List of superparticular intervals: Difference between revisions

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This is a list of [[superparticular]] [[interval]]s ordered by [[prime limit]]. It reaches to the 101-limit and is complete up to the [[23-limit]].
This is a list of [[superparticular]] [[interval]]s ordered by [[prime limit]]. It reaches to the 101-limit and is complete up to the [[23-limit]].


[[Wikipedia:Størmer's theorem|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).
[[Wikipedia: Størmer's theorem|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).


== List of superparticular intervals ==
== List of superparticular intervals ==
{| class="wikitable"
{| class="wikitable"
|-
|-
! Ratio
! [[Ratio]]
! Cents
! [[Cent]]s
! Factorization
! Factorization
! [[Monzo]]
! [[Monzo]]
Line 19: Line 19:
| 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 28: Line 28:
| 701.955
| 701.955
| 3/2
| 3/2
| {{monzo|-1 1}}
| {{Monzo| -1 1 }}
| [[perfect fifth]], octave-reduced 3rd harmonic, diapente
| Perfect fifth, octave-reduced 3rd harmonic, diapente
|
|
|-
|-
Line 35: Line 35:
| 498.045
| 498.045
| 2<sup>2</sup>/3
| 2<sup>2</sup>/3
| {{monzo|2 -1}}
| {{Monzo| 2 -1 }}
| perfect fourth, octave-reduced 3rd subharmonic, diatessaron
| Perfect fourth, octave-reduced 3rd subharmonic, diatessaron
| S2
| S2
|-
|-
Line 51: Line 51:
| 386.314
| 386.314
| 5/2<sup>2</sup>
| 5/2<sup>2</sup>
| {{monzo|-2 0 1}}
| {{Monzo| -2 0 1 }}
| classic(al)/just major third, octave-reduced 5th harmonic
| Classic(al)/just major third, octave-reduced 5th harmonic
|
|
|-
|-
Line 58: Line 58:
| 315.641
| 315.641
| (2*3)/5
| (2*3)/5
| {{monzo|1 1 -1}}
| {{Monzo| 1 1 -1 }}
| classic(al)/just minor third
| Classic(al)/just minor third
|
|
|-
|-
Line 65: Line 65:
| 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(al) (whole) tone, classic major second, minor whole tone
| Classic(al) (whole) tone, classic major second, minor whole tone
|
|
|-
|-
Line 72: Line 72:
| 111.731
| 111.731
| 2<sup>4</sup>/(3*5)
| 2<sup>4</sup>/(3*5)
| {{monzo|4 -1 -1}}
| {{Monzo| 4 -1 -1 }}
| classic(al)/just diatonic semitone, 15th subharmonic
| Classic(al)/just diatonic semitone, 15th subharmonic
| S4
| S4
|-
|-
Line 79: Line 79:
| 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 }}
| classic(al)/just chromatic semitone, chroma, Zarlinian semitone
| Classic(al)/just chromatic semitone, chroma, Zarlinian semitone
| S5
| S5
|-
|-
Line 86: Line 86:
| 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
| S9
| S9
|-
|-
Line 95: Line 95:
| 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 102: Line 102:
| 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, octave-reduced 7th subharmonic
| (Septimal) supermajor second, septimal whole tone, octave-reduced 7th subharmonic
|
|
|-
|-
Line 109: Line 109:
| 119.443
| 119.443
| (3*5)/(2*7)
| (3*5)/(2*7)
| {{monzo|-1 1 1 -1}}
| {{Monzo| -1 1 1 -1 }}
| septimal major semitone, septimal diatonic semitone
| Septimal major semitone, septimal diatonic semitone
|
|
|-
|-
Line 116: Line 116:
| 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 }}
| septimal minor semitone, large septimal chroma
| Septimal minor semitone, large septimal chroma
|
|
|-
|-
Line 123: Line 123:
| 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 1/3-tone, small septimal chroma, (septimal) subminor second, septimal minor second, trienstonic comma
| Septimal 1/3-tone, small septimal chroma, (septimal) subminor second, septimal minor second, trienstonic comma
|
|
|-
|-
Line 130: Line 130:
| 48.770
| 48.770
| (2<sup>2</sup>*3<sup>2</sup>)/(5*7)
| (2<sup>2</sup>*3<sup>2</sup>)/(5*7)
| {{monzo|2 2 -1 -1}}
| {{Monzo| 2 2 -1 -1 }}
| septimal 1/4-tone, septimal diesis
| Septimal 1/4-tone, septimal diesis
| S6
| S6
|-
|-
Line 137: Line 137:
| 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 }}
| slendro diesis, large septimal diesis, large septimal 1/6-tone
| Slendro diesis, large septimal diesis, large septimal 1/6-tone
| S7
| S7
|-
|-
Line 144: Line 144:
| 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 }}
| jubilisma, tritonic diesis, small septimal diesis, small septimal 1/6-tone
| Jubilisma, tritonic diesis, small septimal diesis, small septimal 1/6-tone
|
|
|-
|-
Line 151: Line 151:
| 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
| S8
| S8
|-
|-
Line 158: Line 158:
| 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 165: Line 165:
| 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
| S15
| S15
|-
|-
Line 172: Line 172:
| 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
| S49
| S49
|-
|-
Line 179: Line 179:
| 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 188: Line 188:
| 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, undecimal submajor second, Ptolemy's second
