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User:BudjarnLambeth/Beginners: Difference between revisions

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m Reduce to 50 intervals as that was the number Kite suggested there should be on a subpage like this one
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'''Return to gallery lobby: [[User:BudjarnLambeth/Gallery of just intervals|Gallery of just intervals]]'''
'''Return to gallery lobby: [[User:BudjarnLambeth/Gallery of just intervals|Gallery of just intervals]]'''


The following is an exhibit featuring a small, carefully curated collection of [[just intonation] intervals. It is intended to include those few intervals which stand out above the rest as particularly audible or structurally essential.
The following is an exhibit featuring a small, carefully curated collection of [[just intonation]] intervals. It is intended to include those few intervals which stand out above the rest as particularly audible or structurally essential.


=== Criteria for inclusion ===
=== Criteria for inclusion ===
Line 37: Line 37:
|P1<sup>11</sup>
|P1<sup>11</sup>
|undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, [[octave-reduced]] 33rd [[harmonic]]
|undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, [[octave-reduced]] 33rd [[harmonic]]
|-
|[[28/27]]
|62.960904
|z2, zo 2nd
|m2<sup>7</sup>
|small septimal chroma, septimal third-tone, subminor second, septimal minor second
|-
|[[27/26]]
|65.337341
|3u1, thu unison
|A1<sub>13</sub>
|small tridecimal third tone
|-
|[[26/25]]
|67.900234
|3ogg2, thogugu 2nd
|d2<sup>13</sup><sub>25</sub>
|large tridecimal third tone
|-
|-
|[[25/24]]
|[[25/24]]
Line 61: Line 43:
|A1<sup>25</sup>
|A1<sup>25</sup>
|chroma, classic chromatic semitone, Zarlinian semitone
|chroma, classic chromatic semitone, Zarlinian semitone
|-
|[[24/23]]
|73.680654
|23u1, twethu unison
|m2<sub>23</sub>
|lesser vicesimotertial semitone
|-
|[[23/22]]
|76.956405
|23o1u2, twetholu 2nd
|A1<sup>23</sup><sub>11</sub>
|greater vicesimotertial semitone
|-
|-
|[[22/21]]
|[[22/21]]
Line 151: Line 121:
|M2<sup>5</sup>
|M2<sup>5</sup>
|classic (whole) tone, minor (whole) tone
|classic (whole) tone, minor (whole) tone
|-
|[[19/17]]
|192.557607
|19o17u2, nosu 2nd
|M2<sup>19</sup><sub>17</sub>
|quasi-meantone
|-
|-
|[[9/8]]
|[[9/8]]
Line 163: Line 127:
|M2
|M2
|Pythagorean (whole) tone, major (whole) tone, octave-reduced 9th harmonic
|Pythagorean (whole) tone, major (whole) tone, octave-reduced 9th harmonic
|-
|[[17/15]]
|216.686695
|17og3, sogu 3rd
|d3<sup>17</sup><sub>5</sub>
|septendecimal whole tone, septendecimal eventone
|-
|-
|[[8/7]]
|[[8/7]]
Line 187: Line 145:
|m3<sup>7</sup>
|m3<sup>7</sup>
|subminor third, septimal minor third
|subminor third, septimal minor third
|-
|[[20/17]]
|281.358304
|17uy2, suyo 2nd
|A2<sup>5</sup><sub>17</sub>
|septendecimal augmented second, septendecimal minor third
|-
|-
|[[13/11]]
|[[13/11]]
Line 199: Line 151:
|m3<sup>13</sup><sub>11</sub>
|m3<sup>13</sup><sub>11</sub>
|tridecimal minor third
|tridecimal minor third
|-
|[[19/16]]
|297.513016
|19o3, ino 3rd
|m3<sup>19</sup>
|otonal minor third, octave-reduced 19th harmonic
|-
|-
|[[6/5]]
|[[6/5]]
Line 211: Line 157:
|m3<sub>5</sub>
|m3<sub>5</sub>
|classic minor third, just minor third
|classic minor third, just minor third
|-
|[[23/19]]
