List of superparticular intervals: Difference between revisions

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This '''list of superparticular intervals''' ordered by prime limit. It reaches to the [[101-limit]] and is complete up to the [[17-limit]].
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]].


[[Superparticular]] numbers are ratios of the form (n+1)/n, or 1+1/n, where n is a whole number other than 1. They appear frequently in [[just intonation]] and [[OverToneSeries|Harmonic Series]] music. Adjacent tones in the harmonic series are separated by superparticular intervals: for instance, the 20th and 21st by the superparticular ratio [[21/20]]. As the overtones get closer together, the superparticular intervals get smaller and smaller. Thus, an examination of the superparticular intervals is an examination of some of the simplest small intervals in rational tuning systems. Indeed, many but not all common [[comma]]s are superparticular ratios.
[[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).


The list below is ordered by [[harmonic limit]], or the largest prime involved in the prime factorization. [[36/35]], for instance, is an interval of the [[7-limit]], as it factors to (2<sup>2</sup>*3<sup>2</sup>)/(5*7), while 37/36 would belong to the 37-limit.
== List of superparticular intervals ==
 
=== 2-limit ===
[http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem Størmer's theorem] guarantees 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]]. [http://oeis.org/A002071 A002071 &#45;- OEIS] gives the number of superparticular ratios in each prime limit, [http://oeis.org/A145604 A145604 &#45; OEIS] shows the increment from limit to limit, and [http://oeis.org/A117581 A117581] 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).
{| class="wikitable center-6" style="width:100%"
 
See also [[gallery of just intervals]]. Many of the names below come from [http://www.huygens-fokker.org/docs/intervals.html here].
 
{| class="wikitable"
|-
! Ratio
! Cents
! Factorization
! [[Monzo]]
! Name(s)
|-
|-
! colspan="5" | 2-limit (complete)
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! 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>
|-
|-
| [[2/1]]
| [[2/1]]
| 1200.000
| 1200.000
| 2/1
| 2/1
| {{Monzo|1}}
| {{Monzo| 1 }}
| octave, duple; ''after [[octave reduction]]:'' (perfect) unison, unity, perfect prime, tonic
| Octave, duple, 2nd harmonic, diapason
|-
|
! colspan="5" | 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]]
| 701.995
| 701.955
| 3/2
| 3/2
| {{Monzo|-1 1}}
| {{Monzo| -1 1 }}
| [[perfect fifth]], 3rd harmonic (octave reduced), diapente
| Perfect fifth, octave-reduced 3rd harmonic, diapente
|
|-
|-
| [[4/3]]
| [[4/3]]
| 498.045
| 498.045
| 2<sup>2</sup>/3
| 2<sup>2</sup>/3
| {{Monzo|2 -1}}
| {{Monzo| 2 -1 }}
| perfect fourth, 3rd subharmonic (octave reduced), diatessaron
| Perfect fourth, octave-reduced 3rd subharmonic, diatessaron
| S2
|-
|-
| [[9/8]]
| [[9/8]]
| 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, 9th harmonic or harmonic ninth (octave reduced)