| (Large) undecimal neutral second, undecimal submajor second, Ptolemy's second
|
|
|-
|-
Line 195: Line 195:
| 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
| (Small) undecimal neutral second
|
|
|-
|-
Line 202: Line 202:
| 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 209: Line 209:
| 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 1/4-tone, undecimal diesis, al-Farabi's 1/4-tone, octave-reduced 33rd harmonic
| Undecimal 1/4-tone, undecimal diesis, al-Farabi's 1/4-tone, octave-reduced 33rd harmonic
|
|
|-
|-
Line 216: Line 216:
| 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 223: Line 223:
| 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 }}
| telepathma, eleventyfive comma, undecimal diasecundal comma
| Telepathma, eleventyfive comma, undecimal diasecundal comma
|
|
|-
|-
Line 230: Line 230:
| 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 237: Line 237:
| 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 }}
| mothwellsma, small undecimal comma
| Mothwellsma, small undecimal comma
|
|
|-
|-
Line 244: Line 244:
| 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 }}
| ptolemisma, Ptolemy's comma
| Ptolemisma, Ptolemy's comma
| S10
| S10
|-
|-
Line 251: Line 251:
| 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 }}
| biyatisma, undecimal seconds comma
| Biyatisma, undecimal seconds comma
| S11
| S11
|-
|-
Line 258: Line 258:
| 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 265: Line 265:
| 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 }}
| rastma, neutral thirds comma
| Rastma, neutral thirds comma
|
|
|-
|-
Line 272: Line 272:
| 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 279: Line 279:
| 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 }}
| werckisma, Werckmeister's undecimal septenarian schisma
| Werckisma, Werckmeister's undecimal septenarian schisma
| S21
| S21
|-
|-
Line 286: Line 286:
| 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 }}
| swetisma, Swets' comma
| Swetisma, Swets' comma
|
|
|-
|-
Line 293: Line 293:
| 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
| S55
| S55
|-
|-
Line 300: Line 300:
| 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 }}
| kalisma, Gauss comma
| Kalisma, Gauss comma
| S99
| S99
|-
|-
Line 309: Line 309:
| 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 316: Line 316:
| 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 323: Line 323:
| 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 330: Line 330:
| 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 337: Line 337:
| 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 344: Line 344:
| 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 351: Line 351:
| 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 358: Line 358:
| 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 365: Line 365:
| 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 }}
| Biome comma, superleap comma
| Biome comma, superleap comma
|
|
Line 372: Line 372:
| 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 }}
| animist comma, small tridecimal comma
| Animist comma, small tridecimal comma
|
|
|-
|-
Line 379: Line 379:
| 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
| S12
| S12
|-
|-
Line 386: Line 386:
| 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
| S13
| S13
|-
|-
Line 393: Line 393:
| 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 }}
| mynucuma
| Mynucuma
| S14
| S14
|-
|-
Line 400: Line 400:
| 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 comma
| Marveltwin comma
|
|
|-
|-
Line 407: Line 407:
| 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 414: Line 414:
| 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 421: Line 421:
| 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 428: Line 428:
| 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
| S25
| S25
|-
|-
Line 435: Line 435:
| 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
| S26
| S26
|-
|-
Line 442: Line 442:
| 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
| S27
| S27
|-
|-
Line 449: Line 449:
| 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 456: Line 456:
| 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 463: Line 463:
| 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 470: Line 470:
| 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 }}
| schismina, tridecimal schisma
| Schismina, tridecimal schisma
| S65
| S65
|-
|-
Line 477: Line 477:
| 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
| S66
| S66
|-
|-
Line 484: Line 484:
| 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 491: Line 491:
| 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 498: Line 498:
| 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
| S351
| S351
|-
|-
Line 507: Line 507:
| 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, octave-reduced 17th harmonic
| Large septendecimal semitone, octave-reduced 17th harmonic
|
|
|-
|-
Line 514: Line 514:
| 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 521: Line 521:
| 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 528: Line 528:
| 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 535: Line 535:
| 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 542: Line 542:
| 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 549: Line 549:
| 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 556: Line 556:
| 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 }}
| lynchisma
| Lynchisma
|
|
|-
|-
| 136/135
| [[136/135]]
| 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 570: Line 570:
| 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 577: Line 577:
| 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 584: Line 584:
| 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 591: Line 591:
| 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, octave-reduced 255th subharmonic
| Septendecimal kleisma, octave-reduced 255th subharmonic
| S16
| S16
|-
|-
Line 598: Line 598:
| 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 605: Line 605:
| 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 }}
| semitonisma
| Semitonisma
| S17
| S17
|-
|-
Line 612: Line 612:
| 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 }}
| ursulisma
| Ursulisma
|  
|  
|-
|-
Line 619: Line 619:
| 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 626: Line 626:
| 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 633: Line 633:
| 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 }}
| dakotisma
| Dakotisma
|  
|  
|-
|-
Line 640: Line 640:
| 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 }}
| september comma, septembrisma
| September comma, septembrisma
|
|
|-
|-
Line 647: Line 647:
| 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 }}
| horizma, horizon comma
| Horizma, horizon comma
|
|
|-
|-
Line 654: Line 654:
| 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 661: Line 661:
| 1.5905
| 1.5905
| (3*11)<sup>2</sup>/(2<sup>6</sup>*17)
| (3*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
| S33
| S33
|-
|-
Line 668: Line 668:
| 1.4983
| 1.4983
| (2*17)<sup>2</sup>/(3*5*7*11)
| (2*17)<sup>2</sup>/(3*5*7*11)
| {{monzo|2 -1 -1 -1 -1 0 2}}
| {{Monzo| 2 -1 -1 -1 -1 0 2 }}
| quadrantonisma
| Quadrantonisma
| S34
| S34
|-
|-
Line 675: Line 675:
| 1.4138
| 1.4138
| (5*7)<sup>2</sup>/(2<sup>3</sup>*3<sup>2</sup>*17)
| (5*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 }}
| noellisma
| Noellisma
| S35
| S35
|-
|-
Line 682: Line 682:
| 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 689: Line 689:
| 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 }}
| palingenetic comma, palingenesis
| Palingenetic comma, palingenesis
|
|
|-
|-
Line 696: Line 696:
| 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 703: Line 703:
| 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 710: Line 710:
| 0.69263
| 0.69263
| (2*5<sup>2</sup>)<sup>2</sup>/(3*7<sup>2</sup>*17)
| (2*5<sup>2</sup>)<sup>2</sup>/(3*7<sup>2</sup>*17)
| {{monzo|2 -1 4 -2 0 0 -1}}
| {{Monzo| 2 -1 4 -2 0 0 -1 }}
| sperasma
| Sperasma
| S50
| S50
|-
|-
Line 717: Line 717:
| 0.66573
| 0.66573
| (3*17)<sup>2</sup>/(2<sup>3</sup>*5<sup>2</sup>*13)
| (3*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 }}
| sextantonisma
| Sextantonisma
| S51
| S51
|-
|-
Line 724: Line 724:
| 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 731: Line 731:
| 0.29688
| 0.29688
| (2*3<sup>2</sup>)<sup>3</sup>/(7<sup>3</sup>*17)
| (2*3<sup>2</sup>)<sup>3</sup>/(7<sup>3</sup>*17)
| {{monzo|3 6 0 -3 0 0 -1}}
| {{Monzo| 3 6 0 -3 0 0 -1 }}
| chlorisma
| Chlorisma
|
|
|-
|-
| [[flashma|12376/12375]]
| [[Flashma|12376/12375]]
| 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
|
|
|-
|-
| [[sparkisma|14400/14399]]
| [[Sparkisma|14400/14399]]
| 0.12023
| 0.12023
| (2<sup>3</sup>*3*5)<sup>2</sup>/(7*11<sup>2</sup>*17)
| (2<sup>3</sup>*3*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
| S120
| S120
|-
|-
Line 752: Line 752:
| 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 }}
|  
|  
| S169
| S169
Line 759: Line 759:
| 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 766: Line 766:
| 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 773: Line 773:
| 0.008902
| 0.008902
| (3*7)<sup>4</sup>/(2<sup>4</sup>*5*11*13*17)
| (3*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
| S441
| S441
|-
|-
Line 780: Line 780:
| 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 789: Line 789:
| 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 796: Line 796:
| 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 803: Line 803:
| 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 810: Line 810:
| 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 817: Line 817:
| 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 }}
| large undevicesimal 1/9-tone
| Large undevicesimal 1/9-tone
|
|
|-
|-
Line 824: Line 824:
| 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 }}
| small undevicesimal 1/9-tone
| Small undevicesimal 1/9-tone
|
|
|-
|-
Line 831: Line 831:
| 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 }}
| 19th-partial chroma
| 19th-partial chroma
|
|
Line 838: Line 838:
| 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 845: Line 845:
| 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 }}
| ganassisma, Ganassi's comma
| Ganassisma, Ganassi's comma
|
|
|-
|-
Line 852: Line 852:
| 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 859: Line 859:
| 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 866: Line 866:
| 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 873: Line 873:
| 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 880: Line 880:
| 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 887: Line 887:
| 5.3516
| 5.3516
| (2*3<sup>2</sup>)<sup>2</sup>/(17*19)
| (2*3<sup>2</sup>)<sup>2</sup>/(17*19)
| {{monzo|2 4 0 0 0 0 -1 -1}}
| {{Monzo| 2 4 0 0 0 0 -1 -1 }}
| nusu comma
| Nusu comma
| S18
| S18
|-
|-
Line 894: Line 894:
| 5.0547
| 5.0547
| 7<sup>3</sup>/(2*3<sup>2</sup>*19)
| 7<sup>3</sup>/(2*3<sup>2</sup>*19)
| {{monzo|-1 -2 0 3 0 0 0 -1}}
| {{Monzo| -1 -2 0 3 0 0 0 -1 }}
|  
|  
|
|
Line 901: Line 901:
| 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
| S19
| S19
|-
|-
Line 908: Line 908:
| 4.3335
| 4.3335
| (2<sup>2</sup>*5)<sup>2</sup>/(3*7*19)
| (2<sup>2</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 }}
|  
|  
| S20
| S20
Line 915: Line 915:
| 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 922: Line 922:
| 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 929: Line 929:
| 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 936: Line 936:
| 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, Boethius' comma, 513th harmonic
| Undevicesimal comma, undevicesimal schisma, Boethius' comma, 513th harmonic
|
|
|-
|-
Line 943: Line 943:
| 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 }}
|  
|  
|
|
Line 950: Line 950:
| 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
|
|
|-
|-
Line 957: Line 957:
| 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 }}
|  
|  
|
|
Line 964: Line 964:
| 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 }}
| aureusma
| Aureusma
|
|
|-
|-
Line 971: Line 971:
| 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 }}
| pinkanberry
| Pinkanberry
| S39
| S39
|-
|-
Line 978: Line 978:
| 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 }}
|  
|  
|
|
Line 985: Line 985:
| 1.0016
| 1.0016
| (7*13*19)/(2<sup>2</sup>*3)<sup>3</sup>
| (7*13*19)/(2<sup>2</sup>*3)<sup>3</sup>
| {{monzo|-6 -3 0 1 0 1 0 1}}
| {{Monzo| -6 -3 0 1 0 1 0 1 }}
| ramanujanisma
| Ramanujanisma
|
|
|-
|-
Line 992: Line 992:
| 0.7288
| 0.7288
| (2<sup>3</sup>*3<sup>3</sup>*11)/(5<sup>3</sup>*19)
| (2<sup>3</sup>*3<sup>3</sup>*11)/(5<sup>3</sup>*19)
| {{monzo|3 3 -3 0 1 0 0 -1}}
| {{Monzo| 3 3 -3 0 1 0 0 -1 }}
|  
|  
|
|
Line 999: Line 999:
| 0.7120
| 0.7120
| (2<sup>7</sup>*19)/(11*13*17)
| (2<sup>7</sup>*19)/(11*13*17)
| {{monzo|7 0 0 0 -1 -1 -1 1}}
| {{Monzo| 7 0 0 0 -1 -1 -1 1 }}
| Blumeyer comma
| Blumeyer comma
|
|
Line 1,006: Line 1,006:
| 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 }}
|  
|  
|
|
Line 1,013: Line 1,013:
| 0.5521
| 0.5521
| (2<sup>3</sup>*7)<sup>2</sup>/(3*5*11*19)
| (2<sup>3</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 }}
|  
|  
| S56
| S56
Line 1,020: Line 1,020:
| 0.5328
| 0.5328
| (2*5<sup>3</sup>*13)/(3*19)<sup>2</sup>
| (2*5<sup>3</sup>*13)/(3*19)<sup>2</sup>
| {{monzo|1 -2 3 0 0 1 0 -2}}
| {{Monzo| 1 -2 3 0 0 1 0 -2 }}
|  
|  
|
|
Line 1,027: Line 1,027:
| 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 }}
|  
|  
|
|
Line 1,034: Line 1,034:
| 0.2998
| 0.2998
| (2<sup>2</sup>*19)<sup>2</sup>/(3*5<sup>2</sup>*7*11)
| (2<sup>2</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 }}
|  
|  
| S76
| S76
Line 1,041: Line 1,041:
| 0.2920
| 0.2920
| (7*11)<sup>2</sup>/(2<sup>3</sup>*3*13*19)
| (7*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 }}
|  
|  
| S77
| S77
Line 1,048: Line 1,048:
| 0.2893
| 0.2893
| (3<sup>2</sup>*5*7*19)/(2<sup>5</sup>*11*17)
| (3<sup>2</sup>*5*7*19)/(2<sup>5</sup>*11*17)
| {{monzo|-5 2 1 1 -1 0 -1 1}}
| {{Monzo| -5 2 1 1 -1 0 -1 1 }}
|  
|  
|
|
Line 1,055: Line 1,055:
| 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 }}
|  
|  
|
|
Line 1,062: Line 1,062:
| 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 }}
|  
|  
|
|
Line 1,069: Line 1,069:
| 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 }}
