List of superparticular intervals: Difference between revisions

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Use actual multiplication sign and +subgroup monzos for 31-limit and beyond; 37 -> tricesimoseptimal, 41 -> quadracesimoprimal, 43 -> quadracesimotertial
m Style
Line 57: Line 57:
| [[6/5]]
| [[6/5]]
| 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 64: Line 64:
| [[10/9]]
| [[10/9]]
| 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 71: Line 71:
| [[16/15]]
| [[16/15]]
| 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
Line 78: Line 78:
| [[25/24]]
| [[25/24]]
| 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
Line 94: Line 94:
| [[7/6]]
| [[7/6]]
| 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 108: Line 108:
| [[15/14]]
| [[15/14]]
| 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 115: Line 115:
| [[21/20]]
| [[21/20]]
| 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 122: Line 122:
| [[28/27]]
| [[28/27]]
| 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 129: Line 129:
| [[36/35]]
| [[36/35]]
| 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
Line 136: Line 136:
| [[49/48]]
| [[49/48]]
| 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
Line 143: Line 143:
| [[50/49]]
| [[50/49]]
| 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 150: Line 150:
| [[64/63]]
| [[64/63]]
| 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 157: Line 157:
| [[126/125]]
| [[126/125]]
| 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 164: Line 164:
| [[225/224]]
| [[225/224]]
| 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 171: Line 171:
| [[2401/2400]]
| [[2401/2400]]
| 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 178: Line 178:
| [[4375/4374]]
| [[4375/4374]]
| 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 187: Line 187:
| [[11/10]]
| [[11/10]]
| 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 194: Line 194:
| [[12/11]]
| [[12/11]]
| 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 201: Line 201:
| [[22/21]]
| [[22/21]]
| 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 208: Line 208:
| [[33/32]]
| [[33/32]]
| 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 215: Line 215:
| [[45/44]]
| [[45/44]]
| 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 222: Line 222:
| [[55/54]]
| [[55/54]]
| 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 229: Line 229:
| [[56/55]]
| [[56/55]]
| 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 236: Line 236:
| [[99/98]]
| [[99/98]]
| 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 243: Line 243:
| [[100/99]]
| [[100/99]]
| 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
Line 250: Line 250:
| [[121/120]]
| [[121/120]]
| 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
Line 257: Line 257:
| [[176/175]]
| [[176/175]]
| 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 264: Line 264:
| [[243/242]]
| [[243/242]]
| 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 271: Line 271:
| [[385/384]]
| [[385/384]]
| 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 278: Line 278:
| [[441/440]]
| [[441/440]]
| 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
Line 285: Line 285:
| [[540/539]]
| [[540/539]]
| 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 292: Line 292:
| [[3025/3024]]
| [[3025/3024]]
| 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 299: Line 299:
| [[9801/9800]]
| [[9801/9800]]
| 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
Line 308: Line 308:
| [[13/12]]
| [[13/12]]
| 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 315: Line 315:
| [[14/13]]
| [[14/13]]
| 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 322: Line 322:
| [[26/25]]
| [[26/25]]
| 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 329: Line 329:
| [[27/26]]
| [[27/26]]
| 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 336: Line 336:
| [[40/39]]
| [[40/39]]
| 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 343: Line 343:
| [[65/64]]
| [[65/64]]
| 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 350: Line 350:
| [[66/65]]
| [[66/65]]
| 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 357: Line 357:
| [[78/77]]
| [[78/77]]
| 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 364: Line 364:
| [[91/90]]
| [[91/90]]
| 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 371: Line 371:
| [[105/104]]
| [[105/104]]
| 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 378: Line 378:
| [[144/143]]
| [[144/143]]
| 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 385: Line 385:
| [[169/168]]
| [[169/168]]
| 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 392: Line 392:
| [[196/195]]
| [[196/195]]
| 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
Line 399: Line 399:
| [[325/324]]
| [[325/324]]
| 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 406: Line 406:
