
|z6, zo 6th
| m6<sup>7</sup>
|m6<sup>7</sup>
| subminor sixth, septimal minor sixth
|subminor sixth, septimal minor sixth
|-
|-
| [[25/16]]
|[[25/16]]
| 772.627428
|772.627428
| yy5, yoyo 5th
|yy5, yoyo 5th
|
|A5<sup>25</sup>
| pental augmented fifth, classic augmented fifth, otonal minor sixth, octave-reduced 25th harmonic
|pental augmented fifth, classic augmented fifth, otonal minor sixth, octave-reduced 25th harmonic
|-
|-
| [[36/23]]
|[[36/23]]
| 775.635654
|775.635654
| 23u5, twethu 5th
|23u5, twethu 5th
|  
|m6<sub>23</sub>
| vicesimotertial augmented fifth
|vicesimotertial augmented fifth
|-
|-
| [[11/7]]
|[[11/7]]
| 782.492036
|782.492036
| 1or5, loru 5th
|1or5, loru 5th
| P5<sup>11</sup><sub>7</sub>
|P5<sup>11</sup><sub>7</sub>
| undecimal subminor sixth, undecimal augmented fifth
|undecimal subminor sixth, undecimal augmented fifth
|-
|-
| [[63/40]]
|[[63/40]]
| 786.422194
|786.422194
| zg6, zogu 6th
|zg6, zogu 6th
| m6<sup>7</sup><sub>5</sub>
|m6<sup>7</sup><sub>5</sub>
|  
|
|-
|-
| [[52/33]]
|[[52/33]]
| 787.254719
|787.254719
| 3o1u6, tholu 6th
|3o1u6, tholu 6th
| m6<sup>13</sup><sub>11</sub>
|m6<sup>13</sup><sub>11</sub>
| tridecimal minor sixth
| tridecimal minor sixth
|-
|-
| [[128/81]]
|[[128/81]]
| 792.179997
|792.179997
| sw6, small wa 6th
|sw6, small wa 6th
| m6
|m6
| Pythagorean minor sixth, octave-reduced 81st subharmonic
|Pythagorean minor sixth, octave-reduced 81st subharmonic
|-
|-
| [[8/5]]
|[[8/5]]
| 813.686286
|813.686286
| g6, gu 6th
|g6, gu 6th
| m6<sub>5</sub>
|m6<sub>5</sub>
| classic minor sixth, just minor sixth, octave-reduced 5th subharmonic
|classic minor sixth, just minor sixth, octave-reduced 5th subharmonic
|-
|-
| 413/256
|413/256
| 827.997565
|827.997565
| 59oz6, finozo 6th
|59oz6, finozo 6th
|
|M6<sup>413</sup>
| octave-reduced 413th harmonic, homestuck sixth (2<sup>-8</sup> * 7 * 59)
|octave-reduced 413th harmonic, homestuck sixth (2<sup>-8</sup> * 7 * 59)
|-
|-
| [[13/8]]
|[[13/8]]
| 840.527662
| 840.527662
| 3o6, tho 6th
|3o6, tho 6th
| m6<sup>13</sup>
|m6<sup>13</sup>
| lesser tridecimal neutral sixth, octave-reduced 13th harmonic
|lesser tridecimal neutral sixth, octave-reduced 13th harmonic
|-
|-
| [[80/49]]
|[[80/49]]
| 848.661901
|848.661901
| rry5, ruruyo aug 5th
|rry5, ruruyo aug 5th
|
|A5<sup>5</sup><sub>49</sub>
| (purple 6th)
|(purple 6th)
|-
|-
| [[49/30]]
|[[49/30]]
| 849.383198
|849.383198
| zzg7, zozogu 7th
|zzg7, zozogu 7th
|
|d7<sup>49</sup><sub>5</sub>
| (purple 6th)
|(purple 6th)
|-
|-
| [[18/11]]
|[[18/11]]
| 852.592059
|852.592059
| 1u6, lu 6th
|1u6, lu 6th
| M6<sub>11</sub>
| M6<sub>11</sub>
| undecimal neutral sixth
|undecimal neutral sixth
|-
|-
| [[28/17]]
|[[28/17]]
| 863.870497
|863.870497
| 17uz6, suzo 6th
|17uz6, suzo 6th
|
|M6<sup>7</sup><sub>17</sub>
| septendecimal submajor sixth
|septendecimal submajor sixth
|-
|-
| [[38/23]]
|[[38/23]]
| 869.238669
|869.238669
| 23u19o6, twethuno 6th
|23u19o6, twethuno 6th
|
|d7<sup>19</sup><sub>23</sub>
| vicesimotertial submajor sixth
|vicesimotertial submajor sixth
|-
|-
| [[5/3]]
|[[5/3]]
| 884.358713
|884.358713
| y6, yo 6th
|y6, yo 6th
| M6<sup>5</sup>
|M6<sup>5</sup>
| classic major sixth, just major sixth
|classic major sixth, just major sixth
|-
|-
| [[42/25]]
|[[42/25]]
| 898.153480
|898.153480
| zgg7, zogugu 7th
|zgg7, zogugu 7th
| d7<sup>7</sup><sub>25</sub>
|d7<sup>7</sup><sub>25</sub>
| quasi-tempered major sixth
|quasi-tempered major sixth
|-
|-
| [[32/19]]
|[[32/19]]
| 902.486984
|902.486984
| 19u6, inu 6th
|19u6, inu 6th
|
|M6<sub>19</sub>
| utonal major sixth, octave-reduced 19th subharmonic
|utonal major sixth, octave-reduced 19th subharmonic
|-
|-
| [[27/16]]
|[[27/16]]
| 905.865003
|905.865003
| w6, wa 6th
|w6, wa 6th
| M6
|M6
| Pythagorean major sixth, octave-reduced 27th harmonic
|Pythagorean major sixth, octave-reduced 27th harmonic
|-
|-
| [[22/13]]
|[[22/13]]
| 910.790821
|910.790821
| 3u1o6, thulo 6th
|3u1o6, thulo 6th
| M6<sup>11</sup><sub>13</sub>
|M6<sup>11</sup><sub>13</sub>
| tridecimal major sixth
| tridecimal major sixth
|-
|-
| [[17/10]]
|[[17/10]]
| 918.641696
|918.641696
| 17og7, sogu 7th
|17og7, sogu 7th
| d7<sup>17</sup><sub>5</sub>
|d7<sup>17</sup><sub>5</sub>
| septendecimal diminished seventh, septendecimal major sixth
|septendecimal diminished seventh, septendecimal major sixth
|-
|-
| [[12/7]]
| [[12/7]]
| 933.129094
|933.129094
| r6, ru 6th
|r6, ru 6th
| M6<sub>7</sub>
| M6<sub>7</sub>
| supermajor sixth, septimal major sixth
|supermajor sixth, septimal major sixth
|-
|-
| [[55/32]]
|[[55/32]]
| 937.631656
|937.631656
| 1oy6, loyo 6th
|1oy6, loyo 6th
| M6<sup>55</sup>
|M6<sup>55</sup>
| keenanismic supermajor sixth, octave-reduced 55th harmonic
|keenanismic supermajor sixth, octave-reduced 55th harmonic
|-
|-
| [[19/11]]
|[[19/11]]
| 946.195074
|946.195074
| 19o1u7, nolu 7th
|19o1u7, nolu 7th
| m7<sup>19</sup><sub>11</sub>
|m7<sup>19</sup><sub>11</sub>
| undevicesimal semitwelfth, maximal major sixth
|undevicesimal semitwelfth, maximal major sixth
|-
|-
| [[140/81]]
|[[140/81]]
| 947.319617
|947.319617
| zy7, zoyo 7th
|zy7, zoyo 7th
| m7<sup>35</sup>
|m7<sup>35</sup>
| septimal semidiminished seventh, septimal inframinor seventh
|septimal semidiminished seventh, septimal inframinor seventh
|-
|-
| 97/56
| 97/56
| 951.069504
|951.069504
| 97or6, ninety-soru 6th
|97or6, ninety-soru 6th
| M6<sup>97</sup><sub>7</sub>
|M6<sup>97</sup><sub>7</sub>
| homothetic semitwelth
|homothetic semitwelth
|-
|-
| [[26/15]]
|[[26/15]]
| 952.258947
|952.258947
| 3og7, thogu 7th
|3og7, thogu 7th
| d7<sup>13</sup><sub>5</sub>
|d7<sup>13</sup><sub>5</sub>
| tridecimal semitwelfth
| tridecimal semitwelfth
|-
|-
| [[7/4]]
|[[7/4]]
| 968.825906
|968.825906
| z7, zo 7th
|z7, zo 7th
| m7<sup>7</sup>
|m7<sup>7</sup>
| subminor seventh, septimal minor seventh, harmonic seventh, natural seventh, octave-reduced 7th harmonic
|subminor seventh, septimal minor seventh, harmonic seventh, natural seventh, octave-reduced 7th harmonic
|-
|-
| [[225/128]]
|[[225/128]]
| 976.537429
|976.537429
| Lyy6, large yoyo 6th
|Lyy6, large yoyo 6th
|
|A6<sup>25</sup>
| marvel five-limit harmonic seventh, octave-reduced 225th harmonic ({{Monzo|-7, 2, 2}})
|marvel five-limit harmonic seventh, octave-reduced 225th harmonic ({{Monzo|-7, 2, 2}})
|-
|-
| [[127/72]]
|[[127/72]]
| 982.511622
|982.511622
| 127o7
|127o7
| m7<sup>127</sup>
|m7<sup>127</sup>
| harmonic/Pythagorean minor seventh meantone
|harmonic/Pythagorean minor seventh meantone
|-
|-
| [[30/17]]
|[[30/17]]
| 983.313305
|983.313305
| 17uy6, suyo 6th
|17uy6, suyo 6th
|
|A6<sup>5</sup><sub>17</sub>
| septendecimal minor seventh
|septendecimal minor seventh
|-
|-
| [[71/40]]