|  
|  
|
|
Line 1,076: Line 1,076:
| 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 }}
|  
|  
|
|
Line 1,083: Line 1,083:
| 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 }}
|  
|  
|
|
Line 1,090: Line 1,090:
| 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 }}
|  
|  
|
|
Line 1,097: Line 1,097:
| 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 }}
|  
|  
|
|
Line 1,104: Line 1,104:
| 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 }}
|  
|  
|
|
Line 1,111: Line 1,111:
| 0.07396
| 0.07396
| (3<sup>2</sup>*17)<sup>2</sup>/(2<sup>4</sup>*7*11*19)
| (3<sup>2</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 }}
|  
|  
| S153
| S153
Line 1,118: Line 1,118:
| 0.06306
| 0.06306
| (2<sup>6</sup>*3*11)/(5*17<sup>2</sup>*19)
| (2<sup>6</sup>*3*11)/(5*17<sup>2</sup>*19)
| {{monzo|6 1 -1 0 1 0 -2 -1}}
| {{Monzo| 6 1 -1 0 1 0 -2 -1 }}
|  
|  
|
|
Line 1,125: Line 1,125:
| 0.05991
| 0.05991
| (2*5*17)<sup>2</sup>/(3<sup>2</sup>*13<sup>2</sup>*19)
| (2*5*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 }}
|  
|  
| S170
| S170
Line 1,132: Line 1,132:
| 0.03963
| 0.03963
| (11*19)<sup>2</sup>/(2<sup>5</sup>*3*5*7*13)
| (11*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 }}
|  
|  
| S209
| S209
Line 1,139: Line 1,139:
| 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 }}
|  
|  
|
|
Line 1,146: Line 1,146:
| 0.01649
| 0.01649
| (2*3<sup>2</sup>)<sup>4</sup>/(5<sup>2</sup>*13*17*19)
| (2*3<sup>2</sup>)<sup>4</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 }}
|  
|  
| S324
| S324
Line 1,153: Line 1,153:
| 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 }}
| decimillisma
| Decimillisma
|
|
|-
|-
Line 1,160: Line 1,160:
| 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 }}
|  
|  
|
|
Line 1,167: Line 1,167:
| 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|1 -7 -2 2 -1 0 1 2}}
| {{Monzo| 1 -7 -2 2 -1 0 1 2 }}
|  
|  
|
|
Line 1,174: Line 1,174:
| 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 }}
|  
|  
|
|
Line 1,181: Line 1,181:
| 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 }}
|  
|  
|
|
Line 1,188: Line 1,188:
| 0.0002929
| 0.0002929
| (11*13*17)<sup>2</sup>/(2<sup>8</sup>*3<sup>5</sup>*5*19)
| (11*13*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 }}
|  
|  
| S2431
| S2431
Line 1,195: Line 1,195:
| 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 }}
|  
|  
|
|
Line 1,205: Line 1,205:
| 23/(2*11)
| 23/(2*11)
| {{Monzo| -1 0 0 0 -1 0 0 0 1 }}
| {{Monzo| -1 0 0 0 -1 0 0 0 1 }}
| greater vicesimotertial semitone
| Greater vicesimotertial semitone
|
|
|-
|-
Line 1,212: Line 1,212:
| (2<sup>3</sup>*3)/23
| (2<sup>3</sup>*3)/23
| {{Monzo| 3 1 0 0 0 0 0 0 -1 }}
| {{Monzo| 3 1 0 0 0 0 0 0 -1 }}
| small vicesimotertial semitone
| Small vicesimotertial semitone
|
|
|-
|-
Line 1,219: Line 1,219:
| (2*23)/(3<sup>2</sup>*5)
| (2*23)/(3<sup>2</sup>*5)
| {{Monzo| 1 -2 -1 0 0 0 0 0 1 }}
| {{Monzo| 1 -2 -1 0 0 0 0 0 1 }}
| vicesimotertial 1/5-tone
| Vicesimotertial 1/5-tone
|
|
|-
|-
Line 1,226: Line 1,226:
| (3*23)/(2<sup>2</sup>*17)
| (3*23)/(2<sup>2</sup>*17)
| {{Monzo| -2 1 0 0 0 0 -1 0 1 }}
| {{Monzo| -2 1 0 0 0 0 -1 0 1 }}
| large vicesimotertial 1/8-tone
| Large vicesimotertial 1/8-tone
|
|
|-
|-
Line 1,233: Line 1,233:
| (2*5*7)/(3*23)
| (2*5*7)/(3*23)
| {{Monzo| 1 -1 1 1 0 0 0 0 -1 }}
| {{Monzo| 1 -1 1 1 0 0 0 0 -1 }}
| small vicesimotertial 1/8-tone
| Small vicesimotertial 1/8-tone
|
|
|-
|-
Line 1,725: Line 1,725:
| 29/(2<sup>2</sup>*7)
| 29/(2<sup>2</sup>*7)
|  
|  
| Large vicesimononal 1/4 tone
| Large vicesimononal 1/4-tone
|
|
|-
|-
Line 1,732: Line 1,732:
| (2*3*5)/29
| (2*3*5)/29
|  
|  
| Small vicesimononal 1/4 tone
| Small vicesimononal 1/4-tone
|
|
|-
|-
Line 1,874: Line 1,874:
| 31/(2*3*5)
| 31/(2*3*5)
|  
|  
| large tricesimoprimal 1/4-tone
| Large tricesimoprimal quartertone
|
|
|-
|-
Line 1,881: Line 1,881:
| 2<sup>5</sup>/31
| 2<sup>5</sup>/31
|  
|  
| small tricesimoprimal 1/4-tone, 31st subharmonic
| Small tricesimoprimal quartertone, 31st subharmonic
|
|
|-
|-
Line 1,902: Line 1,902:
| (5<sup>3</sup>)/(2<sup>2</sup>*31)
| (5<sup>3</sup>)/(2<sup>2</sup>*31)
|  
|  
| twizzler
| Twizzler
|
|
|-
|-
Line 1,909: Line 1,909:
| (3³*23)/(2²*5*31)
| (3³*23)/(2²*5*31)
|
|
| owowhatsthisma
| Owowhatsthisma
|
|
|-
|-
Line 1,916: Line 1,916:
| (3<sup>4</sup>*7<sup>2</sup>)/(2<sup>7</sup>*31)
| (3<sup>4</sup>*7<sup>2</sup>)/(2<sup>7</sup>*31)
|  
|  
| yunzee comma
| Yunzee comma
| S63
| S63
|-
|-
Line 1,925: Line 1,925:
| 37/(2<sup>2</sup>*3<sup>2</sup>)
| 37/(2<sup>2</sup>*3<sup>2</sup>)
|  
|  
| Large 37-limit quarter tone, 37th-partial chroma
| Large 37-limit quartertone, 37th-partial chroma
|
|
|-
|-
Line 1,932: Line 1,932:
| (2*19)/37
| (2*19)/37
|  
|  
| Small 37-limit quarter tone
| Small 37-limit quartertone