| [[351/350]]
| [[351/350]]
| 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 413: Line 413:
| [[352/351]]
| [[352/351]]
| 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 420: Line 420:
| [[364/363]]
| [[364/363]]
| 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 427: Line 427:
| [[625/624]]
| [[625/624]]
| 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 434: Line 434:
| [[676/675]]
| [[676/675]]
| 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 441: Line 441:
| [[729/728]]
| [[729/728]]
| 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 448: Line 448:
| [[1001/1000]]
| [[1001/1000]]
| 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 455: Line 455:
| [[1716/1715]]
| [[1716/1715]]
| 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 462: Line 462:
| [[2080/2079]]
| [[2080/2079]]
| 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 469: Line 469:
| [[4096/4095]]
| [[4096/4095]]
| 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
Line 476: Line 476:
| [[4225/4224]]
| [[4225/4224]]
| 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 483: Line 483:
| [[6656/6655]]
| [[6656/6655]]
| 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 490: Line 490:
| [[10648/10647]]
| [[10648/10647]]
| 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 497: Line 497:
| [[123201/123200]]
| [[123201/123200]]
| 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 513: Line 513:
| [[18/17]]
| [[18/17]]
| 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 520: Line 520:
| [[34/33]]
| [[34/33]]
| 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 527: Line 527:
| [[35/34]]
| [[35/34]]
| 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 534: Line 534:
| [[51/50]]
| [[51/50]]
| 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 541: Line 541:
| [[52/51]]
| [[52/51]]
| 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 548: Line 548:
| [[85/84]]
| [[85/84]]
| 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 555: Line 555:
| [[120/119]]
| [[120/119]]
| 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
Line 562: Line 562:
| [[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 569: Line 569:
| 154/153
| 154/153
| 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 576: Line 576:
| 170/169
| 170/169
| 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 583: Line 583:
| 221/220
| 221/220
| 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 590: Line 590:
| [[256/255]]
| [[256/255]]
| 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
Line 597: Line 597:
| [[273/272]]
| [[273/272]]
| 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 611: Line 611:
| [[375/374]]
| [[375/374]]
| 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 618: Line 618:
| 442/441
| 442/441
| 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 625: Line 625:
| 561/560
| 561/560
| 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 632: Line 632:
| [[595/594]]
| [[595/594]]
| 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 639: Line 639:
| [[715/714]]
| [[715/714]]
| 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 646: Line 646:
| [[833/832]]
| [[833/832]]
| 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 653: Line 653:
| [[936/935]]
| [[936/935]]
| 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 660: Line 660:
| [[1089/1088]]
| [[1089/1088]]
| 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
Line 667: Line 667:
| [[1156/1155]]
| [[1156/1155]]
| 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
Line 674: Line 674:
| [[1225/1224]]
| [[1225/1224]]
| 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
Line 681: Line 681:
| 1275/1274
| 1275/1274
| 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 688: Line 688:
| [[1701/1700]]
| [[1701/1700]]
| 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 695: Line 695:
| [[2058/2057]]
| [[2058/2057]]
| 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 702: Line 702:
| 2431/2430
| 2431/2430
| 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 709: Line 709:
| [[2500/2499]]
| [[2500/2499]]
| 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
Line 716: Line 716:
| [[2601/2600]]
| [[2601/2600]]
| 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
Line 723: Line 723:
| 4914/4913
| 4914/4913
| 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 730: Line 730:
| [[5832/5831]]
| [[5832/5831]]
| 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
Line 737: Line 737:
| [[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
Line 744: Line 744:
| [[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
Line 751: Line 751:
| 28561/28560
| 28561/28560
| 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 758: Line 758:
| 31213/31212
| 31213/31212
| 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 765: Line 765:
| 37180/37179
| 37180/37179
