Gallery of just intervals: Difference between revisions
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If any [[FJS]] names are missing, please [https://misotanni.github.io/fjs/en/calc.html add] them. | If any [[FJS]] names are missing, please [https://misotanni.github.io/fjs/en/calc.html add] them. | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|- | |- | ||
! | ! Frequency Ratio | ||
! | ! Cents Value <br> (six decimal places) | ||
! [[ | ! [[Color notation|Color Name]] | ||
! [[Functional Just System|FJS | ! [[Functional Just System|FJS Name]] | ||
! class="unsortable" | | ! class="unsortable" | Some common names | ||
|- | |- | ||
| [[1/1]] | | [[1/1]] | ||
| Line 1,788: | Line 1,787: | ||
=== Intervals larger than an octave === | === Intervals larger than an octave === | ||
In the color names, "co" or "c" stands for compound, | In the color names, "co" or "c" stands for compound, {{w|Interval (music) #Compound intervals|a conventional music term}}. | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|- | |- | ||
! | ! Frequency Ratio | ||
! | ! Cents Value<br>(three decimal places) | ||
! colspan="2" |[[Color notation|Color Name]] | |||
(three decimal places) | ! FJS Name | ||
! colspan="2" |[[Color notation| | ! Some common names | ||
!FJS | |||
! | |||
|- | |- | ||
|[[15/7]] | | [[15/7]] | ||
|1319.443 | | 1319.443 | ||
|ry8 | | ry8 | ||
|ruyo 8ve | | ruyo 8ve | ||
|A8<sup>5</sup><sub>7</sub> | | A8<sup>5</sup><sub>7</sub> | ||
| | | | ||
|- | |- | ||
|[[13/6]] | | [[13/6]] | ||
|1338.573 | | 1338.573 | ||
|3o9 | | 3o9 | ||
|tho 9th | | tho 9th | ||
|m9<sup>13</sup> | | m9<sup>13</sup> | ||
| | | | ||
|- | |- | ||
|[[11/5]] | | [[11/5]] | ||
|1365.004 | | 1365.004 | ||
|1o9 | | 1o9 | ||
|ilo 9th | | ilo 9th | ||
|m9<sup>11</sup><sub>5</sub> | | m9<sup>11</sup><sub>5</sub> | ||
|neutral ninth | | neutral ninth | ||
|- | |- | ||
|[[9/4]] | | [[9/4]] | ||
|1403.910 | | 1403.910 | ||
|w9 | | w9 | ||
|wa 9th | | wa 9th | ||
|M9 | | M9 | ||
|major ninth | | major ninth | ||
|- | |- | ||
| [[16/7]] | | [[16/7]] | ||
|1431.174 | | 1431.174 | ||
|r9 | | r9 | ||
|ru 9th | | ru 9th | ||
|M9<sub>7</sub> | | M9<sub>7</sub> | ||
|septimal major ninth | | septimal major ninth | ||
|- | |- | ||
| [[7/3]] | | [[7/3]] | ||
|1466.871 | | 1466.871 | ||
|z10 | | z10 | ||
|zo 10th | | zo 10th | ||
|m10<sup>7</sup> | | m10<sup>7</sup> | ||
|septimal minor tenth | | septimal minor tenth | ||
|- | |- | ||
|[[12/5]] | | [[12/5]] | ||
|1515.641 | | 1515.641 | ||
|g10 | | g10 | ||
|gu 10th | | gu 10th | ||
|m10<sub>5</sub> | | m10<sub>5</sub> | ||
|classic minor tenth | | classic minor tenth | ||
|- | |- | ||
| [[5/2]] | | [[5/2]] | ||
|1586.314 | | 1586.314 | ||
|y10 | | y10 | ||
|yo 10th | | yo 10th | ||
|M10<sup>5</sup> | | M10<sup>5</sup> | ||
|classic major tenth | | classic major tenth | ||
|- | |- | ||
|[[13/5]] | | [[13/5]] | ||
|1654.214 | | 1654.214 | ||
|3og11 | |3og11 | ||
|thogu 11th | | thogu 11th | ||
|d11<sup>13</sup><sub>5</sub> | | d11<sup>13</sup><sub>5</sub> | ||
| | | | ||
|- | |- | ||
|[[8/3]] | | [[8/3]] | ||
|1698.045 | | 1698.045 | ||
|w11, cw4 | | w11, cw4 | ||
