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 127-limit and is complete up to the [[ | This is a list of [[superparticular]] [[interval]]s ordered by [[prime limit]]. It reaches to the 127-limit and is complete up to the [[37-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). | ||
| Line 18: | Line 18: | ||
| 2/1 | | 2/1 | ||
| {{Monzo| 1 }} | | {{Monzo| 1 }} | ||
| Octave, duple | | Octave, duple, 2nd harmonic, diapason | ||
| | | | ||
|} | |} | ||
| Line 48: | Line 48: | ||
| 203.910 | | 203.910 | ||
| 3<sup>2</sup>/2<sup>3</sup> | | 3<sup>2</sup>/2<sup>3</sup> | ||
| {{monzo|-3 2}} | | {{monzo| -3 2 }} | ||
| | | Pythagorean whole tone, Pythagorean major second, <br>major whole tone, octave-reduced 9th harmonic, harmonic ninth | ||
| S3 | | S3 | ||
|} | |} | ||
| Line 67: | Line 67: | ||
| {{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 | ||
| | | | ||
|- | |- | ||
| [[6/5]] | | [[6/5]] | ||
| Line 74: | Line 74: | ||
| {{Monzo| 1 1 -1 }} | | {{Monzo| 1 1 -1 }} | ||
| Classic(al)/just minor third | | Classic(al)/just minor third | ||
| | | | ||
|- | |- | ||
| [[10/9]] | | [[10/9]] | ||
| Line 81: | Line 81: | ||
| {{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 | ||
| | | | ||
|- | |- | ||
| [[16/15]] | | [[16/15]] | ||
| Line 119: | Line 119: | ||
| {{Monzo| -1 -1 0 1 }} | | {{Monzo| -1 -1 0 1 }} | ||
| (Septimal) subminor third, septimal minor third | | (Septimal) subminor third, septimal minor third | ||
| | | | ||
|- | |- | ||
| [[8/7]] | | [[8/7]] | ||
| Line 125: | Line 125: | ||
| 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, <br>octave-reduced 7th subharmonic | ||
| | | | ||
|- | |- | ||
| [[15/14]] | | [[15/14]] | ||
| Line 133: | Line 133: | ||
| {{Monzo| -1 1 1 -1 }} | | {{Monzo| -1 1 1 -1 }} | ||
| Septimal major semitone, septimal diatonic semitone | | Septimal major semitone, septimal diatonic semitone | ||
| | | | ||
|- | |- | ||
| [[21/20]] | | [[21/20]] | ||
| Line 140: | Line 140: | ||
| {{Monzo| -2 1 -1 1 }} | | {{Monzo| -2 1 -1 1 }} | ||
| Septimal minor semitone, large septimal chroma | | Septimal minor semitone, large septimal chroma | ||
| | | | ||
|- | |- | ||
| [[28/27]] | | [[28/27]] | ||
| Line 146: | Line 146: | ||
| (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, <br>(septimal) subminor second, septimal minor second, <br>trienstonic comma | ||
| | | | ||
|- | |- | ||
| [[36/35]] | | [[36/35]] | ||
| 48.770 | | 48.770 | ||
| ( | | (2×3)<sup>2</sup>/(5×7) | ||
| {{Monzo| 2 2 -1 -1 }} | | {{Monzo| 2 2 -1 -1 }} | ||
| Septimal 1/4-tone, | | Septimal 1/4-tone, mint comma | ||
| S6 | | S6 | ||
|- | |- | ||
| Line 160: | Line 160: | ||
| 7<sup>2</sup>/(2<sup>4</sup>×3) | | 7<sup>2</sup>/(2<sup>4</sup>×3) | ||
| {{Monzo| -4 -1 0 2 }} | | {{Monzo| -4 -1 0 2 }} | ||
| | | Large septimal diesis, large septimal 1/6-tone, slendro diesis, semaphoresma | ||
| S7 | | S7 | ||
|- | |- | ||
| Line 167: | Line 167: | ||
| 2×(5/7)<sup>2</sup> | | 2×(5/7)<sup>2</sup> | ||
| {{Monzo| 1 0 2 -2 }} | | {{Monzo| 1 0 2 -2 }} | ||
| | | Small septimal diesis, small septimal 1/6-tone, septimal tritonic diesis, jubilisma | ||
| | | | ||
|- | |- | ||
| [[64/63]] | | [[64/63]] | ||
| Line 182: | Line 182: | ||
| {{Monzo| 1 2 -3 1 }} | | {{Monzo| 1 2 -3 1 }} | ||
| Starling comma, septimal semicomma | | Starling comma, septimal semicomma | ||
| | | | ||
|- | |- | ||
| [[225/224]] | | [[225/224]] | ||
| Line 203: | Line 203: | ||
| {{Monzo| -1 -7 4 1 }} | | {{Monzo| -1 -7 4 1 }} | ||
| Ragisma | | Ragisma | ||
| | | | ||
|} | |} | ||
| Line 219: | Line 219: | ||
| 11/(2×5) | | 11/(2×5) | ||
| {{Monzo| -1 0 -1 0 1 }} | | {{Monzo| -1 0 -1 0 1 }} | ||
| | | Large undecimal neutral second, <br>undecimal submajor second, Ptolemy's second | ||
| | | | ||
|- | |- | ||
| [[12/11]] | | [[12/11]] | ||
| Line 226: | Line 226: | ||
| (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 | ||
| | | | ||
|- | |- | ||
| [[22/21]] | | [[22/21]] | ||
| Line 234: | Line 234: | ||
| {{Monzo| 1 -1 0 -1 1 }} | | {{Monzo| 1 -1 0 -1 1 }} | ||
| Undecimal minor semitone | | Undecimal minor semitone | ||
| | | | ||
|- | |- | ||
| [[33/32]] | | [[33/32]] | ||
| Line 240: | Line 240: | ||
| (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, <br>al-Farabi's 1/4-tone, octave-reduced 33rd harmonic | ||
| | | | ||
|- | |- | ||
| [[45/44]] | | [[45/44]] | ||
| Line 247: | Line 247: | ||
| (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, cake comma | ||
| | | | ||
|- | |- | ||
| [[55/54]] | | [[55/54]] | ||
| Line 254: | Line 254: | ||
| (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, <br>undecimal diasecundal comma | ||
| | | | ||
|- | |- | ||
| [[56/55]] | | [[56/55]] | ||
| Line 262: | Line 262: | ||
| {{Monzo| 3 0 -1 1 -1 }} | | {{Monzo| 3 0 -1 1 -1 }} | ||
| Undecimal tritonic comma, konbini comma | | Undecimal tritonic comma, konbini comma | ||
| | | | ||
|- | |- | ||
| [[99/98]] | | [[99/98]] | ||
| Line 269: | Line 269: | ||
| {{Monzo| -1 2 0 -2 1 }} | | {{Monzo| -1 2 0 -2 1 }} | ||
| Mothwellsma, small undecimal comma | | Mothwellsma, small undecimal comma | ||
| | | | ||
|- | |- | ||
| [[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 290: | Line 290: | ||
| {{Monzo| 4 0 -2 -1 1 }} | | {{Monzo| 4 0 -2 -1 1 }} | ||
| Valinorsma | | Valinorsma | ||
| | | | ||
|- | |- | ||
| [[243/242]] | | [[243/242]] | ||
| Line 297: | Line 297: | ||
| {{Monzo| -1 5 0 0 -2 }} | | {{Monzo| -1 5 0 0 -2 }} | ||
| Rastma, neutral thirds comma | | Rastma, neutral thirds comma | ||
| | | | ||
|- | |- | ||
| [[385/384]] | | [[385/384]] | ||
| Line 304: | Line 304: | ||
| {{Monzo| -7 -1 1 1 1 }} | | {{Monzo| -7 -1 1 1 1 }} | ||
| Keenanisma | | Keenanisma | ||
| | | | ||
|- | |- | ||
| [[441/440]] | | [[441/440]] | ||
| Line 315: | Line 315: | ||
| [[540/539]] | | [[540/539]] | ||
| 3.2090 | | 3.2090 | ||
| (2/7)<sup>2</sup> | | (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 | ||
| | | | ||
|- | |- | ||
| [[3025/3024]] | | [[3025/3024]] | ||
| 0.57240 | | 0.57240 | ||
| (5×11)<sup>2</sup>/(2<sup>4</sup>×3<sup> | | (5×11)<sup>2</sup>/(2<sup>4</sup>×3<sup>3</sup>×7) | ||
| {{Monzo| -4 -3 2 -1 2 }} | | {{Monzo| -4 -3 2 -1 2 }} | ||
| Lehmerisma | | Lehmerisma | ||
| Line 329: | Line 329: | ||
| [[9801/9800]] | | [[9801/9800]] | ||
| 0.17665 | | 0.17665 | ||
| ( | | ((3<sup>2</sup>×11)/(5×7))<sup>2</sup>/2<sup>3</sup> | ||