| Pythagorean whole tone, Pythagorean major second, <br>major whole tone, octave-reduced 9th harmonic, harmonic ninth
|-
| S3
! colspan="5" | 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]]
| 386.314
| 386.314
| 5/2<sup>2</sup>
| 5/2<sup>2</sup>
| {{Monzo|-2 0 1}}
| {{Monzo| -2 0 1 }}
| (classic) (5-limit) major third, 5th harmonic (octave reduced)
| Classic(al)/just major third, octave-reduced 5th harmonic
|
|-
|-
| [[6/5]]
| [[6/5]]
| 315.641
| 315.641
| (2*3)/5
| (2×3)/5
| {{Monzo|1 1 -1}}
| {{Monzo| 1 1 -1 }}
| (classic) (5-limit) minor third
| Classic(al)/just minor third
|
|-
|-
| [[10/9]]
| [[10/9]]
| 182.404
| 182.404
| (2*5)/3<sup>2</sup>
| (2×5)/3<sup>2</sup>
| {{Monzo|1 -2 1}}
| {{Monzo| 1 -2 1 }}
| classic (whole) tone, classic major second, minor whole tone
| Classic(al) (whole) tone, classic major second, minor whole tone
|
|-
|-
| [[16/15]]
| [[16/15]]
| 111.713
| 111.731
| 2<sup>4</sup>/(3*5)
| 2<sup>4</sup>/(3×5)
| {{Monzo|4 -1 -1}}
| {{Monzo| 4 -1 -1 }}
| minor diatonic semitone, 15th subharmonic
| Classic(al)/just diatonic semitone, 15th subharmonic
| S4
|-
|-
| [[25/24]]
| [[25/24]]
| 70.672
| 70.672
| 5<sup>2</sup>/(2<sup>3</sup>*3)
| 5<sup>2</sup>/(2<sup>3</sup>×3)
| {{Monzo|-3 -1 2}}
| {{Monzo| -3 -1 2 }}
| chroma, (classic) chromatic semitone, Zarlinian semitone
| Classic(al)/just chromatic semitone, chroma, Zarlinian semitone
| S5
|-
|-
| [[81/80]]
| [[81/80]]
| 21.506
| 21.506
| (3/2)<sup>4</sup>/5
| (3/2)<sup>4</sup>/5
| {{Monzo|-4 4 -1}}
| {{Monzo| -4 4 -1 }}
| syntonic comma, Didymus comma
| Syntonic comma, Didymus comma
|-
| S9
! colspan="5" | 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]]
| 266.871
| 266.871
| 7/(2*3)
| 7/(2×3)
| {{Monzo|-1 -1 0 1 }}
| {{Monzo| -1 -1 0 1 }}
| (septimal) subminor third, septimal minor third, augmented second
| (Septimal) subminor third, septimal minor third
|
|-
|-
| [[8/7]]
| [[8/7]]
| 231.174
| 231.174
| 2<sup>3</sup>/7
| 2<sup>3</sup>/7
| {{Monzo|3 0 0 -1}}
| {{Monzo| 3 0 0 -1 }}
| (septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic
| (Septimal) supermajor second, septimal whole tone, <br>octave-reduced 7th subharmonic
|
|-
|-
| [[15/14]]
| [[15/14]]
| 119.443
| 119.443
| (3*5)/(2*7)
| (3×5)/(2×7)
| {{Monzo|-1 1 1 -1}}
| {{Monzo| -1 1 1 -1 }}
| septimal diatonic semitone
| Septimal major semitone, septimal diatonic semitone
|
|-
|-
| [[21/20]]
| [[21/20]]
| 84.467
| 84.467
| (3*7)/(2<sup>2</sup>*5)
| (3×7)/(2<sup>2</sup>×5)
| {{Monzo|-2 1 -1 1}}
| {{Monzo| -2 1 -1 1 }}
| minor semitone, large septimal chromatic semitone
| Septimal minor semitone, large septimal chroma
|
|-
|-
| [[28/27]]
| [[28/27]]
| 62.961
| 62.961
| (2<sup>2</sup>*7)/3<sup>3</sup>
| (2<sup>2</sup>×7)/3<sup>3</sup>
| {{Monzo|2 -3 0 1}}
| {{Monzo| 2 -3 0 1 }}
| septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone
| 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>3</sup>)/(5*7)
| (2×3)<sup>2</sup>/(5×7)
| {{Monzo|2 2 -1 -1}}
| {{Monzo| 2 2 -1 -1 }}
| septimal quarter tone, septimal diesis
| Septimal 1/4-tone, mint comma
| S6
|-
|-
| [[49/48]]
