List of superparticular intervals: Difference between revisions

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


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


== List of superparticular intervals ==
== List of superparticular intervals ==
{| class="wikitable center-6"
=== 2-limit ===
{| class="wikitable center-6" style="width:100%"
|-
|-
! [[Ratio]]
! width="10%" | [[Ratio]]
! [[Cent]]s
! width="10%" | [[Cent]]s
! Factorization
! width="15%" | Factorization
! [[Monzo]]
! width="15%" | [[Monzo]]
! Name(s)
! width="45%" | Name(s)
! Meta<ref>Denoted by s-expressions, where s''k'' is defined as (''k''/(''k'' - 1))/((''k'' + 1)/''k''). See [[square superparticular]] for details.</ref>
! width="5%" | Meta<ref name="ssp">Denoted by S-expressions, where s''k'' is defined as (''k''/(''k'' - 1))/((''k'' + 1)/''k''). See [[square superparticular]] for details.</ref>
|-
! colspan="6" | 2-limit (complete)
|-
|-
| [[2/1]]
| [[2/1]]
Line 20: Line 18:
| 2/1
| 2/1
| {{Monzo| 1 }}
| {{Monzo| 1 }}
| Octave, duple; ''after [[octave reduction]]:'' (perfect) unison, unity, perfect prime, tonic
| Octave, duple, 2nd harmonic, diapason
|
|
|-
|}
! colspan="6" | 3-limit (complete)
 
=== 3-limit ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[3/2]]
| [[3/2]]
Line 42: 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, major whole tone, octave-reduced 9th harmonic or harmonic ninth
| Pythagorean whole tone, Pythagorean major second, <br>major whole tone, octave-reduced 9th harmonic, harmonic ninth
| S3
| S3
|-
|}
! colspan="6" | 5-limit (complete)
 
=== 5-limit ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[5/4]]
| [[5/4]]
Line 53: 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 60: 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 67: 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 89: Line 103:
| Syntonic comma, Didymus comma
| Syntonic comma, Didymus comma
| S9
| S9
|-
|}
! colspan="6" | 7-limit (complete)
 
=== 7-limit ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[7/6]]
| [[7/6]]
Line 97: 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 103: 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 111: 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 118: 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 124: 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<sup>2</sup>×3<sup>2</sup>)/(5×7)
| (2×3)<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, mint comma
| S6
| S6
|-
|-
Line 138: 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 }}
| Slendro diesis, large septimal diesis, large septimal 1/6-tone
| Large septimal diesis, large septimal 1/6-tone, slendro diesis, semaphoresma
| S7
| S7
|-
|-
Line 145: Line 167:
| 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
| Small septimal diesis, small septimal 1/6-tone, septimal tritonic diesis, jubilisma
|
|  
|-
|-
| [[64/63]]
| [[64/63]]
Line 160: 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 181: Line 203:
| {{Monzo| -1 -7 4 1 }}
| {{Monzo| -1 -7 4 1 }}
| Ragisma
| Ragisma
|
|  
|-
|}
! colspan="6" | 11-limit (complete)
 
=== 11-limit ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[11/10]]
| [[11/10]]
Line 189: Line 219:
| 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, <br>undecimal submajor second, Ptolemy's second
|
|  
|-
|-
| [[12/11]]
| [[12/11]]
Line 196: 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
| Small undecimal neutral second
|
|  
|-
|-
| [[22/21]]
| [[22/21]]
Line 204: 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 210: 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 217: 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 224: 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 232: 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 239: 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 260: Line 290:
| {{Monzo| 4 0 -2 -1 1 }}
| {{Monzo| 4 0 -2 -1 1 }}
| Valinorsma
| Valinorsma
|
|  
|-
|-
| [[243/242]]
| [[243/242]]
Line 267: 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 274: Line 304:
| {{Monzo| -7 -1 1 1 1 }}
| {{Monzo| -7 -1 1 1 1 }}
| Keenanisma
| Keenanisma
|
|  
|-
|-
| [[441/440]]
| [[441/440]]
Line 285: Line 315:
| [[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
|
|  
|-
|-
| [[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>3</sup>×7)
| {{Monzo| -4 -3 2 -1 2 }}
| {{Monzo| -4 -3 2 -1 2 }}
| Lehmerisma
| Lehmerisma
Line 299: Line 329:
| [[9801/9800]]
| [[9801/9800]]
| 0.17665
| 0.17665
| (11/(5×7))<sup>2</sup>×3<sup>4</sup>/2<sup>3</sup>
| ((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
| S99
| S99
|-
|}
! colspan="6" | 13-limit (complete)
 
=== 13-limit ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[13/12]]
| [[13/12]]
Line 310: 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 317: Line 355:
| (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
|
|  
|-
|-
| [[26/25]]
| [[26/25]]
Line 324: Line 362:
| (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
|
|  
|-
|-
| [[27/26]]
| [[27/26]]
Line 331: Line 369:
| 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
|
|  
|-
|-
| [[40/39]]
| [[40/39]]
Line 339: 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 346: 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 353: Line 391:
| {{Monzo| 1 1 -1 0 1 -1 }}
| {{Monzo| 1 1 -1 0 1 -1 }}
| Winmeanma
| Winmeanma
|
|  
|-
|-
| [[78/77]]
| [[78/77]]
Line 360: Line 398:
| {{Monzo| 1 1 0 -1 -1 1 }}
| {{Monzo| 1 1 0 -1 -1 1 }}
| Negustma
| Negustma
|
|  
|-
|-
| [[91/90]]
| [[91/90]]
Line 367: 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 374: 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 399: Line 437:
| [[325/324]]
| [[325/324]]
| 5.3351
| 5.3351
| (5<sup>2</sup>×13)/(2<sup>2</sup>×3<sup>4</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
| (3/5)<sup>2</sup>×13/(2×7)
| (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>×13)
| (2<sup>5</sup>×11)/(3<sup>3</sup>×13)
| {{Monzo| 5 -3 0 0 1 -1 }}
| {{Monzo| 5 -3 0 0 1 -1 }}
| Minthma
| Major minthma, major gentle comma
|
|  
|-
|-
| [[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
| Minor minthma, minor gentle comma
|
|  
|-
|-
| [[625/624]]
| [[625/624]]
Line 434: 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 451: Line 489:
| {{Monzo| -3 0 -3 1 1 1 }}
| {{Monzo| -3 0 -3 1 1 1 }}
| Sinbadma
| Sinbadma
|
|  
|-
|-
| [[1716/1715]]
| [[1716/1715]]
Line 458: 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 464: 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 471: 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 }}
| Schismina, tridecimal schisma
| Minisma
| S65
| S64
|-
|-
| [[4225/4224]]
| [[4225/4224]]
Line 479: Line 517:
| {{Monzo| -7 -1 2 0 -1 2 }}
| {{Monzo| -7 -1 2 0 -1 2 }}
| Leprechaun comma
| Leprechaun comma
| S66
| S65
|-
|-
| [[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
|
|  
|-
|-
| [[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 501: Line 539:
| Chalmersia
| Chalmersia
| S351
| S351
|-
|}
! colspan="6" | 17-limit (complete)
 