| 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 772: Line 772:
| 194481/194480
| 194481/194480
| 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
Line 779: Line 779:
| 336141/336140
| 336141/336140
| 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 788: Line 788:
| [[19/18]]
| [[19/18]]
| 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 795: Line 795:
| [[20/19]]
| [[20/19]]
| 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 802: Line 802:
| [[39/38]]
| [[39/38]]
| 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 809: Line 809:
| [[57/56]]
| [[57/56]]
| 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 816: Line 816:
| [[76/75]]
| [[76/75]]
| 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 823: Line 823:
| [[77/76]]
| [[77/76]]
| 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 830: Line 830:
| [[96/95]]
| [[96/95]]
| 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 837: Line 837:
| [[133/132]]
| [[133/132]]
| 13.066
| 13.066
| (19*7)/(2<sup>2</sup>*3*11)
| (7×19)/(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 844: Line 844:
| [[153/152]]
| [[153/152]]
| 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 851: Line 851:
| [[171/170]]
| [[171/170]]
| 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 858: Line 858:
| 190/189
| 190/189
| 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 865: Line 865:
| 209/208
| 209/208
| 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 872: Line 872:
| 210/209
| 210/209
| 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 879: Line 879:
| 286/285
| 286/285
| 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 886: Line 886:
| [[324/323]]
| [[324/323]]
| 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
Line 893: Line 893:
| 343/342
| 343/342
| 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 900: Line 900:
| 361/360
| 361/360
| 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 907: Line 907:
| 400/399
| 400/399
| 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 }}
|  
|  
Line 914: Line 914:
| 456/455
| 456/455
| 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 921: Line 921:
| 476/475
| 476/475
| 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 928: Line 928:
| 495/494
| 495/494
| 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 935: Line 935:
| [[513/512]]
| [[513/512]]
| 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 942: Line 942:
| 969/968
| 969/968
| 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 949: Line 949:
| [[1216/1215]]
| [[1216/1215]]
| 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 956: Line 956:
| 1331/1330
| 1331/1330
| 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 963: Line 963:
| [[1445/1444]]
| [[1445/1444]]
| 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 970: Line 970:
| [[1521/1520]]
| [[1521/1520]]
| 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
Line 977: Line 977:
| 1540/1539
| 1540/1539
| 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 984: Line 984:
| [[1729/1728]]
| [[1729/1728]]
| 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 991: Line 991:
| 2376/2375
| 2376/2375
| 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 998: Line 998:
| 2432/2431
| 2432/2431
| 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 1,005: Line 1,005:
| 2926/2925
| 2926/2925
| 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 1,012: Line 1,012:
| 3136/3135
| 3136/3135
| 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 }}
|  
|  
Line 1,019: Line 1,019:
| 3250/3249
| 3250/3249
| 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 1,026: Line 1,026:
| 4200/4199
| 4200/4199
| 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 1,033: Line 1,033:
| 5776/5775
| 5776/5775
| 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 }}
|  
|  
Line 1,040: Line 1,040:
| 5929/5928
| 5929/5928
| 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 }}
|  
|  
Line 1,047: Line 1,047:
| 5985/5984
| 5985/5984
| 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 1,054: Line 1,054:
| 6175/6174
| 6175/6174
| 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 1,061: Line 1,061:
| 6860/6859
| 6860/6859
| 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 1,068: Line 1,068:
| 10241/10240
| 10241/10240
| 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 1,075: Line 1,075:
| 10830/10829
| 10830/10829
| 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 1,082: Line 1,082:
| 12636/12635
| 12636/12635
| 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 1,089: Line 1,089:
| 13377/13376
| 13377/13376
| 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 1,096: Line 1,096:
| 14080/14079
| 14080/14079
| 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 1,103: Line 1,103:
| 14365/14364
| 14365/14364
| 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 1,110: Line 1,110:
| 23409/23408
| 23409/23408