| [[49/48]]
| 35.697
| 35.697
| 7<sup>2</sup>/(2<sup>4</sup>*3)
| 7<sup>2</sup>/(2<sup>4</sup>×3)
| {{Monzo|-4 -1 0 2}}
| {{Monzo| -4 -1 0 2 }}
| large septimal diesis, slendro diesis, septimal 1/6-tone
| Large septimal diesis, large septimal 1/6-tone, slendro diesis, semaphoresma
| S7
|-
|-
| [[50/49]]
| [[50/49]]
| 34.976
| 34.976
| 2*(5/7)<sup>2</sup>
| 2×(5/7)<sup>2</sup>
| {{Monzo|1 0 2 -2}}
| {{Monzo| 1 0 2 -2 }}
| septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma
| Small septimal diesis, small septimal 1/6-tone, septimal tritonic diesis, jubilisma
|
|-
|-
| [[64/63]]
| [[64/63]]
| 27.264
| 27.264
| 2<sup>6</sup>/(3<sup>2</sup>*7)
| 2<sup>6</sup>/(3<sup>2</sup>×7)
| {{Monzo|6 -2 0 -1}}
| {{Monzo| 6 -2 0 -1 }}
| septimal comma, Archytas' comma
| Septimal comma, Archytas' comma
| S8
|-
|-
| [[126/125]]
| [[126/125]]
| 13.795
| 13.795
| (2*3<sup>2</sup>*7)/5<sup>3</sup>
| (2×3<sup>2</sup>×7)/5<sup>3</sup>
| {{Monzo|1 2 -3 1}}
| {{Monzo| 1 2 -3 1 }}
| starling comma, septimal semicomma
| Starling comma, septimal semicomma
|
|-
|-
| [[225/224]]
| [[225/224]]
| 7.7115
| 7.7115
| (3*5)<sup>2</sup>/(2<sup>5</sup>*7)
| (3×5)<sup>2</sup>/(2<sup>5</sup>×7)
| {{Monzo|-5 2 2 -1}}
| {{Monzo| -5 2 2 -1 }}
| marvel comma, septimal kleisma
| Marvel comma, septimal kleisma
| S15
|-
|-
| [[2401/2400]]
| [[2401/2400]]
| 0.72120
| 0.72120
| 7<sup>4</sup>/(2<sup>5</sup>*3*5<sup>2</sup>)
| 7<sup>4</sup>/(2<sup>5</sup>×3×5<sup>2</sup>)
| {{Monzo|-5 -1 -2 4}}
| {{Monzo| -5 -1 -2 4 }}
| breedsma
| Breedsma
| S49
|-
|-
| [[4375/4374]]
| [[4375/4374]]
| 0.39576
| 0.39576
| (5<sup>4</sup>*7)/(2*3<sup>7</sup>)
| (5<sup>4</sup>×7)/(2×3<sup>7</sup>)
| {{Monzo|-1 -7 4 1}}
| {{Monzo| -1 -7 4 1 }}
| ragisma
| Ragisma
|-
|  
! colspan="5" | 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]]
| 165.004
| 165.004
| 11/(2*5)
| 11/(2×5)
| {{Monzo|-1 0 -1 0 1}}
| {{Monzo| -1 0 -1 0 1 }}
| (large) (undecimal) neutral second, 4/5-tone, Ptolemy's second
| Large undecimal neutral second, <br>undecimal submajor second, Ptolemy's second
|
|-
|-
| [[12/11]]
| [[12/11]]
| 150.637
| 150.637
| (2<sup>2</sup>*3)/11
| (2<sup>2</sup>×3)/11
| {{Monzo|2 1 0 0 -1}}
| {{Monzo| 2 1 0 0 -1 }}
| (small) (undecimal) neutral second, 3/4-tone
| Small undecimal neutral second
|
|-
|-
| [[22/21]]
| [[22/21]]
| 80.537
| 80.537
| (2*11)/(3*7)
| (2×11)/(3×7)
| {{Monzo|1 -1 0 -1 1}}
| {{Monzo| 1 -1 0 -1 1 }}
| undecimal minor semitone
| Undecimal minor semitone
|
|-
|-
| [[33/32]]
| [[33/32]]
| 53.273
| 53.273
| (3*11)/2<sup>5</sup>
| (3×11)/2<sup>5</sup>
| {{Monzo|-5 1 0 0 1}}
| {{Monzo| -5 1 0 0 1 }}
| undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced)
| Undecimal 1/4-tone, undecimal diesis, <br>al-Farabi's 1/4-tone, octave-reduced 33rd harmonic
|
|-
|-
| [[45/44]]
| [[45/44]]
| 38.906
| 38.906
| (3/2)<sup>2</sup>*(5/11)
| (3/2)<sup>2</sup>×(5/11)
| {{Monzo|-2 2 1 0 -1}}
| {{monzo| -2 2 1 0 -1 }}
| 1/5-tone
| Undecimal 1/5-tone, cake comma
|
|-
|-
| [[55/54]]
| [[55/54]]
| 31.767
| 31.767
| (5*11)/(2*3<sup>3</sup>)
| (5×11)/(2×3<sup>3</sup>)
| {{Monzo|-1 -3 1 0 1}}