|[[71/40]]
| 993.382830
|993.382830
| 71oy7
|71oy7
| m7<sup>71</sup><sub>5</sub>
|m7<sup>71</sup><sub>5</sub>
| harmonic/just minor seventh meantone
| harmonic/just minor seventh meantone
|-
|-
| [[959/540]]
|[[959/540]]
| 994.285690
|994.285690
| 137ozy8
|137ozy8
| dd8<sup>959</sup><sub>5</sub>
|dd8<sup>959</sup><sub>5</sub>
| harmonic/Pythagorean/just minor seventh meantone
|harmonic/Pythagorean/just minor seventh meantone
|-
|-
| [[16/9]]
| [[16/9]]
| 996.089998
|996.089998
| w7, wa 7th
|w7, wa 7th
| m7
|m7
| Pythagorean minor seventh, small minor seventh, octave-reduced 9th subharmonic
|Pythagorean minor seventh, small minor seventh, octave-reduced 9th subharmonic
|-
|-
| [[25/14]]
|[[25/14]]
| 1003.801521
|1003.801521
| ryy6, ruyoyo 6th
| ryy6, ruyoyo 6th
|
|A6<sup>25</sup><sub>7</sub>
| middle minor seventh
|middle minor seventh
|-
|-
| [[34/19]]
|[[34/19]]
| 1007.442393
| 1007.442393
| 19u17o7, nuso 7th
|19u17o7, nuso 7th
|
|m7<sup>17</sup><sub>19</sub>
| quasi-meantone minor seventh
|quasi-meantone minor seventh
|-
|-
| [[9/5]]
| [[9/5]]
| 1017.596288
|1017.596288
| g5, gu 7th
|g5, gu 7th
| m7<sub>5</sub>
|m7<sub>5</sub>
| classic minor seventh, large minor seventh
|classic minor seventh, large minor seventh
|-
|-
| [[29/16]]
|[[29/16]]
| 1029.577194
|1029.577194
| 29o7, tweno 7th
|29o7, tweno 7th
|
|m7<sup>29</sup>
| vicesimononal supraminor seventh, octave-reduced 29th harmonic
|vicesimononal supraminor seventh, octave-reduced 29th harmonic
|-
|-
| [[20/11]]
|[[20/11]]
| 1034.995772
|1034.995772
| 1uy7, luyo 7th
|1uy7, luyo 7th
| M7<sup>5</sup><sub>11</sub>
|M7<sup>5</sup><sub>11</sub>
| undecimal supraminor seventh, small undecimal neutral seventh
|undecimal supraminor seventh, small undecimal neutral seventh
|-
|-
| [[64/35]]
|[[64/35]]
| 1044.860380
|1044.860380
| rg7, rugu 7th
|rg7, rugu 7th
|
|m7<sub>35</sub>
| septimal neutral seventh
|septimal neutral seventh
|-
|-
| [[11/6]]
|[[11/6]]
| 1049.362941
|1049.362941
| 1o7, ilo 7th
|1o7, ilo 7th
| m7<sup>11</sup>
| m7<sup>11</sup>
| undecimal neutral seventh, 21/4-tone
|undecimal neutral seventh, 21/4-tone
|-
|-
| [[24/13]]
|[[24/13]]
| 1061.427339
|1061.427339
| 3u7, thu 7th
|3u7, thu 7th
| M7<sub>13</sub>
|M7<sub>13</sub>
| tridecimal neutral seventh
|tridecimal neutral seventh
|-
|-
| [[13/7]]
|[[13/7]]
| 1071.701755
|1071.701755
| 3or7, thoru 7th
|3or7, thoru 7th
| m7<sup>13</sup><sub>7</sub>
|m7<sup>13</sup><sub>7</sub>
| tridecimal submajor seventh, 16/3-tone
|tridecimal submajor seventh, 16/3-tone
|-
|-
| [[28/15]]
|[[28/15]]
| 1080.557192
|1080.557192
| zg8, zogu octave
|zg8, zogu octave
| d8<sup>7</sup><sub>5</sub>
|d8<sup>7</sup><sub>5</sub>
| grave major seventh, octave minus a ruyo aug unison
| grave major seventh, octave minus a ruyo aug unison
|-
|-
| [[15/8]]
|[[15/8]]
| 1088.268715
|1088.268715
| y7, yo 7th
|y7, yo 7th
| M7<sup>5</sup>
|M7<sup>5</sup>
| classic major seventh, just major seventh, octave-reduced 15th harmonic
| classic major seventh, just major seventh, octave-reduced 15th harmonic
|-
|-
| [[32/17]]
|[[32/17]]
| 1095.044590
|1095.044590
| 17u7, su 7th
|17u7, su 7th
| M7<sub>17</sub>
|M7<sub>17</sub>
| septendecimal major seventh (FJS), septendecimal diminished octave (HEJI), [[octave-reduced]] 17th [[subharmonic]]
| septendecimal major seventh (FJS), septendecimal diminished octave (HEJI), [[octave-reduced]] 17th [[subharmonic]]
|-
|-
| [[17/9]]
|[[17/9]]
| 1101.045408
|1101.045408
| 17o8, iso octave
|17o8, iso octave
| d8<sup>17</sup>
|d8<sup>17</sup>
| septendecimal major seventh (HEJI), septendecimal diminished octave (FJS)
| septendecimal major seventh (HEJI), septendecimal diminished octave (FJS)
|-
|-
| [[36/19]]
|[[36/19]]
| 1106.396986
|1106.396986
| 19u7, inu 7th
|19u7, inu 7th
| M7<sub>19</sub>
|M7<sub>19</sub>
| undevicesimal major seventh, Boethius' major seventh
|undevicesimal major seventh, Boethius' major seventh
|-
|-
| [[243/128]]
| [[243/128]]
| 1109.775004
| 1109.775004
| Lw7, large wa 7th
|Lw7, large wa 7th
| M7
|M7
| Pythagorean major seventh, [[octave-reduced]] 243rd harmonic
|Pythagorean major seventh, [[octave-reduced]] 243rd harmonic
|-
|-
| [[19/10]]
|[[19/10]]
| 1111.199302
|1111.199302
| 19og8, nogu 8ve
|19og8, nogu 8ve
| d8<sup>19</sup><sub>5</sub>
|d8<sup>19</sup><sub>5</sub>
| undevicesimal diminished octave, Eratosthenes' major seventh
|undevicesimal diminished octave, Eratosthenes' major seventh
|-
|-
| [[40/21]]
|[[40/21]]
| 1115.532907
|1115.532907
| ry7, ruyo 7th
|ry7, ruyo 7th
| M7<sup>5</sup><sub>7</sub>
|M7<sup>5</sup><sub>7</sub>
| septimal acute major seventh
|septimal acute major seventh
|-
|-
| [[61/32]]
|[[61/32]]
| 1116.884905
|1116.884905
| 61o7, siwo 7th
|61o7, siwo 7th
| M7<sup>61</sup>
|M7<sup>61</sup>
| octave-reduced 61st harmonic
|octave-reduced 61st harmonic
|-
|-
| [[48/25]]
|[[48/25]]
| 1129.327573
|1129.327573
| gg8, gugu octave
|gg8, gugu octave
| d8<sub>25</sub>
|d8<sub>25</sub>
| classic diminished octave
|classic diminished octave
|-
|-
| [[27/14]]
|[[27/14]]
| 1137.039096
|1137.039096
| r7, ru 7th
|r7, ru 7th
| M7<sub>7</sub>
| M7<sub>7</sub>
| supermajor seventh, septimal major seventh
|supermajor seventh, septimal major seventh
|-
|-
| [[31/16]]
|[[31/16]]
| 1145.035572
|1145.035572
| 31o7, thiwo 7th
|31o7, thiwo 7th
| M7<sup>31</sup>
|M7<sup>31</sup>
| tricesimoprimal ultramajor seventh (FJS), tricesimoprimal semidiminished octave (HEJI), octave-reduced 31st harmonic
|tricesimoprimal ultramajor seventh (FJS), tricesimoprimal semidiminished octave (HEJI), octave-reduced 31st harmonic
|-
|-
| [[64/33]]
|[[64/33]]
| 1146.727057
|1146.727057
| 1u8, lu octave
|1u8, lu octave
| P8<sub>11</sub>
| P8<sub>11</sub>
| undecimal semidiminished octave, octave-reduced 33rd subharmonic
|undecimal semidiminished octave, octave-reduced 33rd subharmonic
|-
|-
| [[35/18]]
|[[35/18]]
| 1151.239619
|1151.239619
| zy8, zoyo octave
|zy8, zoyo octave
| P8<sup>35</sup>
|P8<sup>35</sup>
| septimal semidiminished octave
|septimal semidiminished octave
|-
|-
| [[96/49]]
|[[96/49]]
| 1164.303188
|1164.303188
| rr7, ruru 7th
|rr7, ruru 7th
| M7<sub>49</sub>
|M7<sub>49</sub>
|
|
|-
|-
| [[49/25]]
|[[49/25]]
| 1165.024385
| 1165.024385
| zzgg9, bizogu 9th
|zzgg9, bizogu 9th
| d9<sup>49</sup><sub>25</sub>
|d9<sup>49</sup><sub>25</sub>
|  
|
|-
|-
| [[160/81]]
|[[160/81]]
| 1178.493814
|1178.493814
| y8, yo octave
|y8, yo octave
| P8<sup>5</sup>
|P8<sup>5</sup>
| octave minus syntonic comma
|octave minus syntonic comma
|-
|-
| [[2/1]]
|[[2/1]]
| 1200
| 1200
| w8, wa octave
|w8, wa octave
| P8
|P8
| [[Octave|octave]], [[Wikipedia:Diapason|diapason]]
|[[Octave|octave]], [[Wikipedia:Diapason|diapason]]
|}
|}


