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.


<!-- what you could add is [[19-limit]] and more FJS names -->
{| class="wikitable sortable"
{| class="wikitable sortable"
|-
|-
! frequency ratio
! Frequency Ratio
! cents value <br> (six decimal places)
! Cents Value <br> (six decimal places)
! [[color notation]]
! [[Color notation|Color Name]]
! [[Functional Just System|FJS name]]
! [[Functional Just System|FJS Name]]
! class="unsortable" | some common names
! 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, [[wikipedia:Interval_(music)#Compound_intervals|a conventional music term]].
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
! Frequency Ratio
! cents value
! Cents Value<br>(three decimal places)
 
! colspan="2" |[[Color notation|Color Name]]
(three decimal places)
! FJS Name
! colspan="2" |[[Color notation|color name]]
! Some common names
!FJS name
!some common names
|-
|-
|[[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, interval of equivalence of [[173ed49]]
| 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]]