| {{Monzo| -3 4 -2 -2 2 }} | | {{Monzo| -3 4 -2 -2 2 }} | ||
| Kalisma, Gauss comma | | Kalisma, Gauss comma | ||
| Line 348: | Line 348: | ||
| 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, <br>tridecimal neutral second | ||
| | | | ||
|- | |- | ||
| [[14/13]] | | [[14/13]] | ||
| Line 356: | Line 356: | ||
| {{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 | ||
| | | | ||
|- | |- | ||
| [[26/25]] | | [[26/25]] | ||
| Line 363: | Line 363: | ||
| {{Monzo| 1 0 -2 0 0 1 }} | | {{Monzo| 1 0 -2 0 0 1 }} | ||
| Large tridecimal 1/3-tone | | Large tridecimal 1/3-tone | ||
| | | | ||
|- | |- | ||
| [[27/26]] | | [[27/26]] | ||
| Line 370: | Line 370: | ||
| {{Monzo| -1 3 0 0 0 -1 }} | | {{Monzo| -1 3 0 0 0 -1 }} | ||
| Small tridecimal 1/3-tone | | Small tridecimal 1/3-tone | ||
| | | | ||
|- | |- | ||
| [[40/39]] | | [[40/39]] | ||
| Line 377: | Line 377: | ||
| {{Monzo| 3 -1 1 0 0 -1 }} | | {{Monzo| 3 -1 1 0 0 -1 }} | ||
| Tridecimal minor diesis | | Tridecimal minor diesis | ||
| | | | ||
|- | |- | ||
| [[65/64]] | | [[65/64]] | ||
| Line 384: | Line 384: | ||
| {{Monzo| -6 0 1 0 0 1 }} | | {{Monzo| -6 0 1 0 0 1 }} | ||
| Wilsorma, 13th-partial chroma | | Wilsorma, 13th-partial chroma | ||
| | | | ||
|- | |- | ||
| [[66/65]] | | [[66/65]] | ||
| Line 391: | Line 391: | ||
| {{Monzo| 1 1 -1 0 1 -1 }} | | {{Monzo| 1 1 -1 0 1 -1 }} | ||
| Winmeanma | | Winmeanma | ||
| | | | ||
|- | |- | ||
| [[78/77]] | | [[78/77]] | ||
| Line 398: | Line 398: | ||
| {{Monzo| 1 1 0 -1 -1 1 }} | | {{Monzo| 1 1 0 -1 -1 1 }} | ||
| Negustma | | Negustma | ||
| | | | ||
|- | |- | ||
| [[91/90]] | | [[91/90]] | ||
| Line 405: | Line 405: | ||
| {{Monzo| -1 -2 -1 1 0 1 }} | | {{Monzo| -1 -2 -1 1 0 1 }} | ||
| Biome comma, superleap comma | | Biome comma, superleap comma | ||
| | | | ||
|- | |- | ||
| [[105/104]] | | [[105/104]] | ||
| Line 412: | Line 412: | ||
| {{Monzo| -3 1 1 1 0 -1 }} | | {{Monzo| -3 1 1 1 0 -1 }} | ||
| Animist comma, small tridecimal comma | | Animist comma, small tridecimal comma | ||
| | | | ||
|- | |- | ||
| [[144/143]] | | [[144/143]] | ||
| Line 437: | Line 437: | ||
| [[325/324]] | | [[325/324]] | ||
| 5.3351 | | 5.3351 | ||
| (5<sup>2</sup> | | (5/(2×3<sup>2</sup>))<sup>2</sup>×13 | ||
| {{Monzo| -2 -4 2 0 0 1 }} | | {{Monzo| -2 -4 2 0 0 1 }} | ||
| Marveltwin comma | | Marveltwin comma | ||
| | | | ||
|- | |- | ||
| [[351/350]] | | [[351/350]] | ||
| 4.9393 | | 4.9393 | ||
| (3/ | | (3<sup>3</sup>×13)/(2×5<sup>2</sup>×7) | ||
| {{Monzo| -1 3 -2 -1 0 1 }} | | {{Monzo| -1 3 -2 -1 0 1 }} | ||
| Ratwolfsma | | Ratwolfsma | ||
| | | | ||
|- | |- | ||
| [[352/351]] | | [[352/351]] | ||
| 4.9253 | | 4.9253 | ||
| (2<sup>5</sup>×11)/(3<sup> | | (2<sup>5</sup>×11)/(3<sup>3</sup>×13) | ||
| {{Monzo| 5 -3 0 0 1 -1 }} | | {{Monzo| 5 -3 0 0 1 -1 }} | ||
| Major minthma, major gentle comma | | Major minthma, major gentle comma | ||
| | | | ||
|- | |- | ||
| [[364/363]] | | [[364/363]] | ||
| 4.7627 | | 4.7627 | ||
| (2/11)<sup>2</sup> | | (2/11)<sup>2</sup>×((7×13)/3) | ||
| {{Monzo| 2 -1 0 1 -2 1 }} | | {{Monzo| 2 -1 0 1 -2 1 }} | ||
| Minor minthma, minor gentle comma | | Minor minthma, minor gentle comma | ||
| | | | ||
|- | |- | ||
| [[625/624]] | | [[625/624]] | ||
| Line 472: | Line 472: | ||
| [[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 489: | Line 489: | ||
| {{Monzo| -3 0 -3 1 1 1 }} | | {{Monzo| -3 0 -3 1 1 1 }} | ||
| Sinbadma | | Sinbadma | ||
| | | | ||
|- | |- | ||
| [[1716/1715]] | | [[1716/1715]] | ||
| Line 496: | Line 496: | ||
| {{Monzo| 2 1 -1 -3 1 1 }} | | {{Monzo| 2 1 -1 -3 1 1 }} | ||
| Lummic comma | | Lummic comma | ||
| | | | ||
|- | |- | ||
| [[2080/2079]] | | [[2080/2079]] | ||
| Line 502: | Line 502: | ||
| (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, sinaisma | ||
| | | | ||
|- | |- | ||
| [[4096/4095]] | | [[4096/4095]] | ||
| Line 509: | Line 509: | ||
| (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 }} | ||
| | | Minisma | ||
| S64 | | S64 | ||
|- | |- | ||
| Line 521: | Line 521: | ||
| [[6656/6655]] | | [[6656/6655]] | ||
| 0.26012 | | 0.26012 | ||
| (2<sup>3</sup>/11)<sup>3</sup> | | (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 | ||
| | | | ||
|- | |- | ||
| [[10648/10647]] | | [[Harmonisma|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 | ||
| | | | ||
|- | |- | ||
| [[123201/123200]] | | [[Chalmersia|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) | ||
| Line 554: | Line 554: | ||
| 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, <br>octave-reduced 17th harmonic | ||
| | | | ||
|- | |- | ||
| [[18/17]] | | [[18/17]] | ||
| Line 561: | Line 561: | ||
| (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, <br>Arabic lute index finger | ||
| | | | ||
|- | |- | ||
| [[34/33]] | | [[34/33]] | ||
| Line 569: | Line 569: | ||
| {{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 | ||
| | | | ||
|- | |- | ||
| [[35/34]] | | [[35/34]] | ||
| Line 576: | Line 576: | ||
| {{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 | ||
| | | | ||
|- | |- | ||
| [[51/50]] | | [[51/50]] | ||
| Line 583: | Line 583: | ||
| {{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 | ||
| | | | ||
|- | |- | ||
| [[52/51]] | | [[52/51]] | ||
| Line 590: | Line 590: | ||
| {{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 | ||
| | | | ||
|- | |- | ||
| [[85/84]] | | [[85/84]] | ||
| Line 597: | Line 597: | ||
| {{Monzo| -2 -1 1 -1 0 0 1 }} | | {{Monzo| -2 -1 1 -1 0 0 1 }} | ||
| Monk comma | | Monk comma | ||
| | | | ||
|- | |- | ||
| [[120/119]] | | [[120/119]] | ||
| Line 604: | Line 604: | ||
| {{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> | | (2/3)<sup>3</sup>×(17/5) | ||
| {{Monzo| 3 -3 -1 0 0 0 1 }} | | {{Monzo| 3 -3 -1 0 0 0 1 }} | ||
| | | Diatisma, septendecimal major second comma | ||
| | | | ||
|- | |- | ||
| [[154/153]] | | [[154/153]] | ||
| Line 618: | Line 618: | ||
| {{Monzo| 1 -2 0 1 1 0 -1 }} | | {{Monzo| 1 -2 0 1 1 0 -1 }} | ||
| Augustma | | Augustma | ||
| | | | ||
|- | |- | ||
| [[170/169]] | | [[170/169]] | ||
| Line 625: | Line 625: | ||
| {{Monzo| 1 0 1 0 0 -2 1 }} | | {{Monzo| 1 0 1 0 0 -2 1 }} | ||
| Major naiadma | | Major naiadma | ||
| | | | ||
|- | |- | ||
| [[221/220]] | | [[221/220]] | ||
| Line 632: | Line 632: | ||
| {{Monzo| -2 0 -1 0 -1 1 1 }} | | {{Monzo| -2 0 -1 0 -1 1 1 }} | ||
| Minor naiadma | | Minor naiadma | ||
| | | | ||
|- | |- | ||