| 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 }}
|  
|  
Line 1,117: Line 1,117:
| 27456/27455
| 27456/27455
| 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 1,124: Line 1,124:
| 28900/28899
| 28900/28899
| 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 }}
|  
|  
Line 1,131: Line 1,131:
| 43681/43680
| 43681/43680
| 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 }}
|  
|  
Line 1,138: Line 1,138:
| 89376/89375
| 89376/89375
| 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 1,145: Line 1,145:
| 104976/104975
| 104976/104975
| 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 }}
|  
|  
Line 1,152: Line 1,152:
| 165376/165375
| 165376/165375
| 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 1,159: Line 1,159:
| 228096/228095
| 228096/228095
| 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 1,166: Line 1,166:
| 601426/601425
| 601426/601425
| 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 1,173: Line 1,173:
| 633556/633555
| 633556/633555
| 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 1,180: Line 1,180:
| 709632/709631
| 709632/709631
| 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 1,187: Line 1,187:
| 5909761/5909760
| 5909761/5909760
| 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 }}
|  
|  
Line 1,194: Line 1,194:
| 11859211/11859210
| 11859211/11859210
| 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 1,203: Line 1,203:
| [[23/22]]
| [[23/22]]
| 76.956
| 76.956
| 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 1,210: Line 1,210:
| [[24/23]]
| [[24/23]]
| 73.681
| 73.681
| (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 1,217: Line 1,217:
| [[46/45]]
| [[46/45]]
| 38.051
| 38.051
| (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 1,224: Line 1,224:
| [[69/68]]
| [[69/68]]
| 25.274
| 25.274
| (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 1,231: Line 1,231:
| [[70/69]]
| [[70/69]]
| 24.910
| 24.910
| (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 1,238: Line 1,238:
| [[92/91]]
| [[92/91]]
| 18.921
| 18.921
| (2<sup>2</sup>*23)/(7*13)
| (2<sup>2</sup>×23)/(7×13)
| {{Monzo| 2 0 0 -1 0 -1 0 0 1 }}
| {{Monzo| 2 0 0 -1 0 -1 0 0 1 }}
|  
|  
Line 1,245: Line 1,245:
| 115/114
| 115/114
| 15.120
| 15.120
| (5*23)/(2*3*19)
| (5×23)/(2×3×19)
| {{Monzo| -1 -1 1 0 0 0 0 -1 1 }}
| {{Monzo| -1 -1 1 0 0 0 0 -1 1 }}
|  
|  
Line 1,252: Line 1,252:
| 161/160
| 161/160
| 10.787
| 10.787
| (7*23)/(2<sup>5</sup>*5)
| (7×23)/(2<sup>5</sup>×5)
| {{Monzo| -5 0 -1 1 0 0 0 0 1 }}
| {{Monzo| -5 0 -1 1 0 0 0 0 1 }}
|  
|  
Line 1,259: Line 1,259:
| 162/161
| 162/161
| 10.720
| 10.720
| (2*3<sup>4</sup>)/(7*23)
| (2×3<sup>4</sup>)/(7×23)
| {{Monzo| 1 4 0 -1 0 0 0 0 -1 }}
| {{Monzo| 1 4 0 -1 0 0 0 0 -1 }}
|  
|  
Line 1,266: Line 1,266:
| 208/207
| 208/207
| 8.3433
| 8.3433
| (2<sup>4</sup>*13)/(3<sup>2</sup>*23)
| (2<sup>4</sup>×13)/(3<sup>2</sup>×23)
| {{Monzo| 4 -2 0 0 0 1 0 0 -1 }}
| {{Monzo| 4 -2 0 0 0 1 0 0 -1 }}
|  
|  
Line 1,273: Line 1,273:
| 231/230
| 231/230
| 7.5108
| 7.5108
| (3*7*11)/(2*5*23)
| (3×7×11)/(2×5×23)
| {{Monzo| -1 1 -1 1 1 0 0 0 -1 }}
| {{Monzo| -1 1 -1 1 1 0 0 0 -1 }}
|  
|  
Line 1,280: Line 1,280:
| 253/252
| 253/252
| 6.8564
| 6.8564
| (11*23)/((2*3)<sup>2</sup>*7)
| (11×23)/((2×3)<sup>2</sup>×7)
| {{Monzo| -2 -2 0 -1 1 0 0 0 1 }}
| {{Monzo| -2 -2 0 -1 1 0 0 0 1 }}
|  
|  
Line 1,287: Line 1,287:
| 276/275
| 276/275
| 6.2840
| 6.2840
| (2<sup>2</sup>*3*23)/(5<sup>2</sup>*11)
| (2<sup>2</sup>×3×23)/(5<sup>2</sup>×11)
| {{Monzo| 2 1 -2 0 -1 0 0 0 1 }}
| {{Monzo| 2 1 -2 0 -1 0 0 0 1 }}
|  
|  
Line 1,294: Line 1,294:
| 300/299
| 300/299
| 5.7804
| 5.7804
| ((2*5)<sup>2</sup>*3)/(13*23)
| ((2×5)<sup>2</sup>×3)/(13×23)
| {{Monzo| 2 1 2 0 0 -1 0 0 -1 }}
| {{Monzo| 2 1 2 0 0 -1 0 0 -1 }}
|  
|  
Line 1,301: Line 1,301:
| 323/322
| 323/322
| 5.3682
| 5.3682
| (17*19)/(2*7*23)
| (17×19)/(2×7×23)
| {{Monzo| -1 0 0 -1 0 0 1 1 -1 }}
| {{Monzo| -1 0 0 -1 0 0 1 1 -1 }}
|  
|  
Line 1,308: Line 1,308:
| 391/390
| 391/390
| 4.4334
| 4.4334
| (17*23)/(2*3*5*13)
| (17×23)/(2×3×5×13)
| {{Monzo| -1 -1 -1 0 0 -1 1 0 1 }}
| {{Monzo| -1 -1 -1 0 0 -1 1 0 1 }}
|  
|  
Line 1,315: Line 1,315:
| 392/391
| 392/391
| 4.4221
| 4.4221
| (2<sup>3</sup>*7<sup>2</sup>)/(17*23)
| (2<sup>3</sup>×7<sup>2</sup>)/(17×23)
| {{Monzo| 3 0 0 2 0 0 -1 0 -1 }}
| {{Monzo| 3 0 0 2 0 0 -1 0 -1 }}
|  
|  
Line 1,322: Line 1,322:
| 460/459
| 460/459
| 3.7676
| 3.7676
| (2<sup>2</sup>*5*23)/(3<sup>3</sup>*17)
| (2<sup>2</sup>×5×23)/(3<sup>3</sup>×17)
| {{Monzo| 2 -3 1 0 0 0 -1 0 1 }}
| {{Monzo| 2 -3 1 0 0 0 -1 0 1 }}
|  
|  
Line 1,329: Line 1,329:
| 484/483
| 484/483
| 3.5806
| 3.5806
| (2*11)<sup>2</sup>/(3*7*23)
| (2×11)<sup>2</sup>/(3×7×23)
| {{Monzo| 2 -1 0 -1 2 0 0 0 -1 }}
| {{Monzo| 2 -1 0 -1 2 0 0 0 -1 }}
|  
|  
Line 1,336: Line 1,336:
| 507/506
| 507/506
| 3.4180
| 3.4180
| (3*13<sup>2</sup>)/(2*11*23)