=== 17-limit ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[17/16]]
| [[17/16]]
Line 508: 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 515: 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 523: 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 530: 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 537: 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 544: 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 550: Line 596:
| (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 (?)
| Monk comma
|
|  
|-
|-
| [[120/119]]
| [[120/119]]
Line 558: 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>×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
| Diatisma, septendecimal major second comma
|
|  
|-
|-
| 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 }}
| Augustma
|  
|  
|
|-
|-
| [[170/169]]
| [[170/169]]
Line 579: 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 586: 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 592: 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 }}
| Septendecimal kleisma, octave-reduced 255th subharmonic
| Charisma, charic comma, <br>septendecimal kleisma
| S16
| S16
|-
|-
Line 599: Line 645:
| (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, prototannisma
|
|  
|-
|-
| [[289/288]]
| [[289/288]]
Line 621: Line 667:
| {{Monzo| 1 -2 0 -2 0 1 1 }}
| {{Monzo| 1 -2 0 -2 0 1 1 }}
| Seminaiadma
| Seminaiadma
|
|  
|-
|-
| 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 }}
| Monardisma, tsaharuk comma
|  
|  
|
|-
|-
| [[595/594]]
| [[595/594]]
Line 642: 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 649: 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 655: Line 701:
| (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 }}
| Ainic comma, ainos
| Ainisma, ainic comma
|
|  
|-
|-
| [[1089/1088]]
| [[1089/1088]]
Line 679: Line 725:
| S35
| S35
|-
|-
| 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 }}
| Cimbrisma
|  
|  
|
|-
|-
| [[1701/1700]]
| [[1701/1700]]
Line 691: 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 698: Line 744:
| {{Monzo| 1 1 0 3 -2 0 -1 }}
| {{Monzo| 1 1 0 3 -2 0 -1 }}
| Xenisma
| Xenisma
|
|  
|-
|-
| 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 }}
| Heptacircle comma
|  
|  
|
|-
|-
| [[2500/2499]]
| [[2500/2499]]
Line 721: Line 767:
| S51
| S51
|-
|-
| 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 }}
| Baladisma
|  
|  
|
|-
|-
| [[5832/5831]]
| [[5832/5831]]
Line 733: 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 740: 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 751: Line 797:
| [[28561/28560]]
| [[28561/28560]]
| 0.060616
| 0.060616
| 13<sup>4</sup>/(2<sup>4</sup>×3×5×7×17)
| (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 }}
| Neuseisma
| Pisanoisma
| S169
| S169
|-
|-
| 31213/31212
| [[E-shaped comma|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 }}
| 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
|  
|  
|
|-
|-
| [[194481/194480]]
| [[Scintillisma|194481/194480]]
| 0.008902
| 0.0089018
| (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 }}
Line 777: Line 823:
| S441
| S441
|-
|-
| 336141/336140
| [[Aksial comma|336141/336140]]
| 0.005150
| 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
|  
|  
|
|}
|-
 