|
|
|-
|-
Line 1,948: Line 1,948:
| 41/(2<sup>3</sup>*5)
| 41/(2<sup>3</sup>*5)
|  
|  
| Large 41-limit fifth tone
| Large 41-limit fifth-tone
|
|
|-
|-
Line 1,955: Line 1,955:
| (2*3*7)/41
| (2*3*7)/41
|  
|  
| Small 41-limit fifth tone
| Small 41-limit fifth-tone
|
|
|-
|-
Line 1,971: Line 1,971:
| 43/(2*3*7)
| 43/(2*3*7)
|  
|  
| Large 43-limit fifth tone
| Large 43-limit fifth-tone
|
|
|-
|-
Line 1,978: Line 1,978:
| (2<sup>2</sup>*11)/43
| (2<sup>2</sup>*11)/43
|  
|  
| Small 43-limit fifth tone
| Small 43-limit fifth-tone
|
|
|-
|-
Line 1,999: Line 1,999:
| (3*43)/2<sup>7
| (3*43)/2<sup>7
|  
|  
|43rd-partial chroma
| 43rd-partial chroma
|
|
|-
|-

Revision as of 08:04, 18 May 2023

This is a list of superparticular intervals ordered by prime limit. It reaches to the 101-limit and is complete up to the 23-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).

List of superparticular intervals

Ratio Cents Factorization Monzo Name(s) Meta[1]
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, octave-reduced 3rd harmonic, diapente
4/3 498.045 22/3 [2 -1⟩ Perfect fourth, octave-reduced 3rd subharmonic, diatessaron S2
9/8 203.910 32/23 [-3 2⟩ (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, octave-reduced 9th harmonic or harmonic ninth S3
5-limit (complete)
5/4 386.314 5/22 [-2 0 1⟩ Classic(al)/just major third, octave-reduced 5th harmonic
6/5 315.641 (2*3)/5 [1 1 -1⟩ Classic(al)/just minor third
10/9 182.404 (2*5)/32 [1 -2 1⟩ Classic(al) (whole) tone, classic major second, minor whole tone
16/15 111.731 24/(3*5) [4 -1 -1⟩ Classic(al)/just diatonic semitone, 15th subharmonic S4
25/24 70.672 52/(23*3) [-3 -1 2⟩ Classic(al)/just chromatic semitone, chroma, Zarlinian semitone S5
81/80 21.506 (3/2)4/5 [-4 4 -1⟩ Syntonic comma, Didymus comma S9
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, octave-reduced 7th subharmonic
15/14 119.443 (3*5)/(2*7) [-1 1 1 -1⟩ Septimal major semitone, septimal diatonic semitone
21/20 84.467 (3*7)/(22*5) [-2 1 -1 1⟩ Septimal minor semitone, large septimal chroma
28/27 62.961 (22*7)/33 [2 -3 0 1⟩ Septimal 1/3-tone, small septimal chroma, (septimal) subminor second, septimal minor second, trienstonic comma
36/35 48.770 (22*32)/(5*7) [2 2 -1 -1⟩ Septimal 1/4-tone, septimal diesis S6
49/48 35.697 72/(24*3) [-4 -1 0 2⟩ Slendro diesis, large septimal diesis, large septimal 1/6-tone S7
50/49 34.976 2*(5/7)2 [1 0 2 -2⟩ Jubilisma, tritonic diesis, small septimal diesis, small septimal 1/6-tone
64/63 27.264 26/(32*7) [6 -2 0 -1⟩ Septimal comma, Archytas' comma S8
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 S15
2401/2400 0.72120 74/(25*3*52) [-5 -1 -2 4⟩ Breedsma S49
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, undecimal submajor second, Ptolemy's second
12/11 150.637 (22*3)/11 [2 1 0 0 -1⟩ (Small) undecimal neutral second
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 1/4-tone, undecimal diesis, al-Farabi's 1/4-tone, octave-reduced 33rd harmonic
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⟩ Telepathma, eleventyfive comma, undecimal diasecundal 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⟩ Mothwellsma, small undecimal comma
100/99 17.399 (2*5/3)2/11) [2 -2 2 0 -1⟩ Ptolemisma, Ptolemy's comma S10
121/120 14.376 112/(23*3*5) [-3 -1 -1 0 2⟩ Biyatisma, undecimal seconds comma S11
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⟩ Rastma, neutral thirds comma
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⟩ Werckisma, Werckmeister's undecimal septenarian schisma S21
540/539 3.2090 (2/7)2*33*5/11 [2 3 1 -2 -1⟩ Swetisma, Swets' comma
3025/3024 0.57240 (5*11)2/(24*32*7) [-4 -3 2 -1 2⟩ Lehmerisma S55
9801/9800 0.17665 (11/(5*7))2*34/23 [-3 4 -2 -2 2⟩ Kalisma, Gauss comma S99
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⟩ Animist comma, small tridecimal comma
144/143 12.064 (22*3)2/(11*13) [4 2 0 0 -1 -1⟩ Grossma S12
169/168 10.274 132/(23*3*7) [-3 -1 0 -1 0 2⟩ Buzurgisma, dhanvantarisma S13
196/195 8.8554 (2*7)2/(3*5*13) [2 -1 -1 2 0 -1⟩ Mynucuma S14
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 S25
676/675 2.5629 (2*13/5)2/33 [2 -3 -2 0 0 2⟩ Island comma S26
729/728 2.3764 (32/2)3/(7*13) [-3 6 0 -1 0 -1⟩ Squbema S27
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⟩ Schismina, tridecimal schisma S65
4225/4224 0.40981 (5*13)2/(27*3*11) [-7 -1 2 0 -1 2⟩ Leprechaun comma S66
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 S351
17-limit (complete)
17/16 104.955 17/24 [-4 0 0 0 0 0 1⟩ Large septendecimal semitone, octave-reduced 17th harmonic
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⟩ Lynchisma
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, octave-reduced 255th subharmonic S16
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⟩ Semitonisma S17