| [[256/255]] | | [[256/255]] | ||
| Line 638: | Line 638: | ||
| 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 }} | ||
| | | Charisma, charic comma, <br>septendecimal kleisma | ||
| S16 | | S16 | ||
|- | |- | ||
| Line 646: | Line 646: | ||
| {{Monzo| -4 1 0 1 0 1 -1 }} | | {{Monzo| -4 1 0 1 0 1 -1 }} | ||
| Tannisma, prototannisma | | Tannisma, prototannisma | ||
| | | | ||
|- | |- | ||
| [[289/288]] | | [[289/288]] | ||
| Line 667: | Line 667: | ||
| {{Monzo| 1 -2 0 -2 0 1 1 }} | | {{Monzo| 1 -2 0 -2 0 1 1 }} | ||
| Seminaiadma | | Seminaiadma | ||
| | | | ||
|- | |- | ||
| [[561/560]] | | [[561/560]] | ||
| Line 674: | Line 674: | ||
| {{Monzo| -4 1 -1 -1 1 0 1 }} | | {{Monzo| -4 1 -1 -1 1 0 1 }} | ||
| Monardisma, tsaharuk comma | | Monardisma, tsaharuk comma | ||
| | | | ||
|- | |- | ||
| [[595/594]] | | [[595/594]] | ||
| Line 688: | Line 688: | ||
| {{Monzo| -1 -1 1 -1 1 1 -1 }} | | {{Monzo| -1 -1 1 -1 1 1 -1 }} | ||
| September comma, septembrisma | | September comma, septembrisma | ||
| | | | ||
|- | |- | ||
| [[833/832]] | | [[833/832]] | ||
| Line 695: | Line 695: | ||
| {{Monzo| -6 0 0 2 0 -1 1 }} | | {{Monzo| -6 0 0 2 0 -1 1 }} | ||
| Horizma, horizon comma | | Horizma, horizon comma | ||
| | | | ||
|- | |- | ||
| [[936/935]] | | [[936/935]] | ||
| Line 702: | Line 702: | ||
| {{Monzo| 3 2 -1 0 -1 1 -1 }} | | {{Monzo| 3 2 -1 0 -1 1 -1 }} | ||
| Ainisma, ainic comma | | Ainisma, ainic comma | ||
| | | | ||
|- | |- | ||
| [[1089/1088]] | | [[1089/1088]] | ||
| Line 730: | Line 730: | ||
| {{Monzo| -1 1 2 -2 0 -1 1 }} | | {{Monzo| -1 1 2 -2 0 -1 1 }} | ||
| Cimbrisma | | Cimbrisma | ||
| | | | ||
|- | |- | ||
| [[1701/1700]] | | [[1701/1700]] | ||
| Line 737: | Line 737: | ||
| {{Monzo| -2 5 -2 1 0 0 -1 }} | | {{Monzo| -2 5 -2 1 0 0 -1 }} | ||
| Palingenetic comma, palingenesis | | Palingenetic comma, palingenesis | ||
| | | | ||
|- | |- | ||
| [[2058/2057]] | | [[2058/2057]] | ||
| Line 744: | Line 744: | ||
| {{Monzo| 1 1 0 3 -2 0 -1 }} | | {{Monzo| 1 1 0 3 -2 0 -1 }} | ||
| Xenisma | | Xenisma | ||
| | | | ||
|- | |- | ||
| [[2431/2430]] | | [[2431/2430]] | ||
| Line 751: | Line 751: | ||
| {{Monzo| -1 -5 -1 0 1 1 1 }} | | {{Monzo| -1 -5 -1 0 1 1 1 }} | ||
| Heptacircle comma | | Heptacircle comma | ||
| | | | ||
|- | |- | ||
| [[2500/2499]] | | [[2500/2499]] | ||
| Line 772: | Line 772: | ||
| {{Monzo| 1 3 0 1 0 1 -3 }} | | {{Monzo| 1 3 0 1 0 1 -3 }} | ||
| Baladisma | | Baladisma | ||
| | | | ||
|- | |- | ||
| [[5832/5831]] | | [[5832/5831]] | ||
| Line 779: | Line 779: | ||
| {{Monzo| 3 6 0 -3 0 0 -1 }} | | {{Monzo| 3 6 0 -3 0 0 -1 }} | ||
| Chlorisma | | Chlorisma | ||
| | | | ||
|- | |- | ||
| [[Flashma|12376/12375]] | | [[Flashma|12376/12375]] | ||
| Line 786: | Line 786: | ||
| {{Monzo| 3 -2 -3 1 -1 1 1 }} | | {{Monzo| 3 -2 -3 1 -1 1 1 }} | ||
| Flashma | | Flashma | ||
| | | | ||
|- | |- | ||
| [[Sparkisma|14400/14399]] | | [[Sparkisma|14400/14399]] | ||
| Line 795: | Line 795: | ||
| S120 | | S120 | ||
|- | |- | ||
| [[ | | [[28561/28560]] | ||
| 0.060616 | | 0.060616 | ||
| 13<sup>4</sup>/( | | (13/2)<sup>4</sup>/(3×5×7×17) | ||
| {{Monzo| -4 -1 -1 -1 0 4 -1 }} | | {{Monzo| -4 -1 -1 -1 0 4 -1 }} | ||
| | | Pisanoisma | ||
| S169 | | S169 | ||
|- | |- | ||
| Line 807: | Line 807: | ||
| {{Monzo| -2 -3 0 4 0 1 -2 }} | | {{Monzo| -2 -3 0 4 0 1 -2 }} | ||
| E-shaped comma | | E-shaped comma | ||
| | | | ||
|- | |- | ||
| [[37180/37179]] | | [[Lateral comma|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 }} | ||
| Lateral comma | | Lateral comma | ||
| | | | ||
|- | |- | ||
| [[Scintillisma|194481/194480]] | | [[Scintillisma|194481/194480]] | ||
| Line 823: | Line 823: | ||
| S441 | | S441 | ||
|- | |- | ||
| [[336141/336140]] | | [[Aksial comma|336141/336140]] | ||
| 0.0051503 | | 0.0051503 | ||
| (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 }} | ||
| Aksial comma | | Aksial comma | ||
| | | | ||
|} | |} | ||
| Line 845: | Line 845: | ||
| {{Monzo| -1 -2 0 0 0 0 0 1 }} | | {{Monzo| -1 -2 0 0 0 0 0 1 }} | ||
| Large undevicesimal semitone | | Large undevicesimal semitone | ||
| | | | ||
|- | |- | ||
| [[20/19]] | | [[20/19]] | ||
| Line 852: | Line 852: | ||
| {{Monzo| 2 0 1 0 0 0 0 -1 }} | | {{Monzo| 2 0 1 0 0 0 0 -1 }} | ||
| Small undevicesimal semitone | | Small undevicesimal semitone | ||
| | | | ||
|- | |- | ||
| [[39/38]] | | [[39/38]] | ||
| Line 858: | Line 858: | ||
| (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 diesis, <br>undevicesimal 2/9-tone | ||
| | | | ||
|- | |- | ||
| [[57/56]] | | [[57/56]] | ||
| Line 866: | Line 866: | ||
| {{Monzo| -3 1 0 -1 0 0 0 1 }} | | {{Monzo| -3 1 0 -1 0 0 0 1 }} | ||
| Hendrix comma | | Hendrix comma | ||
| | | | ||
|- | |- | ||
| [[76/75]] | | [[76/75]] | ||
| Line 873: | Line 873: | ||
| {{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 | ||
| | | | ||
|- | |- | ||
| [[77/76]] | | [[77/76]] | ||
| Line 880: | Line 880: | ||
| {{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 | ||
| | | | ||
|- | |- | ||
| [[96/95]] | | [[96/95]] | ||
| Line 887: | Line 887: | ||
| {{Monzo| 5 1 -1 0 0 0 0 -1 }} | | {{Monzo| 5 1 -1 0 0 0 0 -1 }} | ||
| 19th-partial chroma | | 19th-partial chroma | ||
| | | | ||
|- | |- | ||
| [[133/132]] | | [[133/132]] | ||
| Line 894: | Line 894: | ||
| {{Monzo| -2 -1 0 1 -1 0 0 1 }} | | {{Monzo| -2 -1 0 1 -1 0 0 1 }} | ||
| Minithirdma | | Minithirdma | ||
| | | | ||
|- | |- | ||
| [[153/152]] | | [[153/152]] | ||
| Line 901: | Line 901: | ||
| {{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 | ||
| | | | ||
|- | |- | ||
| [[171/170]] | | [[171/170]] | ||
| Line 908: | Line 908: | ||
| {{Monzo| -1 2 -1 0 0 0 -1 1 }} | | {{Monzo| -1 2 -1 0 0 0 -1 1 }} | ||
| Malcolmisma | | Malcolmisma | ||
| | | | ||
|- | |- | ||
| [[190/189]] | | [[190/189]] | ||
| Line 915: | Line 915: | ||
| {{Monzo| 1 -3 1 -1 0 0 0 1 }} | | {{Monzo| 1 -3 1 -1 0 0 0 1 }} | ||
| Cotylisma | | Cotylisma | ||
| | | | ||
|- | |- | ||
| [[209/208]] | | [[209/208]] | ||
| Line 922: | Line 922: | ||
| {{Monzo| -4 0 0 0 1 -1 0 1 }} | | {{Monzo| -4 0 0 0 1 -1 0 1 }} | ||
| Yama comma | | Yama comma | ||
| | | | ||
|- | |- | ||
| [[210/209]] | | [[210/209]] | ||
| Line 929: | Line 929: | ||
| {{Monzo| 1 1 1 1 -1 0 0 -1 }} | | {{Monzo| 1 1 1 1 -1 0 0 -1 }} | ||
| Spleen comma | | Spleen comma | ||
| | | | ||
|- | |- | ||
| [[286/285]] | | [[286/285]] | ||
| Line 936: | Line 936: | ||