! colspan="6" | 19-limit (complete)
=== 19-limit ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[19/18]]
| [[19/18]]
Line 791: 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 798: 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 804: 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 812: 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 819: 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 826: 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 833: 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 839: Line 893:
| (7×19)/(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 }}
| Minithirdma
|  
|  
|
|-
|-
| [[153/152]]
| [[153/152]]
Line 847: 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 853: Line 907:
| (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 }}
| Malcolmisma
|  
|  
|
|-
|-
| 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 }}
| Cotylisma
|  
|  
|
|-
|-
| 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
|
|  
|-
|-
| 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
|
|  
|-
|-
| 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 }}
| Chthonisma
|  
|  
|
|-
|-
| [[324/323]]
| [[324/323]]
Line 888: Line 942:
| (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
| Photisma
| S18
| S18
|-
|-
| 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 }}
| Nutrisma
|  
|  
|
|-
|-
| 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, Dudon comma
| S19
| S19
|-
|-
| 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 }}
|  
| Devichroma
| S20
| S20
|-
|-
| 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 }}
| Abnobisma
|  
|  
|
|-
|-
| 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 }}
| Hedwigma
|  
|  
|
|-
|-
| 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 }}
| Eulalisma
|  
|  
|
|-
|-
| [[513/512]]
| [[513/512]]
Line 937: 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]]
| 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 }}
| Kingfisher comma
|  
|  
|
|-
|-
| [[1216/1215]]
| [[1216/1215]]
Line 952: 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]]
| 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 }}
| Solvejgsma
|  
|  
|
|-
|-
| [[1445/1444]]
| [[1445/1444]]
Line 966: 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 975: Line 1,029:
| S39
| S39
|-
|-
| 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 }}
| Kevolisma
|  
|  
|
|-
|-
| [[1729/1728]]
| [[1729/1728]]
Line 987: 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]]
| 0.7288
| 0.72879
| (2<sup>3</sup>×3<sup>3</sup>×11)/(5<sup>3</sup>×19)
| ((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
|  
|  
|
|-
|-
| 2432/2431
| [[2432/2431]]
| 0.7120
| 0.71200
| (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
|
|  
|-
|-
| 2926/2925
| [[2926/2925]]
| 0.5918
| 0.59177
| (2×7×11×19)/(3<sup>2</sup>×5<sup>2</sup>×13)
| (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
|  
|  
|
|-
|-
| 3136/3135
| [[3136/3135]]
| 0.5521
| 0.55214
| (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 }}
|  
| Neomirkwai comma, neomirkwaisma
| S56
| S56
|-
|-
| 3250/3249
| [[3250/3249]]
| 0.5328
| 0.53277
| (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 }}
| Martebisma
|  
|  
|
|-
|-
| 4200/4199
| [[4200/4199]]
| 0.4123
| 0.41225
| (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 }}
| Neosatanisma
|  
|  
|
|-
|-
| 5776/5775
| [[5776/5775]]
| 0.2998
| 0.29975
| (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 }}
|  
| Neovish comma, neovishma
| S76
| S76
|-
|-
| 5929/5928
| [[5929/5928]]
| 0.2920
| 0.29202
| (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
|-
|-
| 5985/5984
| [[5985/5984]]
| 0.2893
| 0.28929
| (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 }}
| Neogrendel comma, neogrendelisma
|  
|  
|
|-
|-
| 6175/6174
| [[6175/6174]]
| 0.2804
| 0.28038
| (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 }}
| Neonewtisma
|  
|  
|
|-
|-
| 6860/6859
| [[6860/6859]]
| 0.2524
| 0.25238
| (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
| 0.1691
| 0.16906
| (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 }}
|  
|  
|
|  
|-
|-
| 10830/10829
| 10830/10829
| 0.1599
| 0.15986
| (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 }}
|  
|  
|
|  
|-
|-
| 12636/12635
| [[12636/12635]]
| 0.1370
| 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
| 0.1294
| 0.12942
| (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 }}
|  
|  
|
|  
|-
|-
| 14080/14079
| 14080/14079
| 0.1230
| 0.12296
| (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 }}
|  
|  
|
|  
|-
|-
| 14365/14364
| 14365/14364
| 0.1205
| 0.12052
| (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 2 1 -1 }}
| {{Monzo| -2 -3 1 -1 0 2 1 -1 }}
|  
|  
|
|  
|-
|-
| 23409/23408
| 23409/23408
| 0.07396
| 0.073957
| (3<sup>2</sup>×17)<sup>2</sup>/(2<sup>4</sup>×7×11×19)
| ((3/2)<sup>2</sup>×17)<sup>2</sup>/(7×11×19)
| {{Monzo| -4 4 0 -1 -1 0 1 -1 }}
| {{Monzo| -4 4 0 -1 -1 0 2 -1 }}
|  
|  
| S153
| S153
|-
|-
| 27456/27455
| 27456/27455
| 0.06306
| 0.063056
| (2<sup>6</sup>×3×11)/(5×17<sup>2</sup>×19)
| (2<sup>6</sup>×3×11×13)/(5×17<sup>2</sup>×19)
| {{Monzo| 6 1 -1 0 1 0 -2 -1 }}
| {{Monzo| 6 1 -1 0 1 1 -2 -1 }}
|
|  
|  
|
|-
|-
| 28900/28899
| 28900/28899
| 0.05991
| 0.059905
| (2×5×17)<sup>2</sup>/(3<sup>2</sup>×13<sup>2</sup>×19)
| ((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 1,130: Line 1,184:
|-
|-
| 43681/43680
| 43681/43680
| 0.03963
| 0.039634
| (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 1,137: Line 1,191:
|-
|-
| 89376/89375
| 89376/89375
| 0.01937
| 0.019370
| (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 }}
|  
|  
|
|  
|-
|-
| 104976/104975
| 104976/104975
| 0.01649
| 0.016492
| (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 -1 -1 -1 }}
|  
|  
| S324
| S324
|-
|-
| 165376/165375
| [[Decimillisma|165376/165375]]
| 0.01047
| 0.010469
| (2<sup>9</sup>×17×19)/(3<sup>3</sup>×5<sup>3</sup>×7<sup>2</sup>)
| (2<sup>9</sup>×17×19)/((3×5)<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
| 0.007590
| 0.0075900
| (2<sup>8</sup>×3<sup>4</sup>×11)/(5×7<sup>4</sup>×19)
| ((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
| 0.002879
| 0.0028786
| (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 }}
|  
|  
|
|  
|-
|-
| 633556/633555
| [[Devicisma|633556/633555]]
| 0.002733
| 0.0027326
| (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 }}
| Devicisma
|  
|  
|
|-
|-
| 709632/709631
| 709632/709631
| 0.002440
| 0.0024396
| (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 }}
|  
|  
|
|  
|-
|-
| 5909761/5909760
| 5909761/5909760
| 0.0002929
| 0.00029294
| (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 1,192: Line 1,246:
| S2431
| S2431
|-
|-
| 11859211/11859210
| <font style="font-size:0.88em">[[11859211/11859210]]</font>
| 0.0001460
| 0.00014598
| (7×13×19<sup>4</sup>)/(2×3<sup>4</sup>×5×11<sup>4</sup>)
| (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
|  
|  
|
|}
|-
 
