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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/Beginners |
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| '''Return to gallery lobby: [[User:BudjarnLambeth/Gallery of just intervals|Gallery of just intervals]]'''
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| | |
| 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.
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| | |
| === Criteria for inclusion ===
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| | |
| The criteria for an interval's inclusion are:
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| * The interval must be between [[1/1]] and [[2/1]] (inclusive)
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| * (''To be determined'')
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| If it meets those criteria, it is welcome to be added.
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| | |
| == The collection ==
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| See also [http://www.huygens-fokker.org/docs/intervals.html List of intervals (Huygens-Fokker foundation)]
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| | |
| If any [[FJS]] names are missing, please [https://misotanni.github.io/fjs/en/calc.html add] them.
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| | |
| {| class="wikitable sortable"
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| |-
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| ! Frequency Ratio
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| ! Cents Value <br> (six decimal places)
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| ! [[Color notation|Color Name]]
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| ! [[Functional Just System|FJS Name]]
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| ! class="unsortable" | Some common names
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| |-
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| | [[1/1]]
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| | 0
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| | w1, wa unison
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| | P1
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| | unity, perfect prime, Tonic
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| |-
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| |[[33/32]]
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| |53.272943
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| |1o1, ilo unison
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| |P1<sup>11</sup>
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| |undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, [[octave-reduced]] 33rd [[harmonic]]
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| |-
| |
| |[[28/27]]
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| |62.960904
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| |z2, zo 2nd
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| |m2<sup>7</sup>
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| |small septimal chroma, septimal third-tone, subminor second, septimal minor second
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| |-
| |
| |[[27/26]]
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| |65.337341
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| |3u1, thu unison
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| |A1<sub>13</sub>
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| |small tridecimal third tone
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| |-
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| |[[26/25]]
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| |67.900234
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| |3ogg2, thogugu 2nd
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| |d2<sup>13</sup><sub>25</sub>
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| |large tridecimal third tone
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| |-
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| |[[25/24]]
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| |70.672427
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| |yy1, yoyo unison
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| |A1<sup>25</sup>
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| |chroma, classic chromatic semitone, Zarlinian semitone
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| |-
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| |[[24/23]]
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| |73.680654
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| |23u1, twethu unison
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| |m2<sub>23</sub>
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| |lesser vicesimotertial semitone
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| |-
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| |[[23/22]]
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| |76.956405
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| |23o1u2, twetholu 2nd
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| |A1<sup>23</sup><sub>11</sub>
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| |greater vicesimotertial semitone
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| |-
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| |[[22/21]]
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| |80.537035
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| |1or1, loru unison
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| |P1<sup>11</sup><sub>7</sub>
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| |undecimal minor semitone
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| |-
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| |[[21/20]]
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| |84.467193
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| |zg2, zogu 2nd
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| |m2<sup>7</sup><sub>5</sub>
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| |minor semitone, large septimal chroma
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| |-
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| |[[20/19]]
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| |88.800698
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| |19uy1, nuyo unison
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| |A1<sup>5</sup><sub>19</sub>
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| |small undevicesimal semitone, undevicesimal chroma, Eratosthenes' semitone
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| |-
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| |[[19/18]]
