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 465: Line 503:
| {{Monzo| 5 -3 1 -1 -1 1 }}
| {{Monzo| 5 -3 1 -1 -1 1 }}
| Ibnsinma
| Ibnsinma
|
|  
|-
|-
| [[4096/4095]]
| [[4096/4095]]
Line 472: Line 510:
| {{Monzo| 12 -2 -1 -1 0 -1 }}
| {{Monzo| 12 -2 -1 -1 0 -1 }}
| Schismina, tridecimal schisma
| Schismina, tridecimal schisma
| 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 }}
| Ainos comma, ainma
| 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 749: Line 795:
| S120
| S120
|-
|-
| 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 }}
|  
| 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 }}
|  
|  
|
|  
|-
|}
! 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 }}
|  
|  
|  
|  
|}
=== 29-limit ===
{{Main|List of superparticular intervals/29-limit}}
=== 31-limit ===
{{Main|List of superparticular intervals/31-limit}}
=== 37-limit ===
{{Main|List of superparticular intervals/37-limit}}
=== 41-limit (incomplete) ===
{| 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"/>
|-
|-
! colspan="6" | 29-limit (incomplete)
| [[41/40]]
|-
| 42.749
| [[29/28]]
| 41/(2<sup>3</sup>×5)
| 60.751
| 2.5.41 {{monzo| -3 -1 1 }}
| 29/(2<sup>2</sup>×7)
| Large quadracesimoprimal 1/5-tone
| 2.7.29 {{monzo| -2 -1 1 }}
| Large vicesimononal 1/4-tone
|
|-
| [[30/29]]
| 58.692
| (2×3×5)/29
| 2.3.5.29 {{monzo| 1 1 1 -1 }}
| Small vicesimononal 1/4-tone
|
|-
| [[58/57]]
| 30.109
| (2×29)/(3×19)
| 2.3.19.29 {{monzo| 1 -1 -1 1 }}
|  
|  
|
|-
|-
| [[88/87]]
| [[42/41]]
| 19.786
| 41.719
| (2<sup>3</sup>×11)/(3×29)
| (2×3×7)/41
| 2.3.11.29 {{monzo| 3 -1 1 -1 }}
| 2.3.7.41 {{monzo| 1 1 1 -1 }}
| Small quadracesimoprimal 1/5-tone
|  
|  
|
|-
|-
| 116/115
| [[82/81]]
| 14.989
| 21.242
| (2<sup>2</sup>×29)/(5×23)
| (2×41)/3<sup>4</sup>
| 2.5.23.29 {{monzo| 2 -1 -1 1 }}
| 2.3.41 {{monzo| 1 -4 1 }}
|
| 41st-partial chroma
|
|-
| 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]]
| [[124/123]]
| 11.981
| 14.018
| (5×29)/(2<sup>2</sup>×3)<sup>2</sup>
| (2<sup>2</sup>×31)/(3×41)
| 2.3.5.29 {{monzo| -4 -2 1 1 }}
| 2.3.31.41 {{monzo| 2 -1 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
| [[165/164]]
| 8.5073
| 10.524
| (3×5×11)/(2<sup>2</sup>×41)
| 2.3.5.11.41 {{monzo| -2 1 1 1 -1 }}
|  
|  
|  
|  
|-
| [[205/204]]
| 8.4657
| (5×41)/(2<sup>2</sup>×3×17)
| 2.3.5.17.41 {{monzo| -2 -1 1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 232/231
| [[246/245]]
| 7.4783
| 7.0519
| (2×3×41)/(5×7<sup>2</sup>)
| 2.3.5.7.41 {{monzo| 1 1 -1 -2 1 }}
|  
|  
|  
|  
|-
| [[247/246]]
| 7.0233
| (13×19)/(2×3×41)
| 2.3.13.19.41 {{monzo| -1 -1 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 261/260
| [[287/286]]
| 6.6458
| 6.0427
| (7×41)/(2×11×13)
| 2.7.11.13.41 {{monzo| -1 1 -1 -1 1 }}
|  
|  
|  
|  
|-
| [[288/287]]
| 6.0217
| (2<sup>5</sup>×3<sup>2</sup>)/(7×41)
| 2.3.7.41 {{monzo| 5 2 -1 -1 }}
|  
|  
|  
|  
|-
|-
| 290/289
| [[369/368]]
| 5.9801
| 4.6981
| (3<sup>2</sup>×41)/(2<sup>4</sup>×23)
| 2.3.23.41 {{monzo| -4 2 -1 1 }}
|  
|  
|  
|  
|-
| [[370/369]]
| 4.6853
| (2×5×37)/(3<sup>2</sup>×41)
| 2.3.5.37.41 {{monzo| 1 -2 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 320/319
| [[451/450]]
| 5.4186
| 3.8429
| (11×41)/(2×(3×5)<sup>2</sup>)
| 2.3.5.11.41 {{monzo| -1 -2 -2 1 1 }}
|  
|  
|  
|  
|-
| [[493/492]]
| 3.5152
| (17×29)/(2<sup>2</sup>×3×41)
| 2.3.17.29.41 {{monzo| -2 -1 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 378/377
| [[533/532]]
| 4.5861
| 3.2511
| (13×41)/(2<sup>2</sup>×7×19)
| 2.7.13.19.41 {{monzo| -2 -1 1 -1 1 }}
|  
|  
|  
|  
|-
| [[575/574]]
| 3.0135
| (5<sup>2</sup>×23)/(2×7×41)
| 2.5.7.23.41 {{monzo| -1 2 -1 1 -1 }}
| Renatisma
|  
|  
|-
| [[616/615]]
| 2.8127
| (2<sup>3</sup>×7×11)/(3×5×41)
| 2.3.5.7.11.41 {{monzo| 3 -1 -1 1 1 -1 }}
| Ellisma
|  
|  
|-
|-
| 406/405
| [[697/696]]
| 4.2694
| 2.4856
|  
| (17×41)/(2<sup>3</sup>×3×29)
| 2.3.17.29.41 {{monzo| -3 -1 1 -1 1 }}
|  
|  
|  
|  
|-
| [[780/779]]
| 2.2210
| (2<sup>2</sup>×3×5×13)/(19×41)
| 2.3.5.13.19.41 {{monzo| 2 1 1 1 -1 -1 }}
| Wiesentisma
|  
|  
|-
|-
| 494/493
| [[820/819]]
| 3.5081
| 2.1125
| (2<sup>2</sup>×5×41)/(3<sup>2</sup>×7×13)
| 2.3.5.7.13.41 {{monzo| 2 -2 1 -1 -1 1 }}
|  
|  
|  
|  
|-
| [[1025/1024]]
| 1.6898
| (5<sup>2</sup>×41)/2<sup>10</sup>
| 2.5.41 {{monzo| -10 2 1 }}
| Kilobytisma
|  
|  
|-
| [[1026/1025]]
| 1.6882
| (2×3<sup>3</sup>×19)/(5<sup>2</sup>×41)
| 2.3.5.19.41 {{monzo| 1 3 -2 1 -1 }}
| Ingridisma
|  
|  
|-
|-
| 551/550
| [[1148/1147]]
| 3.1448
| 1.5087
| (2<sup>2</sup>×7×41)/(31×37)
| 2.7.31.37.41 {{monzo| 2 1 -1 -1 1 }}
|  
|  
|  
|  
|-
| [[1189/1188]]
| 1.4567
| (29×41)/(2<sup>2</sup>×3<sup>3</sup>×11)
| 2.3.11.29.41 {{monzo| -2 -3 -1 1 1 }}
|  
|  
|  
|  
|-
|-
| 552/551
| [[1190/1189]]
| 3.1391
| 1.4554
|  
| (2×5×7×17)/(29×41)
| 2.5.7.17.29.41 {{monzo| 1 1 1 1 -1 -1 }}
| Pelagisma
|  
|  
|-
| [[1312/1311]]
| 1.3200
| (2<sup>5</sup>×41)/(3×19×23)
| 2.3.19.23.41 {{monzo| 5 -1 -1 -1 1 }}
|  
|  
|  
|  
|-
|-
| 609/608
| [[1353/1352]]
| 2.8451
| 1.2800
| (3×11×41)/(2<sup>3</sup>×13<sup>2</sup>)
| 2.3.11.13.41 {{monzo| -3 1 1 -2 1 }}
|  
|  
|  
|  
|-
| [[1395/1394]]
| 1.2415
| (3<sup>2</sup>×5×31)/(2×17×41)
| 2.3.5.17.31.41 {{monzo| -1 2 1 -1 1 -1 }}
|  
|  
|  
|  
|-
|-
| 638/637
| [[1518/1517]]
| 2.7157
| 1.1408
| (2×3×11×23)/(37×41)
| 2.3.11.23.37.41 {{monzo| 1 1 1 1 -1 -1 }}
| Rovaniemisma
|  
|  
|-
| [[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
|-
| [[1682/1681]]
| 1.0296
| (2×29<sup>2</sup>)/41<sup>2</sup>
| 2.29.41 {{monzo| 1 2 -2 }}
| Shaftesburisma
|  
|  
|-
| [[1805/1804]]
| 0.95940
| (5×19<sup>2</sup>)/(2<sup>2</sup>×11×41)
| 2.5.11.19.41 {{monzo| -2 1 -1 2 -1 }}
|  
|  
|  
|  
|-
|-
| 726/725
| [[1886/1885]]
| 2.3863
| 0.91818
| (2×23×41)/(5×13×29)
| 2.5.13.23.29.41 {{monzo| 1 -1 -1 1 -1 1 }}
|  
|  
|  
|  
|-
| [[1887/1886]]
| 0.91770
| (3×17×37)/(2×23×41)
| 2.3.17.23.37.41 {{monzo| -1 1 1 -1 1 -1 }}
|  
|  
|  
|  
|-
|-
! colspan="6" | 31-limit (incomplete)
| [[2091/2090]]
| 0.82814
| (3×17×41)/(2×5×11×19)
| 2.3.5.11.17.19.41 {{monzo| -1 1 -1 -1 1 -1 1 }}
|
|
|-
|-
| [[31/30]]
| [[2255/2254]]
| 56.767
| 0.76790
| 31/(2×3×5)
| (5×11×41)/(2×7<sup>2</sup>×23)
| 2.3.5.31 {{monzo| -1 -1 -1 1 }}
| 2.5.7.11.23.41 {{monzo| -1 1 -2 1 -1 1 }}
| Large tricesimoprimal 1/4-tone
| Qinghaisma
|
|  
|-
|-
| [[32/31]]
| [[2296/2295]]
| 54.964
| 0.75419
| 2<sup>5</sup>/31
| (2<sup>3</sup>×7×41)/(3<sup>3</sup>×5×17)
| 2.31 {{monzo| 5 -1 }}
| 2.3.5.7.17.41 {{monzo| 3 -3 -1 1 -1 1 }}
| Small tricesimoprimal 1/4-tone, octave-reduced 31st subharmonic
|  
|
|  
|-
|-
| [[63/62]]
| [[2542/2541]]
| 27.700
| 0.68119
| (3<sup>2</sup>×7)/(2×31)
| (2×31×41)/(3×7×11<sup>2</sup>)
| 2.3.7.31 {{monzo| -1 2 1 -1 }}
| 2.3.7.11.31.41 {{monzo| 1 -1 -1 -2 1 1 }}
|
|  
|  
|
|-
|-
| [[93/92]]
| [[2584/2583]]
| 18.716
| 0.67011
| (3×31)/(2<sup>2</sup>×23)
| (2<sup>3</sup>×17×19)/(3<sup>2</sup>×7×41)
| 2.3.23.31 {{monzo| -2 1 -1 1 }}
| 2.3.7.17.19.41 {{monzo| 3 -2 -1 1 1 -1 }}
|
|  
|  
|
|-
|-
| [[125/124]]
| [[2625/2624]]
| 13.906
| 0.65964
| 5<sup>3</sup>/(2<sup>2</sup>×31)
| (3×5<sup>3</sup>×7)/(2<sup>6</sup>×41)
| 2.5.31 {{monzo| -2 3 -1 }}
| 2.3.5.7.41 {{monzo| -6 1 3 1 -1 }}
| Twizzler
|  
|
|  
|-
|-
| [[621/620]]
| [[2665/2664]]
| 2.7901
| 0.64974
| (3<sup>3</sup>×23)/(2<sup>2</sup>×5×31)
| (5×13×41)/(2<sup>3</sup>×3<sup>2</sup>×37)
| 2.3.5.23.31 {{monzo| -2 3 -1 1 -1 }}
| 2.3.5.13.37.41 {{monzo| -3 -2 1 1 -1 1 }}
| Owowhatsthisma
|  
|
|  
|-
|-
| [[3969/3968]]
| [[2871/2870]]
| 0.43624
| 0.60311
| (3<sup>4</sup>×7<sup>2</sup>)/(2<sup>7</sup>×31)
| (3<sup>2</sup>×11×29)/(2×5×7×41)
| 2.3.7.31 {{monzo| -7 4 2 -1 }}
| 2.3.5.7.11.29.41 {{monzo| -1 2 -1 -1 1 1 -1 }}
| Yunzee comma
| Schoberisma
| S63
|  
|-
|-
! colspan="6" | 37-limit (incomplete)
| [[3690/3689]]
| 0.46923
| (2×3<sup>2</sup>×5×41)/(7×17×31)
| 2.3.5.7.17.31.41 {{monzo| 1 2 1 -1 -1 -1 1 }}
|
|
|-
|-
| [[37/36]]
| [[3773/3772]]
| 47.434
| 0.45891
| 37/(2<sup>2</sup>×3<sup>2</sup>)
| (7<sup>3</sup>×11)/(2<sup>2</sup>×23×41)
| 2.3.37 {{monzo| -2 -2 1 }}
| 2.7.11.23.41 {{monzo| -2 3 1 -1 -1 }}
| Large tricesimoseptimal 1/4-tone, 37th-partial chroma
| Smithsonianisma
|
|  
|-
|-
| [[38/37]]
| [[4060/4059]]
| 46.169
| 0.42646
| (2×19)/37
| (2<sup>2</sup>×5×7×29)/(3<sup>2</sup>×11×41)
| 2.19.37 {{monzo| 1 1 -1 }}
| 2.3.5.7.11.29.41 {{monzo| 2 -2 1 1 -1 1 -1 }}
| Small tricesimoseptimal 1/4-tone
| Deipylosisma
|
|  
|-
|-
| [[75/74]]
| [[4264/4263]]
| 23.238
| 0.40606
| (3×5<sup>2</sup>)/(2×37)
| (2<sup>3</sup>×13×41)/(3×7<sup>2</sup>×29)
| 2.3.5.37 {{monzo| -1 1 2 -1 }}
| 2.3.7.13.29.41 {{monzo| 3 -1 -2 1 -1 1 }}
|
|  
|  
|
|-
|-
! colspan="6" | 41-limit (incomplete)
| [[4551/4550]]
| 0.38045
| (3×37×41)/(2×5<sup>2</sup>×7×13)
| 2.3.5.7.13.37.41 {{monzo| -1 1 -2 -1 -1 1 1 }}
|
|
|-
|-
| [[41/40]]
| [[4675/4674]]
| 42.749
| 0.37036
| 41/(2<sup>3</sup>×5)
| (5<sup>2</sup>×11×17)/(2×3×19×41)
| 2.5.41 {{monzo| -3 -1 1 }}
| 2.3.5.11.17.19.41 {{monzo| -1 -1 2 1 1 -1 -1 }}
| Large quadracesimoprimal 1/5-tone
| Ohbokisma
|
|  
|-
|-
| [[42/41]]
| [[4921/4920]]
| 41.719
| 0.35184
| (2×3×7)/41
| (7×19×37)/(2<sup>3</sup>×3×5×41)
| 2.3.7.41 {{monzo| 1 1 1 -1 }}
| 2.3.5.7.19.37.41 {{monzo| -3 -1 -1 1 1 1 -1 }}
| Small quadracesimoprimal 1/5-tone
| Volontisma
|
|  
|-
|-
| [[82/81]]
| [[4961/4960]]
| 21.242
| 0.34900
| (2×41)/3<sup>4</sup>
| (11<sup>2</sup>×41)/(2<sup>5</sup>×5×31)
| 2.3.41 {{monzo| 1 -4 1 }}
| 2.5.11.31.41 {{monzo| -5 -1 2 -1 1 }}
| 41st-partial chroma
|  
|
|  
|-
|-
! colspan="6" | 43-limit (incomplete)
| [[5084/5083]]
| 0.34056
| (2<sup>2</sup>×31×41)/(13×17×23)
| 2.13.17.23.31.41 {{monzo| 2 -1 -1 -1 1 1 }}
|
|
|-
|-
| [[43/42]]
| [[5577/5576]]
| 40.737
| 0.31045
| 43/(2×3×7)
| (3×11×13<sup>2</sup>)/(2<sup>3</sup>×17×41)
| 2.3.7.43 {{monzo| -1 -1 -1 1 }}
| 2.3.11.13.17.41 {{monzo| -3 1 1 2 -1 -1 }}
| Large quadracesimotertial 1/5-tone
| Priestlisma
|
|  
|-
|-
| [[44/43]]
| [[6069/6068]]
| 39.800
| 0.28528
| (2<sup>2</sup>×11)/43
| (3×7×17<sup>2</sup>)/(2<sup>2</sup>×37×41)
| 2.11.43 {{monzo| 2 1 -1 }}
| 2.3.7.17.37.41 {{monzo| -2 1 1 2 -1 -1 }}
| Small quadracesimotertial 1/5-tone
| Cevolanisma
|
|  
|-
|-
| [[86/85]]
| [[6273/6272]]
| 20.249
| 0.27600
| (2×43)/(5×17)
| (3<sup>2</sup>×17×41)/(2<sup>7</sup>×7<sup>2</sup>)
| 2.5.17.43 {{monzo| 1 -1 -1 1 }}
| 2.3.7.17.41 {{monzo| -7 2 -2 1 1 }}
|
|  
|  
|
|-
|-
| [[87/86]]
| [[6561/6560]]
| 20.014
| 0.26389
| (3×29)/(2×43)
| 3<sup>8</sup>/(2<sup>5</sup>×5×41)
| 2.3.29.43 {{monzo| -1 1 1 -1 }}
| 2.3.5.41 {{monzo| -5 8 -1 -1 }}
|  
|  
|
| S81
|-
|-
| [[129/128]]
| [[6601/6600]]
| 13.473
| 0.26229
| (3×43)/2<sup>7
| (7×23×41)/(2<sup>3</sup>×3×5<sup>2</sup>×11)
| 2.3.43 {{monzo| -7 1 1 }}
| 2.3.5.7.11.23.41 {{monzo| -3 -1 -2 1 -1 1 1 }}
| 43rd-partial chroma
|  
|
|  
|-
|-
! colspan="6" | 47-limit (incomplete)
| [[6930/6929]]
| 0.24984
| (2×3<sup>2</sup>×5×7×11)/(13<sup>2</sup>×41)
| 2.3.5.7.11.13.41 {{monzo| 1 2 1 1 1 -2 -1 }}
| Bedanisma
|
|-
|-
| [[47/46]]
| [[7176/7175]]
| 37.232
| 0.24127
| 47/(2×23)
| (2<sup>3</sup>×3×13×23)/(5<sup>2</sup>×7×41)
| 2.23.47 {{monzo| -1 -1 1 }}
| 2.3.5.7.13.23.41 {{monzo| 3 1 -2 -1 1 1 -1 }}
| Kunijisma
|  
|  
|
|-
|-
| [[48/47]]
| [[7216/7215]]
| 36.448
| 0.23993
| (2<sup>4</sup>×3)/47
| (2<sup>4</sup>×11×41)/(3×5×13×37)
| 2.3.47 {{monzo| 4 1 -1 }}
| 2.3.5.11.13.37.41 {{monzo| 4 -1 -1 1 -1 -1 1 }}
|
|  
|  
|
|-
|-
| [[94/93]]
| [[7750/7749]]
| 18.516
| 0.22340
| (2×47)/(3×31)
| (2×5<sup>3</sup>×31)/(3<sup>3</sup>×7×41)
| 2.3.31.47 {{monzo| 1 -1 -1 1 }}
| 2.3.5.7.31.41 {{monzo| 1 -3 3 -1 1 -1 }}
|
|  
|  
|
|-
|-
| [[95/94]]
| [[8569/8568]]
| 18.320
| 0.20205
| (5×19)/(2×47)
| (11×19×41)/(2<sup>3</sup>×3<sup>2</sup>×7×17)
| 2.5.19.47 {{monzo| -1 1 1 -1 }}
| 2.3.7.11.17.19.41 {{monzo| -3 -2 -1 1 -1 1 1 }}
| Mamelisma
|  
|  
|
|-
|-
! colspan="6" | 53-limit (incomplete)
| [[8856/8855]]
| 0.19550
| ((2×3)<sup>3</sup>×41)/(5×7×11×23)
| 2.3.5.7.11.23.41 {{monzo| 3 3 -1 -1 -1 -1 1 }}
|
|
|-
|-
| [[53/52]]
| [[9472/9471]]
| 32.977
| 0.18278
| 53/(2<sup>2</sup>×13)
| (2<sup>8</sup>×37)/(3×7×11×41)
| 2.13.53 {{monzo| -2 -1 1 }}
| 2.3.7.11.37.41 {{monzo| 8 -1 -1 -1 1 -1 }}
| Brugesisma
|  
|  
|
|-
|-
| [[54/53]]
| 10045/10044
| 32.360
| 0.17236
| (2×3<sup>3</sup>)/53
| (5×7<sup>2</sup>×41)/(2<sup>2</sup>×3<sup>4</sup>×31)
| 2.3.53 {{monzo| 1 3 -1 }}
| 2.3.5.7.31.41 {{monzo| -2 -4 1 2 -1 1 }}
|
|  
|  
|
|-
|-
! colspan="6" | 59-limit (incomplete)
| [[10374/10373]]
| 0.16689
| (2×3×7×13×19)/(11×23×41)
| 2.3.7.11.13.19.23.41 {{monzo| 1 1 1 -1 1 1 -1 -1}}
| Etampesisma
|
|-
|-
| [[59/58]]
| 10660/10659
| 29.594
| 0.16241
| 59/(2×29)
| (2<sup>2</sup>×5×13×41)/(3×11×17×19)
| 2.29.59 {{monzo| -1 -1 1 }}
| 2.3.5.11.13.17.19.41 {{monzo| 2 -1 1 -1 1 -1 -1 1 }}
|
|  
|  
|
|-
|-
| [[60/59]]
| [[11440/11439]]
| 29.097
| 0.15134
| (2<sup>2</sup>×3×5)/59
| (2<sup>4</sup>×5×11×13)/(3<sup>2</sup>×31×41)
| 2.3.5.59 {{monzo| 2 1 1 -1 }}
| 2.3.5.11.13.31.41 {{monzo| 4 -2 1 1 1 -1 -1 }}
| Massironisma
|  
|  
|
|-
|-
! colspan="6" | 61-limit (incomplete)
| 13776/13775
| 0.12567
| (2<sup>4</sup>×3×7×41)/(5<sup>2</sup>×19×29)
| 2.3.5.7.19.29.41 {{monzo| 4 1 -2 1 -1 -1 1 }}
|
|
|-
|-
| [[61/60]]
| 14145/14144
| 28.616
| 0.12240
| 61/(2<sup>2</sup>×3×5)
| (3×5×23×41)/(2<sup>6</sup>×13×17)
| 2.3.5.61 {{monzo| -2 -1 -1 1 }}
| 2.3.5.13.17.23.41 {{monzo| -6 1 1 -1 -1 1 1 }}
|
|  
|  
|
|-
|-
| [[62/61]]
| 14801/14800
| 28.151
| 0.11697
| (2×31)/61
| (19<sup>2</sup>×41)/(2<sup>4</sup>×5<sup>2</sup>×37)
| 2.31.61 {{monzo| 1 1 -1 }}
| 2.5.19.37.41 {{monzo| -4 -2 2 -1 1 }}
|
|  
|  
|
|-
|-
! colspan="6" | 67-limit (incomplete)
| [[15376/15375]]
| 0.11260
| (2<sup>2</sup>×31)<sup>2</sup>/(3×5<sup>3</sup>×41)
| 2.3.5.31.41 {{monzo| 4 -1 -3 2 -1 }}
| Martakisma
| S124
|-
|-
| [[67/66]]
| 15457/15456
| 26.034
| 0.11201
| 67/(2×3×11)
| (13×29×41)/(2<sup>5</sup>×3×7×23)
| 2.3.11.67 {{monzo| -1 -1 -1 1 }}
| 2.3.7.13.23.29.41 {{monzo| -5 -1 -1 1 -1 1 1 }}
|
|
|-
| 16400/16399
| 0.10557
| (2<sup>4</sup>×5<sup>2</sup>×41)/(23<sup>2</sup>×31)
| 2.5.23.31.41 {{monzo| 4 2 -2 -1 1 }}
|
|  
|  
|
|-
|-
| [[68/67]]
| 16524/16523
| 25.648
| 0.10477
| (2<sup>2</sup>×17)/67
| (2<sup>2</sup>×3<sup>5</sup>×17)/(13×31×41)
| 2.17.67 {{monzo| 2 1 -1 }}
| 2.3.13.17.31.41 {{monzo| 2 5 -1 1 -1 -1 }}
|
|  
|  
|
|-
|-
! colspan="6" | 71-limit (incomplete)
| 16606/16605
| 0.10426
| (2×19<sup>2</sup>×23)/(3<sup>4</sup>×5×41)
| 2.3.5.19.23.41 {{monzo| 1 -4 -1 2 1 -1 }}
|
|
|-
|-
| [[71/70]]
| 17425/17424
| 24.557
| 0.099356
| 71/(2×5×7)
| (5<sup>2</sup>×17×41)/(2<sup>2</sup>×3×11)<sup>2</sup>
| 2.5.7.71 {{monzo| -1 -1 -1 1 }}
| 2.3.5.11.17.41 {{monzo| -4 -2 2 -2 1 1 }}
|
|  
|  
|
|-
|-
| [[72/71]]
| [[17836/17835]]
| 24.213
| 0.097067
| (2<sup>3</sup>×3<sup>2</sup>)/71
| (2<sup>2</sup>×7<sup>3</sup>×13)/(3×5×29×41)
| 2.3.71 {{monzo| 3 2 -1 }}
| 2.3.5.7.13.29.41 {{monzo| 2 -1 -1 3 1 -1 -1 }}
| Canupisma
|  
|  
|
|-
|-
! colspan="6" | 73-limit (incomplete)
| 17918/17917
| 0.096623
| (2×17<sup>2</sup>×31)/(19×23×41)
| 2.17.19.23.31.41 {{monzo| 1 2 -1 -1 1 -1 }}
|
|
|-
|-
| [[73/72]]
| 19721/19720
| 23.879
| 0.087789
| 73/(2<sup>3</sup>×3<sup>2</sup>)
| (13×37×41)/(2<sup>3</sup>×5×17×29)
| 2.3.73 {{monzo| -3 -2 1 }}
| 2.5.13.17.29.37.41 {{monzo| -3 -1 1 -1 -1 1 1 }}
|
|  
|  
|
|-
|-
| [[74/73]]
| 19845/19844
| 23.555
| 0.087240
| (2×37)/73
| (3<sup>4</sup>×5×7<sup>2</sup>)/((2×11)<sup>2</sup>×41)
| 2.37.73 {{monzo| 1 1 -1 }}
| 2.3.5.7.11.41 {{monzo| -2 4 1 2 -2 -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]]
| [[76384/76383]]
| 21.777
| 0.022665
| (2<sup>4</sup>×5)/79
| (2<sup>5</sup>×7×11×31)/(3<sup>4</sup>×23×41)
| 2.5.79 {{monzo| 4 1 -1 }}
| 2.3.7.11.23.31.41 {{monzo| 5 -4 1 1 -1 1 -1 }}
| Vernonisma
|  
|  
|
|-
|-
! colspan="6" | 83-limit (incomplete)
| [[Mebisma|1048576/1048575]]
| 0.0016510
| 2<sup>20</sup>/(3×5<sup>2</sup>×11×31×41)
| 2.3.5.11.31.41 {{monzo| 20 -1 -2 -1 -1 -1 }}
| Mebisma
| S1024
|}
 