| (3×13<sup>2</sup>)/(2×11×23)
| {{Monzo| -1 1 0 0 -1 2 0 0 -1 }}
| {{Monzo| -1 1 0 0 -1 2 0 0 -1 }}
|  
|  
Line 1,343: Line 1,343:
| 529/528
| 529/528
| 3.2758
| 3.2758
| 23<sup>2</sup>/(2<sup>4</sup>*3*11)
| 23<sup>2</sup>/(2<sup>4</sup>×3×11)
| {{Monzo| -4 -1 0 0 -1 0 0 0 2 }}
| {{Monzo| -4 -1 0 0 -1 0 0 0 2 }}
|  
|  
Line 1,350: Line 1,350:
| 576/575
| 576/575
| 3.0082
| 3.0082
| (2<sup>3</sup>*3)<sup>2</sup>/(23*5<sup>2</sup>)
| (2<sup>3</sup>×3)<sup>2</sup>/(23×5<sup>2</sup>)
| {{Monzo| 6 2 -2 0 0 0 0 0 -1 }}
| {{Monzo| 6 2 -2 0 0 0 0 0 -1 }}
|  
|  
Line 1,357: Line 1,357:
| 736/735
| 736/735
| 2.3538
| 2.3538
| (2<sup>5</sup>*23)/(3*5*7<sup>2</sup>)
| (2<sup>5</sup>×23)/(3×5×7<sup>2</sup>)
| {{Monzo| 5 -1 -1 -2 0 0 0 0 1 }}
| {{Monzo| 5 -1 -1 -2 0 0 0 0 1 }}
|
|
Line 1,364: Line 1,364:
| 760/759
| 760/759
| 2.2794
| 2.2794
| (2<sup>3</sup>*5*19)/(3*11*23)
| (2<sup>3</sup>×5×19)/(3×11×23)
| {{Monzo| 3 -1 1 0 -1 0 0 1 -1 }}
| {{Monzo| 3 -1 1 0 -1 0 0 1 -1 }}
|
|
Line 1,371: Line 1,371:
| 875/874
| 875/874
| 1.9797
| 1.9797
| (5<sup>3</sup>*7)/(2*19*23)
| (5<sup>3</sup>×7)/(2×19×23)
| {{Monzo| -1 0 3 1 0 0 0 -1 -1 }}
| {{Monzo| -1 0 3 1 0 0 0 -1 -1 }}
|
|
Line 1,378: Line 1,378:
| 897/896
| 897/896
| 1.9311
| 1.9311
| (3*13*23)/(2<sup>7</sup>*7)
| (3×13×23)/(2<sup>7</sup>×7)
| {{Monzo| -7 1 0 -1 0 1 0 0 1 }}
| {{Monzo| -7 1 0 -1 0 1 0 0 1 }}
|
|
Line 1,385: Line 1,385:
| 1105/1104
| 1105/1104
| 1.5674
| 1.5674
| (5*13*17)/(2<sup>4</sup>*3*23)
| (5×13×17)/(2<sup>4</sup>×3×23)
| {{Monzo| -4 -1 1 0 0 1 1 0 -1 }}
| {{Monzo| -4 -1 1 0 0 1 1 0 -1 }}
|
|
Line 1,392: Line 1,392:
| 1197/1196
| 1197/1196
| 1.4469
| 1.4469
| (3<sup>2</sup>*17*19)/(2<sup>2</sup>*13*23)
| (3<sup>2</sup>×17×19)/(2<sup>2</sup>×13×23)
| {{Monzo| -2 2 0 0 0 -1 1 1 -1 }}
| {{Monzo| -2 2 0 0 0 -1 1 1 -1 }}
|
|
Line 1,399: Line 1,399:
| 1288/1287
| 1288/1287
| 1.3446
| 1.3446
| (2<sup>3</sup>*7*23)/(3<sup>2</sup>*11*13)
| (2<sup>3</sup>×7×23)/(3<sup>2</sup>×11×13)
| {{Monzo| 3 -2 0 1 -1 -1 0 0 1 }}
| {{Monzo| 3 -2 0 1 -1 -1 0 0 1 }}
|
|
Line 1,406: Line 1,406:
| 1496/1495
| 1496/1495
| 1.1576
| 1.1576
| (2<sup>3</sup>*11*17)/(5*13*23)
| (2<sup>3</sup>×11×17)/(5×13×23)
| {{Monzo| 3 0 -1 0 1 -1 1 0 -1 }}
| {{Monzo| 3 0 -1 0 1 -1 1 0 -1 }}
|
|
Line 1,413: Line 1,413:
| 1863/1862
| 1863/1862
| 0.92952
| 0.92952
| (3<sup>4</sup>*23)/(2*7<sup>2</sup>*19)
| (3<sup>4</sup>×23)/(2×7<sup>2</sup>×19)
| {{Monzo| -1 4 0 -2 0 0 0 -1 1 }}
| {{Monzo| -1 4 0 -2 0 0 0 -1 1 }}
|
|
Line 1,420: Line 1,420:
| 2024/2023
| 2024/2023
| 0.85556
| 0.85556
| (2<sup>3</sup>*11*23)/(7*17<sup>2</sup>)
| (2<sup>3</sup>×11×23)/(7×17<sup>2</sup>)
| {{Monzo| 3 0 0 -1 1 0 -2 0 1 }}
| {{Monzo| 3 0 0 -1 1 0 -2 0 1 }}
|
|
Line 1,427: Line 1,427:
| 2025/2024
| 2025/2024
| 0.85514
| 0.85514
| (3<sup>2</sup>*5)<sup>2</sup>/(2<sup>3</sup>*11*23)
| (3<sup>2</sup>×5)<sup>2</sup>/(2<sup>3</sup>×11×23)
| {{Monzo| -3 4 2 0 -1 0 0 0 -1 }}
| {{Monzo| -3 4 2 0 -1 0 0 0 -1 }}
|  
|  
Line 1,434: Line 1,434:
| 2185/2184
| 2185/2184
| 0.79251
| 0.79251
| (5*19*23)/(2<sup>3</sup>*3*7*13)
| (5×19×23)/(2<sup>3</sup>×3×7×13)
| {{Monzo| -3 -1 1 -1 0 -1 0 1 1 }}
| {{Monzo| -3 -1 1 -1 0 -1 0 1 1 }}
|
|
Line 1,441: Line 1,441:
| 2300/2299
| 2300/2299
| 0.75287
| 0.75287
| (2<sup>2</sup>*5<sup>2</sup>*23)/(11<sup>2</sup>*19)
| (2<sup>2</sup>×5<sup>2</sup>×23)/(11<sup>2</sup>×19)
| {{Monzo| 2 0 2 0 -2 0 0 -1 1 }}
| {{Monzo| 2 0 2 0 -2 0 0 -1 1 }}
|  
|  
Line 1,448: Line 1,448:
| 2646/2645
| 2646/2645
| 0.65441
| 0.65441
| (2*3<sup>3</sup>*7<sup>2</sup>)/(5*23<sup>2</sup>)
| (2×3<sup>3</sup>×7<sup>2</sup>)/(5×23<sup>2</sup>)
| {{Monzo| 1 3 -1 2 0 0 0 0 -2 }}
| {{Monzo| 1 3 -1 2 0 0 0 0 -2 }}
|  
|  
Line 1,455: Line 1,455:
| 2737/2736
| 2737/2736
| 0.63265
| 0.63265
| (7*17*23)/(2<sup>4</sup>*3<sup>2</sup>*19)
| (7×17×23)/(2<sup>4</sup>×3<sup>2</sup>×19)
| {{Monzo| -4 -2 0 1 0 0 1 -1 1 }}
| {{Monzo| -4 -2 0 1 0 0 1 -1 1 }}
|  
|  
Line 1,462: Line 1,462:
| 3060/3059
| 3060/3059
| 0.56586
| 0.56586
| (2<sup>2</sup>*3<sup>2</sup>*5*17)/(7*19*23)
| (2<sup>2</sup>×3<sup>2</sup>×5×17)/(7×19×23)
| {{Monzo| 2 2 1 -1 0 0 1 -1 -1 }}
| {{Monzo| 2 2 1 -1 0 0 1 -1 -1 }}
|  
|  
Line 1,469: Line 1,469:
| 3381/3380
| 3381/3380
| 0.51212
| 0.51212
| (3*7<sup>2</sup>*23)/(2<sup>2</sup>*5*13<sup>2</sup>)
| (3×7<sup>2</sup>×23)/(2<sup>2</sup>×5×13<sup>2</sup>)
| {{Monzo| -2 1 -1 2 0 -2 0 0 1 }}
| {{Monzo| -2 1 -1 2 0 -2 0 0 1 }}
|  
|  
Line 1,476: Line 1,476:
| 3520/3519
| 3520/3519
| 0.49190
| 0.49190
| (2<sup>6</sup>*5*11)/(3<sup>2</sup>*17*23)
| (2<sup>6</sup>×5×11)/(3<sup>2</sup>×17×23)
| {{Monzo| 6 -2 1 0 1 0 -1 0 -1 }}
| {{Monzo| 6 -2 1 0 1 0 -1 0 -1 }}
|  
|  
Line 1,483: Line 1,483:
| 3888/3887
| 3888/3887
| 0.44533
| 0.44533
| (2<sup>4</sup>*3<sup>5</sup>)/(13<sup>2</sup>*23)
| (2<sup>4</sup>×3<sup>5</sup>)/(13<sup>2</sup>×23)
| {{Monzo| 4 5 0 0 0 -2 0 0 -1 }}
| {{Monzo| 4 5 0 0 0 -2 0 0 -1 }}