| {{Monzo| -1 -3 1 0 1 }}
| undecimal diasecundal comma, eleventyfive comma
| Telepathma, eleventyfive comma, <br>undecimal diasecundal comma
|
|-
|-
| [[56/55]]
| [[56/55]]
| 31.194
| 31.194
| (2<sup>3</sup>*7)/(5*11)
| (2<sup>3</sup>×7)/(5×11)
| {{Monzo|3 0 -1 1 -1}}
| {{Monzo| 3 0 -1 1 -1 }}
| undecimal tritonic comma, konbini comma
| Undecimal tritonic comma, konbini comma
|
|-
|-
| [[99/98]]
| [[99/98]]
| 17.576
| 17.576
| (3/7)<sup>2</sup>*(11/2)
| (3/7)<sup>2</sup>×(11/2)
| {{Monzo|-1 2 0 -2 1}}
| {{Monzo| -1 2 0 -2 1 }}
| small undecimal comma, mothwellsma
| 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 }}
| Ptolemy's comma, ptolemisma
| Ptolemisma, Ptolemy's comma
| S10
|-
|-
| [[121/120]]
| [[121/120]]
| 14.376
| 14.376
| 11<sup>2</sup>/(2<sup>3</sup>*3*5)
| 11<sup>2</sup>/(2<sup>3</sup>×3×5)
| {{Monzo|-3 -1 -1 0 2}}
| {{Monzo| -3 -1 -1 0 2 }}
| undecimal seconds comma, biyatisma
| Biyatisma, undecimal seconds comma
| S11
|-
|-
| [[176/175]]
| [[176/175]]
| 9.8646
| 9.8646
| (2<sup>4</sup>*11)/(5<sup>2</sup>*7)
| (2<sup>4</sup>×11)/(5<sup>2</sup>×7)
| {{Monzo|4 0 -2 -1 1}}
| {{Monzo| 4 0 -2 -1 1 }}
| valinorsma
| Valinorsma
|
|-
|-
| [[243/242]]
| [[243/242]]
| 7.1391
| 7.1391
| 3<sup>5</sup>/(2*11<sup>2</sup>)
| 3<sup>5</sup>/(2×11<sup>2</sup>)
| {{Monzo|-1 5 0 0 -2}}
| {{Monzo| -1 5 0 0 -2 }}
| neutral third comma, rastma
| Rastma, neutral thirds comma
|
|-
|-
| [[385/384]]
| [[385/384]]
| 4.5026
| 4.5026
| (5*7*11)/(2<sup>7</sup>*3)
| (5×7×11)/(2<sup>7</sup>×3)
| {{Monzo|-7 -1 1 1 1}}
| {{Monzo| -7 -1 1 1 1 }}
| keenanisma
| Keenanisma
|
|-
|-
| [[441/440]]
| [[441/440]]
| 3.9302
| 3.9302
| (3*7)<sup>2</sup>/(2<sup>3</sup>*5*11)
| (3×7)<sup>2</sup>/(2<sup>3</sup>×5×11)
| {{Monzo|-3 2 -1 2 -1}}
| {{Monzo| -3 2 -1 2 -1 }}
| Werckmeister's undecimal septenarian schisma, werckisma
| Werckisma, Werckmeister's undecimal septenarian schisma
| S21
|-
|-
| [[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 }}
| Swets' comma, swetisma
| 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
| S55
|-
|-
| [[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 }}
| Gauss comma, kalisma
| Kalisma, Gauss comma
|-
| S99
! colspan="5" | 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]]
| 138.573
| 138.573
| 13/(2<sup>2</sup>*3)
| 13/(2<sup>2</sup>×3)
| {{Monzo|-2 -1 0 0 0 1}}
| {{Monzo| -2 -1 0 0 0 1 }}
| tridecimal 2/3-tone
| Large tridecimal 2/3-tone, <br>tridecimal neutral second
|
|-
|-
| [[14/13]]
| [[14/13]]
| 128.298
| 128.298
| (2*7)/13
| (2×7)/13
| {{Monzo|1 0 0 1 0 -1}}
| {{Monzo| 1 0 0 1 0 -1 }}
| 2/3-tone, trienthird
| Small tridecimal 2/3-tone, trienthird
|
|-
|-
| [[26/25]]
| [[26/25]]
| 67.900
| 67.900
| (2*13)/5<sup>2</sup>
| (2×13)/5<sup>2</sup>
| {{Monzo|1 0 -2 0 0 1}}
| {{Monzo| 1 0 -2 0 0 1 }}
| tridecimal 1/3-tone
| Large tridecimal 1/3-tone
|
|-
|-
| [[27/26]]
| [[27/26]]
| 65.337
| 65.337
| 3<sup>3</sup>/(2*13)
| 3<sup>3</sup>/(2×13)
| {{Monzo|-1 3 0 0 0 -1}}
| {{Monzo| -1 3 0 0 0 -1 }}
| tridecimal comma
| Small tridecimal 1/3-tone
|
|-
|-
| [[40/39]]
| [[40/39]]
| 43.831
| 43.831