! colspan="6" | 23-limit (complete)
=== 23-limit ===
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp"/>
|-
|-
| [[23/22]]
| [[23/22]]
Line 1,205: 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 }}
| Greater vicesimotertial semitone
| Large vicesimotertial semitone
|
|  
|-
|-
| [[24/23]]
| [[24/23]]
Line 1,213: 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 1,220: 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 1,227: 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 1,234: 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 1,240: Line 1,302:
| (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 }}
| Undinisma
|  
|  
|
|-
|-
| 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 }}
| Yarmanisma
|  
|  
|
|-
|-
| 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 }}
| Major kirnbergerisma
|  
|  
|
|-
|-
| 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 }}
| Minor kirnbergerisma
|  
|  
|
|-
|-
| 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 }}
| Vicetone comma
|  
|  
|
|-
|-
| 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 }}
| Major neutravicema
|  
|  
|
|-
|-
| 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 }}
| Middle neutravicema
|  
|  
|
|-
|-
| 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 }}
| Minor neutravicema
|  
|  
|
|-
|-
| 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 }}
| Major naiadvicema
|  
|  
|
|-
|-
| 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 }}
| Major semivicema
|  
|  
|
|-
|-
| 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 }}
| Minor naiadvicema
|  
|  
|
|-
|-
| 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 }}
| Minor semivicema
|  
|  
|
|-
|-
| 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 }}
| Scanisma, vicewolf comma
|  
|  
|
|-
|-
| 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 }}
|  
| Pittsburghisma
| S22
| S22
|-
|-
| 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 }}
| Laodicisma
|  
|  
|
|-
|-
| 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 }}
|  
| Preziosisma
| S23
| S23
|-
|-
| [[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)/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
| S24
| S24
|-
|-
| 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 }}
|
| Harvardisma
|
|  
|-
|-
| 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 }}
|
| Squadronisma
|
|  
|-
|-
| 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 }}
|
| Nymphisma
|
|  
|-
|-
| 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 }}
|
| Lysistratisma
|
|  
|-
|-
| 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 }}
|
| Fragarisma
|
|  
|-
|-
| 1197/1196
| [[1197/1196]]
| 1.4469
| 1.4469
| (3<sup>2</sup>×17×19)/(2<sup>2</sup>×13×23)
| (3<sup>2</sup>×7×19)/(2<sup>2</sup>×13×23)
| {{Monzo| -2 2 0 0 0 -1 1 1 -1 }}
| {{Monzo| -2 2 0 1 0 -1 0 1 -1 }}
|
| Rodessisma
|
|  
|-
|-
| 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 }}
|
| Santisma, triaphonisma
|
|  
|-
|-
| 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 }}
|
| Turkisma
|
|  
|-
|-
| 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 }}
|
| Antinousisma
|
|  
|-
|-
| 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 }}
|
| Artifisma, insincere comma
|
|  
|-
|-
| 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 }}
|  
| Cupcake comma, cupcakesma
| S45
| S45
|-
|-
| 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 }}
|
| Guangdongisma
|
|  
|-
|-
| 2300/2299
| [[2300/2299]]
| 0.75287
| 0.75287
| (2<sup>2</sup>×5<sup>2</sup>×23)/(11<sup>2</sup>×19)
| ((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
|  
|  
|-
|-
| 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 }}
|  
| Biyativice comma, biyativicema
|  
|  
|-
|-
| 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 }}
|  
| Kotkisma
|  
|  
|-
|-
| 3060/3059
| [[3060/3059]]
| 0.56586
| 0.56586
| (2<sup>2</sup>×3<sup>2</sup>×5×17)/(7×19×23)
| ((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
|  
|  
|-
|-
| 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 }}
|  
| Mikkolisma
|  
|  
|-
|-
| 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 }}
|  
| Vicedim comma, vicedimma
|  
|  
|-
|-
| 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 }}
|  
| Shoalma, vicetride comma
|  
|  
|-
|-
| 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 }}
|  
| Viceaug comma, viceaugma
|  
|  
|-
|-
| 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 }}
|  
| Demiquartervice comma
| S69
| S69
|-
|-
| 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 }}
|  
| Broadviewsma
|  
|  
|-
|-
| 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)
Line 1,516: Line 1,578:
|  
|  
|-
|-
| 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)
Line 1,523: Line 1,585:
| S91
| S91
|-
|-
| 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 }}
|  
| 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 1,547: Line 1,609:
| 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 -1 0 3 0 -2 1 0 -1 }}
|  
|  
|  
|  
|-
|-
| 12168/12167
| [[Vicetertisma|12168/12167]]
| 0.14228
| 0.14228
| (2<sup>3</sup>×3<sup>2</sup>×13<sup>2</sup>)/23<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
|  
|  
|-
|-
Line 1,588: Line 1,650:
| 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)
| ((2×23)/(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 1,623: Line 1,685:
| 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×(3×11)<sup>3</sup>)
| {{Monzo| -1 -3 5 0 -3 0 0 0 1 }}
| {{Monzo| -1 -3 5 0 -3 0 0 0 1 }}
|  
|  
Line 1,645: Line 1,707:
| 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 0 0 2 2 -1 }}
|  
|  
| S323
| S323
Line 1,694: Line 1,756:
| 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 2 -3 }}
|  
|  
|  
|  
Line 1,700: Line 1,762:
| 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)
| ((3×5×23)<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 1,707: Line 1,769:
| 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)/(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 1,714: Line 1,776:
| 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>×((7×13)/(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 }}
|  
|  
|  
|  
|-
|}
! colspan="6" | 29-limit (incomplete)
 