|  
|  
Line 1,490: Line 1,490:
| 4693/4692
| 4693/4692
| 0.36893
| 0.36893
| (13*19<sup>2</sup>)/(2<sup>2</sup>*3*17*23)
| (13×19<sup>2</sup>)/(2<sup>2</sup>×3×17×23)
| {{Monzo| -2 -1 0 0 0 1 -1 2 -1 }}
| {{Monzo| -2 -1 0 0 0 1 -1 2 -1 }}
|  
|  
Line 1,497: Line 1,497:
| 4761/4760
| 4761/4760
| 0.36367
| 0.36367
| (3*23)<sup>2</sup>/(2<sup>3</sup>*5*7*17)
| (3×23)<sup>2</sup>/(2<sup>3</sup>×5×7×17)
| {{Monzo| -3 2 -1 -1 0 0 -1 0 2 }}
| {{Monzo| -3 2 -1 -1 0 0 -1 0 2 }}
|  
|  
Line 1,504: Line 1,504:
| 5083/5082
| 5083/5082
| 0.34063
| 0.34063
| (13*17*23)/(2*3*7*11<sup>2</sup>)
| (13×17×23)/(2×3×7×11<sup>2</sup>)
| {{Monzo| -1 -1 0 -1 -2 1 1 0 1 }}
| {{Monzo| -1 -1 0 -1 -2 1 1 0 1 }}
|  
|  
Line 1,511: Line 1,511:
| 7866/7865
| 7866/7865
| 0.22010
| 0.22010
| (2*3<sup>2</sup>*19*23)/(5*11<sup>2</sup>*13)
| (2×3<sup>2</sup>×19×23)/(5×11<sup>2</sup>×13)
| {{Monzo| 1 2 -1 0 -2 -1 0 1 1 }}
| {{Monzo| 1 2 -1 0 -2 -1 0 1 1 }}
|  
|  
Line 1,518: Line 1,518:
| 8281/8280
| 8281/8280
| 0.20907
| 0.20907
| (7*13)<sup>2</sup>/(2<sup>3</sup>*3<sup>2</sup>*5*23)
| (7×13)<sup>2</sup>/(2<sup>3</sup>×3<sup>2</sup>×5×23)
| {{Monzo| -3 -2 -1 2 0 2 0 0 -1 }}
| {{Monzo| -3 -2 -1 2 0 2 0 0 -1 }}
|  
|  
Line 1,525: Line 1,525:
| 8625/8624
| 8625/8624
| 0.20073
| 0.20073
| (3*5<sup>3</sup>*23)/(2<sup>4</sup>*7<sup>2</sup>*11)
| (3×5<sup>3</sup>×23)/(2<sup>4</sup>×7<sup>2</sup>×11)
| {{Monzo| -4 1 3 -2 -1 0 0 0 1 }}
| {{Monzo| -4 1 3 -2 -1 0 0 0 1 }}
|  
|  
Line 1,532: Line 1,532:
| 10626/10625
| 10626/10625
| 0.16293
| 0.16293
| (2*3*7*11*23)/(5<sup>4</sup>*17)
| (2×3×7×11×23)/(5<sup>4</sup>×17)
| {{Monzo| 1 1 -4 1 1 0 -1 0 1 }}
| {{Monzo| 1 1 -4 1 1 0 -1 0 1 }}
|  
|  
Line 1,539: Line 1,539:
| 11271/11270
| 11271/11270
| 0.15361
| 0.15361
| (3*13*17<sup>2</sup>)/(2*5*7<sup>2</sup>*23)
| (3×13×17<sup>2</sup>)/(2×5×7<sup>2</sup>×23)
| {{Monzo| -1 1 -1 -2 0 1 2 0 -1 }}
| {{Monzo| -1 1 -1 -2 0 1 2 0 -1 }}
|  
|  
Line 1,546: Line 1,546:
| 11662/11661
| 11662/11661
| 0.14846
| 0.14846
| (2*7<sup>3</sup>*17)/(3*13<sup>2</sup>*23)
| (2×7<sup>3</sup>×17)/(3×13<sup>2</sup>×23)
| {{Monzo| 1 0 0 3 0 -2 1 0 -1 }}
| {{Monzo| 1 0 0 3 0 -2 1 0 -1 }}
|  
|  
Line 1,553: Line 1,553:
| 12168/12167
| 12168/12167
| 0.14228
| 0.14228
| (2<sup>3</sup>*3<sup>2</sup>*13<sup>2</sup>)/(23<sup>3</sup>)
| (2<sup>3</sup>×3<sup>2</sup>×13<sup>2</sup>)/(23<sup>3</sup>)
| {{Monzo| 3 2 0 0 0 2 0 0 -3 }}
| {{Monzo| 3 2 0 0 0 2 0 0 -3 }}
|  
|  
Line 1,560: Line 1,560:
| 16929/16928
| 16929/16928
| 0.10227
| 0.10227
| (3<sup>4</sup>*11*19)/(2<sup>5</sup>*23<sup>2</sup>)
| (3<sup>4</sup>×11×19)/(2<sup>5</sup>×23<sup>2</sup>)
| {{Monzo| -5 4 0 0 1 0 0 1 -2 }}
| {{Monzo| -5 4 0 0 1 0 0 1 -2 }}
|  
|  
Line 1,567: Line 1,567:
| 19551/19550
| 19551/19550
| 0.088552
| 0.088552
| (3*7<sup>3</sup>*19)/(2*5<sup>2</sup>*17*23)
| (3×7<sup>3</sup>×19)/(2×5<sup>2</sup>×17×23)
| {{Monzo| -1 1 -2 3 0 0 -1 1 -1 }}
| {{Monzo| -1 1 -2 3 0 0 -1 1 -1 }}
|  
|  
Line 1,574: Line 1,574:
| 21505/21504
| 21505/21504
| 0.080506
| 0.080506
| (5*11*17*23)/(2<sup>10</sup>*3*7)
| (5×11×17×23)/(2<sup>10</sup>×3×7)
| {{Monzo| -10 -1 1 -1 1 0 1 0 1 }}
| {{Monzo| -10 -1 1 -1 1 0 1 0 1 }}
|  
|  
Line 1,581: Line 1,581:
| 21736/21735
| 21736/21735
| 0.079650
| 0.079650
| (2<sup>3</sup>*11*13*19)/(3<sup>3</sup>*5*7*23)
| (2<sup>3</sup>×11×13×19)/(3<sup>3</sup>×5×7×23)
| {{Monzo| 3 -3 -1 -1 1 1 0 1 -1 }}
| {{Monzo| 3 -3 -1 -1 1 1 0 1 -1 }}
|  
|  
Line 1,588: Line 1,588:
| 23276/23275
| 23276/23275
| 0.074380
| 0.074380
| (2<sup>2</sup>*11*23<sup>2</sup>)/(5<sup>2</sup>*7<sup>2</sup>*19)
| (2<sup>2</sup>×11×23<sup>2</sup>)/(5<sup>2</sup>×7<sup>2</sup>×19)
| {{Monzo| 2 0 -2 -2 1 0 0 -1 2 }}
| {{Monzo| 2 0 -2 -2 1 0 0 -1 2 }}
|  
|  
Line 1,595: Line 1,595:
| 25025/25024
| 25025/25024
| 0.069182
| 0.069182
| (5<sup>2</sup>*7*11*13)/(2<sup>6</sup>*17*23)
| (5<sup>2</sup>×7×11×13)/(2<sup>6</sup>×17×23)
| {{Monzo| -6 0 2 1 1 1 -1 0 -1 }}
| {{Monzo| -6 0 2 1 1 1 -1 0 -1 }}
|  
|  
Line 1,602: Line 1,602:
| 25921/25920
| 25921/25920
| 0.066790
| 0.066790
| (7*23)<sup>2</sup>/(2<sup>6</sup>*3<sup>4</sup>*5)
| (7×23)<sup>2</sup>/(2<sup>6</sup>×3<sup>4</sup>×5)
| {{Monzo| -6 -4 -1 2 0 0 0 0 2 }}
| {{Monzo| -6 -4 -1 2 0 0 0 0 2 }}
|  
|  
Line 1,609: Line 1,609:
| 43264/43263
| 43264/43263
| 0.040016
| 0.040016
| (2<sup>4</sup>*13)<sup>2</sup>/(3<sup>2</sup>*11*19*23)
| (2<sup>4</sup>×13)<sup>2</sup>/(3<sup>2</sup>×11×19×23)
| {{Monzo| 8 -2 0 0 -1 2 0 -1 -1 }}
| {{Monzo| 8 -2 0 0 -1 2 0 -1 -1 }}
|  
|  
Line 1,616: Line 1,616:
| 52326/52325
| 52326/52325
| 0.033086
| 0.033086
| (2*3<sup>4</sup>*17*19)/(5<sup>2</sup>*7*13*23)
| (2×3<sup>4</sup>×17×19)/(5<sup>2</sup>×7×13×23)
| {{Monzo| 1 4 -2 -1 0 -1 1 1 -1 }}
| {{Monzo| 1 4 -2 -1 0 -1 1 1 -1 }}
|  
|  
Line 1,623: Line 1,623:
| 71875/71874
| 71875/71874
| 0.024087
| 0.024087
| (5<sup>5</sup>*23)/(2*3<sup>3</sup>*11<sup>3</sup>)