|wa 11th, cowa 4th | | wa 11th, cowa 4th | ||
|P11 | | P11 | ||
|perfect eleventh | | perfect eleventh | ||
|- | |- | ||
|[[11/4]] | | [[11/4]] | ||
|1751.318 | | 1751.318 | ||
|1o11, c1o4 | | 1o11, c1o4 | ||
|ilo 11th, colo 4th | | ilo 11th, colo 4th | ||
|P11<sup>11</sup> | | P11<sup>11</sup> | ||
| | | | ||
|- | |- | ||
|[[14/5]] | | [[14/5]] | ||
|1782.512 | | 1782.512 | ||
|zg12, czg5 | | zg12, czg5 | ||
|zogu 12th, cozogu 5th | | zogu 12th, cozogu 5th | ||
|d12<sup>7</sup><sub>5</sub> | | d12<sup>7</sup><sub>5</sub> | ||
|short hexatone | | short hexatone | ||
|- | |- | ||
|[[3/1]] | | [[3/1]] | ||
|1901.955 | | 1901.955 | ||
|w12, cw5 | | w12, cw5 | ||
|wa 12th, cowa 5th | | wa 12th, cowa 5th | ||
| P12 | | P12 | ||
|tritave, 3rd harmonic | | tritave, 3rd harmonic | ||
|- | |- | ||
|[[16/5]] | | [[16/5]] | ||
|2013.686 | | 2013.686 | ||
|g13, cg6 | | g13, cg6 | ||
|gu 13th, cogu 6th | | gu 13th, cogu 6th | ||
|m13<sub>5</sub> | | m13<sub>5</sub> | ||
|just minor thirteenth | | just minor thirteenth | ||
|- | |- | ||
|[[13/4]] | | [[13/4]] | ||
|2040.528 | | 2040.528 | ||
| 3o13, c3o6 | | 3o13, c3o6 | ||
|tho 13th, cotho 6th | | tho 13th, cotho 6th | ||
|m13<sup>13</sup> | | m13<sup>13</sup> | ||
| | | | ||
|- | |- | ||
|[[10/3]] | | [[10/3]] | ||
|2084.359 | | 2084.359 | ||
|y13, cy6 | | y13, cy6 | ||
|yo 13th, coyo 6th | | yo 13th, coyo 6th | ||
|M13<sup>5</sup> | | M13<sup>5</sup> | ||
|just major thirteenth | | just major thirteenth | ||
|- | |- | ||
| [[7/2]] | | [[7/2]] | ||
|2168.826 | | 2168.826 | ||
|cz7 | | cz7 | ||
|cozo 7th | | cozo 7th | ||
|m14<sup>7</sup> | | m14<sup>7</sup> | ||
|harmonic fourteenth | | harmonic fourteenth | ||
|- | |- | ||
|[[11/3]] | | [[11/3]] | ||
|2249.363 | | 2249.363 | ||
|c1o7 | | c1o7 | ||
|colo 7th | | colo 7th | ||
|m14<sup>11</sup> | | m14<sup>11</sup> | ||
| | | | ||
|- | |- | ||
|[[15/4]] | | [[15/4]] | ||
|2288.269 | | 2288.269 | ||
|cy7 | | cy7 | ||
|coyo 7th | | coyo 7th | ||
|M14<sup>5</sup> | | M14<sup>5</sup> | ||
| | | | ||
|- | |- | ||
| [[4/1]] | | [[4/1]] | ||
|2400.000 | | 2400.000 | ||
|cw8, ccw1 | | cw8, ccw1 | ||
|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 | ||
|cotho 9th, cocotho 2nd | | cotho 9th, cocotho 2nd | ||
|m16<sup>13</sup> | | m16<sup>13</sup> | ||
| | | | ||
|- | |- | ||
|[[9/2]] | | [[9/2]] | ||
|2603.910 | | 2603.910 | ||
|cw9, ccw2 | | cw9, ccw2 | ||
|cowa 9th, cocoyo 2nd | | cowa 9th, cocoyo 2nd | ||
|M16 | | M16 | ||
|major sixteenth | | major sixteenth | ||
|- | |- | ||
|[[14/3]] | | [[14/3]] | ||
|2666.871 | | 2666.871 | ||
|cz10, ccz3 | | cz10, ccz3 | ||
|cozo 10th, cocozo 3rd | | cozo 10th, cocozo 3rd | ||
|m17<sup>7</sup> | | m17<sup>7</sup> | ||
| | | | ||
|- | |- | ||
|[[5/1]] | | [[5/1]] | ||
|2786.314 | | 2786.314 | ||
|cy10, ccy3 | | cy10, ccy3 | ||
|coyo 10th, cocoyo 3rd | | coyo 10th, cocoyo 3rd | ||
|M17<sup>5</sup> | | M17<sup>5</sup> | ||
|pentave, 5th harmonic | | pentave, 5th harmonic | ||
|- | |- | ||
|[[16/3]] | | [[16/3]] | ||
|2898.045 | | 2898.045 | ||
|ccw4 | | ccw4 | ||
|cocowa 4th | | cocowa 4th | ||
|P18 | | P18 | ||
| | | | ||
|- | |- | ||
|[[11/2]] | | [[11/2]] | ||
|2951.318 | | 2951.318 | ||