|-
=== Higher-limit ===
| [[29/28]]
See:
| 60.751
* [[List of superparticular intervals/29-limit]]
| 29/(2<sup>2</sup>×7)
* [[List of superparticular intervals/31-limit]]
| 2.7.29 {{monzo| -2 -1 1 }}
* [[List of superparticular intervals/37-limit]]
| Large vicesimononal 1/4-tone
* [[List of superparticular intervals/41-limit]]
|
* [[List of superparticular intervals/43-limit]]
|-
* [[List of superparticular intervals/47-limit]]
| [[30/29]]
* [[List of superparticular intervals/53-limit]]
| 58.692
* [[List of superparticular intervals/59-limit]]
| (2×3×5)/29
* [[List of superparticular intervals/61-limit]]
| 2.3.5.29 {{monzo| 1 1 1 -1 }}
* [[List of superparticular intervals/67-limit]]
| Small vicesimononal 1/4-tone
* [[List of superparticular intervals/71-limit]]
|
* [[List of superparticular intervals/73-limit]]
|-
* [[List of superparticular intervals/79-limit]]
| [[58/57]]
* [[List of superparticular intervals/83-limit]]
| 30.109
* [[List of superparticular intervals/89-limit]]
| (2×29)/(3×19)
* [[List of superparticular intervals/97-limit]]
| 2.3.19.29 {{monzo| 1 -1 -1 1 }}
* [[List of superparticular intervals/101-limit]]
|
* [[List of superparticular intervals/103-limit]]
|
* [[List of superparticular intervals/107-limit]]
|-
* [[List of superparticular intervals/109-limit]]
| [[88/87]]
* [[List of superparticular intervals/113-limit]]
| 19.786
* [[List of superparticular intervals/127-limit]]
| (2<sup>3</sup>×11)/(3×29)
| 2.3.11.29 {{monzo| 3 -1 1 -1 }}
|
|
|-
| 116/115
| 14.989
| (2<sup>2</sup>×29)/(5×23)
| 2.5.23.29 {{monzo| 2 -1 -1 1 }}
|
|
|-
| 117/116
| 14.860
| (3<sup>3</sup>×13)/(2<sup>2</sup>×29)
| 2.3.13.29 {{monzo| -2 3 1 -1 }}
|
|
|-
| [[145/144]]
| 11.981
| (5×29)/(2<sup>2</sup>×3)<sup>2</sup>
| 2.3.5.29 {{monzo| -4 -2 1 1 }}
| 29th-partial chroma
|
|-
| 175/174
| 9.9211
| (5<sup>2</sup>×7)/(2×3×29)
| 2.3.5.7.29 {{monzo| -1 -1 2 1 -1 }}
|
|
|-
| 204/203
| 8.5073
| (2<sup>2</sup>×3×17)/(7×29)
| 2.3.7.17.29 {{monzo| 2 1 -1 1 -1 }}
|
|
|-
| 232/231
| 7.4783
| (2<sup>3</sup>×29)/(3×7×11)
| 2.3.7.11.29 {{monzo| 3 -1 -1 -1 1 }}
|
|
|-
| 261/260
| 6.6458
| (3<sup>2</sup>×29)/(2<sup>2</sup>×5×13)
| 2.3.5.13.29 {{monzo| -2 2 -1 -1 1 }}
|
|
|-
| 290/289
| 5.9801
| (2×5×29)/17<sup>2</sup>
| 2.5.17.29 {{monzo| 1 1 -2 1 }}
|
|
|-
| 320/319
| 5.4186
| (2<sup>6</sup>×5)/(11×29)
| 2.5.11.29 {{monzo| 6 1 -1 -1 }}
|
|
|-
| 378/377
| 4.5861
| (2×3<sup>3</sup>×7)/(13×29)
| 2.3.7.13.29 {{monzo| 1 3 1 -1 -1 }}
|
|
|-
| 406/405
| 4.2694
| (2×7×29)/(3<sup>4</sup>×5)
| 2.3.5.7.29 {{monzo| 1 -4 -1 1 1 }}
|
|
|-
| 494/493
| 3.5081
| (2×13×19)/(17×29)
| 2.13.17.19.29 {{monzo| 1 1 -1 1 -1 }}
|
|
|-
| 551/550
| 3.1448
| (19×29)/(2×5<sup>2</sup>×11)
| 2.5.11.19.29 {{monzo| -1 -2 -1 1 1 }}
|
|
|-
| [[552/551]]
| 3.1391
| (2<sup>3</sup>×3×23)/(19×29)
| 2.3.19.23.29 {{monzo| 3 1 -1 1 -1 }}
| Marmosarubra
|
|-
| 609/608
| 2.8451
| (3×7×19)/(2<sup>5</sup>×29)
| 2.3.7.19.29 {{monzo| -5 1 1 1 -1 }}
|
|
|-
| 638/637
| 2.7157
| (2×11×29)/(7<sup>2</sup>×13)
| 2.7.11.13.29 {{monzo| 1 -2 1 -1 1 }}
|
|
|-
| 726/725
| 2.3863
| (2×3×11<sup>2</sup>)/(5<sup>2</sup>×29)
| 2.3.5.11.29 {{monzo| 1 1 -2 2 -2 }}
|
|
|-
| 783/782
|
|
| 2.3.17.23.29 {{monzo|-1 3 -1 -1 1}}
|
|
|-
| 784/783
| 2.2096
| (2<sup>2</sup>×7)<sup>2</sup>/(3<sup>3</sup>×29)
| 2.3.7.29 {{monzo| 4 -3 2 -1 }}
|
| S28
|-
| 841/840
| 2.0598
| 29<sup>2</sup>/(2<sup>3</sup>×3×5×7)
| 2.3.5.7.29 {{monzo| -3 -1 -1 -1 2 }}
|
| S29
<!--To be logged:
1015/1014 -1 -1 1 1 0 -2 0 0 0 1
1045/1044 -2 -2 1 0 1 0 0 1 0 -1
