List of superparticular intervals: Difference between revisions

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Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
alternative name for password comma
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
m lc monzo
Line 22: Line 22:
| 1200.000
| 1200.000
| 2/1
| 2/1
| {{Monzo|1}}
| {{monzo|1}}
| octave, duple; ''after [[octave reduction]]:'' (perfect) unison, unity, perfect prime, tonic
| octave, duple; ''after [[octave reduction]]:'' (perfect) unison, unity, perfect prime, tonic
|-
|-
Line 30: Line 30:
| 701.955
| 701.955
| 3/2
| 3/2
| {{Monzo|-1 1}}
| {{monzo|-1 1}}
| [[perfect fifth]], 3rd harmonic (octave reduced), diapente
| [[perfect fifth]], 3rd harmonic (octave reduced), diapente
|-
|-
Line 36: Line 36:
| 498.045
| 498.045
| 2<sup>2</sup>/3
| 2<sup>2</sup>/3
| {{Monzo|2 -1}}
| {{monzo|2 -1}}
| perfect fourth, 3rd subharmonic (octave reduced), diatessaron
| perfect fourth, 3rd subharmonic (octave reduced), diatessaron
|-
|-
Line 42: Line 42:
| 203.910
| 203.910
| 3<sup>2</sup>/2<sup>3</sup>
| 3<sup>2</sup>/2<sup>3</sup>
| {{Monzo|-3 2}}
| {{monzo|-3 2}}
| (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced)
| (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced)
|-
|-
Line 50: Line 50:
| 386.314
| 386.314
| 5/2<sup>2</sup>
| 5/2<sup>2</sup>
| {{Monzo|-2 0 1}}
| {{monzo|-2 0 1}}
| (classic) (5-limit) major third, 5th harmonic (octave reduced)
| (classic) (5-limit) major third, 5th harmonic (octave reduced)
|-
|-
Line 56: Line 56:
| 315.641
| 315.641
| (2*3)/5
| (2*3)/5
| {{Monzo|1 1 -1}}
| {{monzo|1 1 -1}}
| (classic) (5-limit) minor third
| (classic) (5-limit) minor third
|-
|-
Line 62: Line 62:
| 182.404
| 182.404
| (2*5)/3<sup>2</sup>
| (2*5)/3<sup>2</sup>
| {{Monzo|1 -2 1}}
| {{monzo|1 -2 1}}
| classic (whole) tone, classic major second, minor whole tone
| classic (whole) tone, classic major second, minor whole tone
|-
|-
Line 68: Line 68:
| 111.731
| 111.731
| 2<sup>4</sup>/(3*5)
| 2<sup>4</sup>/(3*5)
| {{Monzo|4 -1 -1}}
| {{monzo|4 -1 -1}}
| minor diatonic semitone, 15th subharmonic
| minor diatonic semitone, 15th subharmonic
|-
|-
Line 74: Line 74:
| 70.672
| 70.672
| 5<sup>2</sup>/(2<sup>3</sup>*3)
| 5<sup>2</sup>/(2<sup>3</sup>*3)
| {{Monzo|-3 -1 2}}
| {{monzo|-3 -1 2}}
| chroma, (classic) chromatic semitone, Zarlinian semitone
| chroma, (classic) chromatic semitone, Zarlinian semitone
|-
|-
Line 80: Line 80:
| 21.506
| 21.506
| (3/2)<sup>4</sup>/5
| (3/2)<sup>4</sup>/5
| {{Monzo|-4 4 -1}}
| {{monzo|-4 4 -1}}
| syntonic comma, Didymus comma
| syntonic comma, Didymus comma
|-
|-
Line 88: Line 88:
| 266.871
| 266.871
| 7/(2*3)
| 7/(2*3)
| {{Monzo|-1 -1 0 1 }}
| {{monzo|-1 -1 0 1 }}
| (septimal) subminor third, septimal minor third
| (septimal) subminor third, septimal minor third
|-
|-
Line 94: Line 94:
| 231.174
| 231.174
| 2<sup>3</sup>/7
| 2<sup>3</sup>/7
| {{Monzo|3 0 0 -1}}
| {{monzo|3 0 0 -1}}
| (septimal) supermajor second, septimal whole tone, 7th subharmonic
| (septimal) supermajor second, septimal whole tone, 7th subharmonic
|-
|-
Line 100: Line 100:
| 119.443
| 119.443
| (3*5)/(2*7)
| (3*5)/(2*7)
| {{Monzo|-1 1 1 -1}}
| {{monzo|-1 1 1 -1}}
| septimal diatonic semitone
| septimal diatonic semitone
|-
|-
Line 106: Line 106:
| 84.467
| 84.467
| (3*7)/(2<sup>2</sup>*5)
| (3*7)/(2<sup>2</sup>*5)
| {{Monzo|-2 1 -1 1}}
| {{monzo|-2 1 -1 1}}
| minor semitone, large septimal chroma
| minor semitone, large septimal chroma
|-
|-
Line 112: Line 112:
| 62.961
| 62.961
| (2<sup>2</sup>*7)/3<sup>3</sup>
| (2<sup>2</sup>*7)/3<sup>3</sup>
| {{Monzo|2 -3 0 1}}
| {{monzo|2 -3 0 1}}
| septimal third-tone, small septimal chroma, (septimal) subminor second, septimal minor second, trienstonic comma
| septimal third-tone, small septimal chroma, (septimal) subminor second, septimal minor second, trienstonic comma
|-
|-
Line 118: Line 118:
| 48.770
| 48.770
| (2<sup>2</sup>*3<sup>3</sup>)/(5*7)
| (2<sup>2</sup>*3<sup>3</sup>)/(5*7)
| {{Monzo|2 2 -1 -1}}
| {{monzo|2 2 -1 -1}}
| septimal quarter tone, septimal diesis
| septimal quarter tone, septimal diesis
|-
|-
Line 124: Line 124:
| 35.697
| 35.697
| 7<sup>2</sup>/(2<sup>4</sup>*3)
| 7<sup>2</sup>/(2<sup>4</sup>*3)
| {{Monzo|-4 -1 0 2}}
| {{monzo|-4 -1 0 2}}
| large septimal diesis, slendro diesis, septimal 1/6-tone
| large septimal diesis, slendro diesis, septimal 1/6-tone
|-
|-
Line 130: Line 130:
| 34.976
| 34.976
| 2*(5/7)<sup>2</sup>
| 2*(5/7)<sup>2</sup>
| {{Monzo|1 0 2 -2}}
| {{monzo|1 0 2 -2}}
| septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma
| septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma
|-
|-
Line 136: Line 136:
| 27.264
| 27.264
| 2<sup>6</sup>/(3<sup>2</sup>*7)
| 2<sup>6</sup>/(3<sup>2</sup>*7)
| {{Monzo|6 -2 0 -1}}
| {{monzo|6 -2 0 -1}}
| septimal comma, Archytas' comma
| septimal comma, Archytas' comma
|-
|-
Line 142: Line 142:
| 13.795
| 13.795
| (2*3<sup>2</sup>*7)/5<sup>3</sup>
| (2*3<sup>2</sup>*7)/5<sup>3</sup>
| {{Monzo|1 2 -3 1}}
| {{monzo|1 2 -3 1}}
| starling comma, septimal semicomma
| starling comma, septimal semicomma
|-
|-
Line 148: Line 148:
| 7.7115
| 7.7115
| (3*5)<sup>2</sup>/(2<sup>5</sup>*7)
| (3*5)<sup>2</sup>/(2<sup>5</sup>*7)
| {{Monzo|-5 2 2 -1}}
| {{monzo|-5 2 2 -1}}
| marvel comma, septimal kleisma
| marvel comma, septimal kleisma
|-
|-
Line 154: Line 154:
| 0.72120
| 0.72120
| 7<sup>4</sup>/(2<sup>5</sup>*3*5<sup>2</sup>)
| 7<sup>4</sup>/(2<sup>5</sup>*3*5<sup>2</sup>)
| {{Monzo|-5 -1 -2 4}}
| {{monzo|-5 -1 -2 4}}
| breedsma
| breedsma
|-
|-
Line 160: Line 160:
| 0.39576
| 0.39576
| (5<sup>4</sup>*7)/(2*3<sup>7</sup>)
| (5<sup>4</sup>*7)/(2*3<sup>7</sup>)
| {{Monzo|-1 -7 4 1}}
| {{monzo|-1 -7 4 1}}
| ragisma
| ragisma
|-
|-
Line 168: Line 168:
| 165.004
| 165.004
| 11/(2*5)
| 11/(2*5)
| {{Monzo|-1 0 -1 0 1}}
| {{monzo|-1 0 -1 0 1}}
| (large) (undecimal) neutral second, 4/5-tone, Ptolemy's second
| (large) (undecimal) neutral second, 4/5-tone, Ptolemy's second
|-
|-
Line 174: Line 174:
| 150.637
| 150.637
| (2<sup>2</sup>*3)/11
| (2<sup>2</sup>*3)/11
| {{Monzo|2 1 0 0 -1}}
| {{monzo|2 1 0 0 -1}}
| (small) (undecimal) neutral second, 3/4-tone
| (small) (undecimal) neutral second, 3/4-tone
|-
|-
Line 180: Line 180:
| 80.537
| 80.537
| (2*11)/(3*7)
| (2*11)/(3*7)
| {{Monzo|1 -1 0 -1 1}}
| {{monzo|1 -1 0 -1 1}}
| undecimal minor semitone
| undecimal minor semitone
|-
|-
Line 186: Line 186:
| 53.273
| 53.273
| (3*11)/2<sup>5</sup>
| (3*11)/2<sup>5</sup>
| {{Monzo|-5 1 0 0 1}}
| {{monzo|-5 1 0 0 1}}
| undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced)
| undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced)
|-
|-
Line 192: Line 192:
| 38.906
| 38.906
| (3/2)<sup>2</sup>*(5/11)
| (3/2)<sup>2</sup>*(5/11)
| {{Monzo|-2 2 1 0 -1}}
| {{monzo|-2 2 1 0 -1}}
| undecimal 1/5-tone
| undecimal 1/5-tone
|-
|-
Line 198: Line 198:
| 31.767
| 31.767
| (5*11)/(2*3<sup>3</sup>)
| (5*11)/(2*3<sup>3</sup>)
| {{Monzo|-1 -3 1 0 1}}
| {{monzo|-1 -3 1 0 1}}
| undecimal diasecundal comma, eleventyfive comma
| undecimal diasecundal comma, eleventyfive comma
|-
|-
Line 204: Line 204:
| 31.194
| 31.194
| (2<sup>3</sup>*7)/(5*11)
| (2<sup>3</sup>*7)/(5*11)
| {{Monzo|3 0 -1 1 -1}}
| {{monzo|3 0 -1 1 -1}}
| undecimal tritonic comma, konbini comma
| undecimal tritonic comma, konbini comma
|-
|-
Line 210: Line 210:
| 17.576
| 17.576
| (3/7)<sup>2</sup>*(11/2)
| (3/7)<sup>2</sup>*(11/2)
| {{Monzo|-1 2 0 -2 1}}
| {{monzo|-1 2 0 -2 1}}
| small undecimal comma, mothwellsma
| small undecimal comma, mothwellsma
|-
|-
Line 216: Line 216:
| 17.399
| 17.399
| (2*5/3)<sup>2</sup>/11)
| (2*5/3)<sup>2</sup>/11)
| {{Monzo|2 -2 2 0 -1}}
| {{monzo|2 -2 2 0 -1}}
| Ptolemy's comma, ptolemisma
| Ptolemy's comma, ptolemisma
|-
|-
Line 222: Line 222:
| 14.376
| 14.376
| 11<sup>2</sup>/(2<sup>3</sup>*3*5)
| 11<sup>2</sup>/(2<sup>3</sup>*3*5)
| {{Monzo|-3 -1 -1 0 2}}
| {{monzo|-3 -1 -1 0 2}}
| undecimal seconds comma, [[Biyatismic chords|biyatisma]]
| undecimal seconds comma, [[Biyatismic chords|biyatisma]]
|-
|-
Line 228: Line 228:
| 9.8646
| 9.8646
| (2<sup>4</sup>*11)/(5<sup>2</sup>*7)
| (2<sup>4</sup>*11)/(5<sup>2</sup>*7)
| {{Monzo|4 0 -2 -1 1}}
| {{monzo|4 0 -2 -1 1}}
| valinorsma
| valinorsma
|-
|-
Line 234: Line 234:
| 7.1391
| 7.1391
| 3<sup>5</sup>/(2*11<sup>2</sup>)
| 3<sup>5</sup>/(2*11<sup>2</sup>)
| {{Monzo|-1 5 0 0 -2}}
| {{monzo|-1 5 0 0 -2}}
| neutral third comma, rastma
| neutral third comma, rastma
|-
|-
Line 240: Line 240:
| 4.5026
| 4.5026
| (5*7*11)/(2<sup>7</sup>*3)
| (5*7*11)/(2<sup>7</sup>*3)
| {{Monzo|-7 -1 1 1 1}}
| {{monzo|-7 -1 1 1 1}}
| keenanisma
| keenanisma
|-
|-
Line 246: Line 246:
| 3.9302
| 3.9302
| (3*7)<sup>2</sup>/(2<sup>3</sup>*5*11)
| (3*7)<sup>2</sup>/(2<sup>3</sup>*5*11)
| {{Monzo|-3 2 -1 2 -1}}
| {{monzo|-3 2 -1 2 -1}}
| Werckmeister's undecimal septenarian schisma, werckisma
| Werckmeister's undecimal septenarian schisma, werckisma
|-
|-
Line 252: Line 252:
| 3.2090
| 3.2090
| (2/7)<sup>2</sup>*3<sup>3</sup>*5/11
| (2/7)<sup>2</sup>*3<sup>3</sup>*5/11
| {{Monzo|2 3 1 -2 -1}}
| {{monzo|2 3 1 -2 -1}}
| Swets' comma, swetisma
| Swets' comma, swetisma
|-
|-
Line 258: Line 258:
| 0.57240
| 0.57240
| (5*11)<sup>2</sup>/(2<sup>4</sup>*3<sup>2</sup>*7)
| (5*11)<sup>2</sup>/(2<sup>4</sup>*3<sup>2</sup>*7)
| {{Monzo|-4 -3 2 -1 2}}
| {{monzo|-4 -3 2 -1 2}}
| Lehmerisma
| Lehmerisma
|-
|-
Line 264: Line 264:
| 0.17665
| 0.17665
| (11/(5*7))<sup>2</sup>*3<sup>4</sup>/2<sup>3</sup>
| (11/(5*7))<sup>2</sup>*3<sup>4</sup>/2<sup>3</sup>
| {{Monzo|-3 4 -2 -2 2}}
| {{monzo|-3 4 -2 -2 2}}
| Gauss comma, kalisma
| Gauss comma, kalisma
|-
|-
Line 272: Line 272:
| 138.573
| 138.573
| 13/(2<sup>2</sup>*3)
| 13/(2<sup>2</sup>*3)
| {{Monzo|-2 -1 0 0 0 1}}
| {{monzo|-2 -1 0 0 0 1}}
| (large) tridecimal 2/3-tone, tridecimal neutral second
| (large) tridecimal 2/3-tone, tridecimal neutral second
|-
|-
Line 278: Line 278:
| 128.298
| 128.298
| (2*7)/13
| (2*7)/13
| {{Monzo|1 0 0 1 0 -1}}
| {{monzo|1 0 0 1 0 -1}}
| (small) tridecimal 2/3-tone, trienthird
| (small) tridecimal 2/3-tone, trienthird
|-
|-
Line 284: Line 284:
| 67.900
| 67.900
| (2*13)/5<sup>2</sup>
| (2*13)/5<sup>2</sup>
| {{Monzo|1 0 -2 0 0 1}}
| {{monzo|1 0 -2 0 0 1}}
| (large) tridecimal 1/3-tone
| (large) tridecimal 1/3-tone
|-
|-
Line 290: Line 290:
| 65.337
| 65.337
| 3<sup>3</sup>/(2*13)
| 3<sup>3</sup>/(2*13)
| {{Monzo|-1 3 0 0 0 -1}}
| {{monzo|-1 3 0 0 0 -1}}
| (small) tridecimal 1/3-tone
| (small) tridecimal 1/3-tone
|-
|-
Line 296: Line 296:
| 43.831
| 43.831
| (2<sup>3</sup>*5)/(3*13)
| (2<sup>3</sup>*5)/(3*13)
| {{Monzo|3 -1 1 0 0 -1}}
| {{monzo|3 -1 1 0 0 -1}}
| tridecimal minor diesis
| tridecimal minor diesis
|-
|-
Line 302: Line 302:
| 26.841
| 26.841
| (5*13)/2<sup>6</sup>
| (5*13)/2<sup>6</sup>
| {{Monzo|-6 0 1 0 0 1}}
| {{monzo|-6 0 1 0 0 1}}
| wilsorma, 13th-partial chroma
| wilsorma, 13th-partial chroma
|-
|-
Line 308: Line 308:
| 26.432
| 26.432
| (2*3*11)/(5*13)
| (2*3*11)/(5*13)
| {{Monzo|1 1 -1 0 1 -1}}
| {{monzo|1 1 -1 0 1 -1}}
| winmeanma
| winmeanma
|-
|-
Line 314: Line 314:
| 22.339
| 22.339
| (2*3*13)/(7*11)
| (2*3*13)/(7*11)
| {{Monzo|1 1 0 -1 -1 1}}
| {{monzo|1 1 0 -1 -1 1}}
| negustma
| negustma
|-
|-
Line 320: Line 320:
| 19.130
| 19.130
| (7*13)/(2*3<sup>2</sup>*5)
| (7*13)/(2*3<sup>2</sup>*5)
| {{Monzo|-1 -2 -1 1 0 1}}
| {{monzo|-1 -2 -1 1 0 1}}
| [[The_Biosphere|Biome]] comma, superleap comma
| [[The_Biosphere|Biome]] comma, superleap comma
|-
|-
Line 326: Line 326:
| 16.567
| 16.567
| (3*5*7)/(2<sup>3</sup>*13)
| (3*5*7)/(2<sup>3</sup>*13)
| {{Monzo|-3 1 1 1 0 -1}}
| {{monzo|-3 1 1 1 0 -1}}
| small tridecimal comma, animist comma
| small tridecimal comma, animist comma
|-
|-
Line 332: Line 332:
| 12.064
| 12.064
| (2<sup>2</sup>*3)<sup>2</sup>/(11*13)
| (2<sup>2</sup>*3)<sup>2</sup>/(11*13)
| {{Monzo|4 2 0 0 -1 -1}}
| {{monzo|4 2 0 0 -1 -1}}
| grossma
| grossma
|-
|-
Line 338: Line 338:
| 10.274
| 10.274
| 13<sup>2</sup>/(2<sup>3</sup>*3*7)
| 13<sup>2</sup>/(2<sup>3</sup>*3*7)
| {{Monzo|-3 -1 0 -1 0 2}}
| {{monzo|-3 -1 0 -1 0 2}}
| buzurgisma, dhanvantarisma
| buzurgisma, dhanvantarisma
|-
|-
Line 344: Line 344:
| 8.8554
| 8.8554
| (2*7)<sup>2</sup>/(3*5*13)
| (2*7)<sup>2</sup>/(3*5*13)
| {{Monzo|2 -1 -1 2 0 -1}}
| {{monzo|2 -1 -1 2 0 -1}}
| [[Mynucumic_chords|mynucuma]]
| [[Mynucumic_chords|mynucuma]]
|-
|-
Line 350: Line 350:
| 5.3351
| 5.3351
| (5<sup>2</sup>*13)/(2<sup>2</sup>*3<sup>4</sup>)
| (5<sup>2</sup>*13)/(2<sup>2</sup>*3<sup>4</sup>)
| {{Monzo|-2 -4 2 0 0 1}}
| {{monzo|-2 -4 2 0 0 1}}
| [[Marveltwin|marveltwin comma]]
| [[Marveltwin|marveltwin comma]]
|-
|-
Line 356: Line 356:
| 4.9393
| 4.9393
| (3/5)<sup>2</sup>*13/(2*7)
| (3/5)<sup>2</sup>*13/(2*7)
| {{Monzo|-1 3 -2 -1 0 1}}
| {{monzo|-1 3 -2 -1 0 1}}
| ratwolfsma
| ratwolfsma
|-
|-
Line 362: Line 362:
| 4.9253
| 4.9253
| (2<sup>5</sup>*11)/(3<sup>2</sup>*13)
| (2<sup>5</sup>*11)/(3<sup>2</sup>*13)
| {{Monzo|5 -3 0 0 1 -1}}
| {{monzo|5 -3 0 0 1 -1}}
| minthma
| minthma
|-
|-
Line 368: Line 368:
| 4.7627
| 4.7627
| (2/11)<sup>2</sup>*7*13/3
| (2/11)<sup>2</sup>*7*13/3
| {{Monzo|2 -1 0 1 -2 1}}
| {{monzo|2 -1 0 1 -2 1}}
| gentle comma
| gentle comma
|-
|-
