User:BudjarnLambeth/Above octave: Difference between revisions

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{{Editable user page}}
Cleared this page in case it was the cause of the drop in Google search rankings. I have moved it to: https://aux-xenharmonic.fandom.com/wiki/User:BudjarnLambeth/Above_octave
 
'''Return to gallery lobby: [[User:BudjarnLambeth/Gallery of just intervals|Gallery of just intervals]]'''
 
The following is an exhibit featuring a sampling of [[just intonation] intervals larger than 1200 [[cents]] (so, larger than the just [[octave]], 2/1). It is neither comprehensive nor systematic.  
 
=== Criteria for inclusion ===
 
The criteria for an interval's inclusion are:
* It is a just interval larger than [[2/1]]
* Someone cared enough to write about it
* Its [[ratio]] uses fairly simple numbers (there are no hard and fast rules, but generally the numerator should have 1 or 2 digits, and the denominator should have 1 or 2 digits)
 
If it meets those criteria, it is welcome to be added.
 
=== Dedicated interval pages ===
 
This page lists links to dedicated pages for each interval, under the heading "frequency ratio".
 
Said dedicated pages may 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, fan art, etc. Readers are encouraged to add such things to the interval pages. If your contribution is unconventional, add your name or pseudonym so future readers know where the idea originated.
 
== The collection  ==
See also [http://www.huygens-fokker.org/docs/intervals.html List of intervals (Huygens-Fokker foundation)]
 
If any [[FJS]] names are missing, please [https://misotanni.github.io/fjs/en/calc.html add] them.
 
In the color names, "co" or "c" stands for compound, {{w|Interval (music) #Compound intervals|a conventional music term}}. {{todo|add color name}}
 