| {{Monzo| 1 -1 -1 0 1 1 0 -1 }} | | {{Monzo| 1 -1 -1 0 1 1 0 -1 }} | ||
| Chthonisma | | Chthonisma | ||
| | | | ||
|- | |- | ||
| [[324/323]] | | [[324/323]] | ||
| Line 950: | Line 950: | ||
| {{Monzo| -1 -2 0 3 0 0 0 -1 }} | | {{Monzo| -1 -2 0 3 0 0 0 -1 }} | ||
| Nutrisma | | Nutrisma | ||
| | | | ||
|- | |- | ||
| [[361/360]] | | [[361/360]] | ||
| Line 971: | Line 971: | ||
| {{Monzo| 3 1 -1 -1 0 -1 0 1 }} | | {{Monzo| 3 1 -1 -1 0 -1 0 1 }} | ||
| Abnobisma | | Abnobisma | ||
| | | | ||
|- | |- | ||
| [[476/475]] | | [[476/475]] | ||
| Line 978: | Line 978: | ||
| {{Monzo| 2 0 -2 1 0 0 1 -1 }} | | {{Monzo| 2 0 -2 1 0 0 1 -1 }} | ||
| Hedwigma | | Hedwigma | ||
| | | | ||
|- | |- | ||
| [[495/494]] | | [[495/494]] | ||
| Line 985: | Line 985: | ||
| {{Monzo| -1 2 1 0 1 -1 0 -1 }} | | {{Monzo| -1 2 1 0 1 -1 0 -1 }} | ||
| Eulalisma | | Eulalisma | ||
| | | | ||
|- | |- | ||
| [[513/512]] | | [[513/512]] | ||
| Line 991: | Line 991: | ||
| (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, <br>Boethius' comma, 513th harmonic | ||
| | | | ||
|- | |- | ||
| [[969/968]] | | [[969/968]] | ||
| Line 998: | Line 998: | ||
| (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 }} | ||
| | | Kingfisher comma | ||
| | | | ||
|- | |- | ||
| [[1216/1215]] | | [[1216/1215]] | ||
| Line 1,006: | Line 1,006: | ||
| {{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 | ||
| | | | ||
|- | |- | ||
| [[1331/1330]] | | [[1331/1330]] | ||
| Line 1,013: | Line 1,013: | ||
| {{Monzo| -1 0 -1 -1 3 0 0 -1 }} | | {{Monzo| -1 0 -1 -1 3 0 0 -1 }} | ||
| Solvejgsma | | Solvejgsma | ||
| | | | ||
|- | |- | ||
| [[1445/1444]] | | [[1445/1444]] | ||
| Line 1,020: | Line 1,020: | ||
| {{Monzo| -2 0 1 0 0 0 2 -2 }} | | {{Monzo| -2 0 1 0 0 0 2 -2 }} | ||
| Aureusma | | Aureusma | ||
| | | | ||
|- | |- | ||
| [[1521/1520]] | | [[1521/1520]] | ||
| Line 1,034: | Line 1,034: | ||
| {{Monzo| 2 -4 1 1 1 0 0 -1 }} | | {{Monzo| 2 -4 1 1 1 0 0 -1 }} | ||
| Kevolisma | | Kevolisma | ||
| | | | ||
|- | |- | ||
| [[1729/1728]] | | [[1729/1728]] | ||
| Line 1,041: | Line 1,041: | ||
| {{Monzo| -6 -3 0 1 0 1 0 1 }} | | {{Monzo| -6 -3 0 1 0 1 0 1 }} | ||
| Ramanujanisma | | Ramanujanisma | ||
| | | | ||
|- | |- | ||
| [[2376/2375]] | | [[2376/2375]] | ||
| 0.72879 | | 0.72879 | ||
| ( | | ((2×3)/5)<sup>3</sup>×(11/19) | ||
| {{Monzo| 3 3 -3 0 1 0 0 -1 }} | | {{Monzo| 3 3 -3 0 1 0 0 -1 }} | ||
| Trichthonisma | | Trichthonisma | ||
| | | | ||
|- | |- | ||
| [[2432/2431]] | | [[2432/2431]] | ||
| Line 1,055: | Line 1,055: | ||
| {{Monzo| 7 0 0 0 -1 -1 -1 1 }} | | {{Monzo| 7 0 0 0 -1 -1 -1 1 }} | ||
| Blumeyer comma | | Blumeyer comma | ||
| | | | ||
|- | |- | ||
| [[2926/2925]] | | [[2926/2925]] | ||
| 0.59177 | | 0.59177 | ||
| (2×7×11×19)/( | | (2×7×11×19)/((3×5)<sup>2</sup>×13) | ||
| {{Monzo| 1 -2 -2 1 1 -1 0 1 }} | | {{Monzo| 1 -2 -2 1 1 -1 0 1 }} | ||
| Neovulture comma, neovulturisma | | Neovulture comma, neovulturisma | ||
| | | | ||
|- | |- | ||
| [[3136/3135]] | | [[3136/3135]] | ||
| Line 1,076: | Line 1,076: | ||
| {{Monzo| 1 -2 3 0 0 1 0 -2 }} | | {{Monzo| 1 -2 3 0 0 1 0 -2 }} | ||
| Martebisma | | Martebisma | ||
| | | | ||
|- | |- | ||
| [[4200/4199]] | | [[4200/4199]] | ||
| Line 1,083: | Line 1,083: | ||
| {{Monzo| 3 1 2 1 0 -1 -1 -1 }} | | {{Monzo| 3 1 2 1 0 -1 -1 -1 }} | ||
| Neosatanisma | | Neosatanisma | ||
| | | | ||
|- | |- | ||
| [[5776/5775]] | | [[5776/5775]] | ||
| Line 1,096: | Line 1,096: | ||
| (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 }} | ||
| | | Manzanisma | ||
| S77 | | S77 | ||
|- | |- | ||
| Line 1,104: | Line 1,104: | ||
| {{Monzo| -5 2 1 1 -1 0 -1 1 }} | | {{Monzo| -5 2 1 1 -1 0 -1 1 }} | ||
| Neogrendel comma, neogrendelisma | | Neogrendel comma, neogrendelisma | ||
| | | | ||
|- | |- | ||
| [[6175/6174]] | | [[6175/6174]] | ||
| Line 1,111: | Line 1,111: | ||
| {{Monzo| -1 -2 2 -3 0 1 0 1 }} | | {{Monzo| -1 -2 2 -3 0 1 0 1 }} | ||
| Neonewtisma | | Neonewtisma | ||
| | | | ||
|- | |- | ||
| [[6860/6859]] | | [[6860/6859]] | ||
| Line 1,117: | Line 1,117: | ||
| (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 }} | ||
| Devicubisma | |||
| | | | ||
|- | |- | ||
| 10241/10240 | | 10241/10240 | ||
| Line 1,125: | Line 1,125: | ||
| {{Monzo| -11 0 -1 2 1 0 0 1 }} | | {{Monzo| -11 0 -1 2 1 0 0 1 }} | ||
| | | | ||
| | | | ||
|- | |- | ||
| 10830/10829 | | 10830/10829 | ||
| Line 1,132: | Line 1,132: | ||
| {{Monzo| 1 1 1 -2 0 -1 -1 2 }} | | {{Monzo| 1 1 1 -2 0 -1 -1 2 }} | ||
| | | | ||
| | | | ||
|- | |- | ||
| 12636/12635 | | [[12636/12635]] | ||
| 0.13701 | | 0.13701 | ||
| (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 }} | ||
| Padriellisma | |||
| | | | ||
|- | |- | ||
| 13377/13376 | | 13377/13376 | ||
| Line 1,146: | Line 1,146: | ||
| {{Monzo| -6 1 0 3 -1 1 0 -1 }} | | {{Monzo| -6 1 0 3 -1 1 0 -1 }} | ||
| | | | ||
| | | | ||
|- | |- | ||
| 14080/14079 | | 14080/14079 | ||
| Line 1,153: | Line 1,153: | ||
| {{Monzo| 8 -1 1 0 1 -1 0 -2 }} | | {{Monzo| 8 -1 1 0 1 -1 0 -2 }} | ||
| | | | ||
| | | | ||
|- | |- | ||
| 14365/14364 | | 14365/14364 | ||
| Line 1,160: | Line 1,160: | ||
| {{Monzo| -2 -3 1 -1 0 2 1 -1 }} | | {{Monzo| -2 -3 1 -1 0 2 1 -1 }} | ||
| | | | ||
| | | | ||
|- | |- | ||
| 23409/23408 | | 23409/23408 | ||
| 0.073957 | | 0.073957 | ||
| (3<sup>2</sup>×17)<sup>2</sup>/( | | ((3/2)<sup>2</sup>×17)<sup>2</sup>/(7×11×19) | ||
| {{Monzo| -4 4 0 -1 -1 0 2 -1 }} | | {{Monzo| -4 4 0 -1 -1 0 2 -1 }} | ||
| | | | ||
| Line 1,174: | Line 1,174: | ||
| {{Monzo| 6 1 -1 0 1 1 -2 -1 }} | | {{Monzo| 6 1 -1 0 1 1 -2 -1 }} | ||
| | | | ||
| | | | ||
|- | |- | ||
| 28900/28899 | | 28900/28899 | ||
| 0.059905 | | 0.059905 | ||
| (2×5×17) | | ((2×5×17)/(3×13))<sup>2</sup>/19 | ||
| {{Monzo| 2 -2 2 0 0 -2 2 -1 }} | | {{Monzo| 2 -2 2 0 0 -2 2 -1 }} | ||
| | | | ||
| Line 1,195: | Line 1,195: | ||
| {{Monzo| 5 1 -4 2 -1 -1 0 1 }} | | {{Monzo| 5 1 -4 2 -1 -1 0 1 }} | ||
| | | | ||
| | | | ||
|- | |- | ||
| 104976/104975 | | 104976/104975 | ||
| Line 1,206: | Line 1,206: | ||
| [[Decimillisma|165376/165375]] | | [[Decimillisma|165376/165375]] | ||
| 0.010469 | | 0.010469 | ||
| (2<sup>9</sup>×17×19)/( | | (2<sup>9</sup>×17×19)/((3×5)<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 | ||
| | | | ||
|- | |- | ||
| 228096/228095 | | 228096/228095 | ||
| 0.0075900 | | 0.0075900 | ||
| (2<sup> | | ((2<sup>2</sup>×3)/7)<sup>4</sup>×(11/(5×19)) | ||