|330.761331
|23o19u3, twethonu 3rd
|A2<sup>23</sup><sub>19</sub>
|vicesimotertial supraminor third
|-
|[[17/14]]
|336.129503
|17or3, soru 3rd
|m3<sup>17</sup><sub>5</sub>
|septendecimal supraminor third
|-
|-
|[[11/9]]
|[[11/9]]
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|m3<sup>11</sup>
|m3<sup>11</sup>
|undecimal neutral third
|undecimal neutral third
|-
|[[16/13]]
|359.472338
|3u3, thu 3rd
|M3<sub>13</sub>
|greater tridecimal neutral third, octave reduced 13subharmonic
|-
|[[21/17]]
|365.825498
|17uz3, suzo 3rd
|M3<sup>7</sup><sub>17</sub>
|septendecimal submajor third
|-
|-
|[[5/4]]
|[[5/4]]
Line 247: Line 169:
|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
|-
|[[19/15]]
|409.244301
|19og4, nogu 4th
|d4<sup>19</sup><sub>5</sub>
|Eratosthenes' major third
|-
|-
|[[14/11]]
|[[14/11]]
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|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]]
|424.364346
|23o4, twetho 4th
|M3<sup>23</sup>
|vicesimotertial diminished fourth
|-
|-
|[[9/7]]
|[[9/7]]
Line 277: Line 187:
|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
|-
|[[17/13]]
|464.427748
|17o3u4, sothu 4th
|P4<sup>17</sup><sub>13</sub>
|septendecimal sub-fourth
|-
|[[25/19]]
|475.114412
|19uyy3, nuyoyo 3rd
|A3<sup>5,5</sup><sub>19</sub>
|undevicesimal augmented third, undevicesimal grave fourth
|-
|-
|[[4/3]]
|[[4/3]]
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|P4
|P4
|just perfect fourth, octave-reduced 3rd subharmonic, diatessaron
|just perfect fourth, octave-reduced 3rd subharmonic, diatessaron
|-
|[[23/17]]
|523.318938
|23o17u4, twethosu 4th
|A3<sup>23</sup><sub>17</sub>
|vicesimotertial acute fourth
|-
|-
|[[15/11]]
|[[15/11]]
Line 313: Line 205:
|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]]
|563.382340
|3u4, thu 4th
|A4<sub>13</sub>
|tridecimal augmented fourth
|-
|-
|[[7/5]]
|[[7/5]]
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|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
|-
|[[17/12]]
|603.000409
|17o5, iso 5th
|d5<sup>17</sup>
|larger septendecimal tritone
|-
|-
|[[10/7]]
|[[10/7]]
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|d5<sup>13</sup>
|d5<sup>13</sup>
|tridecimal diminished fifth
|tridecimal diminished fifth
|-
|[[16/11]]
|648.682058
|1u5, lu 5th
|P5<sub>11</sub>
|sub-fifth, octave-reduced 11th subharmonic
|-
|[[19/13]]
|656.985354
|19o3u5, nothu 5th
|P5<sup>19</sup><sub>13</sub>
|undevicesimal subfifth
|-
|[[25/17]]
|667.672018
|17uyy4, suyoyo 4th
|AA4<sup>5,5</sup><sub>17</sub>
|vengeance subfifth
|-
|-
|[[3/2]]
|[[3/2]]
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|P5
|P5
|[[just perfect fifth]], octave-reduced 3rd harmonic, diapente
|[[just perfect fifth]], octave-reduced 3rd harmonic, diapente
|-
|[[26/17]]
|735.572252
|17u3o5, sutho 5th
|P5<sup>13</sup><sub>17</sub>
|septendecimal super-fifth
|-
|[[20/13]]
|745.786052
|3uy5, thuyo 5th
|A5<sup>5</sup><sub>13</sub>
|tridecimal semitenth, Barbados sixth, ratwolf wolf fifth
|-
|[[17/11]]
|753.637467
|17o1u6, solu 6th
|m6<sup>17</sup><sub>11</sub>
|septendecimal subminor sixth
|-
|-
|[[14/9]]
|[[14/9]]
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|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
|-
|[[19/12]]
|795.558015
|19o6, ino 6th
|m6<sup>19</sup>
|large undevicesimal minor sixth, Boethius' minor sixth
|-
|-
|[[8/5]]
|[[8/5]]