1276/1275 2 -1 -2 0 1 0 -1 0 0 1
1450/1449 1 -2 2 -1 0 0 0 0 -1 1
1596/1595 2 1 -1 1 -1 0 0 1 0 -1
1625/1624 -3 0 3 -1 0 1 0 0 0 -1
1683/1682 -1 2 0 0 1 0 1 0 0 -2
2001/2000 -4 1 -3 0 0 0 0 0 1 1
2002/2001 1 -1 0 1 1 1 0 0 -1 -1
2176/2175 7 -1 -2 0 0 0 1 0 0 -1
2205/2204 -2 2 1 2 0 0 0 -1 0 -1
2262/2261 1 1 0 -1 0 1 -1 -1 0 1
2465/2464 -5 0 1 -1 -1 0 1 0 0 1
2640/2639 4 1 1 -1 1 -1 0 0 0 -1
2755/2754 -1 -4 1 0 0 0 -1 1 0 1
2784/2783 5 1 0 0 -2 0 0 0 -1 1
3249/3248 -4 2 0 -1 0 0 0 2 0 -1
3451/3450 -1 -1 -2 1 0 0 1 0 -1 1
3510/3509 1 3 1 0 -2 1 0 0 0 -1
4641/4640 -5 1 -1 1 0 1 1 0 0 -1
4785/4784 -4 1 1 0 1 -1 0 0 -1 1
4901/4900 -2 0 -2 -2 0 2 0 0 0 1
5104/5103 4 -6 0 -1 1 0 0 0 0 1
5888/5887 8 0 0 -1 0 0 0 0 1 -2
5916/5915 2 1 -1 -1 0 -2 1 0 0 1
6670/6669 1 -3 1 0 0 -1 0 -1 1 1
7106/7105 1 0 -1 -2 1 0 1 1 0 -1
7425/7424 -8 3 2 0 1 0 0 0 0 -1
7889/7888 -4 0 0 3 0 0 -1 0 1 -1
8671/8670 -1 -1 -1 0 0 1 -2 0 1 1
9802/9801 1 -4 0 0 -2 2 0 0 0 1
10557/10556 -2 3 0 -1 0 -1 1 0 1 -1
11340/11339 2 4 1 1 0 0 -1 0 -1 -1
12006/12005 1 2 -1 -4 0 0 0 0 1 1
12673/12672 -7 -2 0 0 -1 0 0 1 1 1
13225/13224 -3 -1 2 0 0 0 0 -1 2 -1
13311/13310 -1 3 -1 0 -3 0 1 0 0 1
13312/13311 10 -3 0 0 0 1 -1 0 0 -1-->
|-
|13456/13455
| 0.12866
|
| 2.3.5.13.23.29 {{monzo|4 -2 -1 0 0 -1 0 0 -1 2}}
|
| S116
<!--
19228/19227 2 -1 0 0 1 -1 -1 1 1 -1
20736/20735 8 4 -1 0 -1 -1 0 0 0 -1
23751/23750 -1 2 -4 1 0 1 0 -1 0 1
24795/24794 -1 2 1 -2 -1 0 0 1 -1 1
25840/25839 4 -4 1 0 -1 0 1 1 0 -1
27000/26999 3 3 3 -2 0 0 0 -1 0 -1
30625/30624 -5 -1 4 2 -1 0 0 0 0 -1
30856/30855 3 -1 -1 1 -2 0 -1 1 0 1
35322/35321 1 1 0 1 -1 -2 0 -1 0 2
47125/47124 -2 -2 3 -1 -1 1 -1 0 0 1
53361/53360 -4 2 -1 2 2 0 0 0 -1 -1
72501/72500 -2 1 -4 0 1 3 0 0 0 -1
83521/83520 -6 -2 -1 0 0 0 4 0 0 -1
87465/87464 -3 1 1 3 0 -1 1 0 0 -2
136851/136850 -1 1 -2 -1 2 1 -1 0 -1 1
158950/158949 1 -3 2 -1 1 0 2 0 0 -2
166635/166634 -1 2 1 1 0 -2 -1 0 2 -1
168751/168750 -1 -3 -5 0 1 0 0 0 2 1
176001/176000 -7 1 -3 1 -1 0 2 0 0 1
176176/176175 4 -5 -2 1 2 1 0 0 0 -1
184093/184092 -2 -1 0 2 0 1 2 0 -2 -1
240787/240786 -1 -3 0 -3 0 -1 0 2 1 1
244036/244035 2 -2 -1 0 -1 2 -1 2 0 -1-->
|-
|303601/303600
|
|
| 2.3.5.11.19.23.29 {{monzo|-4 -1 -2 -1 2 -1 2}}
|
| S551
<!--
410670/410669 1 5 1 -2 0 2 -2 0 0 -1
418761/418760 -3 2 -1 1 0 0 2 -2 1 -1-->
|-
| 613089/613088
|
|
| 2.3.7.17.23.29 {{monzo| -5 6 0 -2 0 0 -1 0 -1 2}}
|
| S783<!--
949026/949025 1 1 -2 -1 -1 1 -1 0 3 -1
1163800/1163799 3 -2 2 -3 1 -1 0 0 2 -1
1235169/1235168 -5 5 0 0 -3 1 1 0 1 -1
1243840/1243839 6 -1 1 0 0 2 -1 0 1 -3
1625625/1625624 -3 2 4 -2 -1 -1 2 0 0 -1
1852201/1852200 -3 -3 -2 -3 0 1 3 0 0 1
2697696/2697695 5 2 -1 -3 -2 -1 1 1 0 1
4004001/4004000 -5 2 -3 -1 -1 -1 0 0 2 2
4090625/4090624 -8 0 5 1 1 0 1 -1 0 -2
-->
|-
| 8268800/8268799
| 2.0937×10⁻⁴
|
| 2.5.7.11.17.19.23.29 {{monzo|10 2 -2 -1 1 1 -2 -1}}
|
|
|-
| 10556001/10556000
| 1.6400×10⁻⁴
|
| 2.3.5.7.13.19.29 {{monzo|-5 4 -3 -1 -1 4 -1}}
|
|
|-
| 18085705/18085704
| 9.5724×10⁻⁵
|
| 2.3.5.7.11.13.17.23.29 {{monzo|-3 -1 1 -3 1 -3 1 1 2}}
|
|
|-
| 96059601/96059600
| 1.8022×10⁻⁵
|
| 2.3.5.7.11.13.29 {{monzo|-4 8 -2 -2 4 -2 -1}}
|
| S9801
|-
| 177182721/177182720
| 9.7709×10⁻⁶
|
| 2.3.5.11.13.17.29 {{monzo|-11 6 -1 -3 -1 2 2}}
|
| S13311
|-
! colspan="6" | 31-limit (incomplete)
|-
| [[31/30]]
| 56.767
| 31/(2×3×5)
| 2.3.5.31 {{monzo| -1 -1 -1 1 }}
| Large tricesimoprimal 1/4-tone
|
|-
| [[32/31]]
| 54.964
| 2<sup>5</sup>/31
| 2.31 {{monzo| 5 -1 }}