| (2<sup>3</sup>*5)/(3*13)
| (2<sup>3</sup>×5)/(3×13)
| {{Monzo|3 -1 1 0 0 -1}}
| {{Monzo| 3 -1 1 0 0 -1 }}
| tridecimal minor diesis
| Tridecimal minor diesis
|
|-
|-
| [[65/64]]
| [[65/64]]
| 26.841
| 26.841
| (5*13)/2<sup>6</sup>
| (5×13)/2<sup>6</sup>
| {{Monzo|-6 0 1 0 0 1}}
| {{Monzo| -6 0 1 0 0 1 }}
| wilsorma, 13th-partial chroma
| Wilsorma, 13th-partial chroma
|
|-
|-
| [[66/65]]
| [[66/65]]
| 26.432
| 26.432
| (2*3*11)/(5*13)
| (2×3×11)/(5×13)
| {{Monzo|1 1 -1 0 1 -1}}
| {{Monzo| 1 1 -1 0 1 -1 }}
| winmeanma
| Winmeanma
|
|-
|-
| [[78/77]]
| [[78/77]]
| 22.339
| 22.339
| (2*3*13)/(7*11)
| (2×3×13)/(7×11)
| {{Monzo|1 1 0 -1 -1 1}}
| {{Monzo| 1 1 0 -1 -1 1 }}
| negustma
| Negustma
|
|-
|-
| [[91/90]]
| [[91/90]]
| 19.130
| 19.130
| (7*13)/(2*3<sup>2</sup>*5)
| (7×13)/(2×3<sup>2</sup>×5)
| {{Monzo|-1 -2 -1 1 0 1}}
| {{Monzo| -1 -2 -1 1 0 1 }}
| [[The_Biosphere|Biome]] comma, superleap comma
| Biome comma, superleap comma
|
|-
|-
| [[105/104]]
| [[105/104]]
| 16.567
| 16.567
| (3*5*7)/(2<sup>3</sup>*13)
| (3×5×7)/(2<sup>3</sup>×13)
| {{Monzo|-3 1 1 1 0 -1}}
| {{Monzo| -3 1 1 1 0 -1 }}
| small tridecimal comma, animist comma
| Animist comma, small tridecimal comma
|
|-
|-
| [[144/143]]
| [[144/143]]
| 12.064
| 12.064
| (2<sup>2</sup>*3)<sup>2</sup>/(11*13)
| (2<sup>2</sup>×3)<sup>2</sup>/(11×13)
| {{Monzo|4 2 0 0 -1 -1}}
| {{Monzo| 4 2 0 0 -1 -1 }}
| grossma
| Grossma
| S12
|-
|-
| [[169/168]]
| [[169/168]]
| 10.274
| 10.274
| 13<sup>2</sup>/(2<sup>3</sup>*3*7)
| 13<sup>2</sup>/(2<sup>3</sup>×3×7)
| {{Monzo|-3 -1 0 -1 0 2}}
| {{Monzo| -3 -1 0 -1 0 2 }}
| buzurgisma, dhanvantarisma
| Buzurgisma, dhanvantarisma
| S13
|-
|-
| [[196/195]]
| [[196/195]]
| 8.8554
| 8.8554
| (2*7)<sup>2</sup>/(3*5*13)
| (2×7)<sup>2</sup>/(3×5×13)
| {{Monzo|2 -1 -1 2 0 -1}}
| {{Monzo| 2 -1 -1 2 0 -1 }}
| [[Mynucumic_chords|mynucuma]]
| Mynucuma
| S14
|-
|-
| [[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|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]]
| 2.7722
| 2.7722
| (5/2)<sup>4</sup>/(3*13)
| (5/2)<sup>4</sup>/(3×13)
| {{Monzo|-4 -1 4 0 0 -1}}
| {{Monzo| -4 -1 4 0 0 -1 }}
| tunbarsma
| Tunbarsma
| S25
|-
|-
| [[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
| S26
|-
|-
| [[729/728]]
| [[729/728]]
| 2.3764
| 2.3764
| (3<sup>2</sup>/2)<sup>3</sup>/(7*13)
| (3<sup>2</sup>/2)<sup>3</sup>/(7×13)
| {{Monzo|-3 6 0 -1 0 -1}}
| {{Monzo| -3 6 0 -1 0 -1 }}
| squbema
| Squbema
| S27
|-
|-
| [[1001/1000]]
| [[1001/1000]]
| 1.7304
| 1.7304
| 7*11*13/(2*5)<sup>3</sup>
| (7×11×13)/(2×5)<sup>3</sup>
| {{Monzo|-3 0 -3 1 1 1}}
| {{Monzo| -3 0 -3 1 1 1 }}
| sinbadma
| Sinbadma
|
|-
|-
| [[1716/1715]]
| [[1716/1715]]
| 1.0092
| 1.0092
| 2<sup>2</sup>*3*11*13/(5*7<sup>3</sup>)
| (2<sup>2</sup>×3×11×13)/(5×7<sup>3</sup>)
| {{Monzo|2 1 -1 -3 1 1}}
| {{Monzo| 2 1 -1 -3 1 1 }}
| lummic comma
| Lummic comma
|
|-
|-
| [[2080/2079]]
| [[2080/2079]]
| 0.83252
| 0.83252
| 2<sup>5</sup>*5*13/(3<sup>3</sup>*7*11)
| (2<sup>5</sup>×5×13)/(3<sup>3</sup>×7×11)
| {{Monzo|5 -3 1 -1 -1 1}}
| {{Monzo| 5 -3 1 -1 -1 1 }}
| ibnsinma
| Ibnsinma, sinaisma