| {{Monzo| 8 4 -1 -4 1 0 0 -1 }} | | {{Monzo| 8 4 -1 -4 1 0 0 -1 }} | ||
| | | | ||
| | | | ||
|- | |- | ||
| 601426/601425 | | 601426/601425 | ||
| Line 1,223: | Line 1,223: | ||
| {{Monzo| 1 -7 -2 2 -1 0 1 2 }} | | {{Monzo| 1 -7 -2 2 -1 0 1 2 }} | ||
| | | | ||
| | | | ||
|- | |- | ||
| [[Devicisma|633556/633555]] | | [[Devicisma|633556/633555]] | ||
| Line 1,230: | Line 1,230: | ||
| {{Monzo| 2 -3 -1 1 3 -1 1 -2 }} | | {{Monzo| 2 -3 -1 1 3 -1 1 -2 }} | ||
| Devicisma | | Devicisma | ||
| | | | ||
|- | |- | ||
| 709632/709631 | | 709632/709631 | ||
| Line 1,237: | Line 1,237: | ||
| {{Monzo| 10 2 0 1 1 -3 -1 -1 }} | | {{Monzo| 10 2 0 1 1 -3 -1 -1 }} | ||
| | | | ||
| | | | ||
|- | |- | ||
| 5909761/5909760 | | 5909761/5909760 | ||
| Line 1,246: | Line 1,246: | ||
| S2431 | | S2431 | ||
|- | |- | ||
| 11859211/11859210 | | <font style="font-size:0.88em">[[11859211/11859210]]</font> | ||
| 0.00014598 | | 0.00014598 | ||
| ( | | (19/(3×11))<sup>4</sup>×((7×13)/(2×5)) | ||
| {{Monzo| -1 -4 -1 1 -4 1 0 4 }} | | {{Monzo| -1 -4 -1 1 -4 1 0 4 }} | ||
| Tredekisma | |||
| | | | ||
|} | |} | ||
| Line 1,267: | Line 1,267: | ||
| 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 }} | ||
| | | Large vicesimotertial semitone | ||
| | | | ||
|- | |- | ||
| [[24/23]] | | [[24/23]] | ||
| Line 1,275: | Line 1,275: | ||
| {{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 | ||
| | | | ||
|- | |- | ||
| [[46/45]] | | [[46/45]] | ||
| Line 1,282: | Line 1,282: | ||
| {{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 | ||
| | | | ||
|- | |- | ||
| [[69/68]] | | [[69/68]] | ||
| Line 1,289: | Line 1,289: | ||
| {{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 | ||
| | | | ||
|- | |- | ||
| [[70/69]] | | [[70/69]] | ||
| Line 1,296: | Line 1,296: | ||
| {{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 | ||
| | | | ||
|- | |- | ||
| [[92/91]] | | [[92/91]] | ||
| Line 1,303: | Line 1,303: | ||
| {{Monzo| 2 0 0 -1 0 -1 0 0 1 }} | | {{Monzo| 2 0 0 -1 0 -1 0 0 1 }} | ||
| Undinisma | | Undinisma | ||
| | | | ||
|- | |- | ||
| [[115/114]] | | [[115/114]] | ||
| Line 1,310: | Line 1,310: | ||
| {{Monzo| -1 -1 1 0 0 0 0 -1 1 }} | | {{Monzo| -1 -1 1 0 0 0 0 -1 1 }} | ||
| Yarmanisma | | Yarmanisma | ||
| | | | ||
|- | |- | ||
| [[161/160]] | | [[161/160]] | ||
| Line 1,317: | Line 1,317: | ||
| {{Monzo| -5 0 -1 1 0 0 0 0 1 }} | | {{Monzo| -5 0 -1 1 0 0 0 0 1 }} | ||
| Major kirnbergerisma | | Major kirnbergerisma | ||
| | | | ||
|- | |- | ||
| [[162/161]] | | [[162/161]] | ||
| Line 1,324: | Line 1,324: | ||
| {{Monzo| 1 4 0 -1 0 0 0 0 -1 }} | | {{Monzo| 1 4 0 -1 0 0 0 0 -1 }} | ||
| Minor kirnbergerisma | | Minor kirnbergerisma | ||
| | | | ||
|- | |- | ||
| [[208/207]] | | [[208/207]] | ||
| Line 1,331: | Line 1,331: | ||
| {{Monzo| 4 -2 0 0 0 1 0 0 -1 }} | | {{Monzo| 4 -2 0 0 0 1 0 0 -1 }} | ||
| Vicetone comma | | Vicetone comma | ||
| | | | ||
|- | |- | ||
| [[231/230]] | | [[231/230]] | ||
| Line 1,338: | Line 1,338: | ||
| {{Monzo| -1 1 -1 1 1 0 0 0 -1 }} | | {{Monzo| -1 1 -1 1 1 0 0 0 -1 }} | ||
| Major neutravicema | | Major neutravicema | ||
| | | | ||
|- | |- | ||
| [[253/252]] | | [[253/252]] | ||
| Line 1,345: | Line 1,345: | ||
| {{Monzo| -2 -2 0 -1 1 0 0 0 1 }} | | {{Monzo| -2 -2 0 -1 1 0 0 0 1 }} | ||
| Middle neutravicema | | Middle neutravicema | ||
| | | | ||
|- | |- | ||
| [[276/275]] | | [[276/275]] | ||
| Line 1,352: | Line 1,352: | ||
| {{Monzo| 2 1 -2 0 -1 0 0 0 1 }} | | {{Monzo| 2 1 -2 0 -1 0 0 0 1 }} | ||
| Minor neutravicema | | Minor neutravicema | ||
| | | | ||
|- | |- | ||
| [[300/299]] | | [[300/299]] | ||
| Line 1,359: | Line 1,359: | ||
| {{Monzo| 2 1 2 0 0 -1 0 0 -1 }} | | {{Monzo| 2 1 2 0 0 -1 0 0 -1 }} | ||
| Major naiadvicema | | Major naiadvicema | ||
| | | | ||
|- | |- | ||
| [[323/322]] | | [[323/322]] | ||
| Line 1,366: | Line 1,366: | ||
| {{Monzo| -1 0 0 -1 0 0 1 1 -1 }} | | {{Monzo| -1 0 0 -1 0 0 1 1 -1 }} | ||
| Major semivicema | | Major semivicema | ||
| | | | ||
|- | |- | ||
| [[391/390]] | | [[391/390]] | ||
| Line 1,373: | Line 1,373: | ||
| {{Monzo| -1 -1 -1 0 0 -1 1 0 1 }} | | {{Monzo| -1 -1 -1 0 0 -1 1 0 1 }} | ||
| Minor naiadvicema | | Minor naiadvicema | ||
| | | | ||
|- | |- | ||
| [[392/391]] | | [[392/391]] | ||
| Line 1,380: | Line 1,380: | ||
| {{Monzo| 3 0 0 2 0 0 -1 0 -1 }} | | {{Monzo| 3 0 0 2 0 0 -1 0 -1 }} | ||
| Minor semivicema | | Minor semivicema | ||
| | | | ||
|- | |- | ||
| [[460/459]] | | [[460/459]] | ||
| Line 1,387: | Line 1,387: | ||
| {{Monzo| 2 -3 1 0 0 0 -1 0 1 }} | | {{Monzo| 2 -3 1 0 0 0 -1 0 1 }} | ||
| Scanisma, vicewolf comma | | Scanisma, vicewolf comma | ||
| | | | ||
|- | |- | ||
| [[484/483]] | | [[484/483]] | ||
| Line 1,401: | Line 1,401: | ||
| {{Monzo| -1 1 0 0 -1 2 0 0 -1 }} | | {{Monzo| -1 1 0 0 -1 2 0 0 -1 }} | ||
| Laodicisma | | Laodicisma | ||
| | | | ||
|- | |- | ||
| [[529/528]] | | [[529/528]] | ||
| Line 1,412: | Line 1,412: | ||
| [[576/575]] | | [[576/575]] | ||
| 3.0082 | | 3.0082 | ||
| (2<sup>3</sup>×3)<sup>2</sup>/ | | ((2<sup>3</sup>×3)/5)<sup>2</sup>/23 | ||
| {{Monzo| 6 2 -2 0 0 0 0 0 -1 }} | | {{Monzo| 6 2 -2 0 0 0 0 0 -1 }} | ||
| Worcester comma | | Worcester comma | ||
| Line 1,422: | Line 1,422: | ||
| {{Monzo| 5 -1 -1 -2 0 0 0 0 1 }} | | {{Monzo| 5 -1 -1 -2 0 0 0 0 1 }} | ||
| Harvardisma | | Harvardisma | ||
| | | | ||
|- | |- | ||
| [[760/759]] | | [[760/759]] | ||
| Line 1,429: | Line 1,429: | ||
| {{Monzo| 3 -1 1 0 -1 0 0 1 -1 }} | | {{Monzo| 3 -1 1 0 -1 0 0 1 -1 }} | ||
| Squadronisma | | Squadronisma | ||
| | | | ||
|- | |- | ||
| [[875/874]] | | [[875/874]] | ||
| Line 1,436: | Line 1,436: | ||
| {{Monzo| -1 0 3 1 0 0 0 -1 -1 }} | | {{Monzo| -1 0 3 1 0 0 0 -1 -1 }} | ||
| Nymphisma | | Nymphisma | ||
| | | | ||
|- | |- | ||
| [[897/896]] | | [[897/896]] | ||
| Line 1,443: | Line 1,443: | ||
| {{Monzo| -7 1 0 -1 0 1 0 0 1 }} | | {{Monzo| -7 1 0 -1 0 1 0 0 1 }} | ||
| Lysistratisma | | Lysistratisma | ||
| | | | ||
|- | |- | ||
| [[1105/1104]] | | [[1105/1104]] | ||
| Line 1,450: | Line 1,450: | ||
| {{Monzo| -4 -1 1 0 0 1 1 0 -1 }} | | {{Monzo| -4 -1 1 0 0 1 1 0 -1 }} | ||
| Fragarisma | | Fragarisma | ||
| | | | ||
|- | |- | ||
| [[1197/1196]] | | [[1197/1196]] | ||
| Line 1,456: | Line 1,456: | ||
| (3<sup>2</sup>×7×19)/(2<sup>2</sup>×13×23) | | (3<sup>2</sup>×7×19)/(2<sup>2</sup>×13×23) | ||
| {{Monzo| -2 2 0 1 0 -1 0 1 -1 }} | | {{Monzo| -2 2 0 1 0 -1 0 1 -1 }} | ||