| Small tricesimoprimal 1/4-tone, octave-reduced 31st subharmonic
|
|-
| [[63/62]]
| 27.700
| (3<sup>2</sup>×7)/(2×31)
| 2.3.7.31 {{monzo| -1 2 1 -1 }}
|
|
|-
| [[93/92]]
| 18.716
| (3×31)/(2<sup>2</sup>×23)
| 2.3.23.31 {{monzo| -2 1 -1 1 }}
|
|
|-
| [[125/124]]
| 13.906
| 5<sup>3</sup>/(2<sup>2</sup>×31)
| 2.5.31 {{monzo| -2 3 -1 }}
| Twizzler
|
|-
| [[621/620]]
| 2.7901
| (3<sup>3</sup>×23)/(2<sup>2</sup>×5×31)
| 2.3.5.23.31 {{monzo| -2 3 -1 1 -1 }}
| Owowhatsthisma
|
|-
| 900/899
| 1.9247
| (2×3×5)<sup>2</sup>/(29×31)
| 2.3.5.29.31 {{monzo| 2 2 2 -1 -1 }}
|
| S30
|-
| [[961/960]]
| 1.8024
| 31<sup>2</sup>/(2<sup>6</sup>×3×5)
| 2.3.5.31 {{monzo| -6 -1 -1 2 }}
|
| S31
|-
| 1024/1023
| 1.9247
| 2<sup>10</sup>/(3×11×31)
| 2.3.11.31 {{monzo| 10 -1 -1 -1 }}
|
| S32
|-
| [[3969/3968]]
| 0.43624
| (3<sup>2</sup>×7)<sup>2</sup>/(2<sup>7</sup>×31)
| 2.3.7.31 {{monzo| -7 4 2 -1 }}
| Yunzee comma
| S63
|-
! colspan="6" | 37-limit (incomplete)
|-
| [[37/36]]
| 47.434
| 37/(2<sup>2</sup>×3<sup>2</sup>)
| 2.3.37 {{monzo| -2 -2 1 }}
| Large tricesimoseptimal 1/4-tone, 37th-partial chroma
|
|-
| [[38/37]]
| 46.169
| (2×19)/37
| 2.19.37 {{monzo| 1 1 -1 }}
| Small tricesimoseptimal 1/4-tone
|
|-
| [[75/74]]
| 23.238
| (3×5<sup>2</sup>)/(2×37)
| 2.3.5.37 {{monzo| -1 1 2 -1 }}
|
|
|-
| 1296/1295
| 1.3363
| (2×3)<sup>4</sup>/(5×7×37)
| 2.3.5.7.37 {{monzo| 4 4 -1 -1 -1 }}
|
| S36
|-
| [[1369/1368]]
| 1.2651
| 37<sup>2</sup>/(2<sup>3</sup>×3<sup>2</sup>×19)
| 2.3.19.37 {{monzo| -3 -2 -1 2 }}
|
| S37
|-
| 1444/1443
| 1.1993
| (2×19)<sup>2</sup>/(3×13×37)
| 2.3.13.19.37 {{monzo| 2 -1 -1 2 -1 }}
|
| S38
|-
! colspan="6" | 41-limit (incomplete)
|-
| [[41/40]]
| 42.749
| 41/(2<sup>3</sup>×5)
| 2.5.41 {{monzo| -3 -1 1 }}
| Large quadracesimoprimal 1/5-tone
|
|-
| [[42/41]]
| 41.719
| (2×3×7)/41
| 2.3.7.41 {{monzo| 1 1 1 -1 }}
| Small quadracesimoprimal 1/5-tone
|
|-
| [[82/81]]
| 21.242
| (2×41)/3<sup>4</sup>
| 2.3.41 {{monzo| 1 -4 1 }}
| 41st-partial chroma
|
|-
| 1600/1599
| 1.0824
| (2<sup>3</sup>×5)<sup>2</sup>/(3×13×41)
| 2.3.5.13.41 {{monzo| 6 -1 2 -1 -1 }}
|
| S40
|-
| [[1681/1680]]
| 1.0302
| 41<sup>2</sup>/(2<sup>4</sup>×3×5×7)
| 2.3.5.7.41 {{monzo| -4 -1 -1 -1 2 }}
|
| S41
|-
! colspan="6" | 43-limit (incomplete)
|-
| [[43/42]]
| 40.737
| 43/(2×3×7)
| 2.3.7.43 {{monzo| -1 -1 -1 1 }}
| Large quadracesimotertial 1/5-tone
|
|-
| [[44/43]]
| 39.800
| (2<sup>2</sup>×11)/43
| 2.11.43 {{monzo| 2 1 -1 }}
| Small quadracesimotertial 1/5-tone
|
|-
| [[86/85]]
| 20.249
| (2×43)/(5×17)
| 2.5.17.43 {{monzo| 1 -1 -1 1 }}
|
|
|-
| [[87/86]]
| 20.014
| (3×29)/(2×43)
| 2.3.29.43 {{monzo| -1 1 1 -1 }}
|
|
|-
| [[129/128]]
| 13.473
| (3×43)/2<sup>7
| 2.3.43 {{monzo| -7 1 1 }}
| 43rd-partial chroma
|
|-
| 1764/1763
| 0.98170
| (2×3×7)<sup>2</sup>/(41×43)
| 2.3.7.41.43 {{monzo| 2 2 2 -1 -1 }}
|
| S42
|-
| [[1849/1848]]
| 0.93656
| 43<sup>2</sup>/(2<sup>3</sup>×3×7×11)
| 2.3.7.11.43 {{monzo| -3 -1 -1 -1 2 }}
|
| S43
|-
| 1936/1935
| 0.98170
| (2<sup>2</sup>×11)<sup>2</sup>/(3<sup>2</sup>×5×43)
| 2.3.5.11.43 {{monzo| 4 -2 -1 2 -1 }}
|
| S44
|-
! colspan="6" | 47-limit (incomplete)
|-
| [[47/46]]
| 37.232
| 47/(2×23)
| 2.23.47 {{monzo| -1 -1 1 }}
|
|
|-
| [[48/47]]
| 36.448
| (2<sup>4</sup>×3)/47
| 2.3.47 {{monzo| 4 1 -1 }}
|
|
|-
| [[94/93]]
| 18.516
| (2×47)/(3×31)
| 2.3.31.47 {{monzo| 1 -1 -1 1 }}
|
|
|-
| [[95/94]]
| 18.320
| (5×19)/(2×47)
| 2.5.19.47 {{monzo| -1 1 1 -1 }}
|
|
|-
| 2116/2115
| 0.81836
| (2×23)<sup>2</sup>/(3<sup>2</sup>×5×47)
| 2.3.5.23.47 {{monzo| 2 -2 -1 2 -1 }}
|
| S46