=== 43-limit (incomplete) ===
{| 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"/>
|-
|-
| [[83/82]]
| [[43/42]]
| 20.985
| 40.737
| 83/(2×41)
| 43/(2×3×7)
| 2.41.83 {{monzo| -1 -1 1 }}
| 2.3.7.43 {{monzo| -1 -1 -1 1 }}
| Large quadracesimotertial 1/5-tone
|  
|  
|
|-
|-
| [[84/83]]
| [[44/43]]
| 20.734
| 39.800
| (2<sup>2</sup>*3*7)/83
| (2<sup>2</sup>×11)/43
| 2.3.7.83 {{monzo| 2 1 1 -1 }}
| 2.11.43 {{monzo| 2 1 -1 }}
| Small quadracesimotertial 1/5-tone
|  
|  
|
|-
|-
! colspan="6" | 89-limit (incomplete)
| [[86/85]]
| 20.249
| (2×43)/(5×17)
| 2.5.17.43 {{monzo| 1 -1 -1 1 }}
| Large quadracesimotertial 1/10-tone
|
|-
|-
| [[89/88]]
| [[87/86]]
| 19.562
| 20.014
| 89/(2<sup>3</sup>×11)
| (3×29)/(2×43)
| 2.11.89 {{monzo| -3 -1 1 }}
| 2.3.29.43 {{monzo| -1 1 1 -1 }}
| Small quadracesimotertial 1/10-tone
|  
|  
|
|-
|-
| [[90/89]]
| [[129/128]]
| 19.344
| 13.473
| (2×3<sup>2</sup>×5)/89
| (3×43)/2<sup>7</sup>
| 2.3.43 {{monzo| -7 1 1 }}
| 43rd-partial chroma
|
|-
| [[130/129]]
| 13.369
| (2×5×13)/(3×43)
| 2.3.5.13.43 {{monzo| 1 -1 1 1 -1 }}
|
|
|-
| [[172/171]]
| 10.095
| (2<sup>2</sup>×43)/(3<sup>2</sup>×19)
| 2.3.19.43 {{monzo| 2 -2 -1 1 }}
|
|
|-
| [[216/215]]
| 8.0336
| (2×3)<sup>3</sup>/(5×43)
| 2.3.5.43 {{monzo| 3 3 -1 -1 }}
|
|
|-
| [[259/258]]
| 6.6972
| (7×37)/(2×3×43)
| 2.3.7.37.43 {{monzo| -1 -1 1 1 -1 }}
|
|
|-
| [[301/300]]
| 5.7612
| (7×43)/((2×5)<sup>2</sup>×3)
| 2.3.5.7.43 {{monzo| -2 -1 -2 1 1 }}
|
|
|-
| [[344/343]]
| 5.0400
| (2<sup>3</sup>×43)/7<sup>3</sup>
| 2.7.43 {{monzo| 3 -3 1 }}
|
|
|-
| [[345/344]]
| 5.0254
| (3×5×23)/(2<sup>3</sup>×43)
| 2.3.5.23.43 {{monzo| -3 1 1 1 -1 }}
|
|
|-
| [[430/429]]
| 4.0308
| (2×5×43)/(3×11×13)
| 2.3.5.11.13.43 {{monzo| 1 -1 1 -1 -1 1 }}
|
|
|-
| [[559/558]]
| 3.0998
| (13×43)/(2×3<sup>2</sup>×31)
| 2.3.13.31.43 {{monzo| -1 -2 1 -1 1 }}
|
|
|-
| [[560/559]]
| 3.0943
| (2<sup>4</sup>×5×7)/(13×43)
| 2.5.7.13.43 {{monzo| 4 1 1 -1 -1 }}
|
|
|-
| [[645/644]]
| 2.6862
| (3×5×43)/(2<sup>2</sup>×7×23)
| 2.3.5.7.23.43 {{monzo| -2 1 1 -1 -1 1 }}
|
|
|-
| [[646/645]]
| 2.6820
| (2×17×19)/(3×5×43)
| 2.3.5.17.19.43 {{monzo| 1 -1 -1 1 1 -1 }}
| Kastalisma
|
|-
| [[775/774]]
| 2.2353
| (5<sup>2</sup>×31)/(2×3<sup>2</sup>×43)
| 2.3.5.31.43 {{monzo| -1 -2 2 1 -1 }}
|
|
|-
| [[817/816]]
| 2.1203
| (19×43)/(2<sup>4</sup>×3×17)
| 2.3.17.19.43 {{monzo| -4 -1 -1 1 1 }}
|
|
|-
| [[861/860]]
| 2.0119
| (3×7×41)/(2<sup>2</sup>×5×43)
| 2.3.5.7.41.43 {{monzo| -2 1 -1 1 1 -1 }}
|
|
|-
| [[903/902]]
| 1.9183
| (3×7×43)/(2×11×41)
| 2.3.7.11.41.43 {{monzo| -1 1 1 -1 -1 1 }}
|
|
|-
| [[946/945]]
| 1.8310
| (2×11×43)/(3<sup>3</sup>×5×7)
| 2.3.5.7.11.43 {{monzo| 1 -3 -1 -1 1 1 }}
|
|
|-
| [[989/988]]
| 1.7514
| (23×43)/(2<sup>2</sup>×13×19)
| 2.13.19.23.43 {{monzo| -2 -1 -1 1 1 }}
|
|
|-
| [[990/989]]
| 1.7496
| (2×3<sup>2</sup>×5×11)/(23×43)
| 2.3.5.11.23.43 {{monzo| 1 2 1 1 -1 -1 }}
| Yerkesisma
|
|-
| [[1161/1160]]
| 1.4918
| (3<sup>3</sup>×43)/(2<sup>3</sup>×5×29)
| 2.3.5.29.43 {{monzo| -3 3 -1 -1 1 }}
|
|
|-
| [[1248/1247]]
| 1.3878
| (2<sup>5</sup>×3×13)/(29×43)
| 2.3.13.29.43 {{monzo| 5 1 1 -1 -1 }}
|
|
|-
| [[1333/1332]]
| 1.2992
| (31×43)/((2×3)<sup>2</sup>×37)
| 2.3.31.37.43 {{monzo| -2 -2 1 -1 1 }}
| Cevenolisma
|
|-
| [[1334/1333]]
| 1.2983
| (2×23×29)/(31×43)
| 2.23.29.31.43 {{monzo| 1 1 1 -1 -1 }}
|
|
|-
| [[1376/1375]]
| 1.2586
| (2<sup>5</sup>×43)/(5<sup>3</sup>×11)
| 2.5.11.43 {{monzo| 5 -3 -1 1 }}
|
|
|-
| [[1377/1376]]
| 1.2577
| (3<sup>4</sup>×17)/(2<sup>5</sup>×43)
| 2.3.17.43 {{monzo| -5 4 1 -1 }}
| Roberbauxisma
|
|-
| [[1463/1462]]
| 1.1838
| (7×11×19)/(2×17×43)
| 2.7.11.17.19.43 {{monzo| -1 1 1 -1 1 -1 }}
| Nordenmarkisma
|
|-
| [[1548/1547]]
| 1.1187
| (2<sup>2</sup>×3<sup>2</sup>×43)/(7×13×17)
| 2.3.7.13.17.43 {{monzo| 2 2 -1 -1 -1 1 }}
|
|
|-
| [[1764/1763]]
| 0.98170
| (2×3×7)<sup>2</sup>/(41×43)
| 2.3.7.41.43 {{monzo| 2 2 2 -1 -1 }}
|
| S42
|-
| [[1806/1805]]
| 0.95887
| (2×3×7×43)/(5×19<sup>2</sup>)
| 2.3.5.7.19.43 {{monzo| 1 1 -1 1 -2 1 }}
|
|
|-
| [[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
|-
| [[1850/1849]]
| 0.93606
| (2×5<sup>2</sup>×37)/43<sup>2</sup>
| 2.5.37.43 {{monzo| 1 2 1 -2 }}
|
|
|-
| [[1936/1935]]
| 0.89446
| (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
|-
| [[2925/2924]]
| 0.59198
| (3<sup>2</sup>×5<sup>2</sup>×13)/(2<sup>2</sup>×17×43)
| 2.3.5.13.17.43 {{monzo| -2 2 2 1 -1 -1 }}
| Beattisma
|
|-
| [[3312/3311]]
| 0.52279
| (2<sup>4</sup>×3<sup>2</sup>×23)/(7×11×43)
| 2.3.7.11.23.43 {{monzo| 4 2 -1 -1 1 -1 }}
| Pedersenisma
|
|-
| [[4000/3999]]
| 0.43286
| (2<sup>5</sup>×5<sup>3</sup>)/(3×31×43)
| 2.3.5.31.43 {{monzo| 5 -1 3 -1 -1 }}
| Hipparchusisma
|
|-
| [[4301/4300]]
| 0.40257
| (11×17×23)/(2<sup>2</sup>×5<sup>2</sup>×43)
| 2.5.11.17.23.43 {{monzo| -2 -2 1 1 1 -1 }}
| Boydenisma
|
|-
| [[4774/4773]]
| 0.36268
| (2×7×11×31)/(3×37×43)
| 2.3.7.11.31.37.43 {{monzo| 1 -1 1 1 1 -1 -1 }}
| Hobetsisma
|
|-
| [[5720/5719]]
| 0.30269
| (2<sup>3</sup>×5×11×13)/(7×19×43)
| 2.5.7.11.13.19.43 {{monzo| 3 1 -1 1 1 -1 -1 }}
| Halweaverisma
|
|-
| [[7225/7224]]
| 0.23963
| (5×17)<sup>2</sup>/(2<sup>3</sup>×3×7×43)
| 2.3.5.7.17.43 {{monzo| -3 -1 2 -1 2 -1 }}
| Huntressisma
| S85
|-
| [[7956/7955]]
| 0.21761
| (2<sup>2</sup>×3<sup>2</sup>×13×17)/(5×37×43)
| 2.3.5.13.17.37.43 {{monzo| 2 2 -1 1 1 -1 -1 }}
| Yajinisma
|
|-
| [[9504/9503]]
| 0.18217
| (2<sup>5</sup>×3<sup>3</sup>×11)/(13×17×43)
| 2.3.11.13.17.43 {{monzo| 5 3 1 -1 -1 -1 }}
| Lionelisma
|
|-
| [[9633/9632]]
| 0.17973
| (3×13<sup>2</sup>×19)/(2<sup>5</sup>×7×43)
| 2.3.7.13.19.43 {{monzo| -5 1 -1 2 1 -1 }}
| Coturisma
|
|-
| [[10450/10449]]
| 0.16568
| (2×5<sup>2</sup>×11×19)/(3<sup>5</sup>×43)
| 2.3.5.11.19.43 {{monzo| 1 -5 2 1 1 -1}}
| Girardisma
|
|-
| [[10880/10879]]
| 0.15912
| (2<sup>7</sup>×5×17)/(11×23×43)
| 2.5.11.17.23.43 {{monzo| 7 1 -1 1 -1 -1 }}
| Kaguyisma
|
|-
| [[17545/17544]]
| 0.098677
| (5×11<sup>2</sup>×29)/(2<sup>3</sup>×3×17×43)
| 2.3.5.11.17.29.43 {{monzo| -3 -1 1 2 -1 1 -1 }}
| Manheimisma
|
|-
| [[27048/27047]]
| 0.064007
| (2<sup>3</sup>×3×7<sup>2</sup>×23)/(17×37×43)
| 2.3.7.17.23.37.43 {{monzo| 3 1 2 -1 1 -1 -1 }}
| Jangongisma
|
|-
| [[29241/29240]]
| 0.059207
| (3<sup>2</sup>×19)<sup>2</sup>/(2<sup>3</sup>×5×17×43)
| 2.3.5.17.19.43 {{monzo| -3 4 -1 -1 2 -1 }}
| Locquirecisma
| S171
|}
 