| (5<sup>5</sup>×23)/(2×3<sup>3</sup>×11<sup>3</sup>)
| {{Monzo| -1 -3 5 0 -3 0 0 0 1 }}
| {{Monzo| -1 -3 5 0 -3 0 0 0 1 }}
|  
|  
Line 1,630: Line 1,630:
| 75141/75140
| 75141/75140
| 0.023040
| 0.023040
| (3<sup>3</sup>*11<sup>2</sup>*23)/(2<sup>2</sup>*5*13*17<sup>2</sup>)
| (3<sup>3</sup>×11<sup>2</sup>×23)/(2<sup>2</sup>×5×13×17<sup>2</sup>)
| {{Monzo| -2 3 -1 0 2 -1 -2 0 1 }}
| {{Monzo| -2 3 -1 0 2 -1 -2 0 1 }}
|  
|  
Line 1,637: Line 1,637:
| 76545/76544
| 76545/76544
| 0.022617
| 0.022617
| (3<sup>7</sup>*5*7)/(2<sup>8</sup>*13*23)
| (3<sup>7</sup>×5×7)/(2<sup>8</sup>×13×23)
| {{Monzo| -8 7 1 1 0 -1 0 0 -1 }}
| {{Monzo| -8 7 1 1 0 -1 0 0 -1 }}
|  
|  
Line 1,644: Line 1,644:
| 104329/104328
| 104329/104328
| 0.016594
| 0.016594
| (17*19)<sup>2</sup>/(2<sup>3</sup>*3<sup>4</sup>*7*23)
| (17×19)<sup>2</sup>/(2<sup>3</sup>×3<sup>4</sup>×7×23)
| {{Monzo| -3 -4 0 -1 -1 0 2 2 -1 }}
| {{Monzo| -3 -4 0 -1 -1 0 2 2 -1 }}
|  
|  
Line 1,651: Line 1,651:
| 122452/122451
| 122452/122451
| 0.014138
| 0.014138
| (2<sup>2</sup>*11<sup>3</sup>*23)/(3*7<sup>4</sup>*17)
| (2<sup>2</sup>×11<sup>3</sup>×23)/(3×7<sup>4</sup>×17)
| {{Monzo| 2 -1 0 -4 3 0 -1 0 1 }}
| {{Monzo| 2 -1 0 -4 3 0 -1 0 1 }}
|  
|  
Line 1,658: Line 1,658:
| 126225/126224
| 126225/126224
| 0.013716
| 0.013716
| (3<sup>3</sup>*5<sup>2</sup>*11*17)/(2<sup>4</sup>*7<sup>3</sup>*23)
| (3<sup>3</sup>×5<sup>2</sup>×11×17)/(2<sup>4</sup>×7<sup>3</sup>×23)
| {{Monzo| -4 3 2 -3 1 0 1 0 -1 }}
| {{Monzo| -4 3 2 -3 1 0 1 0 -1 }}
|  
|  
Line 1,665: Line 1,665:
| 152881/152880
| 152881/152880
| 0.011324
| 0.011324
| (17*23)<sup>2</sup>/(2<sup>4</sup>*3*5*7<sup>2</sup>*13)
| (17×23)<sup>2</sup>/(2<sup>4</sup>×3×5×7<sup>2</sup>×13)
| {{Monzo| -4 -1 -1 -2 0 -1 2 0 2 }}
| {{Monzo| -4 -1 -1 -2 0 -1 2 0 2 }}
|  
|  
Line 1,672: Line 1,672:
| 202125/202124
| 202125/202124
| 0.0085652
| 0.0085652
| (3*5<sup>3</sup>*7<sup>2</sup>*11)/(2<sup>2</sup>*13<sup>3</sup>*23)
| (3×5<sup>3</sup>×7<sup>2</sup>×11)/(2<sup>2</sup>×13<sup>3</sup>×23)
| {{Monzo| -2 1 3 2 1 -3 0 0 -1 }}
| {{Monzo| -2 1 3 2 1 -3 0 0 -1 }}
|  
|  
Line 1,679: Line 1,679:
| 264385/264384
| 264385/264384
| 0.0065482
| 0.0065482
| (5*11<sup>2</sup>*19*23)/(2<sup>6</sup>*3<sup>5</sup>*17)
| (5×11<sup>2</sup>×19×23)/(2<sup>6</sup>×3<sup>5</sup>×17)
| {{Monzo| -6 -5 1 0 2 0 -1 1 1 }}
| {{Monzo| -6 -5 1 0 2 0 -1 1 1 }}
|  
|  
Line 1,686: Line 1,686:
| 282625/282624
| 282625/282624
| 0.0061256
| 0.0061256
| (5<sup>3</sup>*7*17*19)/(2<sup>12</sup>*3*23)
| (5<sup>3</sup>×7×17×19)/(2<sup>12</sup>×3×23)
| {{Monzo| -12 -1 3 1 0 0 1 1 -1 }}
| {{Monzo| -12 -1 3 1 0 0 1 1 -1 }}
|  
|  
Line 1,693: Line 1,693:
| 328510/328509
| 328510/328509
| 0.0052700
| 0.0052700
| (2*5*7*13*19<sup>2</sup>)/(3*23)<sup>3</sup>
| (2×5×7×13×19<sup>2</sup>)/(3×23)<sup>3</sup>
| {{Monzo| 1 -3 1 1 0 1 0 0 -3 }}
| {{Monzo| 1 -3 1 1 0 1 0 0 -3 }}
|  
|  
Line 1,700: Line 1,700:
| 2023425/2023424
| 2023425/2023424
| 0.00085560
| 0.00085560
| (3<sup>2</sup>*5<sup>2</sup>*17*23<sup>2</sup>)/(2<sup>13</sup>*13*19)
| (3<sup>2</sup>×5<sup>2</sup>×17×23<sup>2</sup>)/(2<sup>13</sup>×13×19)
| {{Monzo| -13 2 2 0 0 -1 1 -1 2 }}
| {{Monzo| -13 2 2 0 0 -1 1 -1 2 }}
|  
|  
Line 1,707: Line 1,707:
| 4096576/4096575
| 4096576/4096575
| 0.00042261
| 0.00042261
| (2<sup>3</sup>*11*23)<sup>2</sup>/(3<sup>4</sup>*5<sup>2</sup>*7*17<sup>2</sup>)
| (2<sup>3</sup>×11×23)<sup>2</sup>/(3<sup>4</sup>×5<sup>2</sup>×7×17<sup>2</sup>)
| {{Monzo| 6 -4 -2 -1 2 0 -2 0 2 }}
| {{Monzo| 6 -4 -2 -1 2 0 -2 0 2 }}
|  
|  
Line 1,714: Line 1,714:
| 5142501/5142500
| 5142501/5142500
| 0.00033665
| 0.00033665
| (3<sup>3</sup>*7<sup>2</sup>*13<sup>2</sup>*23)/(2<sup>2</sup>*5<sup>4</sup>*11<sup>2</sup>*17)
| (3<sup>3</sup>×7<sup>2</sup>×13<sup>2</sup>×23)/(2<sup>2</sup>×5<sup>4</sup>×11<sup>2</sup>×17)
| {{Monzo| -2 3 -4 2 -2 2 -1 0 1 }}
| {{Monzo| -2 3 -4 2 -2 2 -1 0 1 }}
|  
|  
Line 1,723: Line 1,723:
| [[29/28]]
| [[29/28]]
| 60.751
| 60.751
| 29/(2<sup>2</sup>*7)
| 29/(2<sup>2</sup>×7)
|  
|  
| Large vicesimononal 1/4-tone
| Large vicesimononal 1/4-tone
Line 1,730: Line 1,730:
| [[30/29]]
| [[30/29]]
| 58.692
| 58.692
| (2*3*5)/29
| (2×3×5)/29
|  
|  
| Small vicesimononal 1/4-tone
| Small vicesimononal 1/4-tone
Line 1,737: Line 1,737:
| [[58/57]]
| [[58/57]]
| 30.109
| 30.109
| (2*29)/(3*19)
| (2×29)/(3×19)
|  
|  
|  
|  
Line 1,744: Line 1,744:
| [[88/87]]
| [[88/87]]
| 19.786
| 19.786
| (2<sup>3</sup>*11)/(3*29)
| (2<sup>3</sup>×11)/(3×29)
|  
|  
|  
|  
Line 1,751: Line 1,751:
| 116/115
| 116/115
| 14.989
| 14.989
| (2<sup>2</sup>*29)/(5*23)
| (2<sup>2</sup>×29)/(5×23)
|  
|  
|  
|  
Line 1,758: Line 1,758:
| 117/116
| 117/116
| 14.860
| 14.860
| (3<sup>3</sup>*13)/(2<sup>2</sup>*29)
| (3<sup>3</sup>×13)/(2<sup>2</sup>×29)
|  
|  
|  
|  
Line 1,765: Line 1,765:
| 145/144
| 145/144
| 11.981
| 11.981
| (5*29)/(2<sup>4</sup>*3<sup>2</sup>)