Line 1,380: Line 1,380:
{| class="wikitable sortable"
{| class="wikitable sortable"
|-
|-
! frequency ratio
!frequency ratio
! cents value
! cents value


Line 1,388: Line 1,388:
!some common names
!some common names
|-
|-
| [[13/6]]
|[[13/6]]
| 1338.573
|1338.573
|3o9
|3o9
|tho 9th
|tho 9th
Line 1,395: Line 1,395:
|
|
|-
|-
| [[11/5]]
|[[11/5]]
| 1365.004
|1365.004
|1o9
|1o9
|ilo 9th
|ilo 9th
Line 1,403: Line 1,403:
|-
|-
| [[16/7]]
| [[16/7]]
| 1431.174
|1431.174
|r9
|r9
|ru 9th
|ru 9th
|m9<sub>7</sub>
|M9<sub>7</sub>
|
|
|-
|-
| [[7/3]]
| [[7/3]]
| 1466.871
|1466.871
|z10
|z10
|zo 10th
|zo 10th
Line 1,417: Line 1,417:
|-
|-
| [[5/2]]
| [[5/2]]
| 1586.314
|1586.314
|y10
|y10
|yo 10th
|yo 10th
Line 1,423: Line 1,423:
|just major tenth
|just major tenth
|-
|-
| [[8/3]]
|[[8/3]]
| 1698.045
|1698.045
|w11, cw4
|w11, cw4
|wa 11th, co wa 4th
|wa 11th, co wa 4th
Line 1,430: Line 1,430:
|
|
|-
|-
| [[11/4]]
|[[11/4]]
| 1751.318
|1751.318
|1o11, c1o4
|1o11, c1o4
|ilo 11th, co lo 4th
|ilo 11th, co lo 4th
Line 1,437: Line 1,437:
|
|
|-
|-
| [[3/1]]
|[[3/1]]
| 1901.955
|1901.955
|w12, cw5
|w12, cw5
|wa 12th, co wa 5th
|wa 12th, co wa 5th
|P12
| P12
|tritave
|tritave
|-
|-
| [[16/5]]
|[[16/5]]
| 2013.686
|2013.686
|g13, cg6
|g13, cg6
|gu 13th, co gu 6th
|gu 13th, co gu 6th
Line 1,451: Line 1,451:
|
|
|-
|-
| [[13/4]]
|[[13/4]]
| 2040.528
|2040.528
|3o13, c3o6
| 3o13, c3o6
|tho 13th, co tho 6th
|tho 13th, co tho 6th
|
|m13<sup>13</sup>
|
|
|-
|-
| [[10/3]]
|[[10/3]]
| 2084.359
|2084.359
|y13, cy6
|y13, cy6
|yo 13th, co yo 6th
|yo 13th, co yo 6th
|
|M13<sup>5</sup>
|
|
|-
|-
| [[7/2]]
| [[7/2]]
| 2168.826
|2168.826
|cz7
|cz7
|co zo 7th
|co zo 7th
|
|m14<sup>7</sup>
|
|
|-
|-
| [[11/3]]
|[[11/3]]
| 2249.363
|2249.363
|c1o7
|c1o7
|co ilo 7th
|co ilo 7th
|
|m14<sup>11</sup>
|
|
|-
|-
| [[15/4]]
|[[15/4]]
| 2288.269
|2288.269
|cy7
|cy7
|co yo 7th
| co yo 7th
|
|M14<sup>5</sup>
|
|
|-
|-
| [[4/1]]
| [[4/1]]
| 2400.000
|2400.000
|cw8
| cw8
|wa double 8ve
|wa double 8ve
|P15
|P15
|4th harmonic, two octaves
|4th harmonic, two octaves
|-
|-
| [[13/3]]
|[[13/3]]
| 2538.573
|2538.573
|c3o9, cc3o2
|c3o9, cc3o2
|co tho 9th, coco tho 2nd
|co tho 9th, coco tho 2nd
|
|m16<sup>13</sup>
|
|
|-
|-
| [[9/2]]
|[[9/2]]
| 2603.910
|2603.910
|cw9, ccw2
|cw9, ccw2
|co wa 9th, coco yo 2nd
|co wa 9th, coco yo 2nd
|
|M16
|
|
|-
|-
| [[14/3]]
|[[14/3]]
| 2666.871
| 2666.871
|cz10, ccz3
| cz10, ccz3
|co zo 10th, coco zo 3rd
|co zo 10th, coco zo 3rd
|
|m17<sup>7</sup>
|
|
|-
|-
| [[5/1]]
|[[5/1]]
| 2786.314
| 2786.314
|cy10, ccy3
| cy10, ccy3
|co yo 10th, coco yo 3rd
|co yo 10th, coco yo 3rd
|M17<sup>5</sup>
|M17<sup>5</sup>
|5th harmonic
| 5th harmonic
|-
|-
| [[16/3]]
|[[16/3]]
| 2898.045
|2898.045
|ccw4
|ccw4
|coco wa 4th
|coco wa 4th
|
|P18
|
|
|-
|-
| [[11/2]]
|[[11/2]]
| 2951.318
|2951.318
|cc1o4
| cc1o4
|coco ilo 4th
|coco ilo 4th
|
|P18<sup>11</sup>
|
|
|-
|-
| [[6/1]]
|[[6/1]]
| 3101.955
|3101.955
|ccw5
|ccw5
|coco wa 5th
|coco wa 5th
|
|P19
|
|
|-
|-
| [[13/2]]
|[[13/2]]
| 3240.528
|3240.528
|cc3o6
| cc3o6
|coco tho 6th
|coco tho 6th
|
|m20<sup>13</sup>
|
|
|-
|-
| [[7/1]]
|[[7/1]]
| 3368.826
|3368.826
|ccz7
|ccz7
|coco zo 7th
|coco zo 7th
|
|m21<sup>7</sup>
|
|
|-
|-
| [[15/2]]
|[[15/2]]
| 3488.269
|3488.269
|ccy7
|ccy7
|coco yo 7th
|coco yo 7th
|
|M21<sup>5</sup>
|
|
|-
|-
| [[8/1]]
|[[8/1]]
| 3600.000
|3600.000
|c<sup>3</sup>w1
|c<sup>3</sup>w1
|wa triple 8ve
|wa triple 8ve
|
|P22
|
|
|-
|-
| [[9/1]]
|[[9/1]]
| 3803.910
|3803.910
|c<sup>3</sup>w2
|c<sup>3</sup>w2
|trico wa 2nd
|trico wa 2nd
|
|M23
|
|
|-
|-
| [[10/1]]
|[[10/1]]
| 3986.314
|3986.314
|c<sup>3</sup>y3
|c<sup>3</sup>y3
|trico yo 3rd
|trico yo 3rd
|
|M24<sup>5</sup>
|
|
|-
|-
| [[11/1]]
|[[11/1]]
| 4151.318
|4151.318
|c<sup>3</sup>1o4
|c<sup>3</sup>1o4
|trico ilo 4th
|trico ilo 4th
|
|P25<sup>11</sup>
|
|
|-
|-
| [[12/1]]
|[[12/1]]
| 4301.955
|4301.955
|c<sup>3</sup>w5
|c<sup>3</sup>w5
|trico wa 5th
|trico wa 5th
|
|P26
|
|
|-
|-
| [[13/1]]
|[[13/1]]
| 4440.528
|4440.528
|c<sup>3</sup>3o6
|c<sup>3</sup>3o6
|trico tho 6th
|trico tho 6th
|
|m27<sup>13</sup>
|
|
|-
|-
| [[14/1]]
|[[14/1]]
| 4568.826
|4568.826
|c<sup>3</sup>z7
|c<sup>3</sup>z7
|trico zo 7th
|trico zo 7th
|
|m28<sup>7</sup>
|
|
|-
|-
| [[15/1]]
|[[15/1]]
| 4688.269
|4688.269
|c<sup>3</sup>y7
|c<sup>3</sup>y7
|trico yo 7th
|trico yo 7th
|
|M28<sup>5</sup>
|
|
|-
|-
| [[16/1]]
|[[16/1]]
| 4800.000
|4800.000
|c<sup>4</sup>w1
|c<sup>4</sup>w1
|wa quadruple 8ve
|wa quadruple 8ve
|
|P29
|
|
|}
|}