=== 47-limit (incomplete) ===
{| 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"/>
|-
| [[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 }}
| 47th-partial chroma
|
|-
| [[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 }}
|
|
|-
| [[141/140]]
| 12.322
| (3×47)/(2<sup>2</sup>×5×7)
| 2.3.5.7.47 {{monzo| -2 1 -1 -1 1 }}
|
|
|-
| [[188/187]]
| 9.2333
| (2<sup>2</sup>×47)/(11×17)
| 2.11.37.47 {{monzo| 2 -1 -1 1 }}
|
|
|-
| [[189/188]]
| 9.1843
| (3<sup>3</sup>×7)/(2<sup>2</sup>×47)
| 2.3.7.47 {{monzo| -2 3 1 -1 }}
|
|
|-
| [[235/234]]
| 7.3827
| (5×47)/(2×3<sup>2</sup>×13)
| 2.3.5.13.47 {{monzo| -1 -2 1 -1 1 }}
|
|
|-
| [[329/328]]
| 5.2701
| (7×47)/(2<sup>3</sup>×41)
| 2.7.41.47 {{monzo| -3 1 -1 1 }}
|
|
|-
| [[330/329]]
| 5.2541
| (2×3×5×11)/(7×47)
| 2.3.5.7.11.47 {{monzo| 1 1 1 -1 1 -1 }}
|
|
|-
| [[376/375]]
| 4.6105
| (2<sup>3</sup>×47)/(3×5<sup>3</sup>)
| 2.3.5.47 {{monzo| 3 -1 -3 1 }}
|
|
|-
| [[377/376]]
| 4.5982
| (13×29)/(2<sup>3</sup>×47)
| 2.13.29.47 {{monzo| -3 1 1 -1 }}
|
|
|-
| [[1176/1175]]
| 1.4728
| (2<sup>3</sup>×3×7<sup>2</sup>)/(5<sup>2</sup>×47)
| 2.3.5.7.47 {{monzo| 3 1 -2 2 -1 }}
| Lucidorisma
|
|-
| [[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
|}
 