{| class="wikitable sortable"
|-
! Frequency Ratio
! Cents Value<br>(three decimal places)
! colspan="2" |[[Color notation|Color Name]]
! FJS Name
! Some common names
|-
| [[27/13]]
| 1265.337
| 3u8
| thu8ve
| A8<sub>13</sub>
| Luxembourg eighth
|-
| [[23/11]]
| 1276.956
| 23o1u9
| twetholu 9th
| A8<sup>23</sup><sub>11</sub>
| vicesimotertial minor ninth
|-
| [[19/9]]
| 1293.603
| 19o9
| ino 9th
| m9<sup>19</sup>
| undevicesimal minor ninth
|-
| [[17/8]]
| 1304.955
| 17o9
| iso 9th
| m9<sup>17</sup>
| septendecimal minor ninth
|-
| [[32/15]]
| 1311.731
| g9
| gu 9th
| m9<sub>5</sub>
| classic minor ninth
|-
| [[15/7]]
| 1319.443
| ry8
| ruyo 8ve
| A8<sup>5</sup><sub>7</sub>
| septimal minor ninth
|-
| [[13/6]]
| 1338.573
| 3o9
| tho 9th
| m9<sup>13</sup>
| tridecimal minor ninth, tridecimal neutral ninth
|-
| [[11/5]]
| 1365.004
| 1o9
| ilo 9th
| m9<sup>11</sup><sub>5</sub>
| neutral ninth
|-
| [[20/9]]
| 1382.404
| y9
| yo 9th
| M9<sup>5</sup>
| Ptolemaic ninth
|-
| [[9/4]]
| 1403.910
| w9
| wa 9th
| M9
| major ninth
|-
| [[16/7]]
| 1431.174
| r9
| ru 9th
| M9<sub>7</sub>
| septimal major ninth
|-
| [[7/3]]
| 1466.871
| z10
| zo 10th
| m10<sup>7</sup>
| septimal minor tenth
|-
| [[19/8]]
| 1497.513
|
|
|
| undevicesimal minor tenth
|-
| [[12/5]]
| 1515.641
| g10
| gu 10th
| m10<sub>5</sub>
| classic minor tenth
|-
| [[17/7]]
| 1536.130
| 17or10
| soru 10tg
| m10<sup>17</sup><sub>7</sub>
| septendecimal minor tenth
|-
| [[27/11]]
| 1554.547
| c1u3
| colu 3rd
| M10<sub>11</sub>
| rastmic neutral tenth
|-
| [[5/2]]
| 1586.314
| y10
| yo 10th
| M10<sup>5</sup>
| classic major tenth
|-
| [[18/7]]
| 1635.084
|
|
|
| septimal supermajor tenth
|-
| [[13/5]]
| 1654.214
| 3og11
|  thogu 11th
| d11<sup>13</sup><sub>5</sub>
| tridecimal eleventh
|-
| [[21/8]]
| 1670.781
|
|
|
| septimal subeleventh
|-
| [[8/3]]
| 1698.045
| w11, cw4
| wa 11th, cowa 4th
| P11
| perfect eleventh
|-
| [[19/7]]
| 1728.687
|
|
|
| undevicesimal supereleventh
|-
| [[11/4]]
| 1751.318
| 1o11, c1o4
| ilo 11th, colo 4th
| P11<sup>11</sup>
| undecimal semi-augmented eleventh
|-
| [[14/5]]
| 1782.512
| zg12, czg5
| zogu 12th, cozogu 5th
| d12<sup>7</sup><sub>5</sub>
| short septimal navatone
|-
| [[17/6]]
| 1803.000
| 17o12
| iso 12th
| d12<sup>17</sup>
| septendecimal navatone
|-
| [[20/7]]
| 1817.488
| ry11
| ruyo 11th
| A11<sup>5</sup><sub>7</sub>
| tall septimal navatone
|-
| [[23/8]]
| 1828.274
| 23o12
| twetho 12th
| A11<sup>23</sup>
| trivigintal navatone
|-
| [[35/12]]
| 1853.185
|
|
|
| septimal semi-diminished twelfth
|-
| [[3/1]]
| 1901.955
| w12, cw5
| wa 12th, cowa 5th
| P12
| 3rd harmonic, perfect twelfth, tritave
|-
| [[28/9]]
| 1964.916
|
|
|
| septimal subminor thirteenth
|-
| [[19/6]]
| 1995.558
|
|
|
| undevicesimal minor thirteenth
|-
| [[16/5]]
| 2013.686
| g13, cg6
| gu 13th, cogu 6th
| m13<sub>5</sub>
| classic minor thirteenth
|-
| [[13/4]]
| 2040.528
| 3o13, c3o6
| tho 13th, cotho 6th
| m13<sup>13</sup>
| tridecimal neutral thirteenth
|-
| [[23/7]]
| 2059.448
|
|
|
| trivigintal neutral/submajor thirteenth
|-
| [[10/3]]
| 2084.359
| y13, cy6
| yo 13th, coyo 6th
| M13<sup>5</sup>
| just/classic(al)/ptolemaic major thirteenth
|-
| [[17/5]]
| 2118.642
| c17og7
| cosogu 7th