=See also=
=See also=
* [[List of superparticular intervals]]
*[[List of superparticular intervals]]


=Links=
=Links=
* [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum] by [[Margo Schulter]] [http://www.webcitation.org/5xeoz4zmC Permalink]
*[http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum] by [[Margo Schulter]] [http://www.webcitation.org/5xeoz4zmC Permalink]
* [http://www.huygens-fokker.org/docs/intervals.html Manuel Op de Coul interval list]
*[http://www.huygens-fokker.org/docs/intervals.html Manuel Op de Coul interval list]
* [http://www.kylegann.com/Octave.html Anantomy of an Octave] by [[Kyle Gann]]
*[http://www.kylegann.com/Octave.html Anantomy of an Octave] by [[Kyle Gann]]
* [http://www.tallkite.com/AlternativeTunings.html Alternative Tunings: Theory, Notation and Practice] by [[Kite Giedraitis]]
*[http://www.tallkite.com/AlternativeTunings.html Alternative Tunings: Theory, Notation and Practice] by [[Kite Giedraitis]]
* [https://misotanni.github.io/fjs/en/calc.html FJS interval calculators]
*[https://misotanni.github.io/fjs/en/calc.html FJS interval calculators]
* [http://www.huygens-fokker.org/docs/intervals.html Stichting Huygens-Fokker: List of intervals]
*[http://www.huygens-fokker.org/docs/intervals.html Stichting Huygens-Fokker: List of intervals]


[[Category:Gallery]]
[[Category:Gallery]]
[[Category:Interval collection]]
[[Category:Interval collection]]
[[Category:Just intonation]]
[[Category:Just intonation]]

Revision as of 01:26, 16 May 2021

Introduction

In just intonation, a musical interval is specified as a ratio of two frequencies. When two (or more) pitches are sounded that are in simple proportions to one another, there is a "fusing" quality to the sound which is often described as pleasing; hence the interest in tuning the pitches of musical systems according to such proportions. There is much debate as to what "consonance" means in a musical system, but in Just Intonation, it is generally assumed that lower numbers in frequency ratios lead to greater consonance. In the actual performance of a piece of music, the number of factors involved are enormous, and it is not often helpful to reduce a musical experience to a one-dimensional description of "consonance versus dissonance." Hence the need for this gallery, to give life to conversation about what an interval means beyond the numerical description: "5/3" or "21/16" or what have you.

What follows is a Gallery of Just Intervals in ascending order from 1/1 to 2/1 and beyond. No such list could possibly be complete (as there are infinite possible ratios), so please add intervals of interest as you see fit. Any rational interval is welcome, as long as the wiki author has some interest in it. Contributions to an interval's lore could include: descriptions of common usage, technical notes, poetry, links, reservations, complaints, chords or compositions that feature it, edos that approximate it, intervals that are functionally (or emotionally) related to it, nicknames, love letters, fan art, etc. If your contribution is unconventional, feel free to sign your name to it.

This page lists links to dedicated pages for each interval.

Gallery of Just Intervals

See also list of superparticular intervals and List of intervals (Huygens-Fokker foundation)

Many of the FJS names are still missing, please add them.