Line 374: Line 374:
| 2.7722
| 2.7722
| (5/2)<sup>4</sup>/(3*13)
| (5/2)<sup>4</sup>/(3*13)
| {{Monzo|-4 -1 4 0 0 -1}}
| {{monzo|-4 -1 4 0 0 -1}}
| tunbarsma
| tunbarsma
|-
|-
Line 380: Line 380:
| 2.5629
| 2.5629
| (2*13/5)<sup>2</sup>/3<sup>3</sup>
| (2*13/5)<sup>2</sup>/3<sup>3</sup>
| {{Monzo|2 -3 -2 0 0 2}}
| {{monzo|2 -3 -2 0 0 2}}
| island comma
| island comma
|-
|-
Line 386: Line 386:
| 2.3764
| 2.3764
| (3<sup>2</sup>/2)<sup>3</sup>/(7*13)
| (3<sup>2</sup>/2)<sup>3</sup>/(7*13)
| {{Monzo|-3 6 0 -1 0 -1}}
| {{monzo|-3 6 0 -1 0 -1}}
| squbema
| squbema
|-
|-
Line 392: Line 392:
| 1.7304
| 1.7304
| 7*11*13/(2*5)<sup>3</sup>
| 7*11*13/(2*5)<sup>3</sup>
| {{Monzo|-3 0 -3 1 1 1}}
| {{monzo|-3 0 -3 1 1 1}}
| sinbadma
| sinbadma
|-
|-
Line 398: Line 398:
| 1.0092
| 1.0092
| 2<sup>2</sup>*3*11*13/(5*7<sup>3</sup>)
| 2<sup>2</sup>*3*11*13/(5*7<sup>3</sup>)
| {{Monzo|2 1 -1 -3 1 1}}
| {{monzo|2 1 -1 -3 1 1}}
| lummic comma
| lummic comma
|-
|-
Line 404: Line 404:
| 0.83252
| 0.83252
| 2<sup>5</sup>*5*13/(3<sup>3</sup>*7*11)
| 2<sup>5</sup>*5*13/(3<sup>3</sup>*7*11)
| {{Monzo|5 -3 1 -1 -1 1}}
| {{monzo|5 -3 1 -1 -1 1}}
| ibnsinma
| ibnsinma
|-
|-
Line 410: Line 410:
| 0.42272
| 0.42272
| (2<sup>6</sup>/3)<sup>2</sup>/(5*7*13)
| (2<sup>6</sup>/3)<sup>2</sup>/(5*7*13)
| {{Monzo|12 -2 -1 -1 0 -1}}
| {{monzo|12 -2 -1 -1 0 -1}}
| tridecimal schisma, Sagittal schismina
| tridecimal schisma, Sagittal schismina
|-
|-
Line 416: Line 416:
| 0.40981
| 0.40981
| (5*13)<sup>2</sup>/(2<sup>7</sup>*3*11)
| (5*13)<sup>2</sup>/(2<sup>7</sup>*3*11)
| {{Monzo|-7 -1 2 0 -1 2}}
| {{monzo|-7 -1 2 0 -1 2}}
| leprechaun comma
| leprechaun comma
|-
|-
Line 422: Line 422:
| 0.26012
| 0.26012
| (2<sup>3</sup>/11)<sup>3</sup>*13/5
| (2<sup>3</sup>/11)<sup>3</sup>*13/5
| {{Monzo|9 0 -1 0 -3 1}}
| {{monzo|9 0 -1 0 -3 1}}
| jacobin comma
| jacobin comma
|-
|-
Line 428: Line 428:
| 0.16260
| 0.16260
| (2*11)<sup>3</sup>/((3*13)<sup>2</sup>*7)
| (2*11)<sup>3</sup>/((3*13)<sup>2</sup>*7)
| {{Monzo|3 -2 0 -1 3 -2}}
| {{monzo|3 -2 0 -1 3 -2}}
| harmonisma
| harmonisma
|-
|-
Line 434: Line 434:
| 0.014052
| 0.014052
| (3/2)<sup>6</sup>*(13/5)<sup>2</sup>/(7*11)
| (3/2)<sup>6</sup>*(13/5)<sup>2</sup>/(7*11)
| {{Monzo|-6 6 -2 -1 -1 2}}
| {{monzo|-6 6 -2 -1 -1 2}}
| chalmersia
| chalmersia
|-
|-
Line 442: Line 442:
| 104.955
| 104.955
| 17/2<sup>4</sup>
| 17/2<sup>4</sup>
| {{Monzo|-4 0 0 0 0 0 1}}
| {{monzo|-4 0 0 0 0 0 1}}
| large septendecimal semitone, 17th harmonic (octave reduced)
| large septendecimal semitone, 17th harmonic (octave reduced)
|-
|-
Line 448: Line 448:
| 98.955
| 98.955
| (2*3<sup>2</sup>)/17
| (2*3<sup>2</sup>)/17
| {{Monzo|1 2 0 0 0 0 -1}}
| {{monzo|1 2 0 0 0 0 -1}}
| small septendecimal semitone, Arabic lute index finger
| small septendecimal semitone, Arabic lute index finger
|-
|-
Line 454: Line 454:
| 51.682
| 51.682
| (2*17)/(3*11)
| (2*17)/(3*11)
| {{Monzo|1 -1 0 0 -1 0 1}}
| {{monzo|1 -1 0 0 -1 0 1}}
| large septendecimal 1/4-tone
| large septendecimal 1/4-tone
|-
|-
Line 460: Line 460:
| 50.184
| 50.184
| (5*7)/(2*17)
| (5*7)/(2*17)
| {{Monzo|-1 0 1 1 0 0 -1}}
| {{monzo|-1 0 1 1 0 0 -1}}
| small septendecimal 1/4-tone
| small septendecimal 1/4-tone
|-
|-
Line 466: Line 466:
| 34.283
| 34.283
| (3*17)/(2*5<sup>2</sup>)
| (3*17)/(2*5<sup>2</sup>)
| {{Monzo|-1 1 -2 0 0 0 1}}
| {{monzo|-1 1 -2 0 0 0 1}}
| large septendecimal 1/6-tone
| large septendecimal 1/6-tone
|-
|-
Line 472: Line 472:
| 33.617
| 33.617
| (2<sup>2</sup>*13)/(3*17)
| (2<sup>2</sup>*13)/(3*17)
| {{Monzo|2 -1 0 0 0 1 -1}}
| {{monzo|2 -1 0 0 0 1 -1}}
| small septendecimal 1/6-tone
| small septendecimal 1/6-tone
|-
|-
Line 478: Line 478:
| 20.488
| 20.488
| (5*17)/(2<sup>2</sup>*3*7)
| (5*17)/(2<sup>2</sup>*3*7)
| {{Monzo|-2 -1 1 -1 0 0 1}}
| {{monzo|-2 -1 1 -1 0 0 1}}
| septendecimal comma (?)
| septendecimal comma (?)
|-
|-
Line 484: Line 484:
| 14.487
| 14.487
| (2<sup>3</sup>*3*5)/(7*17)
| (2<sup>3</sup>*3*5)/(7*17)
| {{Monzo|3 1 1 -1 0 0 -1}}
| {{monzo|3 1 1 -1 0 0 -1}}
|  
|  
|-
|-
Line 490: Line 490:
| 12.777
| 12.777
| (2/3)<sup>3</sup>*17/5
| (2/3)<sup>3</sup>*17/5
| {{Monzo|3 -3 -1 0 0 0 1}}
| {{monzo|3 -3 -1 0 0 0 1}}
| septendecimal major second comma
| septendecimal major second comma
|-
|-
Line 496: Line 496:
| 11.278
| 11.278
| (2*7*11)/(3<sup>2</sup>*17)
| (2*7*11)/(3<sup>2</sup>*17)
| {{Monzo|1 -2 0 1 1 0 -1}}
| {{monzo|1 -2 0 1 1 0 -1}}
|  
|  
|-
|-
Line 502: Line 502:
| 10.214
| 10.214
| (2*5*17)/13<sup>2</sup>
| (2*5*17)/13<sup>2</sup>
| {{Monzo|1 0 1 0 0 -2 1}}
| {{monzo|1 0 1 0 0 -2 1}}
|  
|  
|-
|-
Line 508: Line 508:
| 7.8514
| 7.8514
| (13*17)/(2<sup>2</sup>*5*11)
| (13*17)/(2<sup>2</sup>*5*11)
| {{Monzo|-2 0 -1 0 -1 1 1}}
| {{monzo|-2 0 -1 0 -1 1 1}}
|  
|  
|-
|-
Line 514: Line 514:
| 6.7759
| 6.7759
| (2<sup>8</sup>)/(3*5*17)
| (2<sup>8</sup>)/(3*5*17)
| {{Monzo|8 -1 -1 0 0 0 -1}}
| {{monzo|8 -1 -1 0 0 0 -1}}
| septendecimal kleisma, 255th subharmonic
| septendecimal kleisma, 255th subharmonic
|-
|-
Line 520: Line 520:
| 6.3532
| 6.3532
| (3*7*13)/(2<sup>4</sup>*17)
| (3*7*13)/(2<sup>4</sup>*17)
| {{Monzo|-4 1 0 1 0 1 -1}}
| {{monzo|-4 1 0 1 0 1 -1}}
| tannisma
| tannisma
|-
|-
Line 526: Line 526:
| 6.0008
| 6.0008
| (17/3)<sup>2</sup>/2<sup>5</sup>
| (17/3)<sup>2</sup>/2<sup>5</sup>
| {{Monzo|-5 -2 0 0 0 0 2}}
| {{monzo|-5 -2 0 0 0 0 2}}
| septendecimal 6-cent comma
| septendecimal 6-cent comma
|-
|-
Line 532: Line 532:
| 4.6228
| 4.6228
| (3*5<sup>3</sup>)/(2*11*17)
| (3*5<sup>3</sup>)/(2*11*17)
| {{Monzo|-1 1 3 0 -1 0 -1}}
| {{monzo|-1 1 3 0 -1 0 -1}}
|  
|  
|-
|-
Line 538: Line 538:
| 3.9213
| 3.9213
| (2*13*17)/(3*7)<sup>2</sup>
| (2*13*17)/(3*7)<sup>2</sup>
| {{Monzo|1 -2 0 -2 0 1 1}}
| {{monzo|1 -2 0 -2 0 1 1}}
|  
|  
|-
|-
Line 544: Line 544:
| 3.0887
| 3.0887
| (3*11*17)/(2<sup>4</sup>*5*7)
| (3*11*17)/(2<sup>4</sup>*5*7)
| {{Monzo|-4 1 -1 -1 1 0 1}}
| {{monzo|-4 1 -1 -1 1 0 1}}
|  
|  
|-
|-
Line 550: Line 550:
| 2.9121
| 2.9121
| (5*7*17)/(2*3<sup>3</sup>*11)
| (5*7*17)/(2*3<sup>3</sup>*11)
| {{Monzo|-1 -3 1 1 -1 0 1}}
| {{monzo|-1 -3 1 1 -1 0 1}}
|  
|  
|-
|-
Line 556: Line 556:
| 2.4230
| 2.4230
| (5*11*13)/(2*3*7*17)
| (5*11*13)/(2*3*7*17)
| {{Monzo|-1 -1 1 -1 1 1 -1}}
| {{monzo|-1 -1 1 -1 1 1 -1}}
|  
|  
|-
|-
Line 562: Line 562:
| 2.0796
| 2.0796
| (7<sup>2</sup>*17)/(2<sup>6</sup>*13)
| (7<sup>2</sup>*17)/(2<sup>6</sup>*13)
| {{Monzo|-6 0 0 2 0 -1 1}}
| {{monzo|-6 0 0 2 0 -1 1}}
|  
|  
|-
|-
Line 568: Line 568:
| 1.8506
| 1.8506
| (2<sup>3</sup>*3<sup>2</sup>*13)/(5*11*17)
| (2<sup>3</sup>*3<sup>2</sup>*13)/(5*11*17)
| {{Monzo|3 2 -1 0 -1 1 -1}}