=== 53-limit (incomplete) ===
{| 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"/>
|-
| [[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 }}
|
|
|-
| [[106/105]]
| 16.410
| (2×53)/(3×5×7)
| 2.3.5.7.53 {{monzo| 1 -1 -1 -1 1 }}
|
|
|-
| [[160/159]]
| 10.854
| (2<sup>5</sup>×5)/(3×53)
| 2.3.5.53 {{monzo| 5 -1 1 -1 }}
|
|
|-
| [[265/264]]
| 6.5453
| (5×53)/(2<sup>3</sup>×3×11)
| 2.3.5.11.53 {{monzo| -3 -1 1 -1 1 }}
|
|
|-
| [[266/265]]
| 6.5207
| (2×7×19)/(5×53)
| 2.5.7.19.53 {{monzo| 1 -1 1 1 -1 }}
|
|
|-
| [[319/318]]
| 5.4356
| (11×29)/(2×3×53)
| 2.3.11.29.53 {{monzo| -1 -1 1 1 -1 }}
|
|
|-
| [[371/370]]
| 4.6727
| (7×53)/(2×5×37)
| 2.5.7.37.53 {{monzo| -1 -1 1 -1 1 }}
|
|
|-
| [[372/371]]
| 4.6601
| (2<sup>2</sup>×3×31)/(7×53)
| 2.3.7.31.53 {{monzo| 2 1 -1 1 -1 }}
|
|
|-
| [[424/423]]
| 4.0879
| (2<sup>3</sup>×53)/(3<sup>2</sup>×47)
| 2.3.47.53 {{monzo| 3 -2 -1 1 }}
|
|
|-
| [[425/424]]
| 4.0783
| (5<sup>2</sup>×17)/(2<sup>3</sup>×53)
| 2.5.17.53 {{monzo| -3 2 1 -1 }}
|
|
|-
| [[477/476]]
| 3.6332
| (3<sup>2</sup>×53)/(2<sup>2</sup>×7×17)
| 2.3.7.17.53 {{monzo| -2 2 -1 -1 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 }}
|
|
|}
 