|
|-
|-
| [[4096/4095]]
| [[4096/4095]]
| 0.42272
| 0.42272
| (2<sup>6</sup>/3)<sup>2</sup>/(5*7*13)
| (2<sup>6</sup>/3)<sup>2</sup>/(5×7×13)
| {{Monzo|12 -2 -1 -1 0 -1}}
| {{Monzo| 12 -2 -1 -1 0 -1 }}
| tridecimal schisma, Sagittal schismina
| Minisma
| S64
|-
|-
| [[4225/4224]]
| [[4225/4224]]
| 0.40981
| 0.40981
| (5*13)<sup>2</sup>/(2<sup>7</sup>*3*11)
| (5×13)<sup>2</sup>/(2<sup>7</sup>×3×11)
| {{Monzo|-7 -1 2 0 -1 2}}
| {{Monzo| -7 -1 2 0 -1 2 }}
| leprechaun comma
| Leprechaun comma
| 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)
| {{Monzo|-6 6 -2 -1 -1 2}}
| {{Monzo| -6 6 -2 -1 -1 2 }}
| chalmersia
| Chalmersia
|-
| S351
! colspan="5" | 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]]
| 104.955
| 104.955
| 17/2<sup>4</sup>
| 17/2<sup>4</sup>
| {{Monzo|-4 0 0 0 0 0 1}}
| {{Monzo| -4 0 0 0 0 0 1 }}
| 17th harmonic (octave reduced)
| Large septendecimal semitone, <br>octave-reduced 17th harmonic
|
|-
|-
| [[18/17]]
| [[18/17]]
| 98.955
| 98.955
| (2*3<sup>2</sup>)/17
| (2×3<sup>2</sup>)/17
| {{Monzo|1 2 0 0 0 0 -1}}
| {{Monzo| 1 2 0 0 0 0 -1 }}
| Arabic lute index finger
| Small septendecimal semitone, <br>Arabic lute index finger
|
|-
|-
| [[34/33]]
| [[34/33]]
| 51.682
| 51.682
| (2*17)/(3*11)
| (2×17)/(3×11)
| {{Monzo|1 -1 0 0 -1 0 1}}
| {{Monzo| 1 -1 0 0 -1 0 1 }}
| septendecimal 1/4-tone (greater)
| Large septendecimal 1/4-tone
|
|-
|-
| [[35/34]]
| [[35/34]]
| 50.184
| 50.184
| (5*7)/(2*17)
| (5×7)/(2×17)
| {{Monzo|-1 0 1 1 0 0 -1}}
| {{Monzo| -1 0 1 1 0 0 -1 }}
| septendecimal 1/4-tone (lesser)
| Small septendecimal 1/4-tone
|
|-
|-
| [[51/50]]
| [[51/50]]
| 34.283
| 34.283
| (3*17)/(2*5<sup>2</sup>)
| (3×17)/(2×5<sup>2</sup>)
| {{Monzo|-1 1 -2 0 0 0 1}}
| {{Monzo| -1 1 -2 0 0 0 1 }}
| septendecimal 1/6-tone (greater)
| Large septendecimal 1/6-tone
|
|-
|-
| [[52/51]]
| [[52/51]]
| 33.617
| 33.617
| (2<sup>2</sup>*13)/(3*17)
| (2<sup>2</sup>×13)/(3×17)
| {{Monzo|2 -1 0 0 0 1 -1}}
| {{Monzo| 2 -1 0 0 0 1 -1 }}
| septendecimal 1/6-tone (lesser)
| Small septendecimal 1/6-tone
|
|-
|-
| [[85/84]]
| [[85/84]]
| 20.488
| 20.488
| (5*17)/(2<sup>2</sup>*3*7)
| (5×17)/(2<sup>2</sup>×3×7)
| {{Monzo|-2 -1 1 -1 0 0 1}}
| {{Monzo| -2 -1 1 -1 0 0 1 }}
| septendecimal comma
| Monk comma
|
|-
|-
| 120/119
| [[120/119]]
| 14.487
| 14.487
| (2<sup>3</sup>*3*5)/(7*17)
| (2<sup>3</sup>×3×5)/(7×17)
| {{Monzo|3 1 1 -1 0 0 -1}}
| {{Monzo| 3 1 1 -1 0 0 -1 }}
| Lynchisma
|  
|  
|-
|-
| 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 }}
| 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]]
| 10.214
| 10.214
| (2*5*17)/13<sup>2</sup>
| (2×5×17)/13<sup>2</sup>
| {{Monzo|1 0 1 0 0 -2 1}}
| {{Monzo| 1 0 1 0 0 -2 1 }}
| Major naiadma
|  
|  
|-
|-
| 221/220
| [[221/220]]
| 7.8514
| 7.8514
| (13*17)/(2<sup>2</sup>*5*11)
| (13×17)/(2<sup>2</sup>×5×11)
| {{Monzo|-2 0 -1 0 -1 1 1}}
| {{Monzo| -2 0 -1 0 -1 1 1 }}
| Minor naiadma
|  
|  
|-
|-
| 256/255
| [[256/255]]
| 6.7759
| 6.7759
| (2<sup>8</sup>)/(3*5*17)
| 2<sup>8</sup>/(3×5×17)
| {{Monzo|8 -1 -1 0 0 0 -1}}
| {{Monzo| 8 -1 -1 0 0 0 -1 }}
| 255th subharmonic