| {{monzo|3 2 -1 0 -1 1 -1}}
| ainos comma, ainma
| ainos comma, ainma
|-
|-
Line 574: Line 574:
| 1.5905
| 1.5905
| (3<sup>2</sup>*11<sup>2</sup>)/(2<sup>6</sup>*17)
| (3<sup>2</sup>*11<sup>2</sup>)/(2<sup>6</sup>*17)
| {{Monzo|-6 2 0 0 2 0 -1}}
| {{monzo|-6 2 0 0 2 0 -1}}
| twosquare comma
| twosquare comma
|-
|-
Line 580: Line 580:
| 1.4983
| 1.4983
| (2<sup>2</sup>*17<sup>2</sup>)/(3*5*7*11)
| (2<sup>2</sup>*17<sup>2</sup>)/(3*5*7*11)
| {{Monzo|2 -1 -1 -1 -1 0 2}}
| {{monzo|2 -1 -1 -1 -1 0 2}}
|  
|  
|-
|-
Line 586: Line 586:
| 1.4138
| 1.4138
| (5<sup>2</sup>*7<sup>2</sup>)/(2<sup>3</sup>*3<sup>2</sup>*17)
| (5<sup>2</sup>*7<sup>2</sup>)/(2<sup>3</sup>*3<sup>2</sup>*17)
| {{Monzo|-3 -2 2 2 0 0 -1}}
| {{monzo|-3 -2 2 2 0 0 -1}}
|  
|  
|-
|-
Line 592: Line 592:
| 1.3584
| 1.3584
| (3*5<sup>2</sup>*17)/(2*7<sup>2</sup>*13)
| (3*5<sup>2</sup>*17)/(2*7<sup>2</sup>*13)
| {{Monzo|-1 1 2 -2 0 -1 1}}
| {{monzo|-1 1 2 -2 0 -1 1}}
|  
|  
|-
|-
Line 598: Line 598:
| 1.0181
| 1.0181
| (3<sup>5</sup>*7)/[(2*5)<sup>2</sup>*17]
| (3<sup>5</sup>*7)/[(2*5)<sup>2</sup>*17]
| {{Monzo|-2 5 -2 1 0 0 -1}}
| {{monzo|-2 5 -2 1 0 0 -1}}
|  
|  
|-
|-
Line 604: Line 604:
| 0.84143
| 0.84143
| (2*3*7<sup>3</sup>)/(11<sup>2</sup>*17)
| (2*3*7<sup>3</sup>)/(11<sup>2</sup>*17)
| {{Monzo|1 1 0 3 -2 0 -1}}
| {{monzo|1 1 0 3 -2 0 -1}}
| xenisma
| xenisma
|-
|-
Line 610: Line 610:
| 0.71230
| 0.71230
| (11*13*17)/(2*3<sup>5</sup>*5)
| (11*13*17)/(2*3<sup>5</sup>*5)
| {{Monzo|-1 -5 -1 0 1 1 1}}
| {{monzo|-1 -5 -1 0 1 1 1}}
|  
|  
|-
|-
Line 616: Line 616:
| 0.69263
| 0.69263
| (2<sup>2</sup>*5<sup>4</sup>)/(3*7<sup>2</sup>*17)
| (2<sup>2</sup>*5<sup>4</sup>)/(3*7<sup>2</sup>*17)
| {{Monzo|2 -1 4 -2 0 0 -1}}
| {{monzo|2 -1 4 -2 0 0 -1}}
|  
|  
|-
|-
Line 622: Line 622:
| 0.66573
| 0.66573
| (3<sup>2</sup>*17<sup>2</sup>)/(2<sup>3</sup>*5<sup>2</sup>*13)
| (3<sup>2</sup>*17<sup>2</sup>)/(2<sup>3</sup>*5<sup>2</sup>*13)
| {{Monzo|-3 2 -2 0 0 -1 2}}
| {{monzo|-3 2 -2 0 0 -1 2}}
|  
|  
|-
|-
Line 628: Line 628:
| 0.35234
| 0.35234
| (2*3<sup>3</sup>*7*13)/(17<sup>3</sup>)
| (2*3<sup>3</sup>*7*13)/(17<sup>3</sup>)
| {{Monzo|1 3 0 1 0 1 -3}}
| {{monzo|1 3 0 1 0 1 -3}}
|  
|  
|-
|-
Line 634: Line 634:
| 0.29688
| 0.29688
| (2<sup>3</sup>*3<sup>6</sup>)/(7<sup>3</sup>*17)
| (2<sup>3</sup>*3<sup>6</sup>)/(7<sup>3</sup>*17)
| {{Monzo|3 6 0 -3 0 0 -1}}
| {{monzo|3 6 0 -3 0 0 -1}}
|  
|  
|-
|-
Line 640: Line 640:
| 0.13989
| 0.13989
| (2<sup>3</sup>*7*13*17)/(3<sup>2</sup>*5<sup>3</sup>*11)
| (2<sup>3</sup>*7*13*17)/(3<sup>2</sup>*5<sup>3</sup>*11)
| {{Monzo|3 -2 -3 1 -1 1 1}}
| {{monzo|3 -2 -3 1 -1 1 1}}
| flashma
| flashma
|-
|-
Line 646: Line 646:
| 0.12023
| 0.12023
| (2<sup>6</sup>*3<sup>2</sup>*5<sup>2</sup>)/(7*11<sup>2</sup>*17)
| (2<sup>6</sup>*3<sup>2</sup>*5<sup>2</sup>)/(7*11<sup>2</sup>*17)
| {{Monzo|6 2 2 -1 -2 0 -1}}
| {{monzo|6 2 2 -1 -2 0 -1}}
| sparkisma
| sparkisma
|-
|-
Line 652: Line 652:
| 0.060616
| 0.060616
| (13<sup>4</sup>)/(2<sup>4</sup>*3*5*7*17)
| (13<sup>4</sup>)/(2<sup>4</sup>*3*5*7*17)
| {{Monzo|-4 -1 -1 -1 0 4 -1}}
| {{monzo|-4 -1 -1 -1 0 4 -1}}
|  
|  
|-
|-
Line 658: Line 658:
| 0.055466
| 0.055466
| (7<sup>4</sup>*13)/(2<sup>2</sup>*3<sup>3</sup>*17<sup>2</sup>)
| (7<sup>4</sup>*13)/(2<sup>2</sup>*3<sup>3</sup>*17<sup>2</sup>)
| {{Monzo|-2 -3 0 4 0 1 -2}}
| {{monzo|-2 -3 0 4 0 1 -2}}
|  
|  
|-
|-
Line 664: Line 664:
| 0.046564
| 0.046564
| (2<sup>2</sup>*5*11*13<sup>2</sup>)/(3<sup>7</sup>*17)
| (2<sup>2</sup>*5*11*13<sup>2</sup>)/(3<sup>7</sup>*17)
| {{Monzo|2 -7 1 0 1 2 -1}}
| {{monzo|2 -7 1 0 1 2 -1}}
|  
|  
|-
|-
Line 670: Line 670:
| 0.008902
| 0.008902
| (3<sup>4</sup>*7<sup>4</sup>)/(2<sup>4</sup>*5*11*13*17)
| (3<sup>4</sup>*7<sup>4</sup>)/(2<sup>4</sup>*5*11*13*17)
| {{Monzo|-4 4 -1 4 -1 -1 -1}}
| {{monzo|-4 4 -1 4 -1 -1 -1}}
| scintillisma
| scintillisma
|-
|-
Line 676: Line 676:
| 0.005150
| 0.005150
| (3<sup>2</sup>*13<sup>3</sup>*17)/(2<sup>2</sup>*5*7<sup>5</sup>)
| (3<sup>2</sup>*13<sup>3</sup>*17)/(2<sup>2</sup>*5*7<sup>5</sup>)
| {{Monzo|-2 2 -1 -5 0 3 1}}
| {{monzo|-2 2 -1 -5 0 3 1}}
|  
|  
|-
|-
Line 684: Line 684:
| 93.603
| 93.603
| 19/(2*3<sup>2</sup>)
| 19/(2*3<sup>2</sup>)
| {{Monzo|-1 -2 0 0 0 0 0 1}}
| {{monzo|-1 -2 0 0 0 0 0 1}}
| large undevicesimal semitone
| large undevicesimal semitone
|-
|-
Line 690: Line 690:
| 88.801
| 88.801
| (2<sup>2</sup>*5)/19
| (2<sup>2</sup>*5)/19
| {{Monzo|2 0 1 0 0 0 0 -1}}
| {{monzo|2 0 1 0 0 0 0 -1}}
| small undevicesimal semitone
| small undevicesimal semitone
|-
|-
Line 696: Line 696:
| 44.970
| 44.970
| (3*13)/(2*19)
| (3*13)/(2*19)
| {{Monzo|-1 1 0 0 0 1 0 -1}}
| {{monzo|-1 1 0 0 0 1 0 -1}}
| undevicesimal 2/9-tone
| undevicesimal 2/9-tone
|-
|-
Line 702: Line 702:
| 30.642
| 30.642
| (3*19)/(2<sup>3</sup>*7)
| (3*19)/(2<sup>3</sup>*7)
| {{Monzo|-3 1 0 -1 0 0 0 1}}
| {{monzo|-3 1 0 -1 0 0 0 1}}
| hendrix comma
| hendrix comma
|-
|-
Line 708: Line 708:
| 22.931
| 22.931
| (2<sup>2</sup>*19)/(3*5<sup>2</sup>)
| (2<sup>2</sup>*19)/(3*5<sup>2</sup>)
| {{Monzo|2 -1 -2 0 0 0 0 1}}
| {{monzo|2 -1 -2 0 0 0 0 1}}
| undevicesimal 1/9-tone (greater)
| undevicesimal 1/9-tone (greater)
|-
|-
Line 714: Line 714:
| 22.631
| 22.631
| (7*11)/(2<sup>2</sup>*19)
| (7*11)/(2<sup>2</sup>*19)
| {{Monzo|-2 0 0 1 1 0 0 -1}}
| {{monzo|-2 0 0 1 1 0 0 -1}}
| undevicesimal 1/9-tone (lesser)
| undevicesimal 1/9-tone (lesser)
|-
|-
Line 720: Line 720:
| 18.128
| 18.128
| (2<sup>5</sup>*3)/(5*19)
| (2<sup>5</sup>*3)/(5*19)
| {{Monzo|5 1 -1 0 0 0 0 -1}}
| {{monzo|5 1 -1 0 0 0 0 -1}}
|  
|  
|-
|-
Line 726: Line 726:
| 13.066
| 13.066
| (19*7)/(2<sup>2</sup>*3*11)
| (19*7)/(2<sup>2</sup>*3*11)
| {{Monzo|-2 -1 0 1 -1 0 0 1}}
| {{monzo|-2 -1 0 1 -1 0 0 1}}
|  
|  
|-
|-
Line 732: Line 732:
| 11.352
| 11.352
| (3<sup>2</sup>*17)/(2<sup>3</sup>*19)
| (3<sup>2</sup>*17)/(2<sup>3</sup>*19)
| {{Monzo|-3 2 0 0 0 0 1 -1}}
| {{monzo|-3 2 0 0 0 0 1 -1}}
|  
|  
|-
|-
Line 738: Line 738:
| 10.154
| 10.154
| (3<sup>2</sup>*19)/(2*5*17)
| (3<sup>2</sup>*19)/(2*5*17)
| {{Monzo|-1 2 -1 0 0 0 -1 1}}
| {{monzo|-1 2 -1 0 0 0 -1 1}}
|  
|  
|-
|-
Line 744: Line 744:
| 9.1358
| 9.1358
| (2*5*19)/(3<sup>3</sup>*7)
| (2*5*19)/(3<sup>3</sup>*7)
| {{Monzo|1 -3 1 -1 0 0 0 1}}
| {{monzo|1 -3 1 -1 0 0 0 1}}
|  
|  
|-
|-
Line 750: Line 750:
| 8.3033
| 8.3033
| (11*19)/(2<sup>4</sup>*13)
| (11*19)/(2<sup>4</sup>*13)
| {{Monzo|-4 0 0 0 1 -1 0 1}}
| {{monzo|-4 0 0 0 1 -1 0 1}}
| yama comma
| yama comma
|-
|-
Line 756: Line 756:
| 8.2637
| 8.2637
| (2*3*5*7)/(11*19)
| (2*3*5*7)/(11*19)
| {{Monzo|1 1 1 1 -1 0 0 -1}}
| {{monzo|1 1 1 1 -1 0 0 -1}}