=== 59-limit (incomplete) ===
{| 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"/>
|-
| [[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 }}
|
|
|-
| [[118/117]]
| 14.734
| (2×59)/(3<sup>2</sup>×13)
| 2.3.13.59 {{monzo| 1 -2 -1 1 }}
|
|
|-
| [[119/118]]
| 14.610
| (7×17)/(2×59)
| 2.7.17.59 {{monzo| -1 1 1 -1 }}
|
|
|-
| [[177/176]]
| 9.8087
| (3×59)/(2<sup>4</sup>×11)
| 2.3.11.59 {{monzo| -4 1 -1 1 }}
|
|
|-
| [[236/235]]
| 7.3513
| (2<sup>2</sup>×59)/(5×47)
| 2.5.47.59 {{monzo| 2 -1 -1 1 }}
|
|
|-
| [[295/294]]
| 5.8786
| (5×59)/(2×3×7<sup>2</sup>)
| 2.3.5.7.59 {{monzo| -1 -1 1 -2 1 }}
|
|
|-
| [[296/295]]
| 5.8587
| (2<sup>3</sup>×37)/(5×59)
| 2.5.37.59 {{monzo| 3 -1 1 -1 }}
|
|
|-
| [[414/413]]
| 4.1868
| (2×3<sup>2</sup>×23)/(7×59)
| 2.3.7.23.59 {{monzo| 1 2 -1 1 -1 }}
|
|
|-
| [[473/472]]
| 3.6640
| (11×43)/(2<sup>3</sup>×59)
| 2.11.43.59 {{monzo| -3 1 1 -1 }}
|
|
|-
| [[1121/1120]]
| 1.5451
| (19×59)/(2<sup>5</sup>×5×7)
| 2.5.7.19.59 {{monzo| -5 -1 -1 1 1 }}
|
|
|-
| [[1122/1121]]
| 1.5437
| (2×3×11×17)/(19×59)
| 2.3.11.17.19.59 {{monzo| 1 1 1 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
|}
 
=== 61-limit (incomplete) ===
{| 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"/>
|-
| [[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 }}
|
|
|-
| [[122/121]]
| 14.249
| (2×61)/(11<sup>2</sup>)
| 2.11.61 {{monzo| 1 -2 1 }}
|
|
|-
| [[123/122]]
| 14.133
| (3×41)/(2×61)
| 2.3.41.61 {{monzo| -1 1 1 -1 }}
|
|
|-
| [[183/182]]
| 9.4862
| (3×61)/(2×7×13)
| 2.3.7.13.61 {{monzo| -1 1 -1 -1 1 }}
|
|
|-
| [[184/183]]
| 9.4345
| (2<sup>3</sup>×23)/(3×61)
| 2.3.23.61 {{monzo| 3 -1 1 -1 }}
|
|
|-
| [[244/243]]
| 7.1098
| (2<sup>2</sup>×61)/3<sup>5</sup>
| 2.3.61 {{monzo| 2 -5 1 }}
|
|
|-
| [[245/244]]
| 7.0807
| (5×7<sup>2</sup>)/(2<sup>2</sup>×61)
| 2.5.7.61 {{monzo| -2 1 2 -1 }}
|
|
|-
| [[305/304]]
| 5.6855
| (5×61)/(2<sup>4</sup>×19)
| 2.5.19.61 {{monzo| -4 1 -1 1 }}
|
|
|-
| [[306/305]]
| 5.6669
| (2×3<sup>2</sup>×17)/(5×61)
| 2.3.5.17.61 {{monzo| 1 2 -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
|}
 
=== 67-limit (incomplete) ===
{| 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"/>
|-
| [[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 }}
|
|
|-
| [[134/133]]
| 12.968
| (2×67)/(7×19)
| 2.7.19.67 {{monzo| 1 -1 -1 1 }}
|
|
|-
| [[135/134]]
| 12.872
| (3<sup>3</sup>×5)/(2×67)
| 2.3.5.67 {{monzo| -1 3 1 -1 }}
|
|
|-
| [[201/200]]
| 8.6346
| (3×67)/(2<sup>3</sup>×5<sup>2</sup>)
| 2.3.5.67 {{monzo| -3 1 -2 1 }}
|
|
|-
| [[336/335]]
| 5.1602
| (2<sup>4</sup>×3×7)/(5×67)
| 2.3.5.7.67 {{monzo| 4 1 -1 1 -1 }}
|
|
|-
| [[671/670]]
| 2.5820
| (11×61)/(2×5×67)
| 2.5.11.61.67 {{monzo| -1 -1 1 1 -1 }}
|
|
|-
| [[4489/4488]]
| 0.38570
| 67<sup>2</sup>/(2<sup>3</sup>×3×11×17)
| 2.3.11.17.67 {{monzo| -3 -1 -1 -1 2 }}
|
| S67
|}
 
=== 71-limit (incomplete) ===
{| 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"/>
|-
| [[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 }}
|
|
|-
| [[5041/5040]]
| 0.34346
| 71<sup>2</sup>/(2<sup>4</sup>×3<sup>2</sup>×5×7)
| 2.3.5.7.71 {{monzo| -4 -2 -1 -1 2 }}
| Third brown pair comma
| S71
|-
| <font style="font-size:0.85em">[[Borcherdsma|160561400000 / 160561399999]]</font>
| 1.0783×10<sup>-8</sup>
| (2<sup>6</sup>×5<sup>5</sup>×19×29×31×47) / (7×11<sup>2</sup>×13×59<sup>3</sup>×71)
| 2.5.7.11.13.19.29.31.47.59.71 {{monzo| 6 5 -1 -2 -1 1 1 1 1 -3 -1 }}
| Borcherdsma
|
|}
 
=== 73-limit (incomplete) ===
{| 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"/>
|-
| [[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 }}
|
|
|-
| [[366/365]]
| 4.737
| (2×3×61)/(5×73)
| 2.3.5.61.73 [1 1 -1 1 -1⟩
| Sidereal comma
|
|}
 
=== 79-limit (incomplete) ===
{| 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"/>
|-
| [[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 }}
|
|
|}
 
=== 83-limit (incomplete) ===
{| 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"/>
|-
| [[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 }}
|
|
|}
 
=== 89-limit (incomplete) ===
{| 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"/>
|-
| [[89/88]]
| 19.562
| 89/(2<sup>3</sup>×11)
| 2.11.89 {{monzo| -3 -1 1 }}
| Tailwind comma{{idiosyncratic}}
|
|-
| [[90/89]]
| 19.344
| (2×3<sup>2</sup>×5)/89
| 2.3.5.89 {{monzo| 1 2 1 -1 }}
| 2.3.5.89 {{monzo| 1 2 1 -1 }}
|  
|  
|
|
|-
|}
! colspan="6" | 97-limit (incomplete)
 
=== 97-limit (incomplete) ===
{| 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"/>
|-
| [[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 }}
|
|
|}
 
=== 101-limit (incomplete) ===
{| 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"/>
|-
| [[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
|
|}
 
=== 103-limit (incomplete) ===
{| 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"/>
|-
| [[103/102]]
| 16.890
| 103/(2×3×17)
| 2.3.17.103 {{monzo| -1 -1 -1 1 }}
|
|
|-
| [[104/103]]
| 16.727
| (2<sup>3</sup>×13)/103
| 2.13.103 {{monzo| 3 1 -1 }}
|
|
|}
 
=== 107-limit (incomplete) ===
{| 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"/>
|-
| [[107/106]]
| 16.256
| 107/(2×53)
| 2.53.107 {{monzo| -1 -1 1 }}
|
|
|-
| [[108/107]]
| 16.105
| (2<sup>2</sup>×3<sup>3</sup>)/107
| 2.3.107 {{monzo| 2 3 -1 }}
|
|
|-
| [[750/749]]
| 2.3099
| (2×3×5<sup>3</sup>)/(7×107)
| 2.3.5.7.107 {{monzo| 1 1 3 -1 -1 }}
| Ancient Chinese tempering comma
|
|}
 
=== 109-limit (incomplete) ===
{| 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"/>
|-
| [[109/108]]
| 15.956
| 109/(2<sup>2</sup>×3<sup>3</sup>)
| 2.3.109 {{monzo| -2 -3 1 }}
|
|
|-
| [[110/109]]
| 15.810
| (2×5×11)/109
| 2.5.11.109 {{monzo| 1 1 1 -1 }}
|
|
|}
 
=== 113-limit (incomplete) ===
{| 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"/>
|-
| [[113/112]]
| 15.389
| 113/(2<sup>4</sup>×7)
| 2.7.113 {{monzo| -4 -1 1 }}
|
|
|-
| [[114/113]]
| 15.253
| (2×3×19)/113
| 2.3.19.113 {{monzo| 1 1 1 -1 }}
|
|
|-
| [[226/225]]
| 7.6773
| (2×113)/(3×5)<sup>2</sup>
| 2.3.5.113 {{monzo| 1 -2 -2 1 }}
| Reversed marvel comma
|
|}
 