| (5×29)/(2<sup>4</sup>×3<sup>2</sup>)
|  
|  
|  
|  
Line 1,772: Line 1,772:
| 175/174
| 175/174
| 9.9211
| 9.9211
| (5<sup>2</sup>*7)/(2*3*29)
| (5<sup>2</sup>×7)/(2×3×29)
|  
|  
|  
|  
Line 1,874: Line 1,874:
| 31/(2×3×5)
| 31/(2×3×5)
| 2.3.5.31 {{monzo| -1 -1 -1 1 }}
| 2.3.5.31 {{monzo| -1 -1 -1 1 }}
| Large tricesimoprimal quartertone
| Large tricesimoprimal 1/4-tone
|
|
|-
|-
Line 1,881: Line 1,881:
| 2<sup>5</sup>/31
| 2<sup>5</sup>/31
| 2.31 {{monzo| 5 -1 }}
| 2.31 {{monzo| 5 -1 }}
| Small tricesimoprimal quartertone, octave-reduced 31st subharmonic
| Small tricesimoprimal 1/4-tone, octave-reduced 31st subharmonic
|
|
|-
|-
Line 1,925: Line 1,925:
| 37/(2<sup>2</sup>×3<sup>2</sup>)
| 37/(2<sup>2</sup>×3<sup>2</sup>)
| 2.3.37 {{monzo| -2 -2 1 }}
| 2.3.37 {{monzo| -2 -2 1 }}
| Large tricesimoseptimal quartertone, 37th-partial chroma
| Large tricesimoseptimal 1/4-tone, 37th-partial chroma
|
|
|-
|-
Line 1,932: Line 1,932:
| (2×19)/37
| (2×19)/37
| 2.19.37 {{monzo| 1 1 -1 }}
| 2.19.37 {{monzo| 1 1 -1 }}
| Small tricesimoseptimal quartertone
| Small tricesimoseptimal 1/4-tone
|
|
|-
|-
Line 1,948: Line 1,948:
| 41/(2<sup>3</sup>×5)
| 41/(2<sup>3</sup>×5)
| 2.5.41 {{monzo| -3 -1 1 }}
| 2.5.41 {{monzo| -3 -1 1 }}
| Large quadracesimoprimal fifth-tone
| Large quadracesimoprimal 1/5-tone
|
|
|-
|-
Line 1,955: Line 1,955:
| (2×3×7)/41
| (2×3×7)/41
| 2.3.7.41 {{monzo| 1 1 1 -1 }}
| 2.3.7.41 {{monzo| 1 1 1 -1 }}
| Small quadracesimoprimal fifth-tone
| Small quadracesimoprimal 1/5-tone
|
|
|-
|-
Line 1,971: Line 1,971:
| 43/(2×3×7)
| 43/(2×3×7)
| 2.3.7.43 {{monzo| -1 -1 -1 1 }}
| 2.3.7.43 {{monzo| -1 -1 -1 1 }}
| Large quadracesimotertial fifth-tone
| Large quadracesimotertial 1/5-tone
|
|
|-
|-
Line 1,978: Line 1,978:
| (2<sup>2</sup>×11)/43
| (2<sup>2</sup>×11)/43
| 2.11.43 {{monzo| 2 1 -1 }}
| 2.11.43 {{monzo| 2 1 -1 }}
| Small quadracesimotertial fifth-tone
| Small quadracesimotertial 1/5-tone
|
|
|-
|-

Revision as of 09:02, 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 (7×19)/(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) 2.3.5.31 [-1 -1 -1 1⟩ Large tricesimoprimal 1/4-tone
32/31 54.964 25/31 2.31 [5 -1⟩ Small tricesimoprimal 1/4-tone, octave-reduced 31st subharmonic
63/62 27.700 (32×7)/(2×31) 2.3.7.31 [-1 2 1 -1⟩
93/92 18.716 (3×31)/(22×23) 2.3.23.31 [-2 1 -1 1⟩
125/124 13.906 53/(22×31) 2.5.31 [-2 3 -1⟩ Twizzler
621/620 2.7901 (33×23)/(22×5×31) 2.3.5.23.31 [-2 3 -1 1 -1⟩ Owowhatsthisma
3969/3968 0.43624 (34×72)/(27×31) 2.3.7.31 [-7 4 2 -1⟩ Yunzee comma S63
37-limit (incomplete)
37/36 47.434 37/(22×32) 2.3.37 [-2 -2 1⟩ Large tricesimoseptimal 1/4-tone, 37th-partial chroma
38/37 46.169 (2×19)/37 2.19.37 [1 1 -1⟩ Small tricesimoseptimal 1/4-tone
75/74 23.238 (3×52)/(2×37) 2.3.5.37 [-1 1 2 -1⟩
41-limit (incomplete)
41/40 42.749 41/(23×5) 2.5.41 [-3 -1 1⟩ Large quadracesimoprimal 1/5-tone
42/41 41.719 (2×3×7)/41 2.3.7.41 [1 1 1 -1⟩ Small quadracesimoprimal 1/5-tone
82/81 21.242 (2×41)/34 2.3.41 [1 -4 1⟩ 41st-partial chroma
43-limit (incomplete)
43/42 40.737 43/(2×3×7) 2.3.7.43 [-1 -1 -1 1⟩ Large quadracesimotertial 1/5-tone
44/43 39.800 (22×11)/43 2.11.43 [2 1 -1⟩ Small quadracesimotertial 1/5-tone
86/85 20.249 (2×43)/(5×17) 2.5.17.43 [1 -1 -1 1⟩
87/86 20.014 (3×29)/(2×43) 2.3.29.43 [-1 1 1 -1⟩
129/128 13.473 (3×43)/27 2.3.43 [-7 1 1⟩ 43rd-partial chroma
47-limit (incomplete)
47/46 37.232 47/(2×23) 2.23.47 [-1 -1 1⟩
48/47 36.448 (24×3)/47 2.3.47 [4 1 -1⟩
94/93 18.516 (2×47)/(3×31) 2.3.31.47 [1 -1 -1 1⟩
95/94 18.320 (5×19)/(2×47) 2.5.19.47 [-1 1 1 -1⟩
53-limit (incomplete)
53/52 32.977 53/(22×13) 2.13.53 [-2 -1 1⟩
54/53 32.360 (2×33)/53 2.3.53 [1 3 -1⟩
59-limit (incomplete)
59/58 29.594 59/(2×29) 2.29.59 [-1 -1 1⟩
60/59 29.097 (22×3×5)/59 2.3.5.59 [2 1 1 -1⟩
61-limit (incomplete)
61/60 28.616 61/(22×3×5) 2.3.5.61 [-2 -1 -1 1⟩
62/61 28.151 (2×31)/61 2.31.61 [1 1 -1⟩
67-limit (incomplete)
67/66 26.034 67/(2×3×11) 2.3.11.67 [-1 -1 -1 1⟩
68/67 25.648 (22×17)/67 2.17.67 [2 1 -1⟩
71-limit (incomplete)
71/70 24.557 71/(2×5×7) 2.5.7.71 [-1 -1 -1 1⟩
72/71 24.213 (23×32)/71 2.3.71 [3 2 -1⟩
73-limit (incomplete)
73/72 23.879 73/(23×32) 2.3.73 [-3 -2 1⟩
74/73 23.555 (2×37)/73 2.37.73 [1 1 -1⟩
79-limit (incomplete)
79/78 22.054 79/(2×3×13) 2.3.13.79 [-1 -1 -1 1⟩
80/79 21.777 (24×5)/79 2.5.79 [4 1 -1⟩
83-limit (incomplete)
83/82 20.985 83/(2×41) 2.41.83 [-1 -1 1⟩
84/83 20.734 (22*3*7)/83 2.3.7.83 [2 1 1 -1⟩
89-limit (incomplete)
89/88 19.562 89/(23×11) 2.11.89 [-3 -1 1⟩
90/89 19.344 (2×32×5)/89 2.3.5.89 [1 2 1 -1⟩
97-limit (incomplete)
97/96 17.940 97/(25×3) 2.3.97 [-5 -1 1⟩
98/97 17.756 (2×72)/97 2.7.97 [1 2 -1⟩
101-limit (incomplete)
101/100 17.226 101/(2×5)2 2.5.101 [-2 -2 1⟩
102/101 17.057 (2×3×17)/101 2.3.17.101 [1 1 1 -1⟩
7777/7776 0.223 7×11×101/(2×3)5 2.3.7.11.101 [-5 -5 1 1 1⟩ Pulsar comma

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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