| spleen comma
| spleen comma
|-
|-
Line 762: Line 762:
| 6.0639
| 6.0639
| (2*11*13)/(3*5*19)
| (2*11*13)/(3*5*19)
| {{Monzo|1 -1 -1 0 1 1 0 -1}}
| {{monzo|1 -1 -1 0 1 1 0 -1}}
|  
|  
|-
|-
Line 768: Line 768:
| 5.3516
| 5.3516
| (2<sup>2</sup>*3<sup>4</sup>)/(17*19)
| (2<sup>2</sup>*3<sup>4</sup>)/(17*19)
| {{Monzo|2 4 0 0 0 0 -1 -1}}
| {{monzo|2 4 0 0 0 0 -1 -1}}
|  
|  
|-
|-
Line 774: Line 774:
| 5.0547
| 5.0547
| 7<sup>4</sup>/(2*3<sup>3</sup>*19)
| 7<sup>4</sup>/(2*3<sup>3</sup>*19)
| {{Monzo|-1 -2 0 3 0 0 0 -1}}
| {{monzo|-1 -2 0 3 0 0 0 -1}}
|  
|  
|-
|-
Line 780: Line 780:
| 4.8023
| 4.8023
| 19<sup>2</sup>/(2<sup>3</sup>*3<sup>2</sup>*5)
| 19<sup>2</sup>/(2<sup>3</sup>*3<sup>2</sup>*5)
| {{Monzo|-3 -2 -1 0 0 0 0 2}}
| {{monzo|-3 -2 -1 0 0 0 0 2}}
| go comma
| go comma
|-
|-
Line 786: Line 786:
| 4.3335
| 4.3335
| (2<sup>4</sup>*5<sup>2</sup>)/(3*7*19)
| (2<sup>4</sup>*5<sup>2</sup>)/(3*7*19)
| {{Monzo|4 -1 2 -1 0 0 0 -1}}
| {{monzo|4 -1 2 -1 0 0 0 -1}}
|  
|  
|-
|-
Line 792: Line 792:
| 3.8007
| 3.8007
| (2<sup>3</sup>*3*19)/(5*7*13)
| (2<sup>3</sup>*3*19)/(5*7*13)
| {{Monzo|3 1 -1 -1 0 -1 0 1}}
| {{monzo|3 1 -1 -1 0 -1 0 1}}
|  
|  
|-
|-
Line 798: Line 798:
| 3.6409
| 3.6409
| (2<sup>2</sup>*7*17)/(5<sup>2</sup>*19)
| (2<sup>2</sup>*7*17)/(5<sup>2</sup>*19)
| {{Monzo|2 0 -2 1 0 0 1 -1}}
| {{monzo|2 0 -2 1 0 0 1 -1}}
|  
|  
|-
|-
Line 804: Line 804:
| 3.5010
| 3.5010
| (3<sup>2</sup>*5*11)/(2*13*19)
| (3<sup>2</sup>*5*11)/(2*13*19)
| {{Monzo|-1 2 1 0 1 -1 0 -1}}
| {{monzo|-1 2 1 0 1 -1 0 -1}}
|  
|  
|-
|-
Line 810: Line 810:
| 3.3780
| 3.3780
| (3<sup>3</sup>*19)/2<sup>9</sup>
| (3<sup>3</sup>*19)/2<sup>9</sup>
| {{Monzo|-9 3 0 0 0 0 0 1}}
| {{monzo|-9 3 0 0 0 0 0 1}}
| undevicesimal comma, undevicesimal schisma, 513th harmonic
| undevicesimal comma, undevicesimal schisma, 513th harmonic
|-
|-
Line 816: Line 816:
| 1.7875
| 1.7875
| (3*17*19)/(2<sup>3</sup>*11<sup>2</sup>)
| (3*17*19)/(2<sup>3</sup>*11<sup>2</sup>)
| {{Monzo|-3 1 0 0 -2 0 1 1}}
| {{monzo|-3 1 0 0 -2 0 1 1}}
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Line 822: Line 822:
| 1.4243
| 1.4243
| (2<sup>6</sup>*19)/(3<sup>5</sup>*5)
| (2<sup>6</sup>*19)/(3<sup>5</sup>*5)
| {{Monzo|6 -5 -1 0 0 0 0 1}}
| {{monzo|6 -5 -1 0 0 0 0 1}}
| password comma, Eratosthenes' comma
| password comma, Eratosthenes' comma
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Line 828: Line 828:
| 1.3012
| 1.3012
| 11<sup>3</sup>/(2*5*7*19)
| 11<sup>3</sup>/(2*5*7*19)
| {{Monzo|-1 0 -1 -1 3 0 0 -1}}
| {{monzo|-1 0 -1 -1 3 0 0 -1}}
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Line 834: Line 834:
| 1.1985
| 1.1985
| 5*(17/(2*19))<sup>2</sup>
| 5*(17/(2*19))<sup>2</sup>
| {{Monzo|-2 0 1 0 0 0 2 -2}}
| {{monzo|-2 0 1 0 0 0 2 -2}}
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Line 840: Line 840:
| 1.1386
| 1.1386
| (3*13)<sup>2</sup>/(2<sup>4</sup>*5*19)
| (3*13)<sup>2</sup>/(2<sup>4</sup>*5*19)
| {{Monzo|-4 2 -1 0 0 2 0 -1}}
| {{monzo|-4 2 -1 0 0 2 0 -1}}
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Line 846: Line 846:
| 1.1245
| 1.1245
| (2<sup>2</sup>*5*7*11)/(3<sup>4</sup>*19)
| (2<sup>2</sup>*5*7*11)/(3<sup>4</sup>*19)
| {{Monzo|2 -4 1 1 1 0 0 -1}}
| {{monzo|2 -4 1 1 1 0 0 -1}}
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Line 852: Line 852:
| 1.0016
| 1.0016
| (7*13*19)/(2<sup>6</sup>*3<sup>3</sup>)
| (7*13*19)/(2<sup>6</sup>*3<sup>3</sup>)
| {{Monzo|-6 -3 0 1 0 1 0 1}}
| {{monzo|-6 -3 0 1 0 1 0 1}}
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Line 858: Line 858:
| 0.7288
| 0.7288
| (5<sup>3</sup>*19)/(2<sup>3</sup>*3<sup>3</sup>*11)
| (5<sup>3</sup>*19)/(2<sup>3</sup>*3<sup>3</sup>*11)
| {{Monzo|-3 -3 3 0 -1 0 0 1}}
| {{monzo|-3 -3 3 0 -1 0 0 1}}
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Line 864: Line 864:
| 0.7120
| 0.7120
| (11*13*17)/(2<sup>7</sup>*19)
| (11*13*17)/(2<sup>7</sup>*19)
| {{Monzo|-7 0 0 0 1 1 1 -1}}
| {{monzo|-7 0 0 0 1 1 1 -1}}
| Blumeyer comma
| Blumeyer comma
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Line 870: Line 870:
| 0.5918
| 0.5918
| (2*7*11*19)/(3<sup>2</sup>*5<sup>2</sup>*13)
| (2*7*11*19)/(3<sup>2</sup>*5<sup>2</sup>*13)
| {{Monzo|1 -2 -2 1 1 -1 0 1}}
| {{monzo|1 -2 -2 1 1 -1 0 1}}
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Line 876: Line 876:
| 0.5521
| 0.5521
| (2<sup>6</sup>*7<sup>2</sup>)/(3*5*11*19)
| (2<sup>6</sup>*7<sup>2</sup>)/(3*5*11*19)
| {{Monzo|6 -1 -1 2 -1 0 0 -1}}
| {{monzo|6 -1 -1 2 -1 0 0 -1}}
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Line 882: Line 882:
| 0.5328
| 0.5328
| (2*5<sup>3</sup>*13)/(3<sup>2</sup>*19<sup>2</sup>)
| (2*5<sup>3</sup>*13)/(3<sup>2</sup>*19<sup>2</sup>)
| {{Monzo|1 -2 3 0 0 1 0 -2}}
| {{monzo|1 -2 3 0 0 1 0 -2}}
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Line 888: Line 888:
| 0.4123
| 0.4123
| (2<sup>3</sup>*3*5<sup>2</sup>*7)/(13*17*19)
| (2<sup>3</sup>*3*5<sup>2</sup>*7)/(13*17*19)
| {{Monzo|3 1 2 1 0 -1 -1 -1}}
| {{monzo|3 1 2 1 0 -1 -1 -1}}
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Line 894: Line 894:
| 0.2998
| 0.2998
| (2<sup>4</sup>*19<sup>2</sup>)/(3*5<sup>2</sup>*7*11)
| (2<sup>4</sup>*19<sup>2</sup>)/(3*5<sup>2</sup>*7*11)
| {{Monzo|4 -1 -2 -1 -1 0 0 2}}
| {{monzo|4 -1 -2 -1 -1 0 0 2}}
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Line 900: Line 900:
| 0.2920
| 0.2920
| (7<sup>2</sup>*11<sup>2</sup>)/(2<sup>3</sup>*3*13*19)
| (7<sup>2</sup>*11<sup>2</sup>)/(2<sup>3</sup>*3*13*19)
| {{Monzo|-3 -1 0 2 2 -1 0 -1}}
| {{monzo|-3 -1 0 2 2 -1 0 -1}}
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Line 906: Line 906:
| 0.2893
| 0.2893
| (2<sup>5</sup>*11*17)/(3<sup>2</sup>*5*7*19)
| (2<sup>5</sup>*11*17)/(3<sup>2</sup>*5*7*19)
| {{Monzo|5 -2 -1 -1 1 0 1 -1}}
| {{monzo|5 -2 -1 -1 1 0 1 -1}}
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Line 912: Line 912:
| 0.2804
| 0.2804
| (5<sup>2</sup>*13*19)/(2*3<sup>2</sup>*7<sup>3</sup>)
| (5<sup>2</sup>*13*19)/(2*3<sup>2</sup>*7<sup>3</sup>)
| {{Monzo|-1 -2 2 -3 0 1 0 1}}
| {{monzo|-1 -2 2 -3 0 1 0 1}}
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Line 918: Line 918:
| 0.2524
| 0.2524
| (2<sup>2</sup>*5*7<sup>3</sup>)/(19<sup>3</sup>)
| (2<sup>2</sup>*5*7<sup>3</sup>)/(19<sup>3</sup>)
| {{Monzo|2 0 1 3 0 0 0 -3}}
| {{monzo|2 0 1 3 0 0 0 -3}}
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Line 924: Line 924:
| 0.1691
| 0.1691
| (7<sup>2</sup>*11*19)/(2<sup>11</sup>*5)
| (7<sup>2</sup>*11*19)/(2<sup>11</sup>*5)
| {{Monzo|-11 0 -1 2 1 0 0 1}}
| {{monzo|-11 0 -1 2 1 0 0 1}}
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Line 930: Line 930:
| 0.1599
| 0.1599
| (2*3*5*19<sup>2</sup>)/(7<sup>2</sup>*13*17)
| (2*3*5*19<sup>2</sup>)/(7<sup>2</sup>*13*17)
| {{Monzo|1 1 1 -2 0 -1 -1 2}}
| {{monzo|1 1 1 -2 0 -1 -1 2}}
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Line 936: Line 936:
| 0.1370
| 0.1370
| (2<sup>2</sup>*3<sup>5</sup>*13)/(5*7*19<sup>2</sup>)
| (2<sup>2</sup>*3<sup>5</sup>*13)/(5*7*19<sup>2</sup>)
| {{Monzo|2 5 -1 -1 0 1 0 -2}}
| {{monzo|2 5 -1 -1 0 1 0 -2}}
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Line 942: Line 942:
| 0.1294
| 0.1294
| (3*7<sup>3</sup>*13)/(2<sup>6</sup>*11*19)
| (3*7<sup>3</sup>*13)/(2<sup>6</sup>*11*19)
| {{Monzo|-6 1 0 3 -1 1 0 -1}}
| {{monzo|-6 1 0 3 -1 1 0 -1}}
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Line 948: Line 948:
| 0.1230
| 0.1230
| (2<sup>8</sup>*5*11)/(3*13*19<sup>2</sup>)
| (2<sup>8</sup>*5*11)/(3*13*19<sup>2</sup>)
| {{Monzo|8 -1 1 0 1 -1 0 -2}}
| {{monzo|8 -1 1 0 1 -1 0 -2}}
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Line 954: Line 954:
| 0.1205
| 0.1205
| (5*13<sup>2</sup>*17)/(2<sup>2</sup>*3<sup>3</sup>*7*19)
| (5*13<sup>2</sup>*17)/(2<sup>2</sup>*3<sup>3</sup>*7*19)
| {{Monzo|-2 -3 1 -1 0 1 1 -1}}
| {{monzo|-2 -3 1 -1 0 1 1 -1}}
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Line 960: Line 960:
| 0.07396
| 0.07396
| (3<sup>4</sup>*17<sup>2</sup>)/(2<sup>4</sup>*7*11*19)
| (3<sup>4</sup>*17<sup>2</sup>)/(2<sup>4</sup>*7*11*19)
| {{Monzo|-4 4 0 -1 -1 0 1 -1}}
| {{monzo|-4 4 0 -1 -1 0 1 -1}}
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Line 966: Line 966:
| 0.06306
| 0.06306
| (2<sup>6</sup>*3*11*17)/(5*17<sup>2</sup>*19)
| (2<sup>6</sup>*3*11*17)/(5*17<sup>2</sup>*19)
| {{Monzo|6 1 -1 0 1 0 -2 -1}}
| {{monzo|6 1 -1 0 1 0 -2 -1}}
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Line 972: Line 972:
| 0.05991
| 0.05991
| (2<sup>2</sup>*5<sup>2</sup>*17<sup>2</sup>)/(3<sup>2</sup>*13<sup>2</sup>*19)
| (2<sup>2</sup>*5<sup>2</sup>*17<sup>2</sup>)/(3<sup>2</sup>*13<sup>2</sup>*19)
| {{Monzo|2 -2 2 0 0 -2 2 -1}}
| {{monzo|2 -2 2 0 0 -2 2 -1}}
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Line 978: Line 978:
| 0.03963
| 0.03963
| (11<sup>2</sup>*19<sup>2</sup>)/(2<sup>5</sup>*3*5*7*13)
| (11<sup>2</sup>*19<sup>2</sup>)/(2<sup>5</sup>*3*5*7*13)
| {{Monzo|-5 -1 -1 -1 2 -1 0 2}}
| {{monzo|-5 -1 -1 -1 2 -1 0 2}}
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Line 984: Line 984:
| 0.01937
| 0.01937
| (2<sup>5</sup>*3*7<sup>2</sup>*19)/(5<sup>4</sup>*11*13)
| (2<sup>5</sup>*3*7<sup>2</sup>*19)/(5<sup>4</sup>*11*13)
| {{Monzo|5 1 -4 2 -1 -1 0 1}}
| {{monzo|5 1 -4 2 -1 -1 0 1}}
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Line 990: Line 990:
| 0.01649
| 0.01649
| (2<sup>4</sup>*3<sup>8</sup>)/(5<sup>2</sup>*13*17*19)
| (2<sup>4</sup>*3<sup>8</sup>)/(5<sup>2</sup>*13*17*19)
| {{Monzo|4 8 -2 0 0 0 -1 -1 -1}}
| {{monzo|4 8 -2 0 0 0 -1 -1 -1}}
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Line 996: Line 996:
| 0.01047
| 0.01047
| (2<sup>9</sup>*17*19)/(3<sup>3</sup>*5<sup>3</sup>*7<sup>2</sup>)
| (2<sup>9</sup>*17*19)/(3<sup>3</sup>*5<sup>3</sup>*7<sup>2</sup>)
| {{Monzo|9 -3 -3 -2 0 0 1 1}}
| {{monzo|9 -3 -3 -2 0 0 1 1}}
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Line 1,002: Line 1,002:
| 0.007590
| 0.007590
| (2<sup>8</sup>*3<sup>4</sup>*11)/(5*7<sup>4</sup>*19)
| (2<sup>8</sup>*3<sup>4</sup>*11)/(5*7<sup>4</sup>*19)
| {{Monzo|8 4 -1 -4 1 0 0 -1}}
| {{monzo|8 4 -1 -4 1 0 0 -1}}
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Line 1,008: Line 1,008:
| 0.002879
| 0.002879
| (2*7<sup>2</sup>*17*19<sup>2</sup>)/(3<sup>7</sup>*5<sup>2</sup>*11)
| (2*7<sup>2</sup>*17*19<sup>2</sup>)/(3<sup>7</sup>*5<sup>2</sup>*11)
| {{Monzo|2 -7 -2 2 -1 0 1 2}}
| {{monzo|2 -7 -2 2 -1 0 1 2}}
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Line 1,014: Line 1,014:
| 0.002733
| 0.002733
| (2<sup>2</sup>*7*11<sup>3</sup>*17)/(3<sup>3</sup>*5*13*19<sup>2</sup>)
| (2<sup>2</sup>*7*11<sup>3</sup>*17)/(3<sup>3</sup>*5*13*19<sup>2</sup>)
| {{Monzo|2 -3 -1 1 3 -1 1 -2}}
| {{monzo|2 -3 -1 1 3 -1 1 -2}}
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Line 1,020: Line 1,020:
| 0.002440
| 0.002440
| (2<sup>10</sup>*3<sup>2</sup>*7*11)/(13<sup>3</sup>*17*19)
| (2<sup>10</sup>*3<sup>2</sup>*7*11)/(13<sup>3</sup>*17*19)
| {{Monzo|10 2 0 1 1 -3 -1 -1}}
| {{monzo|10 2 0 1 1 -3 -1 -1}}
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Line 1,026: Line 1,026:
| 0.0002929
| 0.0002929
| (11<sup>2</sup>*13<sup>2</sup>*17<sup>2</sup>)/(2<sup>8</sup>*3<sup>5</sup>*5*19)
| (11<sup>2</sup>*13<sup>2</sup>*17<sup>2</sup>)/(2<sup>8</sup>*3<sup>5</sup>*5*19)
| {{Monzo|-8 -5 -1 0 2 2 2 -1}}
| {{monzo|-8 -5 -1 0 2 2 2 -1}}
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Line 1,032: Line 1,032:
| 0.0001460
| 0.0001460
| (7*13*19<sup>4</sup>)/(2*3<sup>4</sup>*5*11<sup>4</sup>)
| (7*13*19<sup>4</sup>)/(2*3<sup>4</sup>*5*11<sup>4</sup>)
| {{Monzo|-1 -4 -1 1 -4 1 0 4}}
| {{monzo|-1 -4 -1 1 -4 1 0 4}}
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Revision as of 12:18, 17 January 2021

This list of superparticular intervals ordered by prime limit. It reaches to the 101-limit and is complete up to the 19-limit.

Superparticular numbers are ratios of the form (n + 1)/n, or 1 + 1/n, where n is a whole number other than 1. They appear frequently in just intonation and harmonic series music. Adjacent tones in the harmonic series are separated by superparticular intervals: for instance, the 20th and 21st by the superparticular ratio 21/20. As the overtones get closer together, the superparticular intervals get smaller and smaller. Thus, an examination of the superparticular intervals is an examination of some of the simplest small intervals in rational tuning systems. Indeed, many but not all common commas are superparticular ratios.

The list below is ordered by harmonic limit, or the largest prime involved in the prime factorization. 36/35, for instance, is an interval of the 7-limit, as it factors to (22×32)/(5×7), while 37/36 would belong to the 37-limit.

Størmer's theorem states that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. OEIS: A002071 gives the number of superparticular ratios in each prime limit, OEIS: A145604 shows the increment from limit to limit, and OEIS: A117581 gives the largest numerator for each prime limit (with some exceptions, such as the 23-limit, where the largest value is smaller than that of a smaller prime limit, in this case the 19-limit).

See also gallery of just intervals. Many of the names below come from the Scala website.