=== 127-limit (incomplete) ===
{| 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"/>
|-
| [[127/126]]
| 13.686
| 127/(2×3<sup>2</sup>×7)
| 2.3.7.127 {{monzo| -1 -2 -1 1 }}
|
|
|-
|-
| [[97/96]]
| [[128/127]]
| 17.940
| 13.578
| 97/(2<sup>5</sup>×3)
| 2<sup>7</sup>/127
| 2.3.97 {{monzo| -5 -1 1 }}
| 2.127 {{monzo| 7 -1 }}
|  
|  
|
|-
| [[98/97]]
| 17.756
| (2×7<sup>2</sup>)/97
| 2.7.97 {{monzo| 1 2 -1 }}
|  
|  
|
|-
|-
! colspan="6" | 101-limit (incomplete)
| [[381/380]]
|-
| 4.5499
| [[101/100]]
| (3×127)/(2<sup>2</sup>×5×19)
| 17.226
| 2.3.5.19.127 {{monzo| -2 1 -1 -1 1 }}
| 101/(2×5)<sup>2</sup>
| Five feet comma
| 2.5.101 {{monzo| -2 -2 1 }}
|  
|  
|
|-
|-
| [[102/101]]
| 500000/499999
| 17.057
| 0.0034625
| (2×3×17)/101
| (2<sup>5</sup>×5<sup>6</sup>)/(31×127<sup>2</sup>)
| 2.3.17.101 {{monzo| 1 1 1 -1 }}
| 2.5.31.127 {{monzo| 5 6 -1 -2 }}
|  
|  
|
|-
| [[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
|  
|  
|}
|}

Latest revision as of 12:44, 2 August 2025

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
4096/4095 0.42272 (26/3)2/(5×7×13) [12 -2 -1 -1 0 -1⟩ Schismina, tridecimal schisma 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⟩

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⟩

29-limit

Main article: List of superparticular intervals/29-limit

31-limit

Main article: List of superparticular intervals/31-limit

37-limit

Main article: List of superparticular intervals/37-limit

41-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
41/40 42.749 41/(23×5) 2.5.41 [-3 -1 1⟩ Large quadracesimoprimal 1/5-tone
42/41 41.719 (2×3×7)/41 2.3.7.41 [1 1 1 -1⟩ Small quadracesimoprimal 1/5-tone
82/81 21.242 (2×41)/34 2.3.41 [1 -4 1⟩ 41st-partial chroma
124/123 14.018 (22×31)/(3×41) 2.3.31.41 [2 -1 1 -1⟩
165/164 10.524 (3×5×11)/(22×41) 2.3.5.11.41 [-2 1 1 1 -1⟩
205/204 8.4657 (5×41)/(22×3×17) 2.3.5.17.41 [-2 -1 1 -1 1⟩
246/245 7.0519 (2×3×41)/(5×72) 2.3.5.7.41 [1 1 -1 -2 1⟩
247/246 7.0233 (13×19)/(2×3×41) 2.3.13.19.41 [-1 -1 1 1 -1⟩
287/286 6.0427 (7×41)/(2×11×13) 2.7.11.13.41 [-1 1 -1 -1 1⟩
288/287 6.0217 (25×32)/(7×41) 2.3.7.41 [5 2 -1 -1⟩
369/368 4.6981 (32×41)/(24×23) 2.3.23.41 [-4 2 -1 1⟩
370/369 4.6853 (2×5×37)/(32×41) 2.3.5.37.41 [1 -2 1 1 -1⟩
451/450 3.8429 (11×41)/(2×(3×5)2) 2.3.5.11.41 [-1 -2 -2 1 1⟩
493/492 3.5152 (17×29)/(22×3×41) 2.3.17.29.41 [-2 -1 1 1 -1⟩
533/532 3.2511 (13×41)/(22×7×19) 2.7.13.19.41 [-2 -1 1 -1 1⟩
575/574 3.0135 (52×23)/(2×7×41) 2.5.7.23.41 [-1 2 -1 1 -1⟩ Renatisma
616/615 2.8127 (23×7×11)/(3×5×41) 2.3.5.7.11.41 [3 -1 -1 1 1 -1⟩ Ellisma
697/696 2.4856 (17×41)/(23×3×29) 2.3.17.29.41 [-3 -1 1 -1 1⟩
780/779 2.2210 (22×3×5×13)/(19×41) 2.3.5.13.19.41 [2 1 1 1 -1 -1⟩ Wiesentisma
820/819 2.1125 (22×5×41)/(32×7×13) 2.3.5.7.13.41 [2 -2 1 -1 -1 1⟩
1025/1024 1.6898 (52×41)/210 2.5.41 [-10 2 1⟩ Kilobytisma
1026/1025 1.6882 (2×33×19)/(52×41) 2.3.5.19.41 [1 3 -2 1 -1⟩ Ingridisma
1148/1147 1.5087 (22×7×41)/(31×37) 2.7.31.37.41 [2 1 -1 -1 1⟩
1189/1188 1.4567 (29×41)/(22×33×11) 2.3.11.29.41 [-2 -3 -1 1 1⟩
1190/1189 1.4554 (2×5×7×17)/(29×41) 2.5.7.17.29.41 [1 1 1 1 -1 -1⟩ Pelagisma
1312/1311 1.3200 (25×41)/(3×19×23) 2.3.19.23.41 [5 -1 -1 -1 1⟩
1353/1352 1.2800 (3×11×41)/(23×132) 2.3.11.13.41 [-3 1 1 -2 1⟩
1395/1394 1.2415 (32×5×31)/(2×17×41) 2.3.5.17.31.41 [-1 2 1 -1 1 -1⟩
1518/1517 1.1408 (2×3×11×23)/(37×41) 2.3.11.23.37.41 [1 1 1 1 -1 -1⟩ Rovaniemisma
1600/1599 1.0824 (23×5)2/(3×13×41) 2.3.5.13.41 [6 -1 2 -1 -1⟩ S40
1681/1680 1.0302 412/(24×3×5×7) 2.3.5.7.41 [-4 -1 -1 -1 2⟩ S41
1682/1681 1.0296 (2×292)/412 2.29.41 [1 2 -2⟩ Shaftesburisma
1805/1804 0.95940 (5×192)/(22×11×41) 2.5.11.19.41 [-2 1 -1 2 -1⟩
1886/1885 0.91818 (2×23×41)/(5×13×29) 2.5.13.23.29.41 [1 -1 -1 1 -1 1⟩
1887/1886 0.91770 (3×17×37)/(2×23×41) 2.3.17.23.37.41 [-1 1 1 -1 1 -1⟩
2091/2090 0.82814 (3×17×41)/(2×5×11×19) 2.3.5.11.17.19.41 [-1 1 -1 -1 1 -1 1⟩
2255/2254 0.76790 (5×11×41)/(2×72×23) 2.5.7.11.23.41 [-1 1 -2 1 -1 1⟩ Qinghaisma
2296/2295 0.75419 (23×7×41)/(33×5×17) 2.3.5.7.17.41 [3 -3 -1 1 -1 1⟩
2542/2541 0.68119 (2×31×41)/(3×7×112) 2.3.7.11.31.41 [1 -1 -1 -2 1 1⟩
2584/2583 0.67011 (23×17×19)/(32×7×41) 2.3.7.17.19.41 [3 -2 -1 1 1 -1⟩
2625/2624 0.65964 (3×53×7)/(26×41) 2.3.5.7.41 [-6 1 3 1 -1⟩
2665/2664 0.64974 (5×13×41)/(23×32×37) 2.3.5.13.37.41 [-3 -2 1 1 -1 1⟩
2871/2870 0.60311 (32×11×29)/(2×5×7×41) 2.3.5.7.11.29.41 [-1 2 -1 -1 1 1 -1⟩ Schoberisma
3690/3689 0.46923 (2×32×5×41)/(7×17×31) 2.3.5.7.17.31.41 [1 2 1 -1 -1 -1 1⟩
3773/3772 0.45891 (73×11)/(22×23×41) 2.7.11.23.41 [-2 3 1 -1 -1⟩ Smithsonianisma
4060/4059 0.42646 (22×5×7×29)/(32×11×41) 2.3.5.7.11.29.41 [2 -2 1 1 -1 1 -1⟩ Deipylosisma
4264/4263 0.40606 (23×13×41)/(3×72×29) 2.3.7.13.29.41 [3 -1 -2 1 -1 1⟩
4551/4550 0.38045 (3×37×41)/(2×52×7×13) 2.3.5.7.13.37.41 [-1 1 -2 -1 -1 1 1⟩
4675/4674 0.37036 (52×11×17)/(2×3×19×41) 2.3.5.11.17.19.41 [-1 -1 2 1 1 -1 -1⟩ Ohbokisma
4921/4920 0.35184 (7×19×37)/(23×3×5×41) 2.3.5.7.19.37.41 [-3 -1 -1 1 1 1 -1⟩ Volontisma
4961/4960 0.34900 (112×41)/(25×5×31) 2.5.11.31.41 [-5 -1 2 -1 1⟩
5084/5083 0.34056 (22×31×41)/(13×17×23) 2.13.17.23.31.41 [2 -1 -1 -1 1 1⟩
5577/5576 0.31045 (3×11×132)/(23×17×41) 2.3.11.13.17.41 [-3 1 1 2 -1 -1⟩ Priestlisma
6069/6068 0.28528 (3×7×172)/(22×37×41) 2.3.7.17.37.41 [-2 1 1 2 -1 -1⟩ Cevolanisma
6273/6272 0.27600 (32×17×41)/(27×72) 2.3.7.17.41 [-7 2 -2 1 1⟩
6561/6560 0.26389 38/(25×5×41) 2.3.5.41 [-5 8 -1 -1⟩ S81
6601/6600 0.26229 (7×23×41)/(23×3×52×11) 2.3.5.7.11.23.41 [-3 -1 -2 1 -1 1 1⟩
6930/6929 0.24984 (2×32×5×7×11)/(132×41) 2.3.5.7.11.13.41 [1 2 1 1 1 -2 -1⟩ Bedanisma
7176/7175 0.24127 (23×3×13×23)/(52×7×41) 2.3.5.7.13.23.41 [3 1 -2 -1 1 1 -1⟩ Kunijisma
7216/7215 0.23993 (24×11×41)/(3×5×13×37) 2.3.5.11.13.37.41 [4 -1 -1 1 -1 -1 1⟩
7750/7749 0.22340 (2×53×31)/(33×7×41) 2.3.5.7.31.41 [1 -3 3 -1 1 -1⟩
8569/8568 0.20205 (11×19×41)/(23×32×7×17) 2.3.7.11.17.19.41 [-3 -2 -1 1 -1 1 1⟩ Mamelisma
8856/8855 0.19550 ((2×3)3×41)/(5×7×11×23) 2.3.5.7.11.23.41 [3 3 -1 -1 -1 -1 1⟩
9472/9471 0.18278 (28×37)/(3×7×11×41) 2.3.7.11.37.41 [8 -1 -1 -1 1 -1⟩ Brugesisma
10045/10044 0.17236 (5×72×41)/(22×34×31) 2.3.5.7.31.41 [-2 -4 1 2 -1 1⟩
10374/10373 0.16689 (2×3×7×13×19)/(11×23×41) 2.3.7.11.13.19.23.41 [1 1 1 -1 1 1 -1 -1⟩ Etampesisma
10660/10659 0.16241 (22×5×13×41)/(3×11×17×19) 2.3.5.11.13.17.19.41 [2 -1 1 -1 1 -1 -1 1⟩
11440/11439 0.15134 (24×5×11×13)/(32×31×41) 2.3.5.11.13.31.41 [4 -2 1 1 1 -1 -1⟩ Massironisma
13776/13775 0.12567 (24×3×7×41)/(52×19×29) 2.3.5.7.19.29.41 [4 1 -2 1 -1 -1 1⟩
14145/14144 0.12240 (3×5×23×41)/(26×13×17) 2.3.5.13.17.23.41 [-6 1 1 -1 -1 1 1⟩
14801/14800 0.11697 (192×41)/(24×52×37) 2.5.19.37.41 [-4 -2 2 -1 1⟩
15376/15375 0.11260 (22×31)2/(3×53×41) 2.3.5.31.41 [4 -1 -3 2 -1⟩ Martakisma S124
15457/15456 0.11201 (13×29×41)/(25×3×7×23) 2.3.7.13.23.29.41 [-5 -1 -1 1 -1 1 1⟩
16400/16399 0.10557 (24×52×41)/(232×31) 2.5.23.31.41 [4 2 -2 -1 1⟩
16524/16523 0.10477 (22×35×17)/(13×31×41) 2.3.13.17.31.41 [2 5 -1 1 -1 -1⟩
16606/16605 0.10426 (2×192×23)/(34×5×41) 2.3.5.19.23.41 [1 -4 -1 2 1 -1⟩
17425/17424 0.099356 (52×17×41)/(22×3×11)2 2.3.5.11.17.41 [-4 -2 2 -2 1 1⟩
17836/17835 0.097067 (22×73×13)/(3×5×29×41) 2.3.5.7.13.29.41 [2 -1 -1 3 1 -1 -1⟩ Canupisma
17918/17917 0.096623 (2×172×31)/(19×23×41) 2.17.19.23.31.41 [1 2 -1 -1 1 -1⟩
19721/19720 0.087789 (13×37×41)/(23×5×17×29) 2.5.13.17.29.37.41 [-3 -1 1 -1 -1 1 1⟩
19845/19844 0.087240 (34×5×72)/((2×11)2×41) 2.3.5.7.11.41 [-2 4 1 2 -2 -1⟩
76384/76383 0.022665 (25×7×11×31)/(34×23×41) 2.3.7.11.23.31.41 [5 -4 1 1 -1 1 -1⟩ Vernonisma
1048576/1048575 0.0016510 220/(3×52×11×31×41) 2.3.5.11.31.41 [20 -1 -2 -1 -1 -1⟩ Mebisma S1024