|cc1o4 | | cc1o4 | ||
|cocolo 4th | | cocolo 4th | ||
|P18<sup>11</sup> | | P18<sup>11</sup> | ||
| | | | ||
|- | |- | ||
|[[6/1]] | | [[6/1]] | ||
|3101.955 | | 3101.955 | ||
|ccw5 | | ccw5 | ||
|cocowa 5th | | cocowa 5th | ||
|P19 | | P19 | ||
|6th harmonic | | 6th harmonic | ||
|- | |- | ||
|[[13/2]] | | [[13/2]] | ||
|3240.528 | | 3240.528 | ||
|cc3o6 | | cc3o6 | ||
|cocotho 6th | | cocotho 6th | ||
|m20<sup>13</sup> | | m20<sup>13</sup> | ||
| | | | ||
|- | |- | ||
|[[7/1]] | | [[7/1]] | ||
|3368.826 | | 3368.826 | ||
|ccz7 | | ccz7 | ||
|cocozo 7th | | cocozo 7th | ||
|m21<sup>7</sup> | | m21<sup>7</sup> | ||
|7th harmonic | | 7th harmonic | ||
|- | |- | ||
|[[15/2]] | | [[15/2]] | ||
|3488.269 | | 3488.269 | ||
|ccy7 | | ccy7 | ||
|cocoyo 7th | | cocoyo 7th | ||
|M21<sup>5</sup> | | 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 | | P22 | ||
|8th harmonic, three octaves | | 8th harmonic, three octaves | ||
|- | |- | ||
|[[9/1]] | | [[9/1]] | ||
|3803.910 | | 3803.910 | ||
|c<sup>3</sup>w2 | | c<sup>3</sup>w2 | ||
|tricowa 2nd | | tricowa 2nd | ||
|M23 | | M23 | ||
|9th harmonic | | 9th harmonic | ||
|- | |- | ||
|[[10/1]] | | [[10/1]] | ||
|3986.314 | | 3986.314 | ||
|c<sup>3</sup>y3 | | c<sup>3</sup>y3 | ||
|tricoyo 3rd | | tricoyo 3rd | ||
|M24<sup>5</sup> | | M24<sup>5</sup> | ||
|10th harmonic | | 10th harmonic | ||
|- | |- | ||
|[[11/1]] | | [[11/1]] | ||
|4151.318 | | 4151.318 | ||
|c<sup>3</sup>1o4 | | c<sup>3</sup>1o4 | ||
|tricolo 4th | | tricolo 4th | ||
|P25<sup>11</sup> | | P25<sup>11</sup> | ||
|11th harmonic | | 11th harmonic | ||
|- | |- | ||
|[[12/1]] | | [[12/1]] | ||
|4301.955 | | 4301.955 | ||
|c<sup>3</sup>w5 | | c<sup>3</sup>w5 | ||
|tricowa 5th | | tricowa 5th | ||
|P26 | | P26 | ||
|12th harmonic | | 12th harmonic | ||
|- | |- | ||
|[[13/1]] | | [[13/1]] | ||
|4440.528 | | 4440.528 | ||
|c<sup>3</sup>3o6 | | c<sup>3</sup>3o6 | ||
|tricotho 6th | | tricotho 6th | ||
|m27<sup>13</sup> | | m27<sup>13</sup> | ||
|13th harmonic | | 13th harmonic | ||
|- | |- | ||
|[[14/1]] | | [[14/1]] | ||
|4568.826 | | 4568.826 | ||
|c<sup>3</sup>z7 | | c<sup>3</sup>z7 | ||
|tricozo 7th | | tricozo 7th | ||
|m28<sup>7</sup> | | m28<sup>7</sup> | ||
|14th harmonic | | 14th harmonic | ||
|- | |- | ||
|[[15/1]] | | [[15/1]] | ||
|4688.269 | | 4688.269 | ||
|c<sup>3</sup>y7 | | c<sup>3</sup>y7 | ||
|tricoyo 7th | | tricoyo 7th | ||
|M28<sup>5</sup> | | M28<sup>5</sup> | ||
|15th harmonic | | 15th harmonic | ||
|- | |- | ||
|[[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 | | P29 | ||
|16th harmonic, four octaves | | 16th harmonic, four octaves | ||
|- | |- | ||
|[[49/1]] | | [[49/1]] | ||
|6737.652 | | 6737.652 | ||
| | | | ||
| | | | ||
| | | | ||
|49th harmonic | | 49th harmonic | ||
|} | |} | ||
== 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]] [https://www.webcitation.org/5xeoz4zmC Permalink] | * [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum] by [[Margo Schulter]] [https://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:Lists of intervals| ]] | [[Category:Lists of intervals| ]] | ||
[[Category:Just intonation]] | [[Category:Just intonation]] | ||