| Charisma, charic comma, <br>septendecimal kleisma
| S16
|-
|-
| 273/272
| [[273/272]]
| 6.3532
| 6.3532
| (3*7*13)/(2<sup>4</sup>*17)
| (3×7×13)/(2<sup>4</sup>×17)
| {{Monzo|-4 1 0 1 0 1 -1}}
| {{Monzo| -4 1 0 1 0 1 -1 }}
| Tannisma, prototannisma
|  
|  
|-
|-
| 289/288
| [[289/288]]
| 6.0008
| 6.0008
| (17/3)<sup>2</sup>/2<sup>5</sup>
| (17/3)<sup>2</sup>/2<sup>5</sup>
| {{Monzo|-5 -2 0 0 0 0 2}}
| {{Monzo| -5 -2 0 0 0 0 2 }}
|  
| Semitonisma
| S17
|-
|-
| 375/374
| [[375/374]]
| 4.6228
| 4.6228
| (3*5<sup>3</sup>)/(2*11*17)
| (3×5<sup>3</sup>)/(2×11×17)
| {{Monzo|-1 1 3 0 -1 0 -1}}
| {{Monzo| -1 1 3 0 -1 0 -1 }}
| Ursulisma
|  
|  
|-
|-
| 442/441
| [[442/441]]
| 3.9213
| 3.9213
| (2*13*17)/(3*7)<sup>2</sup>
| (2×13×17)/(3×7)<sup>2</sup>
| {{Monzo|1 -2 0 -2 0 1 1}}
| {{Monzo| 1 -2 0 -2 0 1 1 }}
| 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]]
| 2.9121
| 2.9121
| (5*7*17)/(2*3<sup>3</sup>*11)
| (5×7×17)/(2×3<sup>3</sup>×11)
| {{Monzo|-1 -3 1 1 -1 0 1}}
| {{Monzo| -1 -3 1 1 -1 0 1 }}
| Dakotisma
|  
|  
|-
|-
| 715/714
| [[715/714]]
| 2.4230
| 2.4230
| (5*11*13)/(2*3*7*17)
| (5×11×13)/(2×3×7×17)
| {{Monzo|-1 -1 1 -1 1 1 -1}}
| {{Monzo| -1 -1 1 -1 1 1 -1 }}
| September comma, septembrisma
|  
|  
|-
|-
| 833/832
| [[833/832]]
| 2.0796
| 2.0796
| (7<sup>2</sup>*17)/(2<sup>6</sup>*13)
| (7<sup>2</sup>×17)/(2<sup>6</sup>×13)
| {{Monzo|-6 0 0 2 0 -1 1}}
| {{Monzo| -6 0 0 2 0 -1 1 }}
| Horizma, horizon comma
|  
|  
|-
|-
| 936/935
| [[936/935]]
| 1.8506
| 1.8506
| (2<sup>3</sup>*3<sup>2</sup>*13)/(5*11*17)
| (2<sup>3</sup>×3<sup>2</sup>×13)/(5×11×17)
| {{Monzo|3 2 -1 0 -1 1 -1}}
| {{Monzo| 3 2 -1 0 -1 1 -1 }}
| Ainisma, ainic comma
|  
|  
|-
|-
| 1089/1088
| [[1089/1088]]
| 1.5905
| 1.5905
| (3<sup>2</sup>*11<sup>2</sup>)/(2<sup>6</sup>*17)
| (3×11)<sup>2</sup>/(2<sup>6</sup>×17)
| {{Monzo|-6 2 0 0 2 0 -1}}
| {{Monzo| -6 2 0 0 2 0 -1 }}
| twosquare comma
| Twosquare comma
| S33
|-
|-
| 1156/1155
| [[1156/1155]]
| 1.4983
| 1.4983
| (2<sup>2</sup>*17<sup>2</sup>)/(3*5*7*11)
| (2×17)<sup>2</sup>/(3×5×7×11)
| {{Monzo|2 -1 -1 -1 -1 0 2}}
| {{Monzo| 2 -1 -1 -1 -1 0 2 }}
|  
| Quadrantonisma
| S34
|-
|-
| 1225/1224
| [[1225/1224]]
| 1.4138
| 1.4138
| (5<sup>2</sup>*7<sup>2</sup>)/(2<sup>3</sup>*3<sup>2</sup>*17)
| (5×7)<sup>2</sup>/(2<sup>3</sup>×3<sup>2</sup>×17)
| {{Monzo|-3 -2 2 2 0 0 -1}}
| {{Monzo| -3 -2 2 2 0 0 -1 }}
|  
| Noellisma
| 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]]
| 1.0181
| 1.0181
| (3<sup>5</sup>*7)/[(2*5)<sup>2</sup>*17]
| (3<sup>5</sup>×7)/((2×5)<sup>2</sup>×17)
| {{Monzo|-2 5 -2 1 0 0 -1}}
| {{Monzo| -2 5 -2 1 0 0 -1 }}
| Palingenetic comma, palingenesis
|  
|  
|-
|-
| 2058/2057
| [[2058/2057]]
| 0.8414
| 0.84143
| (2*3*7<sup>3</sup>)/(11<sup>2</sup>*17)
| (2×3×7<sup>3</sup>)/(11<sup>2</sup>×17)
| {{Monzo|1 1 0 3 -2 0 -1}}
| {{Monzo| 1 1 0 3 -2 0 -1 }}
| xenisma
| Xenisma
|
|-
|-
| 2431/2430
| [[2431/2430]]
| 0.7123
| 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]]
| 0.6926
| 0.69263
| (2<sup>2</sup>*5<sup>4</sup>)/(3*7<sup>2</sup>*17)
| (2×5<sup>2</sup>)<sup>2</sup>/(3×7<sup>2</sup>×17)