frequency ratio cents value
(six decimal places) 		color notation FJS name some common names
1/1 0 w1, wa unison P1 unity, perfect prime, Tonic
32805/32768 1.953721 Ly-2, layo comma d-25 schisma ([-15, 8, 1⟩)
225/224 7.711523 ryy-2, ruyoyo comma d-2257 septimal kleisma, marvel comma ([-5, 2, 2, -1⟩)
126/125 13.794767 zg32, zotrigu comma d27125 septimal semicomma, starling comma ([1, 2, -3, 1⟩)
100/99 17.399484 1uyy1, luyoyo comma A12511 Ptolemy's comma, ptolemisma
99/98 17.576131 1orr-2, loruru comma m-21149 mothwellsma
2048/2025 19.552569 sgg2, sagugu comma d225 diaschisma ([11, -4, -2⟩)
81/80 21.506286 g1, gu comma P15 meantone comma, syntonic comma, Didymus comma
531441/524288 23.460010 LLw-2, wa comma d-2 Pythagorean comma, ditonic comma ([-19, 12⟩)
66/65 26.431568 3u1og1, thulogu comma P11165 winmeanma
65/64 26.841376 3oy1, thoyo comma P165 wilsorma, 13th-partial chroma
64/63 27.264092 r1, ru comma P17 septimal comma, Archytas' comma
3125/3072 29.613568 Ly5-2, laquinyo comma dd-23125 magic comma, small diesis ([-10, -1, 5⟩)
50/49 34.975615 rryy-2, biruyo comma d-22549 septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis
49/48 35.696812 zz2, zozo comma m249 large septimal diesis, slendro diesis
45/44 38.905773 1uy1, luyo comma A1511 undecimal 1/5th tone
128/125 41.058858 g32, trigu comma d2125 diesis, minor diesis, augmented comma, enharmonic comma ([7, 0, -3⟩)
525/512 43.408335 Lzyy1, lazoyoyo comma A1175 Avicenna's enharmonic diesis, avicennma ([-9, 1, 2, 1⟩)
1053/1024 48.347665 L3o1, latho comma P113 tridecimal quartertone, tridecimal comma
36/35 48.770381 rg1, rugu comma P135 septimal quarter tone, double comma
250/243 49.166137 y31, triyo comma A1125 porcupine comma ([1, -5, 3⟩)
59049/57344 50.724102 Lr-2, laru comma d-27 Harrison's comma ([-13, 10, 0, -1⟩)
100/97 52.732017 97uyy1, ninety-suyoyo unison A12597 shrutar quarter tone
33/32 53.272943 1o1, ilo unison P111 undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, octave-reduced 33rd harmonic
648/625 62.565148 g42, quadgu 2nd d2625 diminished comma, major diesis ([8, 4, -4⟩)
28/27 62.960904 z2, zo 2nd m27 small septimal chroma, septimal third-tone, subminor second, septimal minor second
27/26 65.337341 3u1, thu unison A113 small tridecimal third tone
26/25 67.900234 3ogg2, thogugu 2nd d21325 large tridecimal third tone
25/24 70.672427 yy1, yoyo unison A125 chroma, classic chromatic semitone, Zarlinian semitone
24/23 73.680654 23u1, twethu unison m223 lesser vicesimotertial semitone
68/65 78.114034 17o3ug2, sothugu 2nd m21765 valentine semitone
22/21 80.537035 1or1, loru unison P1117 undecimal minor semitone
64/61 83.115195 61u2, siwu 2nd m261 harry minor semitone
21/20 84.467193 zg2, zogu 2nd m275 minor semitone, large septimal chroma
20/19 88.800698 19uy1, nuyo unison A1519 small undevicesimal semitone, undevicesimal chroma, Eratosthenes' semitone
256/243 90.224996 sw2, small wa 2nd m2 Pythagorean limma, Pythagorean diatonic semitone, Pythagorean minor second ([8, -5⟩)
135/128 92.178716 Ly1, layo unison A15 major limma ([-7, 3, 1⟩)
19/18 93.603014 19o2, ino 2nd m219 large undevicesimal semitone, undevicesimal limma, Boethius' semitone
18/17 98.954592 17u1, su unison A117 small septendecimal semitone, Arabic lute index finger
17/16 104.955410 17o2, iso 2nd m217 large septendecimal semitone, octave-reduced 17th harmonic
16/15 111.731285 g2, gu 2nd m25 classic diatonic semitone, classic minor second, octave-reduced 15th subharmonic
2187/2048 113.685006 Lw1, large wa unison A1 apotome, Pythagorean chromatic semitone, Pythagorean augmented unison ([-11, 7⟩)
77/72 116.233847 1oz2, lozo 2nd m277 undecimal secor
15/14 119.442808 ry1, ruyo unison A157 septimal diatonic semitone
14/13 128.298245 3uz2, thuzo 2nd M2713 tridecimal 2/3-tone, trienthird, tridecimal supraminor second
27/25 133.237575 gg2, gugu 2nd m225 large limma
13/12 138.572661 3o2, tho 2nd m213 tridecimal neutral second, tridecimal 2/3-tone
243/224 140.949098 Lr1, large ru unison A17 septimal subtone ([-5, 5, 0, -1⟩)
88/81 143.497939 1o2, ilo 2nd m211 undecimal subtone
49/45 147.428097 zzg3, zozogu 3rd d3495 swetismic neutral second
12/11 150.637059 1u2, lu 2nd M211 small undecimal neutral second, 3/4-tone
35/32 155.139620 zy2, zoyo 2nd M235 septimal neutral second
78/71 162.786119 71u3o2, seventy-wutho 2nd m21371 porcupine neutral second
11/10 165.004228 1og2, logu 2nd m2115 undecimal submajor second, large undecimal neutral second, 4/5-tone, Ptolemy's second
54/49 168.213190 rr1, ruru unison A149 Zalzal's mujannab
10/9 182.403712 y2, yo 2nd M25 classic (whole) tone, minor (whole) tone
49/44 186.333871 1uzz3, luzozo 3rd m34911 werckismic minor second
6272/5625 188.486956 szzg44, small bizogugu 4th ddd449625 double marvelous second, double marvelous (whole) tone
19/17 192.557607 19o17u2, nosu 2nd M21917 quasi-meantone
28/25 196.198479 zgg3, zogugu 3rd d3725 middle major second
55/49 199.979843 1orry1, loruruyo unison A15549 werckismic tone
64/57 200.531983 19u2, inu 2nd M219 quasi-tempered whole tone, octave-reduced 57th subharmonic
9/8 203.910002 w2, wa 2nd M2 Pythagorean (whole) tone, major (whole) tone, octave-reduced 9th harmonic
17/15 216.686695 17og3, sogu 3rd d3175 septendecimal whole tone, septendecimal eventone
8/7 231.174094 r2, ru 2nd M27 supermajor second, septimal whole tone, octave-reduced 7th subharmonic
63/55 235.104252 1uzg3, luzogu 3rd m3755 werckismic supermajor second
55/48 235.676655 1oy2, loyo 2nd M255 keenanismic supermajor second
15/13 247.741053 3uy2, thuyo 2nd A2513 tridecimal semifourth, tridecimal ultramajor second, tridecimal inframinor third
97/84 249.114503 97or2, ninety-soru 2nd M2977 homothetic semifourth
81/70 252.268038 rg2, rugu 2nd M235 septimal semi-augmented second, septimal ultramajor second
22/19 253.804926 19u1o2, nulo 2nd M21119 undevicesimal semifourth, minimal minor third, godzilla semifourth
64/55 262.368344 1ug3, lugu 3rd m355 keenanismic subminor third, octave-reduced 55th subharmonic