| | | Rodessisma | ||
| | | | ||
|- | |- | ||
| [[1288/1287]] | | [[1288/1287]] | ||
| Line 1,464: | Line 1,464: | ||
| {{Monzo| 3 -2 0 1 -1 -1 0 0 1 }} | | {{Monzo| 3 -2 0 1 -1 -1 0 0 1 }} | ||
| Santisma, triaphonisma | | Santisma, triaphonisma | ||
| | | | ||
|- | |- | ||
| [[1496/1495]] | | [[1496/1495]] | ||
| Line 1,471: | Line 1,471: | ||
| {{Monzo| 3 0 -1 0 1 -1 1 0 -1 }} | | {{Monzo| 3 0 -1 0 1 -1 1 0 -1 }} | ||
| Turkisma | | Turkisma | ||
| | | | ||
|- | |- | ||
| [[1863/1862]] | | [[1863/1862]] | ||
| Line 1,478: | Line 1,478: | ||
| {{Monzo| -1 4 0 -2 0 0 0 -1 1 }} | | {{Monzo| -1 4 0 -2 0 0 0 -1 1 }} | ||
| Antinousisma | | Antinousisma | ||
| | | | ||
|- | |- | ||
| [[2024/2023]] | | [[2024/2023]] | ||
| Line 1,485: | Line 1,485: | ||
| {{Monzo| 3 0 0 -1 1 0 -2 0 1 }} | | {{Monzo| 3 0 0 -1 1 0 -2 0 1 }} | ||
| Artifisma, insincere comma | | Artifisma, insincere comma | ||
| | | | ||
|- | |- | ||
| [[2025/2024]] | | [[2025/2024]] | ||
| Line 1,499: | Line 1,499: | ||
| {{Monzo| -3 -1 1 -1 0 -1 0 1 1 }} | | {{Monzo| -3 -1 1 -1 0 -1 0 1 1 }} | ||
| Guangdongisma | | Guangdongisma | ||
| | | | ||
|- | |- | ||
| [[2300/2299]] | | [[2300/2299]] | ||
| 0.75287 | | 0.75287 | ||
| ( | | ((2×5)/11)<sup>2</sup>×(23/19) | ||
| {{Monzo| 2 0 2 0 -2 0 0 -1 1 }} | | {{Monzo| 2 0 2 0 -2 0 0 -1 1 }} | ||
| Travellisma | | Travellisma | ||
| Line 1,512: | Line 1,512: | ||
| (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 }} | ||
| Biyativice comma | | Biyativice comma, biyativicema | ||
| | | | ||
|- | |- | ||
| Line 1,524: | Line 1,524: | ||
| [[3060/3059]] | | [[3060/3059]] | ||
| 0.56586 | | 0.56586 | ||
| ( | | ((2×3)<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 }} | ||
| Vicious comma, viciousma | | Vicious comma, viciousma | ||
| Line 1,540: | Line 1,540: | ||
| (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 }} | ||
| Vicedim comma | | Vicedim comma, vicedimma | ||
| | | | ||
|- | |- | ||
| Line 1,547: | Line 1,547: | ||
| (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 }} | ||
| | | Shoalma, vicetride comma | ||
| | | | ||
|- | |- | ||
| Line 1,554: | Line 1,554: | ||
| (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 }} | ||
| Viceaug comma | | Viceaug comma, viceaugma | ||
| | | | ||
|- | |- | ||
| Line 1,589: | Line 1,589: | ||
| (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 }} | ||
| | | Beerglass comma | ||
| | | | ||
|- | |- | ||
| 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 }} | ||
| | | Demiglace comma | ||
| | | | ||
|- | |- | ||
| Line 1,615: | Line 1,615: | ||
| [[Vicetertisma|12168/12167]] | | [[Vicetertisma|12168/12167]] | ||
| 0.14228 | | 0.14228 | ||
| (2<sup>3</sup> | | (2/23)<sup>3</sup>×(3×13)<sup>2</sup> | ||
| {{Monzo| 3 2 0 0 0 2 0 0 -3 }} | | {{Monzo| 3 2 0 0 0 2 0 0 -3 }} | ||
| Vicetertisma | | Vicetertisma | ||
| Line 1,650: | Line 1,650: | ||
| 23276/23275 | | 23276/23275 | ||
| 0.074380 | | 0.074380 | ||
| ( | | ((2×23)/(5×7))<sup>2</sup>×(11/19) | ||
| {{Monzo| 2 0 -2 -2 1 0 0 -1 2 }} | | {{Monzo| 2 0 -2 -2 1 0 0 -1 2 }} | ||
| | | | ||
| | | | ||
|- | |- | ||
| 25025/25024 | | [[Joshuavoisma|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 }} | ||
| | | Joshuavoisma | ||
| | | | ||
|- | |- | ||
| 25921/25920 | | [[Diarithmedia|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 }} | ||
| | | Diarithmedia | ||
| S161 | | S161 | ||
|- | |- | ||
| Line 1,685: | Line 1,685: | ||
| 71875/71874 | | 71875/71874 | ||
| 0.024087 | | 0.024087 | ||
| (5<sup>5</sup>×23)/( | | (5<sup>5</sup>×23)/(2×(3×11)<sup>3</sup>) | ||
| {{Monzo| -1 -3 5 0 -3 0 0 0 1 }} | | {{Monzo| -1 -3 5 0 -3 0 0 0 1 }} | ||
| | | | ||
| Line 1,762: | Line 1,762: | ||
| 2023425/2023424 | | 2023425/2023424 | ||
| 0.00085560 | | 0.00085560 | ||
| ( | | ((3×5×23)<sup>2</sup>×17)/(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 1,769: | Line 1,769: | ||
| 4096576/4096575 | | 4096576/4096575 | ||
| 0.00042261 | | 0.00042261 | ||
| (2<sup>3</sup>×11×23) | | ((2<sup>3</sup>×11×23)/(3<sup>2</sup>×5×17))<sup>2</sup>/7 | ||
| {{Monzo| 6 -4 -2 -1 2 0 -2 0 2 }} | | {{Monzo| 6 -4 -2 -1 2 0 -2 0 2 }} | ||
| | | | ||
| Line 1,776: | Line 1,776: | ||
| 5142501/5142500 | | 5142501/5142500 | ||
| 0.00033665 | | 0.00033665 | ||
| | | 3<sup>3</sup>×((7×13)/(2×5<sup>2</sup>×11))<sup>2</sup>×(23/17) | ||
| {{Monzo| -2 3 -4 2 -2 2 -1 0 1 }} | | {{Monzo| -2 3 -4 2 -2 2 -1 0 1 }} | ||
| | | | ||
| Line 1,782: | Line 1,782: | ||
|} | |} | ||
=== | === Higher-limit === | ||
See: | |||
* [[List of superparticular intervals/29-limit]] | |||
* [[List of superparticular intervals/31-limit]] | |||
* [[List of superparticular intervals/37-limit]] | |||
* [[List of superparticular intervals/41-limit]] | |||
* [[List of superparticular intervals/43-limit]] | |||
* [[List of superparticular intervals/47-limit]] | |||
* [[List of superparticular intervals/53-limit]] | |||
* [[List of superparticular intervals/59-limit]] | |||
* [[List of superparticular intervals/61-limit]] | |||
* [[List of superparticular intervals/67-limit]] | |||
* [[List of superparticular intervals/71-limit]] | |||
* [[List of superparticular intervals/73-limit]] | |||
* [[List of superparticular intervals/79-limit]] | |||
* [[List of superparticular intervals/83-limit]] | |||
* [[List of superparticular intervals/89-limit]] | |||
* [[List of superparticular intervals/97-limit]] | |||
* [[List of superparticular intervals/101-limit]] | |||
* [[List of superparticular intervals/103-limit]] | |||
* [[List of superparticular intervals/107-limit]] | |||
* [[List of superparticular intervals/109-limit]] | |||
* [[List of superparticular intervals/113-limit]] | |||
* [[List of superparticular intervals/127-limit]] | |||
== See also == | == See also == | ||
Latest revision as of 08:38, 28 March 2026
This is a list of superparticular intervals ordered by prime limit. It reaches to the 127-limit and is complete up to the 37-limit.
Størmer's theorem states that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. OEIS: A002071 gives the number of superparticular ratios in each prime limit, OEIS: A145604 shows the increment from limit to limit, and OEIS: A117581 gives the largest numerator for each prime limit (with some exceptions, such as the 23-limit, where the largest value is smaller than that of a smaller prime limit, in this case the 19-limit).