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| |93.603014
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| |19o2, ino 2nd
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| |m2<sup>19</sup>
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| |large undevicesimal semitone, undevicesimal limma, Boethius' semitone
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| |-
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| |[[18/17]]
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| |98.954592
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| |17u1, su unison
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| |A1<sub>17</sub>
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| |small septendecimal semitone, Arabic lute index finger
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| |-
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| |[[17/16]]
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| |104.955410
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| |17o2, iso 2nd
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| |m2<sup>17</sup>
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| |large septendecimal semitone, octave-reduced 17th harmonic
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| |-
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| |[[16/15]]
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| |111.731285
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| |g2, gu 2nd
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| |m2<sub>5</sub>
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| |classic diatonic semitone, classic minor second, octave-reduced 15th subharmonic
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| |-
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| |[[15/14]]
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| |119.442808
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| |ry1, ruyo unison
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| |A1<sup>5</sup><sub>7</sub>
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| |septimal diatonic semitone
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| |-
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| |[[14/13]]
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| |128.298245
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| |3uz2, thuzo 2nd
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| |M2<sup>7</sup><sub>13</sub>
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| |tridecimal 2/3-tone, trienthird, tridecimal supraminor second
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| |-
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| |[[13/12]]
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| |138.572661
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| |3o2, tho 2nd
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| |m2<sup>13</sup>
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| |tridecimal neutral second, tridecimal 2/3-tone
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| |-
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| |[[12/11]]
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| |150.637059
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| |1u2, lu 2nd
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| |M2<sub>11</sub>
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| |small undecimal neutral second, 3/4-tone
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| |-
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| |[[11/10]]
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| |165.004228
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| |1og2, logu 2nd
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| |m2<sup>11</sup><sub>5</sub>
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| |undecimal submajor second, large undecimal neutral second, 4/5-tone, Ptolemy's second
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| |-
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| |[[10/9]]
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| |182.403712
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| |y2, yo 2nd
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| |M2<sup>5</sup>
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| |classic (whole) tone, minor (whole) tone
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| |-
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| |[[19/17]]
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| |192.557607
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| |19o17u2, nosu 2nd
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| |M2<sup>19</sup><sub>17</sub>
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| |quasi-meantone
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| |-
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| |[[9/8]]
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| |203.910002
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| |w2, wa 2nd
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| |M2
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| |Pythagorean (whole) tone, major (whole) tone, octave-reduced 9th harmonic
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| |-
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| |[[17/15]]
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| |216.686695
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| |17og3, sogu 3rd
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| |d3<sup>17</sup><sub>5</sub>
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| |septendecimal whole tone, septendecimal eventone
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| |-
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| |[[8/7]]
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| |231.174094
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| |r2, ru 2nd
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| |M2<sub>7</sub>
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| |supermajor second, septimal whole tone, octave-reduced 7th subharmonic
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| |-
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| |[[15/13]]
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| |247.741053
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| |3uy2, thuyo 2nd
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| |A2<sup>5</sup><sub>13</sub>
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| |tridecimal semifourth, tridecimal ultramajor second, tridecimal inframinor third
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| |-
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| |[[7/6]]
