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]]
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|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]]
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|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]]
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|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]]
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|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]]
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|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]]
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|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]]
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|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]]
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|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]]

Revision as of 04:16, 22 January 2025

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Return to gallery lobby: 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.

Criteria for inclusion

The criteria for an interval's inclusion are:

  • The interval must be between 1/1 and 2/1 (inclusive)
  • (To be determined)

If it meets those criteria, it is welcome to be added.

The collection

See also List of intervals (Huygens-Fokker foundation)

If any FJS names are missing, please add them.

Frequency Ratio Cents Value
(six decimal places) 		Color Name FJS Name Some common names
1/1 0 w1, wa unison P1 unity, perfect prime, Tonic
33/32 53.272943 1o1, ilo unison P111 undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, octave-reduced 33rd harmonic
25/24 70.672427 yy1, yoyo unison A125 chroma, classic chromatic semitone, Zarlinian semitone
22/21 80.537035 1or1, loru unison P1117 undecimal 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
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
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
13/12 138.572661 3o2, tho 2nd m213 tridecimal neutral second, tridecimal 2/3-tone
12/11 150.637059 1u2, lu 2nd M211 small undecimal neutral second, 3/4-tone
11/10 165.004228 1og2, logu 2nd m2115 undecimal submajor second, large undecimal neutral second, 4/5-tone, Ptolemy's second
10/9 182.403712 y2, yo 2nd M25 classic (whole) tone, minor (whole) tone
9/8 203.910002 w2, wa 2nd M2 Pythagorean (whole) tone, major (whole) tone, octave-reduced 9th harmonic
8/7 231.174094 r2, ru 2nd M27 supermajor second, septimal whole tone, octave-reduced 7th subharmonic
15/13 247.741053 3uy2, thuyo 2nd A2513 tridecimal semifourth, tridecimal ultramajor second, tridecimal inframinor third
7/6 266.870906 z3, zo 3rd m37 subminor third, septimal minor third
13/11 289.209719 3o1u3, tholu 3rd m31311 tridecimal minor third
6/5 315.641287 g3, gu 3rd m35 classic minor third, just minor third
11/9 347.407941 1o3, ilo 3rd m311 undecimal neutral third
5/4 386.313714 y3, yo 3rd M35 classic major third, just major third, octave-reduced 5th harmonic
14/11 417.507964 1uz4, luzo 4th P4711 undecimal major third, undecimal diminished fourth
9/7 435.084095 r3, ru 3rd M37 supermajor third, septimal major third
13/10 454.213948 3og4, thogu 4th d4135 tridecimal semisixth, Barbados third, tridecimal 9/4 tone
4/3 498.044999 w4, wa 4th P4 just perfect fourth, octave-reduced 3rd subharmonic, diatessaron
15/11 536.950772 1uy4, luyo 4th A4511 undecimal augmented fourth, subaugmented fourth
11/8 551.317942 1o4, ilo 4th P411 super-fourth, undecimal semi-augmented fourth, octave-reduced 11th harmonic or harmonic 11th, Alphorn-Fa
7/5 582.512193 zg5, zogu 5th d575 augmented fourth, septimal tritone, Huygen's tritone
10/7 617.487807 ry4, ruyo 4th A457 diminished fifth, Euler's tritone, superaugmented fourth
13/9 636.617660 3o5, tho 5th d513 tridecimal diminished fifth
3/2 701.955001 w5, wa 5th P5 just perfect fifth, octave-reduced 3rd harmonic, diapente
14/9 764.915905 z6, zo 6th m67 subminor sixth, septimal minor sixth
11/7 782.492036 1or5, loru 5th P5117 undecimal subminor sixth, undecimal augmented fifth
8/5 813.686286 g6, gu 6th m65 classic minor sixth, just minor sixth, octave-reduced 5th subharmonic
13/8 840.527662 3o6, tho 6th m613 lesser tridecimal neutral sixth, octave-reduced 13th harmonic
5/3 884.358713 y6, yo 6th M65 classic major sixth, just 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
7/4 968.825906 z7, zo 7th m77 subminor seventh, septimal minor seventh, harmonic seventh, natural seventh, octave-reduced 7th harmonic
16/9 996.089998 w7, wa 7th m7 Pythagorean minor seventh, small minor seventh, octave-reduced 9th subharmonic
9/5 1017.596288 g5, gu 7th m75 classic minor seventh, large minor seventh
11/6 1049.362941 1o7, ilo 7th m711 undecimal neutral seventh, 21/4-tone
13/7 1071.701755 3or7, thoru 7th m7137 tridecimal submajor seventh, 16/3-tone
15/8 1088.268715 y7, yo 7th M75 classic major seventh, just major seventh, octave-reduced 15th harmonic
21/11 1119.462965 1uz8, luzo 8ve P8711 large undecimal diminished octave, undecimal major seventh
25/13 1132.099766 3uyy7, thuyoyo 7th A75,513 lesser tridecimal diminished octave
2/1 1200 w8, wa octave P8 octave, diapason
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