Ratio Cents Factorization Monzo Name(s)
2-limit (complete)
2/1 1200.000 2/1 [1⟩ octave, duple; after octave reduction: (perfect) unison, unity, perfect prime, tonic
3-limit (complete)
3/2 701.955 3/2 [-1 1⟩ perfect fifth, 3rd harmonic (octave reduced), diapente
4/3 498.045 22/3 [2 -1⟩ perfect fourth, 3rd subharmonic (octave reduced), diatessaron
9/8 203.910 32/23 [-3 2⟩ (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced)
5-limit (complete)
5/4 386.314 5/22 [-2 0 1⟩ (classic) (5-limit) major third, 5th harmonic (octave reduced)
6/5 315.641 (2*3)/5 [1 1 -1⟩ (classic) (5-limit) minor third
10/9 182.404 (2*5)/32 [1 -2 1⟩ classic (whole) tone, classic major second, minor whole tone
16/15 111.731 24/(3*5) [4 -1 -1⟩ minor diatonic semitone, 15th subharmonic
25/24 70.672 52/(23*3) [-3 -1 2⟩ chroma, (classic) chromatic semitone, Zarlinian semitone
81/80 21.506 (3/2)4/5 [-4 4 -1⟩ syntonic comma, Didymus comma
7-limit (complete)
7/6 266.871 7/(2*3) [-1 -1 0 1⟩ (septimal) subminor third, septimal minor third
8/7 231.174 23/7 [3 0 0 -1⟩ (septimal) supermajor second, septimal whole tone, 7th subharmonic
15/14 119.443 (3*5)/(2*7) [-1 1 1 -1⟩ septimal diatonic semitone
21/20 84.467 (3*7)/(22*5) [-2 1 -1 1⟩ minor semitone, large septimal chroma
28/27 62.961 (22*7)/33 [2 -3 0 1⟩ septimal third-tone, small septimal chroma, (septimal) subminor second, septimal minor second, trienstonic comma
36/35 48.770 (22*33)/(5*7) [2 2 -1 -1⟩ septimal quarter tone, septimal diesis
49/48 35.697 72/(24*3) [-4 -1 0 2⟩ large septimal diesis, slendro diesis, septimal 1/6-tone
50/49 34.976 2*(5/7)2 [1 0 2 -2⟩ septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma
64/63 27.264 26/(32*7) [6 -2 0 -1⟩ septimal comma, Archytas' comma
126/125 13.795 (2*32*7)/53 [1 2 -3 1⟩ starling comma, septimal semicomma
225/224 7.7115 (3*5)2/(25*7) [-5 2 2 -1⟩ marvel comma, septimal kleisma
2401/2400 0.72120 74/(25*3*52) [-5 -1 -2 4⟩ breedsma
4375/4374 0.39576 (54*7)/(2*37) [-1 -7 4 1⟩ ragisma
11-limit (complete)
11/10 165.004 11/(2*5) [-1 0 -1 0 1⟩ (large) (undecimal) neutral second, 4/5-tone, Ptolemy's second
12/11 150.637 (22*3)/11 [2 1 0 0 -1⟩ (small) (undecimal) neutral second, 3/4-tone
22/21 80.537 (2*11)/(3*7) [1 -1 0 -1 1⟩ undecimal minor semitone
33/32 53.273 (3*11)/25 [-5 1 0 0 1⟩ undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced)
45/44 38.906 (3/2)2*(5/11) [-2 2 1 0 -1⟩ undecimal 1/5-tone
55/54 31.767 (5*11)/(2*33) [-1 -3 1 0 1⟩ undecimal diasecundal comma, eleventyfive comma
56/55 31.194 (23*7)/(5*11) [3 0 -1 1 -1⟩ undecimal tritonic comma, konbini comma
99/98 17.576 (3/7)2*(11/2) [-1 2 0 -2 1⟩ small undecimal comma, mothwellsma
100/99 17.399 (2*5/3)2/11) [2 -2 2 0 -1⟩ Ptolemy's comma, ptolemisma
121/120 14.376 112/(23*3*5) [-3 -1 -1 0 2⟩ undecimal seconds comma, biyatisma
176/175 9.8646 (24*11)/(52*7) [4 0 -2 -1 1⟩ valinorsma
243/242 7.1391 35/(2*112) [-1 5 0 0 -2⟩ neutral third comma, rastma
385/384 4.5026 (5*7*11)/(27*3) [-7 -1 1 1 1⟩ keenanisma
441/440 3.9302 (3*7)2/(23*5*11) [-3 2 -1 2 -1⟩ Werckmeister's undecimal septenarian schisma, werckisma
540/539 3.2090 (2/7)2*33*5/11 [2 3 1 -2 -1⟩ Swets' comma, swetisma
3025/3024 0.57240 (5*11)2/(24*32*7) [-4 -3 2 -1 2⟩ Lehmerisma
9801/9800 0.17665 (11/(5*7))2*34/23 [-3 4 -2 -2 2⟩ Gauss comma, kalisma
13-limit (complete)
13/12 138.573 13/(22*3) [-2 -1 0 0 0 1⟩ (large) tridecimal 2/3-tone, tridecimal neutral second
14/13 128.298 (2*7)/13 [1 0 0 1 0 -1⟩ (small) tridecimal 2/3-tone, trienthird
26/25 67.900 (2*13)/52 [1 0 -2 0 0 1⟩ (large) tridecimal 1/3-tone
27/26 65.337 33/(2*13) [-1 3 0 0 0 -1⟩ (small) tridecimal 1/3-tone
40/39 43.831 (23*5)/(3*13) [3 -1 1 0 0 -1⟩ tridecimal minor diesis
65/64 26.841 (5*13)/26 [-6 0 1 0 0 1⟩ wilsorma, 13th-partial chroma
66/65 26.432 (2*3*11)/(5*13) [1 1 -1 0 1 -1⟩ winmeanma
78/77 22.339 (2*3*13)/(7*11) [1 1 0 -1 -1 1⟩ negustma
91/90 19.130 (7*13)/(2*32*5) [-1 -2 -1 1 0 1⟩ Biome comma, superleap comma
105/104 16.567 (3*5*7)/(23*13) [-3 1 1 1 0 -1⟩ small tridecimal comma, animist comma
144/143 12.064 (22*3)2/(11*13) [4 2 0 0 -1 -1⟩ grossma
169/168 10.274 132/(23*3*7) [-3 -1 0 -1 0 2⟩ buzurgisma, dhanvantarisma
196/195 8.8554 (2*7)2/(3*5*13) [2 -1 -1 2 0 -1⟩ mynucuma
325/324 5.3351 (52*13)/(22*34) [-2 -4 2 0 0 1⟩ marveltwin comma
351/350 4.9393 (3/5)2*13/(2*7) [-1 3 -2 -1 0 1⟩ ratwolfsma
352/351 4.9253 (25*11)/(32*13) [5 -3 0 0 1 -1⟩ minthma
364/363 4.7627 (2/11)2*7*13/3 [2 -1 0 1 -2 1⟩ gentle comma
625/624 2.7722 (5/2)4/(3*13) [-4 -1 4 0 0 -1⟩ tunbarsma
676/675 2.5629 (2*13/5)2/33 [2 -3 -2 0 0 2⟩ island comma
729/728 2.3764 (32/2)3/(7*13) [-3 6 0 -1 0 -1⟩ squbema
1001/1000 1.7304 7*11*13/(2*5)3 [-3 0 -3 1 1 1⟩ sinbadma
1716/1715 1.0092 22*3*11*13/(5*73) [2 1 -1 -3 1 1⟩ lummic comma
2080/2079 0.83252 25*5*13/(33*7*11) [5 -3 1 -1 -1 1⟩ ibnsinma
4096/4095 0.42272 (26/3)2/(5*7*13) [12 -2 -1 -1 0 -1⟩ tridecimal schisma, Sagittal schismina
4225/4224 0.40981 (5*13)2/(27*3*11) [-7 -1 2 0 -1 2⟩ leprechaun comma
6656/6655 0.26012 (23/11)3*13/5 [9 0 -1 0 -3 1⟩ jacobin comma
10648/10647 0.16260 (2*11)3/((3*13)2*7) [3 -2 0 -1 3 -2⟩ harmonisma
123201/123200 0.014052 (3/2)6*(13/5)2/(7*11) [-6 6 -2 -1 -1 2⟩ chalmersia
17-limit (complete)
17/16 104.955 17/24 [-4 0 0 0 0 0 1⟩ large septendecimal semitone, 17th harmonic (octave reduced)
18/17 98.955 (2*32)/17 [1 2 0 0 0 0 -1⟩ small septendecimal semitone, Arabic lute index finger
34/33 51.682 (2*17)/(3*11) [1 -1 0 0 -1 0 1⟩ large septendecimal 1/4-tone
35/34 50.184 (5*7)/(2*17) [-1 0 1 1 0 0 -1⟩ small septendecimal 1/4-tone
51/50 34.283 (3*17)/(2*52) [-1 1 -2 0 0 0 1⟩ large septendecimal 1/6-tone
52/51 33.617 (22*13)/(3*17) [2 -1 0 0 0 1 -1⟩ small septendecimal 1/6-tone
85/84 20.488 (5*17)/(22*3*7) [-2 -1 1 -1 0 0 1⟩ septendecimal comma (?)
120/119 14.487 (23*3*5)/(7*17) [3 1 1 -1 0 0 -1⟩
136/135 12.777 (2/3)3*17/5 [3 -3 -1 0 0 0 1⟩ septendecimal major second comma
154/153 11.278 (2*7*11)/(32*17) [1 -2 0 1 1 0 -1⟩
170/169 10.214 (2*5*17)/132 [1 0 1 0 0 -2 1⟩
221/220 7.8514 (13*17)/(22*5*11) [-2 0 -1 0 -1 1 1⟩
256/255 6.7759 (28)/(3*5*17) [8 -1 -1 0 0 0 -1⟩ septendecimal kleisma, 255th subharmonic
273/272 6.3532 (3*7*13)/(24*17) [-4 1 0 1 0 1 -1⟩ tannisma
289/288 6.0008 (17/3)2/25 [-5 -2 0 0 0 0 2⟩ septendecimal 6-cent comma
375/374 4.6228 (3*53)/(2*11*17) [-1 1 3 0 -1 0 -1⟩
442/441 3.9213 (2*13*17)/(3*7)2 [1 -2 0 -2 0 1 1⟩
561/560 3.0887 (3*11*17)/(24*5*7) [-4 1 -1 -1 1 0 1⟩
595/594 2.9121 (5*7*17)/(2*33*11) [-1 -3 1 1 -1 0 1⟩
715/714 2.4230 (5*11*13)/(2*3*7*17) [-1 -1 1 -1 1 1 -1⟩
833/832 2.0796 (72*17)/(26*13) [-6 0 0 2 0 -1 1⟩
936/935 1.8506 (23*32*13)/(5*11*17) [3 2 -1 0 -1 1 -1⟩ ainos comma, ainma
1089/1088 1.5905 (32*112)/(26*17) [-6 2 0 0 2 0 -1⟩ twosquare comma
1156/1155 1.4983 (22*172)/(3*5*7*11) [2 -1 -1 -1 -1 0 2⟩
1225/1224 1.4138 (52*72)/(23*32*17) [-3 -2 2 2 0 0 -1⟩
1275/1274 1.3584 (3*52*17)/(2*72*13) [-1 1 2 -2 0 -1 1⟩
1701/1700 1.0181 (35*7)/[(2*5)2*17] [-2 5 -2 1 0 0 -1⟩
2058/2057 0.84143 (2*3*73)/(112*17) [1 1 0 3 -2 0 -1⟩ xenisma