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| |266.870906
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| |z3, zo 3rd
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| |m3<sup>7</sup>
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| |subminor third, septimal minor third
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| |-
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| |[[20/17]]
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| |281.358304
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| |17uy2, suyo 2nd
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| |A2<sup>5</sup><sub>17</sub>
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| |septendecimal augmented second, septendecimal minor third
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| |-
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| |[[13/11]]
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| |289.209719
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| |3o1u3, tholu 3rd
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| |m3<sup>13</sup><sub>11</sub>
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| |tridecimal minor third
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| |-
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| |[[19/16]]
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| |297.513016
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| |19o3, ino 3rd
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| |m3<sup>19</sup>
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| |otonal minor third, octave-reduced 19th harmonic
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| |-
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| |[[6/5]]
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| |315.641287
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| |g3, gu 3rd
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| |m3<sub>5</sub>
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| |classic minor third, just minor third
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| |-
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| |[[23/19]]
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| |330.761331
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| |23o19u3, twethonu 3rd
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| |A2<sup>23</sup><sub>19</sub>
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| |vicesimotertial supraminor third
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| |-
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| |[[17/14]]
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| |336.129503
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| |17or3, soru 3rd
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| |m3<sup>17</sup><sub>5</sub>
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| |septendecimal supraminor third
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| |-
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| |[[11/9]]
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| |347.407941
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| |1o3, ilo 3rd
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| |m3<sup>11</sup>
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| |undecimal neutral third
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| |-
| |
| |[[16/13]]
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| |359.472338
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| |3u3, thu 3rd
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| |M3<sub>13</sub>
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| |greater tridecimal neutral third, octave reduced 13subharmonic
| |
| |-
| |
| |[[21/17]]
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| |365.825498
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| |17uz3, suzo 3rd
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| |M3<sup>7</sup><sub>17</sub>
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| |septendecimal submajor third
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| |-
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| |[[5/4]]
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| |386.313714
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| |y3, yo 3rd
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| |M3<sup>5</sup>
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| |classic major third, just major third, octave-reduced 5th harmonic
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| |-
| |
| |[[19/15]]
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| |409.244301
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| |19og4, nogu 4th
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| |d4<sup>19</sup><sub>5</sub>
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| |Eratosthenes' major third
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| |-
| |
| |[[14/11]]
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| |417.507964
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| |1uz4, luzo 4th
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| |P4<sup>7</sup><sub>11</sub>
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| |undecimal major third, undecimal diminished fourth
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| |-
| |
| |[[23/18]]
| |
| |424.364346
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| |23o4, twetho 4th
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| |M3<sup>23</sup>
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| |vicesimotertial diminished fourth
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| |-
| |
| |[[9/7]]
| |
| |435.084095
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| |r3, ru 3rd
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| |M3<sub>7</sub>
| |
| |supermajor third, septimal major third
| |
| |-
| |
| |[[13/10]]
| |
| |454.213948
| |
| |3og4, thogu 4th
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| |d4<sup>13</sup><sub>5</sub>
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| |tridecimal semisixth, Barbados third, tridecimal 9/4 tone
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| |-
| |
| |[[17/13]]
| |
| |464.427748
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| |17o3u4, sothu 4th
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| |P4<sup>17</sup><sub>13</sub>
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| |septendecimal sub-fourth
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| |-
| |
| |[[25/19]]
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| |475.114412
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| |19uyy3, nuyoyo 3rd
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| |A3<sup>5,5</sup><sub>19</sub>