43-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
43/42 40.737 43/(2×3×7) 2.3.7.43 [-1 -1 -1 1⟩ Large quadracesimotertial 1/5-tone
44/43 39.800 (22×11)/43 2.11.43 [2 1 -1⟩ Small quadracesimotertial 1/5-tone
86/85 20.249 (2×43)/(5×17) 2.5.17.43 [1 -1 -1 1⟩ Large quadracesimotertial 1/10-tone
87/86 20.014 (3×29)/(2×43) 2.3.29.43 [-1 1 1 -1⟩ Small quadracesimotertial 1/10-tone
129/128 13.473 (3×43)/27 2.3.43 [-7 1 1⟩ 43rd-partial chroma
130/129 13.369 (2×5×13)/(3×43) 2.3.5.13.43 [1 -1 1 1 -1⟩
172/171 10.095 (22×43)/(32×19) 2.3.19.43 [2 -2 -1 1⟩
216/215 8.0336 (2×3)3/(5×43) 2.3.5.43 [3 3 -1 -1⟩
259/258 6.6972 (7×37)/(2×3×43) 2.3.7.37.43 [-1 -1 1 1 -1⟩
301/300 5.7612 (7×43)/((2×5)2×3) 2.3.5.7.43 [-2 -1 -2 1 1⟩
344/343 5.0400 (23×43)/73 2.7.43 [3 -3 1⟩
345/344 5.0254 (3×5×23)/(23×43) 2.3.5.23.43 [-3 1 1 1 -1⟩
430/429 4.0308 (2×5×43)/(3×11×13) 2.3.5.11.13.43 [1 -1 1 -1 -1 1⟩
559/558 3.0998 (13×43)/(2×32×31) 2.3.13.31.43 [-1 -2 1 -1 1⟩
560/559 3.0943 (24×5×7)/(13×43) 2.5.7.13.43 [4 1 1 -1 -1⟩
645/644 2.6862 (3×5×43)/(22×7×23) 2.3.5.7.23.43 [-2 1 1 -1 -1 1⟩
646/645 2.6820 (2×17×19)/(3×5×43) 2.3.5.17.19.43 [1 -1 -1 1 1 -1⟩ Kastalisma
775/774 2.2353 (52×31)/(2×32×43) 2.3.5.31.43 [-1 -2 2 1 -1⟩
817/816 2.1203 (19×43)/(24×3×17) 2.3.17.19.43 [-4 -1 -1 1 1⟩
861/860 2.0119 (3×7×41)/(22×5×43) 2.3.5.7.41.43 [-2 1 -1 1 1 -1⟩
903/902 1.9183 (3×7×43)/(2×11×41) 2.3.7.11.41.43 [-1 1 1 -1 -1 1⟩
946/945 1.8310 (2×11×43)/(33×5×7) 2.3.5.7.11.43 [1 -3 -1 -1 1 1⟩
989/988 1.7514 (23×43)/(22×13×19) 2.13.19.23.43 [-2 -1 -1 1 1⟩
990/989 1.7496 (2×32×5×11)/(23×43) 2.3.5.11.23.43 [1 2 1 1 -1 -1⟩ Yerkesisma
1161/1160 1.4918 (33×43)/(23×5×29) 2.3.5.29.43 [-3 3 -1 -1 1⟩
1248/1247 1.3878 (25×3×13)/(29×43) 2.3.13.29.43 [5 1 1 -1 -1⟩
1333/1332 1.2992 (31×43)/((2×3)2×37) 2.3.31.37.43 [-2 -2 1 -1 1⟩ Cevenolisma
1334/1333 1.2983 (2×23×29)/(31×43) 2.23.29.31.43 [1 1 1 -1 -1⟩
1376/1375 1.2586 (25×43)/(53×11) 2.5.11.43 [5 -3 -1 1⟩
1377/1376 1.2577 (34×17)/(25×43) 2.3.17.43 [-5 4 1 -1⟩ Roberbauxisma
1463/1462 1.1838 (7×11×19)/(2×17×43) 2.7.11.17.19.43 [-1 1 1 -1 1 -1⟩ Nordenmarkisma
1548/1547 1.1187 (22×32×43)/(7×13×17) 2.3.7.13.17.43 [2 2 -1 -1 -1 1⟩
1764/1763 0.98170 (2×3×7)2/(41×43) 2.3.7.41.43 [2 2 2 -1 -1⟩ S42
1806/1805 0.95887 (2×3×7×43)/(5×192) 2.3.5.7.19.43 [1 1 -1 1 -2 1⟩
1849/1848 0.93656 432/(23×3×7×11) 2.3.7.11.43 [-3 -1 -1 -1 2⟩ S43
1850/1849 0.93606 (2×52×37)/432 2.5.37.43 [1 2 1 -2⟩
1936/1935 0.89446 (22×11)2/(32×5×43) 2.3.5.11.43 [4 -2 -1 2 -1⟩ S44
2925/2924 0.59198 (32×52×13)/(22×17×43) 2.3.5.13.17.43 [-2 2 2 1 -1 -1⟩ Beattisma
3312/3311 0.52279 (24×32×23)/(7×11×43) 2.3.7.11.23.43 [4 2 -1 -1 1 -1⟩ Pedersenisma
4000/3999 0.43286 (25×53)/(3×31×43) 2.3.5.31.43 [5 -1 3 -1 -1⟩ Hipparchusisma
4301/4300 0.40257 (11×17×23)/(22×52×43) 2.5.11.17.23.43 [-2 -2 1 1 1 -1⟩ Boydenisma
4774/4773 0.36268 (2×7×11×31)/(3×37×43) 2.3.7.11.31.37.43 [1 -1 1 1 1 -1 -1⟩ Hobetsisma
5720/5719 0.30269 (23×5×11×13)/(7×19×43) 2.5.7.11.13.19.43 [3 1 -1 1 1 -1 -1⟩ Halweaverisma
7225/7224 0.23963 (5×17)2/(23×3×7×43) 2.3.5.7.17.43 [-3 -1 2 -1 2 -1⟩ Huntressisma S85
7956/7955 0.21761 (22×32×13×17)/(5×37×43) 2.3.5.13.17.37.43 [2 2 -1 1 1 -1 -1⟩ Yajinisma
9504/9503 0.18217 (25×33×11)/(13×17×43) 2.3.11.13.17.43 [5 3 1 -1 -1 -1⟩ Lionelisma
9633/9632 0.17973 (3×132×19)/(25×7×43) 2.3.7.13.19.43 [-5 1 -1 2 1 -1⟩ Coturisma
10450/10449 0.16568 (2×52×11×19)/(35×43) 2.3.5.11.19.43 [1 -5 2 1 1 -1⟩ Girardisma
10880/10879 0.15912 (27×5×17)/(11×23×43) 2.5.11.17.23.43 [7 1 -1 1 -1 -1⟩ Kaguyisma
17545/17544 0.098677 (5×112×29)/(23×3×17×43) 2.3.5.11.17.29.43 [-3 -1 1 2 -1 1 -1⟩ Manheimisma
27048/27047 0.064007 (23×3×72×23)/(17×37×43) 2.3.7.17.23.37.43 [3 1 2 -1 1 -1 -1⟩ Jangongisma
29241/29240 0.059207 (32×19)2/(23×5×17×43) 2.3.5.17.19.43 [-3 4 -1 -1 2 -1⟩ Locquirecisma S171