| d14<sup>17</sup><sub>5</sub>
| septendecimal major thirteenth
|-
| [[24/7]]
| 2133.129
|
|
|
| septimal supermajor thirteenth
|-
| [[7/2]]
| 2168.826
| cz7
| cozo 7th
| m14<sup>7</sup>
| harmonic fourteenth
|-
| [[32/9]]
| 2196.090
|
|
|
| 3-limit minor fourteenth
|-
| [[18/5]]
| 2217.596
|
|
| m14<sub>5</sub>
| 5-limit minor fourteenth
|-
| [[11/3]]
| 2249.363
| c1o7
| colo 7th
| m14<sup>11</sup>
| undecimal neutral fourteenth
|-
| [[15/4]]
| 2288.269
| cy7
| coyo 7th
| M14<sup>5</sup>
| just/classic(al)/ptolemaic major fourteenth
|-
| [[19/5]]
| 2311.199
|
|
|
| undevicesimal major fourteenth
|-
| [[35/9]]
| 2351.230
|
|
|
| septimal semi-augmented fourteenth
|-
| [[4/1]]
| 2400.000
| cw8, ccw1
| wa double 8ve
| P15
| 4th harmonic, two octaves, just double octave
|-
| [[81/20]]
| 2421.506
| g15
| gu double 8ve
| P15<sub>5</sub>
| syntonic double octave
|-
| [[25/6]]
| 2470.672
|
|
|
| classic chromatic minor sixteenth
|-
| [[17/4]]
| 2504.955
| cc17o2
| cocoso 2nd
| m16<sup>17</sup>
| septendecimal minor sixteenth
|-
| [[64/15]]
| 2511.731
| cc17o2
| cocoso 2nd
| m16<sub>5</sub>
| classic minor sixteenth
|-
| [[13/3]]
| 2538.573
| c3o9, cc3o2
| cotho 9th, cocotho 2nd
| m16<sup>13</sup>
| tridecimal minor sixteenth
|-
| [[22/5]]
| 2565.004
|
|
|
| large undecimal neutral sixteenth
|-
| [[9/2]]
| 2603.910
| cw9, ccw2
| cowa 9th, cocoyo 2nd
| M16
| classic large major sixteenth
|-
| [[23/5]]
| 2641.961
|
|
|
| trivigintal supermajor sixteenth
|-
| [[14/3]]
| 2666.871
| cz10, ccz3
| cozo 10th, cocozo 3rd
| m17<sup>7</sup>
| septimal subminor seventeenth
|-
| [[19/4]]
| 2696.513
|
|
|
| undevicesimal minor seventeenth
|-
| [[24/5]]
| 2715.641
|
|
|
| classic minor seventeenth
|-
| [[44/9]]
| 2747.408
|
|
|
| undecimal neutral seventeenth
|-
| [[5/1]]
| 2786.314
| cy10, ccy3
| coyo 10th, cocoyo 3rd
| M17<sup>5</sup>
| 5th harmonic, pentave
|-
| [[36/7]]
| 2835.084
|
|
|
| septimal supermajor seventeenth
|-
| [[21/4]]
| 2870.781
|
|
|
| septimal subeighteenth
|-
| [[16/3]]
| 2898.045
| ccw4
| cocowa 4th
| P18
| perfect eighteenth
|-
| [[27/5]]
| 2919.551
|
|
|
| 5-limit supereighteenth
|-
| [[11/2]]
| 2951.318
| cc1o4
| cocolo 4th
| P18<sup>11</sup>
| undecimal semi-augmented eighteenth
|-
| [[28/5]]
| 2982.512
| cczg5
| coco-zogu 5th
| d19<sup>7</sup><sub>5</sub>
| short septimal panchadashatone
|-
| [[45/8]]
| 2990.224
| ccy4
| cocoyo 4th
| A18<sup>5</sup>
| quinquadragintimal panchadashatone
|-
| [[17/3]]
| 3003.000
| cc17o5
| cocoso 5th
| d19<sup>17</sup>
| septendecimal panchadasatone
|-
| [[40/7]]
| 3017.488
| ccry4
| coco-ruyo 4th
| A18<sup>5</sup><sub>7</sub>
| tall septimal panchadashatone
|-
| [[23/4]]
| 3028.274
|
|
|
| vicesimotertial panchadashatone
|-
| [[35/6]]
| 3053.185
|
|
|
| septimal semi-diminished nineteenth
|-
| [[6/1]]
| 3101.955
| ccw5
| cocowa 5th
| P19
| 6th harmonic
|-
| [[55/9]]
| 3133.722
|
|
|
| undecimal superninteenth
|-
| [[25/4]]
| 3172.627
|
|
|
| 5-limit subminor twentieth
|-
| [[19/3]]
| 3195.558
|
|
|
| undevicesimal minor twentieth
|-
| [[32/5]]
| 3213.686
|
|
|
| classic minor twentieth
|-
| [[13/2]]
| 3240.528
| cc3o6
| cocotho 6th
| m20<sup>13</sup>
| tridecimal neutral twentieth
|-
| [[20/3]]
| 3284.359
|
|
|
| classic major twentieth
|-
| [[48/7]]