375/374 4.6228 (3*53)/(2*11*17) [-1 1 3 0 -1 0 -1⟩ Ursulisma
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⟩ Dakotisma
715/714 2.4230 (5*11*13)/(2*3*7*17) [-1 -1 1 -1 1 1 -1⟩ September comma, septembrisma
833/832 2.0796 (72*17)/(26*13) [-6 0 0 2 0 -1 1⟩ Horizma, horizon comma
936/935 1.8506 (23*32*13)/(5*11*17) [3 2 -1 0 -1 1 -1⟩ Ainos comma, ainma
1089/1088 1.5905 (3*11)2/(26*17) [-6 2 0 0 2 0 -1⟩ Twosquare comma S33
1156/1155 1.4983 (2*17)2/(3*5*7*11) [2 -1 -1 -1 -1 0 2⟩ Quadrantonisma S34
1225/1224 1.4138 (5*7)2/(23*32*17) [-3 -2 2 2 0 0 -1⟩ Noellisma S35
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⟩ Palingenetic comma, palingenesis
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 (2*52)2/(3*72*17) [2 -1 4 -2 0 0 -1⟩ Sperasma S50
2601/2600 0.66573 (3*17)2/(23*52*13) [-3 2 -2 0 0 -1 2⟩ Sextantonisma S51
4914/4913 0.35234 (2*33*7*13)/173 [1 3 0 1 0 1 -3⟩
5832/5831 0.29688 (2*32)3/(73*17) [3 6 0 -3 0 0 -1⟩ Chlorisma
12376/12375 0.13989 (23*7*13*17)/(32*53*11) [3 -2 -3 1 -1 1 1⟩ flashma
14400/14399 0.12023 (23*3*5)2/(7*112*17) [6 2 2 -1 -2 0 -1⟩ Sparkisma S120
28561/28560 0.060616 134/(24*3*5*7*17) [-4 -1 -1 -1 0 4 -1⟩ S169
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 (3*7)4/(24*5*11*13*17) [-4 4 -1 4 -1 -1 -1⟩ Scintillisma S441
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⟩ Large undevicesimal 1/9-tone
77/76 22.631 (7*11)/(22*19) [-2 0 0 1 1 0 0 -1⟩ Small undevicesimal 1/9-tone
96/95 18.128 (25*3)/(5*19) [5 1 -1 0 0 0 0 -1⟩ 19th-partial chroma
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⟩ Ganassisma, Ganassi's comma
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 (2*32)2/(17*19) [2 4 0 0 0 0 -1 -1⟩ Nusu comma S18
343/342 5.0547 73/(2*32*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 S19
400/399 4.3335 (22*5)2/(3*7*19) [4 -1 2 -1 0 0 0 -1⟩ S20
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, Boethius' comma, 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⟩ Aureusma
1521/1520 1.1386 (3*13)2/(24*5*19) [-4 2 -1 0 0 2 0 -1⟩ Pinkanberry S39
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)/(22*3)3 [-6 -3 0 1 0 1 0 1⟩ Ramanujanisma
2376/2375 0.7288 (23*33*11)/(53*19) [3 3 -3 0 1 0 0 -1⟩
2432/2431 0.7120 (27*19)/(11*13*17) [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 (23*7)2/(3*5*11*19) [6 -1 -1 2 -1 0 0 -1⟩ S56
3250/3249 0.5328 (2*53*13)/(3*19)2 [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 (22*19)2/(3*52*7*11) [4 -1 -2 -1 -1 0 0 2⟩ S76
5929/5928 0.2920 (7*11)2/(23*3*13*19) [-3 -1 0 2 2 -1 0 -1⟩ S77
5985/5984 0.2893 (32*5*7*19)/(25*11*17) [-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 (32*17)2/(24*7*11*19) [-4 4 0 -1 -1 0 1 -1⟩ S153
27456/27455 0.06306 (26*3*11)/(5*172*19) [6 1 -1 0 1 0 -2 -1⟩
28900/28899 0.05991 (2*5*17)2/(32*132*19) [2 -2 2 0 0 -2 2 -1⟩ S170
43681/43680 0.03963 (11*19)2/(25*3*5*7*13) [-5 -1 -1 -1 2 -1 0 2⟩ S209
89376/89375 0.01937 (25*3*72*19)/(54*11*13) [5 1 -4 2 -1 -1 0 1⟩
104976/104975 0.01649 (2*32)4/(52*13*17*19) [4 8 -2 0 0 0 -1 -1 -1⟩ S324
165376/165375 0.01047 (29*17*19)/(33*53*72) [9 -3 -3 -2 0 0 1 1⟩ Decimillisma
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) [1 -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 (11*13*17)2/(28*35*5*19) [-8 -5 -1 0 2 2 2 -1⟩ S2431
11859211/11859210 0.0001460 (7*13*194)/(2*34*5*114) [-1 -4 -1 1 -4 1 0 4⟩
23-limit (complete)
23/22 76.956 23/(2*11) [-1 0 0 0 -1 0 0 0 1⟩ Greater vicesimotertial semitone
24/23 73.681 (23*3)/23 [3 1 0 0 0 0 0 0 -1⟩ Small vicesimotertial semitone
46/45 38.051 (2*23)/(32*5) [1 -2 -1 0 0 0 0 0 1⟩ Vicesimotertial 1/5-tone
69/68 25.274 (3*23)/(22*17) [-2 1 0 0 0 0 -1 0 1⟩ Large vicesimotertial 1/8-tone
70/69 24.910 (2*5*7)/(3*23) [1 -1 1 1 0 0 0 0 -1⟩ Small vicesimotertial 1/8-tone
92/91 18.921 (22*23)/(7*13) [2 0 0 -1 0 -1 0 0 1⟩
115/114 15.120 (5*23)/(2*3*19) [-1 -1 1 0 0 0 0 -1 1⟩
161/160 10.787 (7*23)/(25*5) [-5 0 -1 1 0 0 0 0 1⟩
162/161 10.720 (2*34)/(7*23) [1 4 0 -1 0 0 0 0 -1⟩
208/207 8.3433 (24*13)/(32*23) [4 -2 0 0 0 1 0 0 -1⟩
231/230 7.5108 (3*7*11)/(2*5*23) [-1 1 -1 1 1 0 0 0 -1⟩
253/252 6.8564 (11*23)/((2*3)2*7) [-2 -2 0 -1 1 0 0 0 1⟩
276/275 6.2840 (22*3*23)/(52*11) [2 1 -2 0 -1 0 0 0 1⟩
300/299 5.7804 ((2*5)2*3)/(13*23) [2 1 2 0 0 -1 0 0 -1⟩
323/322 5.3682 (17*19)/(2*7*23) [-1 0 0 -1 0 0 1 1 -1⟩
391/390 4.4334 (17*23)/(2*3*5*13) [-1 -1 -1 0 0 -1 1 0 1⟩
392/391 4.4221 (23*72)/(17*23) [3 0 0 2 0 0 -1 0 -1⟩
460/459 3.7676 (22*5*23)/(33*17) [2 -3 1 0 0 0 -1 0 1⟩
484/483 3.5806 (2*11)2/(3*7*23) [2 -1 0 -1 2 0 0 0 -1⟩ S22
507/506 3.4180 (3*132)/(2*11*23) [-1 1 0 0 -1 2 0 0 -1⟩
529/528 3.2758 232/(24*3*11) [-4 -1 0 0 -1 0 0 0 2⟩ S23
576/575 3.0082 (23*3)2/(23*52) [6 2 -2 0 0 0 0 0 -1⟩ S24
736/735 2.3538 (25*23)/(3*5*72) [5 -1 -1 -2 0 0 0 0 1⟩
760/759 2.2794 (23*5*19)/(3*11*23) [3 -1 1 0 -1 0 0 1 -1⟩
875/874 1.9797 (53*7)/(2*19*23) [-1 0 3 1 0 0 0 -1 -1⟩