2431/2430 0.71230 (11*13*17)/(2*35*5) [-1 -5 -1 0 1 1 1⟩
2500/2499 0.69263 (22*54)/(3*72*17) [2 -1 4 -2 0 0 -1⟩
2601/2600 0.66573 (32*172)/(23*52*13) [-3 2 -2 0 0 -1 2⟩
4914/4913 0.35234 (2*33*7*13)/(173) [1 3 0 1 0 1 -3⟩
5832/5831 0.29688 (23*36)/(73*17) [3 6 0 -3 0 0 -1⟩
12376/12375 0.13989 (23*7*13*17)/(32*53*11) [3 -2 -3 1 -1 1 1⟩ flashma
14400/14399 0.12023 (26*32*52)/(7*112*17) [6 2 2 -1 -2 0 -1⟩ sparkisma
28561/28560 0.060616 (134)/(24*3*5*7*17) [-4 -1 -1 -1 0 4 -1⟩
31213/31212 0.055466 (74*13)/(22*33*172) [-2 -3 0 4 0 1 -2⟩
37180/37179 0.046564 (22*5*11*132)/(37*17) [2 -7 1 0 1 2 -1⟩
194481/194480 0.008902 (34*74)/(24*5*11*13*17) [-4 4 -1 4 -1 -1 -1⟩ scintillisma
336141/336140 0.005150 (32*133*17)/(22*5*75) [-2 2 -1 -5 0 3 1⟩
19-limit (complete)
19/18 93.603 19/(2*32) [-1 -2 0 0 0 0 0 1⟩ large undevicesimal semitone
20/19 88.801 (22*5)/19 [2 0 1 0 0 0 0 -1⟩ small undevicesimal semitone
39/38 44.970 (3*13)/(2*19) [-1 1 0 0 0 1 0 -1⟩ undevicesimal 2/9-tone
57/56 30.642 (3*19)/(23*7) [-3 1 0 -1 0 0 0 1⟩ hendrix comma
76/75 22.931 (22*19)/(3*52) [2 -1 -2 0 0 0 0 1⟩ undevicesimal 1/9-tone (greater)
77/76 22.631 (7*11)/(22*19) [-2 0 0 1 1 0 0 -1⟩ undevicesimal 1/9-tone (lesser)
96/95 18.128 (25*3)/(5*19) [5 1 -1 0 0 0 0 -1⟩
133/132 13.066 (19*7)/(22*3*11) [-2 -1 0 1 -1 0 0 1⟩
153/152 11.352 (32*17)/(23*19) [-3 2 0 0 0 0 1 -1⟩
171/170 10.154 (32*19)/(2*5*17) [-1 2 -1 0 0 0 -1 1⟩
190/189 9.1358 (2*5*19)/(33*7) [1 -3 1 -1 0 0 0 1⟩
209/208 8.3033 (11*19)/(24*13) [-4 0 0 0 1 -1 0 1⟩ yama comma
210/209 8.2637 (2*3*5*7)/(11*19) [1 1 1 1 -1 0 0 -1⟩ spleen comma
286/285 6.0639 (2*11*13)/(3*5*19) [1 -1 -1 0 1 1 0 -1⟩
324/323 5.3516 (22*34)/(17*19) [2 4 0 0 0 0 -1 -1⟩
343/342 5.0547 74/(2*33*19) [-1 -2 0 3 0 0 0 -1⟩
361/360 4.8023 192/(23*32*5) [-3 -2 -1 0 0 0 0 2⟩ go comma
400/399 4.3335 (24*52)/(3*7*19) [4 -1 2 -1 0 0 0 -1⟩
456/455 3.8007 (23*3*19)/(5*7*13) [3 1 -1 -1 0 -1 0 1⟩
476/475 3.6409 (22*7*17)/(52*19) [2 0 -2 1 0 0 1 -1⟩
495/494 3.5010 (32*5*11)/(2*13*19) [-1 2 1 0 1 -1 0 -1⟩
513/512 3.3780 (33*19)/29 [-9 3 0 0 0 0 0 1⟩ undevicesimal comma, undevicesimal schisma, 513th harmonic
969/968 1.7875 (3*17*19)/(23*112) [-3 1 0 0 -2 0 1 1⟩
1216/1215 1.4243 (26*19)/(35*5) [6 -5 -1 0 0 0 0 1⟩ password comma, Eratosthenes' comma
1331/1330 1.3012 113/(2*5*7*19) [-1 0 -1 -1 3 0 0 -1⟩
1445/1444 1.1985 5*(17/(2*19))2 [-2 0 1 0 0 0 2 -2⟩
1521/1520 1.1386 (3*13)2/(24*5*19) [-4 2 -1 0 0 2 0 -1⟩
1540/1539 1.1245 (22*5*7*11)/(34*19) [2 -4 1 1 1 0 0 -1⟩
1729/1728 1.0016 (7*13*19)/(26*33) [-6 -3 0 1 0 1 0 1⟩
2376/2375 0.7288 (53*19)/(23*33*11) [-3 -3 3 0 -1 0 0 1⟩
2432/2431 0.7120 (11*13*17)/(27*19) [-7 0 0 0 1 1 1 -1⟩ Blumeyer comma
2926/2925 0.5918 (2*7*11*19)/(32*52*13) [1 -2 -2 1 1 -1 0 1⟩
3136/3135 0.5521 (26*72)/(3*5*11*19) [6 -1 -1 2 -1 0 0 -1⟩
3250/3249 0.5328 (2*53*13)/(32*192) [1 -2 3 0 0 1 0 -2⟩
4200/4199 0.4123 (23*3*52*7)/(13*17*19) [3 1 2 1 0 -1 -1 -1⟩
5776/5775 0.2998 (24*192)/(3*52*7*11) [4 -1 -2 -1 -1 0 0 2⟩
5929/5928 0.2920 (72*112)/(23*3*13*19) [-3 -1 0 2 2 -1 0 -1⟩
5985/5984 0.2893 (25*11*17)/(32*5*7*19) [5 -2 -1 -1 1 0 1 -1⟩
6175/6174 0.2804 (52*13*19)/(2*32*73) [-1 -2 2 -3 0 1 0 1⟩
6860/6859 0.2524 (22*5*73)/(193) [2 0 1 3 0 0 0 -3⟩
10241/10240 0.1691 (72*11*19)/(211*5) [-11 0 -1 2 1 0 0 1⟩
10830/10829 0.1599 (2*3*5*192)/(72*13*17) [1 1 1 -2 0 -1 -1 2⟩
12636/12635 0.1370 (22*35*13)/(5*7*192) [2 5 -1 -1 0 1 0 -2⟩
13377/13376 0.1294 (3*73*13)/(26*11*19) [-6 1 0 3 -1 1 0 -1⟩
14080/14079 0.1230 (28*5*11)/(3*13*192) [8 -1 1 0 1 -1 0 -2⟩
14365/14364 0.1205 (5*132*17)/(22*33*7*19) [-2 -3 1 -1 0 1 1 -1⟩
23409/23408 0.07396 (34*172)/(24*7*11*19) [-4 4 0 -1 -1 0 1 -1⟩
27456/27455 0.06306 (26*3*11*17)/(5*172*19) [6 1 -1 0 1 0 -2 -1⟩
28900/28899 0.05991 (22*52*172)/(32*132*19) [2 -2 2 0 0 -2 2 -1⟩
43681/43680 0.03963 (112*192)/(25*3*5*7*13) [-5 -1 -1 -1 2 -1 0 2⟩
89376/89375 0.01937 (25*3*72*19)/(54*11*13) [5 1 -4 2 -1 -1 0 1⟩
104976/104975 0.01649 (24*38)/(52*13*17*19) [4 8 -2 0 0 0 -1 -1 -1⟩
165376/165375 0.01047 (29*17*19)/(33*53*72) [9 -3 -3 -2 0 0 1 1⟩
228096/228095 0.007590 (28*34*11)/(5*74*19) [8 4 -1 -4 1 0 0 -1⟩
601426/601425 0.002879 (2*72*17*192)/(37*52*11) [2 -7 -2 2 -1 0 1 2⟩
633556/633555 0.002733 (22*7*113*17)/(33*5*13*192) [2 -3 -1 1 3 -1 1 -2⟩
709632/709631 0.002440 (210*32*7*11)/(133*17*19) [10 2 0 1 1 -3 -1 -1⟩
5909761/5909760 0.0002929 (112*132*172)/(28*35*5*19) [-8 -5 -1 0 2 2 2 -1⟩
11859211/11859210 0.0001460 (7*13*194)/(2*34*5*114) [-1 -4 -1 1 -4 1 0 4⟩
23-limit (incomplete)
23/22 76.956 23/(2*11) greater vicesimotertial semitone
24/23 73.681 (23*3)/23 small vicesimotertial semitone
46/45 38.051 (2*23)/(32*5) vicesimotertial 1/5-tone
69/68 25.274 (3*23)/(22*17) vicesimotertial 1/8-tone (greater)
70/69 24.910 (2*5*7)/(3*23) vicesimotertial 1/8-tone (lesser)
92/91 18.921 (22*23)/(7*13)
115/114 15.120 (5*23)/(2*3*19)
161/160 10.787 (7*23)/(25*5)
162/161 10.720 (2*34)/(7*23)
208/207 8.3433 (24*13)/(32*23)
231/230 7.5108 (3*7*11)/(2*5*23)
253/252 6.8564 (11*23)/((2*3)2*7)
276/275 6.2840 (22*3*23)/(52*11)
300/299 5.7804 ((2*5)2*3)/(13*23)
323/322 5.3682 (17*19)/(2*7*23)
391/390 4.4334 (17*23)/(2*3*5*13)
392/391 4.4221 (23*7*7)/(17*23)
460/459 3.7676 (22*5*23)/(33*17)
484/483 3.5806 (2*11)2/(3*7*23)
507/506 3.4180 (3*132)/(2*11*23)
529/528 3.2758 232/(24*3*11)
576/575 3.0082 (26*32)/(23*52)
29-limit (incomplete)
29/28 60.751 29/(22*7)
30/29 58.692 (2*3*5)/29
58/57 30.109 (2*29)/(3*19)
88/87 19.786 (23*11)/(3*29)
116/115 14.989 (22*29)/(5*23)
117/116 14.860 (33*13)/(22*29)
145/144 11.981 (5*29)/(24*32)
31-limit (incomplete)
31/30 56.767 31/(2*3*5)
32/31 54.964 25/31 31st subharmonic
63/62 27.700 (32*7)/(2*31)
93/92 18.716 (3*31)/(22*23)
125/124 13.906 (53)/(22*31) Twizzler
37-limit (incomplete)
37/36 47.434 37/(22*32)
38/37 46.169 (2*19)/37
75/74 23.238 (3*52)/(2*37)
41-limit (incomplete)
41/40 42.749 41/(23*5)
42/41 41.719 (2*3*7)/41
82/81 21.242 (2*41)/34
43-limit (incomplete)
43/42 40.737 43/(2*3*7)
44/43 39.800 (22*11)/43
86/85 20.249 (2*43)/(5*17)
87/86 20.014 (3*29)/(2*43)
47-limit (incomplete)
47/46 37.232 47/(2*23)
48/47 36.448 (24*3)/47
94/93 18.516 (2*47)/(3*31)
95/94 18.320 (5*19)/(2*47)
53-limit (incomplete)
53/52 32.977 53/(22*13)
54/53 32.360 (2*33)/53
59-limit (incomplete)
59/58 29.594 59/(2*29)
60/59 29.097 (22*3*5)/59
61-limit (incomplete)
61/60 28.616 61/(22*3*5)
62/61 28.151 (2*31)/61
67-limit (incomplete)
67/66 26.034 67/(2*3*11)
68/67 25.648 (22*17)/67
71-limit (incomplete)
71/70 24.557 71/(2*5*7)
72/71 24.213 (23*32)/71
73-limit (incomplete)
73/72 23.879 73/(23*32)
74/73 23.555 (2*37)/73
79-limit (incomplete)
79/78 22.054 79/(2*3*13)
80/79 21.777 (24*5)/79
83-limit (incomplete)
83/82 20.985 83/(2*41)
84/83 20.734 (22*3*7)/83
89-limit (incomplete)
89/88 19.562 89/(23*11)
90/89 19.344 (2*32*5)/89
97-limit (incomplete)
97/96 17.940 97/(25*3)
98/97 17.756 (2*72)/97
101-limit (incomplete)
101/100 17.226 101/(22*52)
102/101 17.057 (2*3*17)/101
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