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| |undevicesimal augmented third, undevicesimal grave fourth
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| |-
| |
| |[[4/3]]
| |
| |498.044999
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| |w4, wa 4th
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| |P4
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| |just perfect fourth, octave-reduced 3rd subharmonic, diatessaron
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| |-
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| |[[23/17]]
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| |523.318938
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| |23o17u4, twethosu 4th
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| |A3<sup>23</sup><sub>17</sub>
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| |vicesimotertial acute fourth
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| |-
| |
| |[[15/11]]
| |
| |536.950772
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| |1uy4, luyo 4th
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| |A4<sup>5</sup><sub>11</sub>
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| |undecimal augmented fourth, subaugmented fourth
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| |-
| |
| |[[11/8]]
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| |551.317942
| |
| |1o4, ilo 4th
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| |P4<sup>11</sup>
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| |super-fourth, undecimal semi-augmented fourth, octave-reduced 11th harmonic or harmonic 11th, Alphorn-Fa
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| |-
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| |[[18/13]]
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| |563.382340
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| |3u4, thu 4th
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| |A4<sub>13</sub>
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| |tridecimal augmented fourth
| |
| |-
| |
| |[[7/5]]
| |
| |582.512193
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| |zg5, zogu 5th
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| |d5<sup>7</sup><sub>5</sub>
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| |augmented fourth, septimal tritone, Huygen's tritone
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| |-
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| |[[17/12]]
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| |603.000409
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| |17o5, iso 5th
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| |d5<sup>17</sup>
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| |larger septendecimal tritone
| |
| |-
| |
| |[[10/7]]
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| |617.487807
| |
| |ry4, ruyo 4th
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| |A4<sup>5</sup><sub>7</sub>
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| |diminished fifth, Euler's tritone, superaugmented fourth
| |
| |-
| |
| |[[13/9]]
| |
| |636.617660
| |
| |3o5, tho 5th
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| |d5<sup>13</sup>
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| |tridecimal diminished fifth
| |
| |-
| |
| |[[16/11]]
| |
| |648.682058
| |
| |1u5, lu 5th
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| |P5<sub>11</sub>
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| |sub-fifth, octave-reduced 11th subharmonic
| |
| |-
| |
| |[[19/13]]
| |
| |656.985354
| |
| |19o3u5, nothu 5th
| |
| |P5<sup>19</sup><sub>13</sub>
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| |undevicesimal subfifth
| |
| |-
| |
| |[[25/17]]
| |
| |667.672018
| |
| |17uyy4, suyoyo 4th
| |
| |AA4<sup>5,5</sup><sub>17</sub>
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| |vengeance subfifth
| |
| |-
| |
| |[[3/2]]
| |
| |701.955001
| |
| |w5, wa 5th
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| |P5
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| |[[just perfect fifth]], octave-reduced 3rd harmonic, diapente
| |
| |-
| |
| |[[26/17]]
| |
| |735.572252
| |
| |17u3o5, sutho 5th
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| |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]]
| |
| |764.915905
| |
| |z6, zo 6th
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| |m6<sup>7</sup>
| |
| |subminor sixth, septimal minor sixth
| |
| |-
| |
| |[[11/7]]
| |
| |782.492036
| |
| |1or5, loru 5th
| |
| |P5<sup>11</sup><sub>7</sub>
| |
| |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]]
| |
| |813.686286
| |
| |g6, gu 6th
| |
| |m6<sub>5</sub>
| |
| |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]]
| |
| |840.527662
| |
| |3o6, tho 6th
| |
| |m6<sup>13</sup>
| |
| |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]]
| |
| |884.358713
| |
| |y6, yo 6th
| |
| |M6<sup>5</sup>
| |
| |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]]
| |
| |918.641696
| |
| |17og7, sogu 7th
| |
| |d7<sup>17</sup><sub>5</sub>
| |
| |septendecimal diminished seventh, septendecimal major sixth
| |
| |-
| |
| |[[12/7]]
| |
| |933.129094
| |
| |r6, ru 6th
| |
| |M6<sub>7</sub>
| |
| |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]]
| |
| |968.825906
| |
| |z7, zo 7th
| |
| |m7<sup>7</sup>
| |
| |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]]
| |
| |996.089998
| |
| |w7, wa 7th
| |
| |m7
| |
| |Pythagorean minor seventh, small minor seventh, octave-reduced 9th subharmonic
| |
| |-
| |
| |[[9/5]]
| |
| |1017.596288
| |
| |g5, gu 7th
| |
| |m7<sub>5</sub>
| |
| |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]]
| |
| |1049.362941
| |
| |1o7, ilo 7th
| |
| |m7<sup>11</sup>
| |
| |undecimal neutral seventh, 21/4-tone
| |
| |-
| |
| |[[24/13]]
| |
| |1061.427339
| |
| |3u7, thu 7th
| |
| |M7<sub>13</sub>
| |
| |tridecimal neutral seventh
| |
| |-
| |
| |[[13/7]]
| |
| |1071.701755
| |
| |3or7, thoru 7th
| |
| |m7<sup>13</sup><sub>7</sub>
| |
| |tridecimal submajor seventh, 16/3-tone
| |
| |-
| |
| |[[15/8]]
| |
| |1088.268715
| |
| |y7, yo 7th
| |
| |M7<sup>5</sup>
| |
| |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]]
| |
| |1119.462965
| |
| |1uz8, luzo 8ve
| |
| |P8<sup>7</sup><sub>11</sub>
| |
| |large undecimal diminished octave, undecimal major seventh
| |
| |-
| |
| |[[23/12]]
| |
| |1126.319346
| |
| |23o8, twetho 8ve
| |
| |M7<sup>23</sup>
| |
| |large vicesimotertial major seventh
| |
| |-
| |
| |[[25/13]]
| |
| |1132.099766
| |
| |3uyy7, thuyoyo 7th
| |
| |A7<sup>5,5</sup><sub>13</sub>
| |
| |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]]
| |
| |1200
| |
| |w8, wa octave
| |
| |P8
| |
| |[[octave]], [[Wikipedia:Diapason|diapason]]
| |
| |}
| |