897/896 1.9311 (3*13*23)/(27*7) [-7 1 0 -1 0 1 0 0 1⟩
1105/1104 1.5674 (5*13*17)/(24*3*23) [-4 -1 1 0 0 1 1 0 -1⟩
1197/1196 1.4469 (32*17*19)/(22*13*23) [-2 2 0 0 0 -1 1 1 -1⟩
1288/1287 1.3446 (23*7*23)/(32*11*13) [3 -2 0 1 -1 -1 0 0 1⟩
1496/1495 1.1576 (23*11*17)/(5*13*23) [3 0 -1 0 1 -1 1 0 -1⟩
1863/1862 0.92952 (34*23)/(2*72*19) [-1 4 0 -2 0 0 0 -1 1⟩
2024/2023 0.85556 (23*11*23)/(7*172) [3 0 0 -1 1 0 -2 0 1⟩
2025/2024 0.85514 (32*5)2/(23*11*23) [-3 4 2 0 -1 0 0 0 -1⟩ S45
2185/2184 0.79251 (5*19*23)/(23*3*7*13) [-3 -1 1 -1 0 -1 0 1 1⟩
2300/2299 0.75287 (22*52*23)/(112*19) [2 0 2 0 -2 0 0 -1 1⟩
2646/2645 0.65441 (2*33*72)/(5*232) [1 3 -1 2 0 0 0 0 -2⟩
2737/2736 0.63265 (7*17*23)/(24*32*19) [-4 -2 0 1 0 0 1 -1 1⟩
3060/3059 0.56586 (22*32*5*17)/(7*19*23) [2 2 1 -1 0 0 1 -1 -1⟩
3381/3380 0.51212 (3*72*23)/(22*5*132) [-2 1 -1 2 0 -2 0 0 1⟩
3520/3519 0.49190 (26*5*11)/(32*17*23) [6 -2 1 0 1 0 -1 0 -1⟩
3888/3887 0.44533 (24*35)/(132*23) [4 5 0 0 0 -2 0 0 -1⟩
4693/4692 0.36893 (13*192)/(22*3*17*23) [-2 -1 0 0 0 1 -1 2 -1⟩
4761/4760 0.36367 (3*23)2/(23*5*7*17) [-3 2 -1 -1 0 0 -1 0 2⟩ S69
5083/5082 0.34063 (13*17*23)/(2*3*7*112) [-1 -1 0 -1 -2 1 1 0 1⟩
7866/7865 0.22010 (2*32*19*23)/(5*112*13) [1 2 -1 0 -2 -1 0 1 1⟩
8281/8280 0.20907 (7*13)2/(23*32*5*23) [-3 -2 -1 2 0 2 0 0 -1⟩ S91
8625/8624 0.20073 (3*53*23)/(24*72*11) [-4 1 3 -2 -1 0 0 0 1⟩
10626/10625 0.16293 (2*3*7*11*23)/(54*17) [1 1 -4 1 1 0 -1 0 1⟩
11271/11270 0.15361 (3*13*172)/(2*5*72*23) [-1 1 -1 -2 0 1 2 0 -1⟩
11662/11661 0.14846 (2*73*17)/(3*132*23) [1 0 0 3 0 -2 1 0 -1⟩
12168/12167 0.14228 (23*32*132)/(233) [3 2 0 0 0 2 0 0 -3⟩
16929/16928 0.10227 (34*11*19)/(25*232) [-5 4 0 0 1 0 0 1 -2⟩
19551/19550 0.088552 (3*73*19)/(2*52*17*23) [-1 1 -2 3 0 0 -1 1 -1⟩
21505/21504 0.080506 (5*11*17*23)/(210*3*7) [-10 -1 1 -1 1 0 1 0 1⟩
21736/21735 0.079650 (23*11*13*19)/(33*5*7*23) [3 -3 -1 -1 1 1 0 1 -1⟩
23276/23275 0.074380 (22*11*232)/(52*72*19) [2 0 -2 -2 1 0 0 -1 2⟩
25025/25024 0.069182 (52*7*11*13)/(26*17*23) [-6 0 2 1 1 1 -1 0 -1⟩
25921/25920 0.066790 (7*23)2/(26*34*5) [-6 -4 -1 2 0 0 0 0 2⟩ S161
43264/43263 0.040016 (24*13)2/(32*11*19*23) [8 -2 0 0 -1 2 0 -1 -1⟩ S208
52326/52325 0.033086 (2*34*17*19)/(52*7*13*23) [1 4 -2 -1 0 -1 1 1 -1⟩
71875/71874 0.024087 (55*23)/(2*33*113) [-1 -3 5 0 -3 0 0 0 1⟩
75141/75140 0.023040 (33*112*23)/(22*5*13*172) [-2 3 -1 0 2 -1 -2 0 1⟩
76545/76544 0.022617 (37*5*7)/(28*13*23) [-8 7 1 1 0 -1 0 0 -1⟩
104329/104328 0.016594 (17*19)2/(23*34*7*23) [-3 -4 0 -1 -1 0 2 2 -1⟩ S323
122452/122451 0.014138 (22*113*23)/(3*74*17) [2 -1 0 -4 3 0 -1 0 1⟩
126225/126224 0.013716 (33*52*11*17)/(24*73*23) [-4 3 2 -3 1 0 1 0 -1⟩
152881/152880 0.011324 (17*23)2/(24*3*5*72*13) [-4 -1 -1 -2 0 -1 2 0 2⟩ S391
202125/202124 0.0085652 (3*53*72*11)/(22*133*23) [-2 1 3 2 1 -3 0 0 -1⟩
264385/264384 0.0065482 (5*112*19*23)/(26*35*17) [-6 -5 1 0 2 0 -1 1 1⟩
282625/282624 0.0061256 (53*7*17*19)/(212*3*23) [-12 -1 3 1 0 0 1 1 -1⟩
328510/328509 0.0052700 (2*5*7*13*192)/(3*23)3 [1 -3 1 1 0 1 0 0 -3⟩
2023425/2023424 0.00085560 (32*52*17*232)/(213*13*19) [-13 2 2 0 0 -1 1 -1 2⟩
4096576/4096575 0.00042261 (23*11*23)2/(34*52*7*172) [6 -4 -2 -1 2 0 -2 0 2⟩ S2024
5142501/5142500 0.00033665 (33*72*132*23)/(22*54*112*17) [-2 3 -4 2 -2 2 -1 0 1⟩
29-limit (incomplete)
29/28 60.751 29/(22*7) Large vicesimononal 1/4-tone
30/29 58.692 (2*3*5)/29 Small vicesimononal 1/4-tone
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)
175/174 9.9211 (52*7)/(2*3*29)
204/203 8.5073
232/231 7.4783
261/260 6.6458
290/289 5.9801
320/319 5.4186
378/377 4.5861
406/405 4.2694
494/493 3.5081
551/550 3.1448
552/551 3.1391
609/608 2.8451
638/637 2.7157
726/725 2.3863
31-limit (incomplete)
31/30 56.767 31/(2*3*5) Large tricesimoprimal quartertone
32/31 54.964 25/31 Small tricesimoprimal quartertone, 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
621/620 2.7901 (3³*23)/(2²*5*31) Owowhatsthisma
3969/3968 0.43624 (34*72)/(27*31) Yunzee comma S63
37-limit (incomplete)
37/36 47.434 37/(22*32) Large 37-limit quartertone, 37th-partial chroma
38/37 46.169 (2*19)/37 Small 37-limit quartertone
75/74 23.238 (3*52)/(2*37)
41-limit (incomplete)
41/40 42.749 41/(23*5) Large 41-limit fifth-tone
42/41 41.719 (2*3*7)/41 Small 41-limit fifth-tone
82/81 21.242 (2*41)/34 41st-partial chroma
43-limit (incomplete)
43/42 40.737 43/(2*3*7) Large 43-limit fifth-tone
44/43 39.800 (22*11)/43 Small 43-limit fifth-tone
86/85 20.249 (2*43)/(5*17)
87/86 20.014 (3*29)/(2*43)
129/128 13.473 (3*43)/27 43rd-partial chroma
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
7777/7776 0.223 7*11*101/(25*35)

See also

Notes

  1. ↑ Denoted by s-expressions, where sk is defined as (k/(k - 1))/((k + 1)/k). See square superparticular for details.

External links

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