47-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
47/46 37.232 47/(2×23) 2.23.47 [-1 -1 1⟩
48/47 36.448 (24×3)/47 2.3.47 [4 1 -1⟩ 47th-partial chroma
94/93 18.516 (2×47)/(3×31) 2.3.31.47 [1 -1 -1 1⟩
95/94 18.320 (5×19)/(2×47) 2.5.19.47 [-1 1 1 -1⟩
141/140 12.322 (3×47)/(22×5×7) 2.3.5.7.47 [-2 1 -1 -1 1⟩
188/187 9.2333 (22×47)/(11×17) 2.11.37.47 [2 -1 -1 1⟩
189/188 9.1843 (33×7)/(22×47) 2.3.7.47 [-2 3 1 -1⟩
235/234 7.3827 (5×47)/(2×32×13) 2.3.5.13.47 [-1 -2 1 -1 1⟩
329/328 5.2701 (7×47)/(23×41) 2.7.41.47 [-3 1 -1 1⟩
330/329 5.2541 (2×3×5×11)/(7×47) 2.3.5.7.11.47 [1 1 1 -1 1 -1⟩
376/375 4.6105 (23×47)/(3×53) 2.3.5.47 [3 -1 -3 1⟩
377/376 4.5982 (13×29)/(23×47) 2.13.29.47 [-3 1 1 -1⟩
1176/1175 1.4728 (23×3×72)/(52×47) 2.3.5.7.47 [3 1 -2 2 -1⟩ Lucidorisma
2116/2115 0.81836 (2×23)2/(32×5×47) 2.3.5.23.47 [2 -2 -1 2 -1⟩ S46
2209/2208 0.78390 472/(25×3×5) 2.3.23.47 [-5 -1 -1 2⟩ S47
2304/2303 0.75157 (24×3)2/(72×47) 2.3.7.47 [8 2 -2 -1⟩ S48

53-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
53/52 32.977 53/(22×13) 2.13.53 [-2 -1 1⟩
54/53 32.360 (2×33)/53 2.3.53 [1 3 -1⟩
106/105 16.410 (2×53)/(3×5×7) 2.3.5.7.53 [1 -1 -1 -1 1⟩
160/159 10.854 (25×5)/(3×53) 2.3.5.53 [5 -1 1 -1⟩
265/264 6.5453 (5×53)/(23×3×11) 2.3.5.11.53 [-3 -1 1 -1 1⟩
266/265 6.5207 (2×7×19)/(5×53) 2.5.7.19.53 [1 -1 1 1 -1⟩
319/318 5.4356 (11×29)/(2×3×53) 2.3.11.29.53 [-1 -1 1 1 -1⟩
371/370 4.6727 (7×53)/(2×5×37) 2.5.7.37.53 [-1 -1 1 -1 1⟩
372/371 4.6601 (22×3×31)/(7×53) 2.3.7.31.53 [2 1 -1 1 -1⟩
424/423 4.0879 (23×53)/(32×47) 2.3.47.53 [3 -2 -1 1⟩
425/424 4.0783 (52×17)/(23×53) 2.5.17.53 [-3 2 1 -1⟩
477/476 3.6332 (32×53)/(22×7×17) 2.3.7.17.53 [-2 2 -1 -1 1⟩
2809/2808 0.61643 532/(23×33×13) 2.3.13.53 [-3 -3 -1 2⟩ S53
4081/4080 0.42427 (7×11×53)/(24×3×5×17) 2.3.5.7.11.17.53 [-4 -1 -1 1 1 -1 1⟩

59-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
59/58 29.594 59/(2×29) 2.29.59 [-1 -1 1⟩
60/59 29.097 (22×3×5)/59 2.3.5.59 [2 1 1 -1⟩
118/117 14.734 (2×59)/(32×13) 2.3.13.59 [1 -2 -1 1⟩
119/118 14.610 (7×17)/(2×59) 2.7.17.59 [-1 1 1 -1⟩
177/176 9.8087 (3×59)/(24×11) 2.3.11.59 [-4 1 -1 1⟩
236/235 7.3513 (22×59)/(5×47) 2.5.47.59 [2 -1 -1 1⟩
295/294 5.8786 (5×59)/(2×3×72) 2.3.5.7.59 [-1 -1 1 -2 1⟩
296/295 5.8587 (23×37)/(5×59) 2.5.37.59 [3 -1 1 -1⟩
414/413 4.1868 (2×32×23)/(7×59) 2.3.7.23.59 [1 2 -1 1 -1⟩
473/472 3.6640 (11×43)/(23×59) 2.11.43.59 [-3 1 1 -1⟩
1121/1120 1.5451 (19×59)/(25×5×7) 2.5.7.19.59 [-5 -1 -1 1 1⟩
1122/1121 1.5437 (2×3×11×17)/(19×59) 2.3.11.17.19.59 [1 1 1 1 -1 -1⟩
3481/3480 0.49741 592/(23×3×5×29) 2.3.5.29.59 [-3 -1 -1 -1 2⟩ S59

61-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
61/60 28.616 61/(22×3×5) 2.3.5.61 [-2 -1 -1 1⟩
62/61 28.151 (2×31)/61 2.31.61 [1 1 -1⟩
122/121 14.249 (2×61)/(112) 2.11.61 [1 -2 1⟩
123/122 14.133 (3×41)/(2×61) 2.3.41.61 [-1 1 1 -1⟩
183/182 9.4862 (3×61)/(2×7×13) 2.3.7.13.61 [-1 1 -1 -1 1⟩
184/183 9.4345 (23×23)/(3×61) 2.3.23.61 [3 -1 1 -1⟩
244/243 7.1098 (22×61)/35 2.3.61 [2 -5 1⟩
245/244 7.0807 (5×72)/(22×61) 2.5.7.61 [-2 1 2 -1⟩
305/304 5.6855 (5×61)/(24×19) 2.5.19.61 [-4 1 -1 1⟩
306/305 5.6669 (2×32×17)/(5×61) 2.3.5.17.61 [1 2 -1 1 -1⟩
672/671 2.5782 (25×3×7)/(11×61) 2.3.7.11.61 [5 1 1 -1 -1⟩
1404/1403 1.2335 (22×33×13)/(23×61) 2.3.13.23.61 [2 3 1 -1 -1⟩
3721/3720 0.46532 612/(23×3×5×31) 2.3.5.31.61 [-3 -1 -1 -1 2⟩ S61

67-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
67/66 26.034 67/(2×3×11) 2.3.11.67 [-1 -1 -1 1⟩
68/67 25.648 (22×17)/67 2.17.67 [2 1 -1⟩
134/133 12.968 (2×67)/(7×19) 2.7.19.67 [1 -1 -1 1⟩
135/134 12.872 (33×5)/(2×67) 2.3.5.67 [-1 3 1 -1⟩
201/200 8.6346 (3×67)/(23×52) 2.3.5.67 [-3 1 -2 1⟩
336/335 5.1602 (24×3×7)/(5×67) 2.3.5.7.67 [4 1 -1 1 -1⟩
671/670 2.5820 (11×61)/(2×5×67) 2.5.11.61.67 [-1 -1 1 1 -1⟩
4489/4488 0.38570 672/(23×3×11×17) 2.3.11.17.67 [-3 -1 -1 -1 2⟩ S67

71-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
71/70 24.557 71/(2×5×7) 2.5.7.71 [-1 -1 -1 1⟩
72/71 24.213 (23×32)/71 2.3.71 [3 2 -1⟩
5041/5040 0.34346 712/(24×32×5×7) 2.3.5.7.71 [-4 -2 -1 -1 2⟩ Third brown pair comma S71
160561400000 / 160561399999 1.0783×10-8 (26×55×19×29×31×47) / (7×112×13×593×71) 2.5.7.11.13.19.29.31.47.59.71 [6 5 -1 -2 -1 1 1 1 1 -3 -1⟩ Borcherdsma

73-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
73/72 23.879 73/(23×32) 2.3.73 [-3 -2 1⟩
74/73 23.555 (2×37)/73 2.37.73 [1 1 -1⟩
366/365 4.737 (2×3×61)/(5×73) 2.3.5.61.73 [1 1 -1 1 -1⟩ Sidereal comma

79-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
79/78 22.054 79/(2×3×13) 2.3.13.79 [-1 -1 -1 1⟩
80/79 21.777 (24×5)/79 2.5.79 [4 1 -1⟩

83-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
83/82 20.985 83/(2×41) 2.41.83 [-1 -1 1⟩
84/83 20.734 (22×3×7)/83 2.3.7.83 [2 1 1 -1⟩

89-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
89/88 19.562 89/(23×11) 2.11.89 [-3 -1 1⟩ Tailwind comma[idiosyncratic term]
90/89 19.344 (2×32×5)/89 2.3.5.89 [1 2 1 -1⟩

97-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
97/96 17.940 97/(25×3) 2.3.97 [-5 -1 1⟩
98/97 17.756 (2×72)/97 2.7.97 [1 2 -1⟩

101-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
101/100 17.226 101/(2×5)2 2.5.101 [-2 -2 1⟩
102/101 17.057 (2×3×17)/101 2.3.17.101 [1 1 1 -1⟩
7777/7776 0.223 7×11×101/(2×3)5 2.3.7.11.101 [-5 -5 1 1 1⟩ Pulsar comma

103-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
103/102 16.890 103/(2×3×17) 2.3.17.103 [-1 -1 -1 1⟩
104/103 16.727 (23×13)/103 2.13.103 [3 1 -1⟩

107-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
107/106 16.256 107/(2×53) 2.53.107 [-1 -1 1⟩
108/107 16.105 (22×33)/107 2.3.107 [2 3 -1⟩
750/749 2.3099 (2×3×53)/(7×107) 2.3.5.7.107 [1 1 3 -1 -1⟩ Ancient Chinese tempering comma

109-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
109/108 15.956 109/(22×33) 2.3.109 [-2 -3 1⟩
110/109 15.810 (2×5×11)/109 2.5.11.109 [1 1 1 -1⟩

113-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
113/112 15.389 113/(24×7) 2.7.113 [-4 -1 1⟩
114/113 15.253 (2×3×19)/113 2.3.19.113 [1 1 1 -1⟩
226/225 7.6773 (2×113)/(3×5)2 2.3.5.113 [1 -2 -2 1⟩ Reversed marvel comma

127-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
127/126 13.686 127/(2×32×7) 2.3.7.127 [-1 -2 -1 1⟩
128/127 13.578 27/127 2.127 [7 -1⟩
381/380 4.5499 (3×127)/(22×5×19) 2.3.5.19.127 [-2 1 -1 -1 1⟩ Five feet comma
500000/499999 0.0034625 (25×56)/(31×1272) 2.5.31.127 [5 6 -1 -2⟩

See also

Notes

  1. ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 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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