| 3333.129
|
|
|
| septimal supermajor twentieth
|-
| [[7/1]]
| 3368.826
| ccz7
| cocozo 7th
| m21<sup>7</sup>
| 7th harmonic
|-
| [[36/5]]
| 3417.596
|
|
|
| 5-limit minor twentyfirst
|-
| [[22/3]]
| 3449.363
|
|
|
| undecimal neutral twentyfirst
|-
| [[15/2]]
| 3488.269
| ccy7
| cocoyo 7th
| M21<sup>5</sup>
| just/classic(al)/ptolemaic major twentyfirst
|-
| [[23/3]]
| 3526.319
|
|
|
| vicesimotertial supermajor twentyfirst
|-
| [[31/4]]
| 3545.036
|
|
|
| 31-limit semi-augmented twentyfirst
|-
| [[8/1]]
| 3600.000
| c<sup>3</sup>w1
| wa triple 8ve
| P22
| 8th harmonic, three octaves
|-
| [[33/4]]
| 3653.273
|
|
|
| undecimal semi-diminished twentythird
|-
| [[25/3]]
| 3670.672
|
|
|
| classic chromatic twentythird
|-
| [[17/2]]
| 3704.955
|
|
|
| septendecimal minor twentythird
|-
| [[128/15]]
| 3711.731
| c3g2
| tricogu 2nd
| m23<sub>5</sub>
| classic minor twenty-third
|-
| [[26/3]]
| 3738.573
|
|
|
| tridecimal neutral twentythird
|-
| [[35/4]]
| 3755.140
|
|
|
| septimal neutral twentythird
|-
| [[9/1]]
| 3803.910
| c<sup>3</sup>w2
| tricowa 2nd
| M23
| 9th harmonic
|-
| [[10/1]]
| 3986.314
| c<sup>3</sup>y3
| tricoyo 3rd
| M24<sup>5</sup>
| 10th harmonic, decade
|-
| [[11/1]]
| 4151.318
| c<sup>3</sup>1o4
| tricolo 4th
| P25<sup>11</sup>
| 11th harmonic
|-
| [[12/1]]
| 4301.955
| c<sup>3</sup>w5
| tricowa 5th
| P26
| 12th harmonic
|-
| [[13/1]]
| 4440.528
| c<sup>3</sup>3o6
| tricotho 6th
| m27<sup>13</sup>
| 13th harmonic
|-
| [[14/1]]
| 4568.826
| c<sup>3</sup>z7
| tricozo 7th
| m28<sup>7</sup>
| 14th harmonic
|-
| [[15/1]]
| 4688.269
| c<sup>3</sup>y7
| tricoyo 7th
| M28<sup>5</sup>
| 15th harmonic
|-
| [[16/1]]
| 4800.000
| c<sup>4</sup>w1
| wa quadruple 8ve
| P29
| 16th harmonic, four octaves
|-
| [[17/1]]
| 4904.955
| c^417o2
| quadcoso 2nd
| m30<sup>17</sup>
| 17th harmonic
|-
| [[256/15]]
| 4911.731
| c4g2
| quadcogu 2nd
| m30<sub>5</sub>
| classic minor thirtieth
|-
| [[18/1]]
| 5004.910
|
|
| M30
| 18th harmonic
|-
| [[19/1]]
| 5097.513
| c<sup>4</sup>19o3
| quadcono 3rd
| m31<sup>19</sup>
| 19th harmonic
|-
| [[20/1]]
| 5186.314
|
|
| M31<sup>5</sup>
| 20th harmonic
|-
| [[21/1]]
| 5270.781
| c<sup>4</sup>z4
| quadcozo 4th
| P32<sup>7</sup>
| 21st harmonic
|-
| [[22/1]]
| 5351.318
|
|
| P32<sup>11</sup>
| 22nd harmonic
|-
| [[23/1]]
| 5428.274
| c<sup>4</sup>23o5
| quadcotwetho
| A32<sup>23</sup>
| 23rd harmonic
|-
| [[24/1]]
| 5501.955
| c<sup>4</sup>w5
| quadcowa 5th
| P33
| 24th harmonic
|-
| [[25/1]]
| 5572.617
| c<sup>4</sup>yy5
| quadco-yoyo 5th
| A33<sup>5,5</sup>
| 25th harmonic
|-
| [[27/1]]
| 5705.865
| c<sup>4</sup>w6
| quadcowa 6th
| M34
| 27th harmonic
|-
| [[29/1]]
| 5829.577
| c<sup>4</sup>29o7
| quadcotweno 7th
| m35<sup>29</sup>
| 29th harmonic
|-
| [[31/1]]
| 5945.036
| c<sup>4</sup>31o7
| quadcothiwo 7th
| M35<sup>31</sup>
| 31st harmonic
|-
| [[49/1]]
| 6737.652
|
|
| M41<sup>7,7</sup>
| 49th harmonic
|-
| [[1536/1]]
| 12701.955
|
|
| P75
| 1536th harmonic
|}

Latest revision as of 06:56, 24 January 2025

Cleared this page in case it was the cause of the drop in Google search rankings. I have moved it to: https://aux-xenharmonic.fandom.com/wiki/User:BudjarnLambeth/Above_octave

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