List of superparticular intervals
2-limit
| Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
|---|---|---|---|---|---|
| 2/1 | 1200.000 | 2/1 | [1⟩ | Octave, duple, 2nd harmonic, diapason |
3-limit
| Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
|---|---|---|---|---|---|
| 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, harmonic ninth |
S3 |
5-limit
| Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
|---|---|---|---|---|---|
| 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
| Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
|---|---|---|---|---|---|
| 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 | (2×3)2/(5×7) | [2 2 -1 -1⟩ | Septimal 1/4-tone, mint comma | S6 |
| 49/48 | 35.697 | 72/(24×3) | [-4 -1 0 2⟩ | Large septimal diesis, large septimal 1/6-tone, slendro diesis, semaphoresma | S7 |
| 50/49 | 34.976 | 2×(5/7)2 | [1 0 2 -2⟩ | Small septimal diesis, small septimal 1/6-tone, septimal tritonic diesis, jubilisma | |
| 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
| Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
|---|---|---|---|---|---|
| 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, cake comma | |
| 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/(24×33×7) | [-4 -3 2 -1 2⟩ | Lehmerisma | S55 |
| 9801/9800 | 0.17665 | ((32×11)/(5×7))2/23 | [-3 4 -2 -2 2⟩ | Kalisma, Gauss comma | S99 |
13-limit
| Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
|---|---|---|---|---|---|
| 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 | (5/(2×32))2×13 | [-2 -4 2 0 0 1⟩ | Marveltwin comma | |
| 351/350 | 4.9393 | (33×13)/(2×52×7) | [-1 3 -2 -1 0 1⟩ | Ratwolfsma | |
| 352/351 | 4.9253 | (25×11)/(33×13) | [5 -3 0 0 1 -1⟩ | Major minthma, major gentle comma | |
| 364/363 | 4.7627 | (2/11)2×((7×13)/3) | [2 -1 0 1 -2 1⟩ | Minor minthma, minor 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, sinaisma | |
| 4096/4095 | 0.42272 | (26/3)2/(5×7×13) | [12 -2 -1 -1 0 -1⟩ | Minisma | S64 |
| 4225/4224 | 0.40981 | (5×13)2/(27×3×11) | [-7 -1 2 0 -1 2⟩ | Leprechaun comma | S65 |
| 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
| Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
|---|---|---|---|---|---|
| 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⟩ | Monk 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⟩ | Diatisma, septendecimal major second comma | |
| 154/153 | 11.278 | (2×7×11)/(32×17) | [1 -2 0 1 1 0 -1⟩ | Augustma | |
| 170/169 | 10.214 | (2×5×17)/132 | [1 0 1 0 0 -2 1⟩ | Major naiadma | |
| 221/220 | 7.8514 | (13×17)/(22×5×11) | [-2 0 -1 0 -1 1 1⟩ | Minor naiadma | |
| 256/255 | 6.7759 | 28/(3×5×17) | [8 -1 -1 0 0 0 -1⟩ | Charisma, charic comma, septendecimal kleisma |
S16 |
| 273/272 | 6.3532 | (3×7×13)/(24×17) | [-4 1 0 1 0 1 -1⟩ | Tannisma, prototannisma | |
| 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⟩ | Seminaiadma | |
| 561/560 | 3.0887 | (3×11×17)/(24×5×7) | [-4 1 -1 -1 1 0 1⟩ | Monardisma, tsaharuk comma | |
| 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⟩ | Ainisma, ainic comma | |
| 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⟩ | Cimbrisma | |
| 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⟩ | Heptacircle comma | |
| 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⟩ | Baladisma | |
| 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 | (13/2)4/(3×5×7×17) | [-4 -1 -1 -1 0 4 -1⟩ | Pisanoisma | S169 |
| 31213/31212 | 0.055466 | (74×13)/(22×33×172) | [-2 -3 0 4 0 1 -2⟩ | E-shaped comma | |
| 37180/37179 | 0.046564 | (22×5×11×132)/(37×17) | [2 -7 1 0 1 2 -1⟩ | Lateral comma | |
| 194481/194480 | 0.0089018 | (3×7)4/(24×5×11×13×17) | [-4 4 -1 4 -1 -1 -1⟩ | Scintillisma | S441 |
| 336141/336140 | 0.0051503 | (32×133×17)/(22×5×75) | [-2 2 -1 -5 0 3 1⟩ | Aksial comma |
19-limit
| Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
|---|---|---|---|---|---|
| 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 diesis, 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⟩ | Minithirdma | |
| 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⟩ | Malcolmisma | |
| 190/189 | 9.1358 | (2×5×19)/(33×7) | [1 -3 1 -1 0 0 0 1⟩ | Cotylisma | |
| 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⟩ | Chthonisma | |
| 324/323 | 5.3516 | (2×32)2/(17×19) | [2 4 0 0 0 0 -1 -1⟩ | Photisma | S18 |
| 343/342 | 5.0547 | 73/(2×32×19) | [-1 -2 0 3 0 0 0 -1⟩ | Nutrisma | |
| 361/360 | 4.8023 | 192/(23×32×5) | [-3 -2 -1 0 0 0 0 2⟩ | Go comma, Dudon comma | S19 |
| 400/399 | 4.3335 | (22×5)2/(3×7×19) | [4 -1 2 -1 0 0 0 -1⟩ | Devichroma | S20 |
| 456/455 | 3.8007 | (23×3×19)/(5×7×13) | [3 1 -1 -1 0 -1 0 1⟩ | Abnobisma | |
| 476/475 | 3.6409 | (22×7×17)/(52×19) | [2 0 -2 1 0 0 1 -1⟩ | Hedwigma | |
| 495/494 | 3.5010 | (32×5×11)/(2×13×19) | [-1 2 1 0 1 -1 0 -1⟩ | Eulalisma | |
| 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⟩ | Kingfisher comma | |
| 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⟩ | Solvejgsma | |
| 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⟩ | Kevolisma | |
| 1729/1728 | 1.0016 | (7×13×19)/(22×3)3 | [-6 -3 0 1 0 1 0 1⟩ | Ramanujanisma | |
| 2376/2375 | 0.72879 | ((2×3)/5)3×(11/19) | [3 3 -3 0 1 0 0 -1⟩ | Trichthonisma | |
| 2432/2431 | 0.71200 | (27×19)/(11×13×17) | [7 0 0 0 -1 -1 -1 1⟩ | Blumeyer comma | |
| 2926/2925 | 0.59177 | (2×7×11×19)/((3×5)2×13) | [1 -2 -2 1 1 -1 0 1⟩ | Neovulture comma, neovulturisma | |
| 3136/3135 | 0.55214 | (23×7)2/(3×5×11×19) | [6 -1 -1 2 -1 0 0 -1⟩ | Neomirkwai comma, neomirkwaisma | S56 |
| 3250/3249 | 0.53277 | (2×53×13)/(3×19)2 | [1 -2 3 0 0 1 0 -2⟩ | Martebisma | |
| 4200/4199 | 0.41225 | (23×3×52×7)/(13×17×19) | [3 1 2 1 0 -1 -1 -1⟩ | Neosatanisma | |
| 5776/5775 | 0.29975 | (22×19)2/(3×52×7×11) | [4 -1 -2 -1 -1 0 0 2⟩ | Neovish comma, neovishma | S76 |
| 5929/5928 | 0.29202 | (7×11)2/(23×3×13×19) | [-3 -1 0 2 2 -1 0 -1⟩ | Manzanisma | S77 |
| 5985/5984 | 0.28929 | (32×5×7×19)/(25×11×17) | [-5 2 1 1 -1 0 -1 1⟩ | Neogrendel comma, neogrendelisma | |
| 6175/6174 | 0.28038 | (52×13×19)/(2×32×73) | [-1 -2 2 -3 0 1 0 1⟩ | Neonewtisma | |
| 6860/6859 | 0.25238 | (22×5×73)/193 | [2 0 1 3 0 0 0 -3⟩ | Devicubisma | |
| 10241/10240 | 0.16906 | (72×11×19)/(211×5) | [-11 0 -1 2 1 0 0 1⟩ | ||
| 10830/10829 | 0.15986 | (2×3×5×192)/(72×13×17) | [1 1 1 -2 0 -1 -1 2⟩ | ||
| 12636/12635 | 0.13701 | (22×35×13)/(5×7×192) | [2 5 -1 -1 0 1 0 -2⟩ | Padriellisma | |
| 13377/13376 | 0.12942 | (3×73×13)/(26×11×19) | [-6 1 0 3 -1 1 0 -1⟩ | ||
| 14080/14079 | 0.12296 | (28×5×11)/(3×13×192) | [8 -1 1 0 1 -1 0 -2⟩ | ||
| 14365/14364 | 0.12052 | (5×132×17)/(22×33×7×19) | [-2 -3 1 -1 0 2 1 -1⟩ | ||
| 23409/23408 | 0.073957 | ((3/2)2×17)2/(7×11×19) | [-4 4 0 -1 -1 0 2 -1⟩ | S153 | |
| 27456/27455 | 0.063056 | (26×3×11×13)/(5×172×19) | [6 1 -1 0 1 1 -2 -1⟩ | ||