|-
| [[2209/2208]]
| 0.78390
| 47<sup>2</sup>/(2<sup>5</sup>×3×5)
| 2.3.23.47 {{monzo| -5 -1 -1 2 }}
|
| S47
|-
| [[2304/2303]]
| 0.75157
| (2<sup>4</sup>×3)<sup>2</sup>/(7<sup>2</sup>×47)
| 2.3.7.47 {{monzo| 8 2 -2 -1 }}
|
| S48
|-
! colspan="6" | 53-limit (incomplete)
|-
| [[53/52]]
| 32.977
| 53/(2<sup>2</sup>×13)
| 2.13.53 {{monzo| -2 -1 1 }}
|
|
|-
| [[54/53]]
| 32.360
| (2×3<sup>3</sup>)/53
| 2.3.53 {{monzo| 1 3 -1 }}
|
|
|-
| [[2809/2808]]
| 0.61643
| 53<sup>2</sup>/(2<sup>3</sup>×3<sup>3</sup>×13)
| 2.3.13.53 {{monzo| -3 -3 -1 2 }}
|
| S53
|-
| [[4081/4080]]
| 0.42427
| (7×11×53)/(2<sup>4</sup>×3×5×17)
| 2.3.5.7.11.17.53 {{monzo| -4 -1 -1 1 1 -1 1 }}
|
|
|-
! colspan="6" | 59-limit (incomplete)
|-
| [[59/58]]
| 29.594
| 59/(2×29)
| 2.29.59 {{monzo| -1 -1 1 }}
|
|
|-
| [[60/59]]
| 29.097
| (2<sup>2</sup>×3×5)/59
| 2.3.5.59 {{monzo| 2 1 1 -1 }}
|
|
|-
| [[3481/3480]]
| 0.49741
| 59<sup>2</sup>/(2<sup>3</sup>×3×5×29)
| 2.3.5.29.59 {{monzo| -3 -1 -1 -1 2}}
|
| S59
|-
! colspan="6" | 61-limit (incomplete)
|-
| [[61/60]]
| 28.616
| 61/(2<sup>2</sup>×3×5)
| 2.3.5.61 {{monzo| -2 -1 -1 1 }}
|
|
|-
| [[62/61]]
| 28.151
| (2×31)/61
| 2.31.61 {{monzo| 1 1 -1 }}
|
|
|-
| [[672/671]]
| 2.5782
| (2<sup>5</sup>×3×7)/(11×61)
| 2.3.7.11.61 {{monzo| 5 1 1 -1 -1 }}
|
|
|-
| [[1404/1403]]
| 1.2335
| (2<sup>2</sup>×3<sup>3</sup>×13)/(23×61)
| 2.3.13.23.61 {{monzo| 2 3 1 -1 -1 }}
|
|
|-
| [[3721/3720]]
| 0.46532
| 61<sup>2</sup>/(2<sup>3</sup>×3×5×31)
| 2.3.5.31.61 {{monzo| -3 -1 -1 -1 2 }}
|
| S61
|-
! colspan="6" | 67-limit (incomplete)
|-
| [[67/66]]
| 26.034
| 67/(2×3×11)
| 2.3.11.67 {{monzo| -1 -1 -1 1 }}
|
|
|-
| [[68/67]]
| 25.648
| (2<sup>2</sup>×17)/67
| 2.17.67 {{monzo| 2 1 -1 }}
|
|
|-
! colspan="6" | 71-limit (incomplete)
|-
| [[71/70]]
| 24.557
| 71/(2×5×7)
| 2.5.7.71 {{monzo| -1 -1 -1 1 }}
|
|
|-
| [[72/71]]
| 24.213
| (2<sup>3</sup>×3<sup>2</sup>)/71
| 2.3.71 {{monzo| 3 2 -1 }}
|
|
|-
! colspan="6" | 73-limit (incomplete)
|-
| [[73/72]]
| 23.879
| 73/(2<sup>3</sup>×3<sup>2</sup>)
| 2.3.73 {{monzo| -3 -2 1 }}
|
|
|-
| [[74/73]]
| 23.555
| (2×37)/73
| 2.37.73 {{monzo| 1 1 -1 }}
|
|
|-
! colspan="6" | 79-limit (incomplete)
|-
| [[79/78]]
| 22.054
| 79/(2×3×13)
| 2.3.13.79 {{monzo| -1 -1 -1 1 }}
|
|
|-
| [[80/79]]
| 21.777
| (2<sup>4</sup>×5)/79
| 2.5.79 {{monzo| 4 1 -1 }}
|
|
|-
! colspan="6" | 83-limit (incomplete)
|-
| [[83/82]]
| 20.985
| 83/(2×41)
| 2.41.83 {{monzo| -1 -1 1 }}
|
|
|-
| [[84/83]]
| 20.734
| (2<sup>2</sup>×3×7)/83
| 2.3.7.83 {{monzo| 2 1 1 -1 }}
|
|
|-
! colspan="6" | 89-limit (incomplete)
|-
| [[89/88]]
| 19.562
| 89/(2<sup>3</sup>×11)
| 2.11.89 {{monzo| -3 -1 1 }}
| Sky comma
|
|-
| [[90/89]]
| 19.344
| (2×3<sup>2</sup>×5)/89
| 2.3.5.89 {{monzo| 1 2 1 -1 }}
|
|
|-
! colspan="6" | 97-limit (incomplete)
|-
| [[97/96]]
| 17.940
| 97/(2<sup>5</sup>×3)
| 2.3.97 {{monzo| -5 -1 1 }}
|
|
|-
| [[98/97]]
| 17.756
| (2×7<sup>2</sup>)/97
| 2.7.97 {{monzo| 1 2 -1 }}
|
|
|-
! colspan="6" | 101-limit (incomplete)
|-
| [[101/100]]
| 17.226
| 101/(2×5)<sup>2</sup>
| 2.5.101 {{monzo| -2 -2 1 }}
|
|
|-
| [[102/101]]
| 17.057
| (2×3×17)/101
| 2.3.17.101 {{monzo| 1 1 1 -1 }}
|
|
|-
| [[7777/7776]]
| 0.223
| 7×11×101/(2×3)<sup>5</sup>
| 2.3.7.11.101 {{monzo| -5 -5 1 1 1 }}
| Pulsar comma
|
|}


== 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:

See also

Notes

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 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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