7/6 266.870906 z3, zo 3rd m37 subminor third, septimal minor third
90/77 270.079867 1ury2, luruyo 2nd A2577 swetismic subminor third
62/53 271.531027 53u31o2, fithu-thiwo 2nd M23153 orwell subminor third
75/64 274.582429 yy2, yoyo 2nd A225 classic augmented second
20/17 281.358304 17uy2, suyo 2nd A2517 septendecimal augmented second, septendecimal minor third
13/11 289.209179 3o1u3, tholu 3rd m31311 tridecimal minor third
32/27 294.134997 w3, wa 3rd m3 Pythagorean minor third, octave-reduced 27th subharmonic
19/16 297.513016 19o3, ino 3rd m319 otonal minor third, octave-reduced 19th harmonic
25/21 301.846520 ryy2, ruyoyo 2nd A2257 quasi-tempered minor third
61/51 309.974395 61o17u2, siwosu 2nd A26117 myna third
6/5 315.641287 g3, gu 3rd m35 classic minor third, just minor third
77/64 320.143849 1oz3, lozo 3rd m377 keenanismic minor third, octave-reduced 77th harmonic
135/112 323.352810 ry2, ruyo 2nd A257 large septimal minor third, marvelous minor third ([-4, 3, 1, -1⟩)
35/29 325.562426 29uzy3, twenuzoyo 3rd M33529 doublewide minor third
23/19 330.761331 23o19u3, twethonu 3rd A22319 vicesimotertial supraminor third
17/14 336.129503 17or3, soru 3rd m3175 septendecimal supraminor third
73/60 339.520756 73og3, seventy-thogu 3rd m3735 amity supraminor third
39/32 342.482663 3o3, tho 3rd m313 lesser tridecimal neutral third, octave-reduced 39th harmonic
625/512 345.254855 Ly42, large quadyo 2nd AA2625 5-limit neutral third ([-9, 0, 4⟩)
11/9 347.407941 1o3, ilo 3rd m311 undecimal neutral third
60/49 350.616902 rry2, ruruyo 2nd A2549 smaller septimal neutral third, (purple 3rd)
49/40 351.338099 zzg4, zozogu 4th d4495 larger septimal neutral third, (purple 3rd)
27/22 354.547060 1u3, lu 3rd M311 rastmic neutral third
16/13 359.472338 3u3, thu 3rd M313 greater tridecimal neutral third, octave reduced 13subharmonic
21/17 365.825498 17uz3, suzo 3rd M3717 septendecimal submajor third
51/41 377.848005 41u17o4, fowuso 4th d41741 maja third
56/45 378.602191 zg4, zogu 4th d475 narrow perde segah, marvelous major third
71/57 380.228526 71o19u3, seventy-wonu 3rd M37119 witchcraft major third
76/61 380.628211 61u19o4, siwuno 4th d41961 magic major third
96/77 381.811152 1ur3, luru 3rd M377 undecimal perde segah, keenanismic major third
5/4 386.313714 y3, yo 3rd M35 classic major third, just major third, octave-reduced 5th harmonic
161/128 397.100254 23oz4, twethozo 4th M3161 just/Pythagorean major third meantone, octave-reduced 161th harmonic
63/50 400.108480 zgg4, zogugu 4th d4725 quasi-tempered major third
81/64 407.820003 Lw3, large wa 3rd M3 Pythagorean major third, octave-reduced 81st harmonic
33/26 412.745281 3u1o3, thulo 3rd M31113 tridecimal major third
80/63 413.577806 ry3, ruyo 3rd M357 werckismic sharp major third
14/11 417.507964 1uz4, luzo 4th P4711 undecimal major third, undecimal diminished fourth
23/18 424.364346 23o4, twetho 4th M323 vicesimotertial diminished fourth
32/25 427.372572 gg4, gugu 4th d425 classic diminished fourth
77/60 431.875134 1ozg4, lozogu 4th d4775 swetismic supermajor third
9/7 435.084095 r3, ru 3rd M37 supermajor third, septimal major third
31/24 443.080572 31o3, thiwo 3rd M331 sensi supermajor third
22/17 446.362533 17u1o3, sulo 3rd M31117 septendecimal supermajor third
35/27 449.274618 zy4, zoyo 4th P435 septimal semidiminished fourth
13/10 454.213948 3og4, thogu 4th d4135 tridecimal semisixth, Barbados third, tridecimal 9/4 tone
64/49 462.348187 rr3, ruru 3rd M349 septatonic major third
17/13 464.427748 17o3u4, sothu 4th P41713 septendecimal sub-fourth
21/16 470.780907 z4, zo 4th P47 sub-fourth, narrow fourth, 8ve-reduced 21st harmonic
33/25 480.645516 1ogg4, logugu 4th d41125 "5-EDO"-esque fourth
117/88 493.119721 3o1u4, tholu 4th P41311 minthmic fourth ([-3, 2, 0, 0, -1, 1⟩)
4/3 498.044999 w4, wa 4th P4 just perfect fourth, octave-reduced 3rd subharmonic, diatessaron
75/56 505.756522 ryy3, ruyoyo 3rd A3257 marvelous fourth
980/729 512.235522 zzy5, zozoyo 5th d5245 sensamagic fourth, septimal sesquidiminished grave fifth
27/20 519.551289 g4, gu 4th P45 acute fourth
19/14 528.687110 19or4, noru 4th P4197 hendrix fourth
49/36 533.741811 zz5, zozo 5th d549 Arabic lute acute fourth
15/11 536.950772 1uy4, luyo 4th A4511 undecimal augmented fourth, subaugmented fourth
48/35 546.815381 rg4, rugu 4th P435 septimal super-fourth
11/8 551.317942 1o4, ilo 4th P411 super-fourth, undecimal semi-augmented fourth, octave-reduced 11th harmonic or harmonic 11th, Alphorn-Fa
18/13 563.382340 3u4, thu 4th A413 tridecimal augmented fourth
25/18 568.717426 yy4, yoyo 4th A425 classic augmented fourth, pental augmented fourth ([-1 -2 2⟩)
88/63 578.582034 1or4, loru 4th P4117 werckismic augmented fourth
7/5 582.512193 zg5, zogu 5th d575 augmented fourth, septimal tritone, Huygen's tritone
45/32 590.223716 y4, yo 4th A45 smaller pental tritone, diatonic tritone ([-5 2 1⟩)
108/77 585.721154 1ur4, luru 4th A477 swetismic augmented fourth ([2, 3, 0, -1, -1⟩)
24/17 596.999591 17u4, su 4th A417 smaller septendecimal tritone
99/70 600.088324 1org4, lorugu 4th P41135 homothetic quasi-tempered tritone
17/12 603.000409 17o5, iso 5th d517 larger septendecimal tritone
64/45 609.776284 g5, gu 5th d55 larger pental tritone, diatonic tritone ([6 -2 -1⟩)
10/7 617.487807 ry4, ruyo 4th A457 diminished fifth, Euler's tritone, superaugmented fourth
23/16 628.274347 23o5, twetho 5th A423 vicesimotertial superaugmented fourth, octave-reduced 23rd harmonic
36/25 631.282574 gg5, gugu 5th d525 pental diminished fifth, classic diminshed fifth ([2 2 -2⟩)
13/9 636.617660 3o5, tho 5th d513 tridecimal diminished fifth
16/11 648.682058 1u5, lu 5th P511 sub-fifth, octave-reduced 11th subharmonic
35/24 653.184619 zy5, zoyo 5th P535 septimal sub-fifth
22/15 663.049228 1og5, logu 5th d5115 undecimal diminished fifth, semidiminished fifth
72/49 666.258889 rr4, ruru 4th A449 septimal catafifth
81/55 670.188347 1ug5, lugu 5th P555 undecimal catafifth
28/19 671.312890 19uz5, nuzo 5th P5719 hendrix fifth
40/27 680.448711 y5, yo 5th P55 grave fifth