| 28900/28899 | 0.059905 | ((2×5×17)/(3×13))2/19 | [2 -2 2 0 0 -2 2 -1⟩ | S170 | |
| 43681/43680 | 0.039634 | (11×19)2/(25×3×5×7×13) | [-5 -1 -1 -1 2 -1 0 2⟩ | S209 | |
| 89376/89375 | 0.019370 | (25×3×72×19)/(54×11×13) | [5 1 -4 2 -1 -1 0 1⟩ | ||
| 104976/104975 | 0.016492 | (2×32)4/(52×13×17×19) | [4 8 -2 0 0 -1 -1 -1⟩ | S324 | |
| 165376/165375 | 0.010469 | (29×17×19)/((3×5)3×72) | [9 -3 -3 -2 0 0 1 1⟩ | Decimillisma | |
| 228096/228095 | 0.0075900 | ((22×3)/7)4×(11/(5×19)) | [8 4 -1 -4 1 0 0 -1⟩ | ||
| 601426/601425 | 0.0028786 | (2×72×17×192)/(37×52×11) | [1 -7 -2 2 -1 0 1 2⟩ | ||
| 633556/633555 | 0.0027326 | (22×7×113×17)/(33×5×13×192) | [2 -3 -1 1 3 -1 1 -2⟩ | Devicisma | |
| 709632/709631 | 0.0024396 | (210×32×7×11)/(133×17×19) | [10 2 0 1 1 -3 -1 -1⟩ | ||
| 5909761/5909760 | 0.00029294 | (11×13×17)2/(28×35×5×19) | [-8 -5 -1 0 2 2 2 -1⟩ | S2431 | |
| 11859211/11859210 | 0.00014598 | (19/(3×11))4×((7×13)/(2×5)) | [-1 -4 -1 1 -4 1 0 4⟩ | Tredekisma |
23-limit
| Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
|---|---|---|---|---|---|
| 23/22 | 76.956 | 23/(2×11) | [-1 0 0 0 -1 0 0 0 1⟩ | Large 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⟩ | Undinisma | |
| 115/114 | 15.120 | (5×23)/(2×3×19) | [-1 -1 1 0 0 0 0 -1 1⟩ | Yarmanisma | |
| 161/160 | 10.787 | (7×23)/(25×5) | [-5 0 -1 1 0 0 0 0 1⟩ | Major kirnbergerisma | |
| 162/161 | 10.720 | (2×34)/(7×23) | [1 4 0 -1 0 0 0 0 -1⟩ | Minor kirnbergerisma | |
| 208/207 | 8.3433 | (24×13)/(32×23) | [4 -2 0 0 0 1 0 0 -1⟩ | Vicetone comma | |
| 231/230 | 7.5108 | (3×7×11)/(2×5×23) | [-1 1 -1 1 1 0 0 0 -1⟩ | Major neutravicema | |
| 253/252 | 6.8564 | (11×23)/((2×3)2×7) | [-2 -2 0 -1 1 0 0 0 1⟩ | Middle neutravicema | |
| 276/275 | 6.2840 | (22×3×23)/(52×11) | [2 1 -2 0 -1 0 0 0 1⟩ | Minor neutravicema | |
| 300/299 | 5.7804 | ((2×5)2×3)/(13×23) | [2 1 2 0 0 -1 0 0 -1⟩ | Major naiadvicema | |
| 323/322 | 5.3682 | (17×19)/(2×7×23) | [-1 0 0 -1 0 0 1 1 -1⟩ | Major semivicema | |
| 391/390 | 4.4334 | (17×23)/(2×3×5×13) | [-1 -1 -1 0 0 -1 1 0 1⟩ | Minor naiadvicema | |
| 392/391 | 4.4221 | (23×72)/(17×23) | [3 0 0 2 0 0 -1 0 -1⟩ | Minor semivicema | |
| 460/459 | 3.7676 | (22×5×23)/(33×17) | [2 -3 1 0 0 0 -1 0 1⟩ | Scanisma, vicewolf comma | |
| 484/483 | 3.5806 | (2×11)2/(3×7×23) | [2 -1 0 -1 2 0 0 0 -1⟩ | Pittsburghisma | S22 |
| 507/506 | 3.4180 | (3×132)/(2×11×23) | [-1 1 0 0 -1 2 0 0 -1⟩ | Laodicisma | |
| 529/528 | 3.2758 | 232/(24×3×11) | [-4 -1 0 0 -1 0 0 0 2⟩ | Preziosisma | S23 |
| 576/575 | 3.0082 | ((23×3)/5)2/23 | [6 2 -2 0 0 0 0 0 -1⟩ | Worcester comma | S24 |
| 736/735 | 2.3538 | (25×23)/(3×5×72) | [5 -1 -1 -2 0 0 0 0 1⟩ | Harvardisma | |
| 760/759 | 2.2794 | (23×5×19)/(3×11×23) | [3 -1 1 0 -1 0 0 1 -1⟩ | Squadronisma | |
| 875/874 | 1.9797 | (53×7)/(2×19×23) | [-1 0 3 1 0 0 0 -1 -1⟩ | Nymphisma | |
| 897/896 | 1.9311 | (3×13×23)/(27×7) | [-7 1 0 -1 0 1 0 0 1⟩ | Lysistratisma | |
| 1105/1104 | 1.5674 | (5×13×17)/(24×3×23) | [-4 -1 1 0 0 1 1 0 -1⟩ | Fragarisma | |
| 1197/1196 | 1.4469 | (32×7×19)/(22×13×23) | [-2 2 0 1 0 -1 0 1 -1⟩ | Rodessisma | |
| 1288/1287 | 1.3446 | (23×7×23)/(32×11×13) | [3 -2 0 1 -1 -1 0 0 1⟩ | Santisma, triaphonisma | |
| 1496/1495 | 1.1576 | (23×11×17)/(5×13×23) | [3 0 -1 0 1 -1 1 0 -1⟩ | Turkisma | |
| 1863/1862 | 0.92952 | (34×23)/(2×72×19) | [-1 4 0 -2 0 0 0 -1 1⟩ | Antinousisma | |
| 2024/2023 | 0.85556 | (23×11×23)/(7×172) | [3 0 0 -1 1 0 -2 0 1⟩ | Artifisma, insincere comma | |
| 2025/2024 | 0.85514 | (32×5)2/(23×11×23) | [-3 4 2 0 -1 0 0 0 -1⟩ | Cupcake comma, cupcakesma | S45 |
| 2185/2184 | 0.79251 | (5×19×23)/(23×3×7×13) | [-3 -1 1 -1 0 -1 0 1 1⟩ | Guangdongisma | |
| 2300/2299 | 0.75287 | ((2×5)/11)2×(23/19) | [2 0 2 0 -2 0 0 -1 1⟩ | Travellisma | |
| 2646/2645 | 0.65441 | (2×33×72)/(5×232) | [1 3 -1 2 0 0 0 0 -2⟩ | Biyativice comma, biyativicema | |
| 2737/2736 | 0.63265 | (7×17×23)/(24×32×19) | [-4 -2 0 1 0 0 1 -1 1⟩ | Kotkisma | |
| 3060/3059 | 0.56586 | ((2×3)2×5×17)/(7×19×23) | [2 2 1 -1 0 0 1 -1 -1⟩ | Vicious comma, viciousma | |
| 3381/3380 | 0.51212 | (3×72×23)/(22×5×132) | [-2 1 -1 2 0 -2 0 0 1⟩ | Mikkolisma | |
| 3520/3519 | 0.49190 | (26×5×11)/(32×17×23) | [6 -2 1 0 1 0 -1 0 -1⟩ | Vicedim comma, vicedimma | |
| 3888/3887 | 0.44533 | (24×35)/(132×23) | [4 5 0 0 0 -2 0 0 -1⟩ | Shoalma, vicetride comma | |
| 4693/4692 | 0.36893 | (13×192)/(22×3×17×23) | [-2 -1 0 0 0 1 -1 2 -1⟩ | Viceaug comma, viceaugma | |
| 4761/4760 | 0.36367 | (3×23)2/(23×5×7×17) | [-3 2 -1 -1 0 0 -1 0 2⟩ | Demiquartervice comma | S69 |
| 5083/5082 | 0.34063 | (13×17×23)/(2×3×7×112) | [-1 -1 0 -1 -2 1 1 0 1⟩ | Broadviewsma | |
| 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⟩ | Beerglass comma | |
| 10626/10625 | 0.16293 | (2×3×7×11×23)/(54×17) | [1 1 -4 1 1 0 -1 0 1⟩ | Demiglace comma | |
| 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 -1 0 3 0 -2 1 0 -1⟩ | ||
| 12168/12167 | 0.14228 | (2/23)3×(3×13)2 | [3 2 0 0 0 2 0 0 -3⟩ | Vicetertisma | |
| 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 | ((2×23)/(5×7))2×(11/19) | [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⟩ | Joshuavoisma | |
| 25921/25920 | 0.066790 | (7×23)2/(26×34×5) | [-6 -4 -1 2 0 0 0 0 2⟩ | Diarithmedia | 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×(3×11)3) | [-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 0 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 2 -3⟩ | ||
| 2023425/2023424 | 0.00085560 | ((3×5×23)2×17)/(213×13×19) | [-13 2 2 0 0 -1 1 -1 2⟩ | ||
| 4096576/4096575 | 0.00042261 | ((23×11×23)/(32×5×17))2/7 | [6 -4 -2 -1 2 0 -2 0 2⟩ | S2024 | |
| 5142501/5142500 | 0.00033665 | 33×((7×13)/(2×52×11))2×(23/17) | [-2 3 -4 2 -2 2 -1 0 1⟩ |
Higher-limit
See:
- List of superparticular intervals/29-limit
- List of superparticular intervals/31-limit
- List of superparticular intervals/37-limit
- List of superparticular intervals/41-limit
- List of superparticular intervals/43-limit
- List of superparticular intervals/47-limit
- List of superparticular intervals/53-limit
- List of superparticular intervals/59-limit
- List of superparticular intervals/61-limit
- List of superparticular intervals/67-limit
- List of superparticular intervals/71-limit
- List of superparticular intervals/73-limit
- List of superparticular intervals/79-limit
- List of superparticular intervals/83-limit
- List of superparticular intervals/89-limit
- List of superparticular intervals/97-limit
- List of superparticular intervals/101-limit
- List of superparticular intervals/103-limit
- List of superparticular intervals/107-limit
- List of superparticular intervals/109-limit
- List of superparticular intervals/113-limit
- List of superparticular intervals/127-limit
See also
Notes
External links
- List of intervals on the Huygens-Fokker Foundation website