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|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
|-
|[[21/13]]
|830.253246
|3uz6, thuzo 6th
|M6<sup>7</sup><sub>13</sub>
|tridecimal supraminor sixth
|-
|-
|[[13/8]]
|[[13/8]]
Line 421: Line 253:
|m6<sup>13</sup>
|m6<sup>13</sup>
|lesser tridecimal neutral sixth, octave-reduced 13th harmonic
|lesser tridecimal neutral sixth, octave-reduced 13th harmonic
|-
|[[18/11]]
|852.592059
|1u6, lu 6th
|M6<sub>11</sub>
|undecimal neutral sixth
|-
|[[23/14]]
|859.448441
|23or6, twethoru 6th
|A5<sup>23</sup><sub>7</sub>
|vicesimotertial neutral sixth
|-
|-
|[[5/3]]
|[[5/3]]
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|M6<sup>5</sup>
|M6<sup>5</sup>
|classic major sixth, just major sixth
|classic major sixth, just major sixth
|-
|[[22/13]]
|910.790821
|3u1o6, thulo 6th
|M6<sup>11</sup><sub>13</sub>
|tridecimal major sixth
|-
|-
|[[17/10]]
|[[17/10]]
Line 457: Line 271:
|M6<sub>7</sub>
|M6<sub>7</sub>
|supermajor sixth, septimal major sixth
|supermajor sixth, septimal major sixth
|-
|[[19/11]]
|946.195074
|19o1u7, nolu 7th
|m7<sup>19</sup><sub>11</sub>
|undevicesimal semitwelfth, maximal major sixth
|-
|[[26/15]]
|952.258947
|3og7, thogu 7th
|d7<sup>13</sup><sub>5</sub>
|tridecimal semitwelfth
|-
|-
|[[7/4]]
|[[7/4]]
Line 475: Line 277:
|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
|-
|[[23/13]]
|987.746686
|23o3u7, twethothu 7th
|A6<sup>23</sup><sub>13</sub>
|vicesimotertial minor seventh
|-
|-
|[[16/9]]
|[[16/9]]
Line 493: Line 289:
|m7<sub>5</sub>
|m7<sub>5</sub>
|classic minor seventh, large minor seventh
|classic minor seventh, large minor seventh
|-
|[[20/11]]
|1034.995772
|1uy7, luyo 7th
|M7<sup>5</sup><sub>11</sub>
|undecimal supraminor seventh, small undecimal neutral seventh
|-
|-
|[[11/6]]
|[[11/6]]
Line 505: Line 295:
|m7<sup>11</sup>
|m7<sup>11</sup>
|undecimal neutral seventh, 21/4-tone
|undecimal neutral seventh, 21/4-tone
|-
|[[24/13]]
|1061.427339
|3u7, thu 7th
|M7<sub>13</sub>
|tridecimal neutral seventh
|-
|-
|[[13/7]]
|[[13/7]]
Line 523: Line 307:
|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
|-
|[[17/9]]
|1101.045408
|17o8, iso octave
|d8<sup>17</sup>
|septendecimal major seventh (HEJI), septendecimal diminished octave (FJS)
|-
|[[19/10]]
|1111.199302
|19og8, nogu 8ve
|d8<sup>19</sup><sub>5</sub>
|undevicesimal diminished octave, Eratosthenes' major seventh
|-
|-
|[[21/11]]
|[[21/11]]
Line 541: Line 313:
|P8<sup>7</sup><sub>11</sub>
|P8<sup>7</sup><sub>11</sub>
|large undecimal diminished octave, undecimal major seventh
|large undecimal diminished octave, undecimal major seventh
|-
|[[23/12]]
|1126.319346
|23o8, twetho 8ve
|M7<sup>23</sup>
|large vicesimotertial major seventh
|-
|-
|[[25/13]]
|[[25/13]]
Line 553: Line 319:
|A7<sup>5,5</sup><sub>13</sub>
|A7<sup>5,5</sup><sub>13</sub>
|lesser tridecimal diminished octave
|lesser tridecimal diminished octave
|-
|[[27/14]]
|1137.039096
|r7, ru 7th
|M7<sub>7</sub>
|supermajor seventh, septimal major seventh
|-
|[[31/16]]
|1145.035572
|31o7, thiwo 7th
|M7<sup>31</sup>
|tricesimoprimal ultramajor seventh (FJS), tricesimoprimal semidiminished octave (HEJI), octave-reduced 31st harmonic
|-
|[[35/18]]
|1151.239619
|zy8, zoyo octave
|P8<sup>35</sup>
|septimal semidiminished octave
|-
|-
|[[2/1]]
|[[2/1]]
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