729/490 687.764478 rrg5, rurugu 4th A4245 sensamagic fifth, septimal sesquiaugmented acute fourth
112/75 694.243478 zgg6, zogugu 6th d6725 marvelous fifth
16384/10935 700.001280 sg6, sagu 6th d65 Kirnberger's fifth ("12-EDO"-esque fifth)
3/2 701.955001 w5, wa 5th P5 just perfect fifth, octave-reduced 3rd harmonic, diapente
182/121 706.717684 3o1uuz6, tholuluzo 6th m691121 tridecimal gentle fifth ([1, 0, 0, 1, -2, 1⟩)
176/117 706.880279 3u1o5, thulo 5th P51113 minthmic fifth ([4, -2, 0, 0, 1, -1⟩)
50/33 719.354484 1uyy5, luyoyo 5th A52511 "5-EDO"-esque fifth
32/21 729.219093 r5, ru 5th P57 super-fifth, wide fifth, octave-reduced 21st subharmonic
26/17 735.572252 17u3o5, sutho 5th P51317 septendecimal super-fifth
49/32 737.651813 zz6, zozo 6th m649 superduper fifth, octave-reduced 49th harmonic
20/13 745.786052 3uy5, thuyo 5th A5513 tridecimal semitenth, Barbados sixth, ratwolf wolf fifth
17/11 753.637467 17o1u6, solu 6th m61711 septendecimal subminor sixth
14/9 764.915905 z6, zo 6th m67 subminor sixth, septimal minor sixth
25/16 772.627428 yy5, yoyo 5th A525 pental augmented fifth, classic augmented fifth, otonal minor sixth, octave-reduced 25th harmonic
36/23 775.635654 23u5, twethu 5th m623 vicesimotertial augmented fifth
11/7 782.492036 1or5, loru 5th P5117 undecimal subminor sixth, undecimal augmented fifth
63/40 786.422194 zg6, zogu 6th m675
52/33 787.254719 3o1u6, tholu 6th m61311 tridecimal minor sixth
128/81 792.179997 sw6, small wa 6th m6 Pythagorean minor sixth, octave-reduced 81st subharmonic
8/5 813.686286 g6, gu 6th m65 classic minor sixth, just minor sixth, octave-reduced 5th subharmonic
413/256 827.997565 59oz6, finozo 6th M6413 octave-reduced 413th harmonic, homestuck sixth (2-8 * 7 * 59)
13/8 840.527662 3o6, tho 6th m613 lesser tridecimal neutral sixth, octave-reduced 13th harmonic
80/49 848.661901 rry5, ruruyo aug 5th A5549 (purple 6th)
49/30 849.383198 zzg7, zozogu 7th d7495 (purple 6th)
18/11 852.592059 1u6, lu 6th M611 undecimal neutral sixth
28/17 863.870497 17uz6, suzo 6th M6717 septendecimal submajor sixth
38/23 869.238669 23u19o6, twethuno 6th d71923 vicesimotertial submajor sixth
5/3 884.358713 y6, yo 6th M65 classic major sixth, just major sixth
42/25 898.153480 zgg7, zogugu 7th d7725 quasi-tempered major sixth
32/19 902.486984 19u6, inu 6th M619 utonal major sixth, octave-reduced 19th subharmonic
27/16 905.865003 w6, wa 6th M6 Pythagorean major sixth, octave-reduced 27th harmonic
22/13 910.790821 3u1o6, thulo 6th M61113 tridecimal major sixth
17/10 918.641696 17og7, sogu 7th d7175 septendecimal diminished seventh, septendecimal major sixth
12/7 933.129094 r6, ru 6th M67 supermajor sixth, septimal major sixth
55/32 937.631656 1oy6, loyo 6th M655 keenanismic supermajor sixth, octave-reduced 55th harmonic
19/11 946.195074 19o1u7, nolu 7th m71911 undevicesimal semitwelfth, maximal major sixth
140/81 947.319617 zy7, zoyo 7th m735 septimal semidiminished seventh, septimal inframinor seventh
97/56 951.069504 97or6, ninety-soru 6th M6977 homothetic semitwelth
26/15 952.258947 3og7, thogu 7th d7135 tridecimal semitwelfth
7/4 968.825906 z7, zo 7th m77 subminor seventh, septimal minor seventh, harmonic seventh, natural seventh, octave-reduced 7th harmonic
225/128 976.537429 Lyy6, large yoyo 6th A625 marvel five-limit harmonic seventh, octave-reduced 225th harmonic ([-7, 2, 2⟩)
127/72 982.511622 127o7 m7127 harmonic/Pythagorean minor seventh meantone
30/17 983.313305 17uy6, suyo 6th A6517 septendecimal minor seventh
71/40 993.382830 71oy7 m7715 harmonic/just minor seventh meantone
959/540 994.285690 137ozy8 dd89595 harmonic/Pythagorean/just minor seventh meantone
16/9 996.089998 w7, wa 7th m7 Pythagorean minor seventh, small minor seventh, octave-reduced 9th subharmonic
25/14 1003.801521 ryy6, ruyoyo 6th A6257 middle minor seventh
34/19 1007.442393 19u17o7, nuso 7th m71719 quasi-meantone minor seventh
9/5 1017.596288 g5, gu 7th m75 classic minor seventh, large minor seventh
29/16 1029.577194 29o7, tweno 7th m729 vicesimononal supraminor seventh, octave-reduced 29th harmonic
20/11 1034.995772 1uy7, luyo 7th M7511 undecimal supraminor seventh, small undecimal neutral seventh
64/35 1044.860380 rg7, rugu 7th m735 septimal neutral seventh
11/6 1049.362941 1o7, ilo 7th m711 undecimal neutral seventh, 21/4-tone
24/13 1061.427339 3u7, thu 7th M713 tridecimal neutral seventh
13/7 1071.701755 3or7, thoru 7th m7137 tridecimal submajor seventh, 16/3-tone
28/15 1080.557192 zg8, zogu octave d875 grave major seventh, octave minus a ruyo aug unison
15/8 1088.268715 y7, yo 7th M75 classic major seventh, just major seventh, octave-reduced 15th harmonic
32/17 1095.044590 17u7, su 7th M717 septendecimal major seventh (FJS), septendecimal diminished octave (HEJI), octave-reduced 17th subharmonic
17/9 1101.045408 17o8, iso octave d817 septendecimal major seventh (HEJI), septendecimal diminished octave (FJS)
36/19 1106.396986 19u7, inu 7th M719 undevicesimal major seventh, Boethius' major seventh
243/128 1109.775004 Lw7, large wa 7th M7 Pythagorean major seventh, octave-reduced 243rd harmonic
19/10 1111.199302 19og8, nogu 8ve d8195 undevicesimal diminished octave, Eratosthenes' major seventh
40/21 1115.532907 ry7, ruyo 7th M757 septimal acute major seventh
61/32 1116.884905 61o7, siwo 7th M761 octave-reduced 61st harmonic
48/25 1129.327573 gg8, gugu octave d825 classic diminished octave
27/14 1137.039096 r7, ru 7th M77 supermajor seventh, septimal major seventh
31/16 1145.035572 31o7, thiwo 7th M731 tricesimoprimal ultramajor seventh (FJS), tricesimoprimal semidiminished octave (HEJI), octave-reduced 31st harmonic
64/33 1146.727057 1u8, lu octave P811 undecimal semidiminished octave, octave-reduced 33rd subharmonic
35/18 1151.239619 zy8, zoyo octave P835 septimal semidiminished octave
96/49 1164.303188 rr7, ruru 7th M749
49/25 1165.024385 zzgg9, bizogu 9th d94925
160/81 1178.493814 y8, yo octave P85 octave minus syntonic comma
2/1 1200 w8, wa octave P8 octave, diapason

Intervals larger than an octave

In the color names, "co" or "c" stands for compound, a conventional music term.

frequency ratio cents value

(three decimal places)

color name FJS name some common names
13/6 1338.573 3o9 tho 9th m913
11/5 1365.004 1o9 ilo 9th m9115
16/7 1431.174 r9 ru 9th M97
7/3 1466.871 z10 zo 10th m107 septimal minor tenth
5/2 1586.314 y10 yo 10th M105 just major tenth
8/3 1698.045 w11, cw4 wa 11th, co wa 4th P11
11/4 1751.318 1o11, c1o4 ilo 11th, co lo 4th P1111
3/1 1901.955 w12, cw5 wa 12th, co wa 5th P12 tritave
16/5 2013.686 g13, cg6 gu 13th, co gu 6th m135
13/4 2040.528 3o13, c3o6 tho 13th, co tho 6th m1313
10/3 2084.359 y13, cy6 yo 13th, co yo 6th M135
7/2 2168.826 cz7 co zo 7th m147
11/3 2249.363 c1o7 co ilo 7th m1411
15/4 2288.269 cy7 co yo 7th M145
4/1 2400.000 cw8 wa double 8ve P15 4th harmonic, two octaves
13/3 2538.573 c3o9, cc3o2 co tho 9th, coco tho 2nd m1613
9/2 2603.910 cw9, ccw2 co wa 9th, coco yo 2nd M16
14/3 2666.871 cz10, ccz3 co zo 10th, coco zo 3rd m177
5/1 2786.314 cy10, ccy3 co yo 10th, coco yo 3rd M175 5th harmonic
16/3 2898.045 ccw4 coco wa 4th P18
11/2 2951.318 cc1o4 coco ilo 4th P1811
6/1 3101.955 ccw5 coco wa 5th P19
13/2 3240.528 cc3o6 coco tho 6th m2013
7/1 3368.826 ccz7 coco zo 7th m217
15/2 3488.269 ccy7 coco yo 7th M215
8/1 3600.000 c3w1 wa triple 8ve P22
9/1 3803.910 c3w2 trico wa 2nd M23
10/1 3986.314 c3y3 trico yo 3rd M245
11/1 4151.318 c31o4 trico ilo 4th P2511
12/1 4301.955 c3w5 trico wa 5th P26
13/1 4440.528 c33o6 trico tho 6th m2713
14/1 4568.826 c3z7 trico zo 7th m287
15/1 4688.269 c3y7 trico yo 7th M285
16/1 4800.000 c4w1 wa quadruple 8ve P29

See also

Links

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