| {{Monzo|2 -1 4 -2 0 0 -1}}
| {{Monzo| 2 -1 4 -2 0 0 -1 }}
|  
| Sperasma
| S50
|-
|-
| 2601/2600
| [[2601/2600]]
| 0.6657
| 0.66573
| (3<sup>2</sup>*17<sup>2</sup>)/(2<sup>3</sup>*5<sup>2</sup>*13)
| (3×17)<sup>2</sup>/(2<sup>3</sup>×5<sup>2</sup>×13)
| {{Monzo|-3 2 -2 0 0 -1 2}}
| {{Monzo| -3 2 -2 0 0 -1 2 }}
|  
| Sextantonisma
| S51
|-
|-
| 4914/4913
| [[4914/4913]]
| 0.3523
| 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]]
| 0.2969
| 0.29688
| (2<sup>3</sup>*3<sup>6</sup>)/(7<sup>3</sup>*17)
| (2×3<sup>2</sup>)<sup>3</sup>/(7<sup>3</sup>×17)
| {{Monzo|3 6 0 -3 0 0 -1}}
| {{Monzo| 3 6 0 -3 0 0 -1 }}
| Chlorisma
|  
|  
|-
|-
| 12376/12375
| [[Flashma|12376/12375]]
| 0.1399
| 0.13989
| (2<sup>3</sup>*7*13*17)/(3<sup>2</sup>*5<sup>3</sup>*11)
| (2<sup>3</sup>×7×13×17)/(3<sup>2</sup>×5<sup>3</sup>×11)
| {{Monzo|3 -2 -3 1 -1 1 1}}
| {{Monzo| 3 -2 -3 1 -1 1 1 }}
| Flashma
|  
|  
|-
|-
| 14400/14399
| [[Sparkisma|14400/14399]]
| 0.1202
| 0.12023
| (2<sup>6</sup>*3<sup>2</sup>*5<sup>2</sup>)/(7*11<sup>2</sup>*17)
| (2<sup>3</sup>×3×5)<sup>2</sup>/(7×11<sup>2</sup>×17)
| {{Monzo|6 2 2 -1 -2 0 -1}}
| {{monzo| 6 2 2 -1 -2 0 -1 }}
|  
| Sparkisma
| S120
|-
|-
| 28561/28560
| [[28561/28560]]
| 0.0606
| 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
|-
|-
| 31213/31212
| [[E-shaped comma|31213/31212]]
| 0.0555
| 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]]
| 0.0466
| 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]]
| 0.0089
| 0.0089018
| (3<sup>4</sup>*7<sup>4</sup>)/(2<sup>4</sup>*5*11*13*17)
| (3×7)<sup>4</sup>/(2<sup>4</sup>×5×11×13×17)
| {{Monzo|-4 4 -1 4 -1 -1 -1}}
| {{Monzo| -4 4 -1 4 -1 -1 -1 }}
| scintillisma
| Scintillisma
| S441
|-
|-
| 336141/336140
| [[Aksial comma|336141/336140]]
| 0.0052
| 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="5" | 19-limit (incomplete)
 
=== 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]]
| 93.603
| 93.603
| 19/(2*3<sup>2</sup>)
| 19/(2×3<sup>2</sup>)
| {{Monzo|-1 -2 0 0 0 0 0 1}}
| {{Monzo| -1 -2 0 0 0 0 0 1 }}
| undevicesimal semitone
| Large undevicesimal semitone
|
|-
|-
| [[20/19]]
| [[20/19]]
| 88.801
| 88.801
| (2<sup>2</sup>*5)/19
| (2<sup>2</sup>×5)/19
| {{Monzo|2 0 1 0 0 0 0 -1}}
| {{Monzo| 2 0 1 0 0 0 0 -1 }}
| small undevicesimal semitone
| Small undevicesimal semitone
|
|-
|-
| [[39/38]]
| [[39/38]]
| 44.970
| 44.970
| (3*13)/(2*19)
| (3×13)/(2×19)
| {{Monzo|-1 1 0 0 0 1 0 -1}}
| {{Monzo| -1 1 0 0 0 1 0 -1 }}
| undevicesimal 2/9-tone
| Undevicesimal diesis, <br>undevicesimal 2/9-tone
|
|-
|-
| [[57/56]]
| [[57/56]]
| 30.642
| 30.642
| (3*19)/(2<sup>3</sup>*7)
| (3×19)/(2<sup>3</sup>×7)
| {{Monzo|-3 1 0 -1 0 0 0 1}}
| {{Monzo| -3 1 0 -1 0 0 0 1 }}
| Hendrix comma
|  
|  
|-
|-
| [[76/75]]
| [[76/75]]
| 22.931
| 22.931
| (2<sup>2</sup>*19)/(3*5<sup>2</sup>)
| (2<sup>2</sup>×19)/(3×5<sup>2</sup>)
| {{Monzo|2 -1 -2 0 0 0 0 1}}
| {{Monzo| 2 -1 -2 0 0 0 0 1 }}
| Large undevicesimal 1/9-tone
|  
|  
|-
|-
| [[77/76]]
| [[77/76]]
| 22.631
| 22.631
| (7*11)/(2<sup>2</sup>*19)
| (7×11)/(2<sup>2</sup>×19)
| {{Monzo|-2 0 0 1 1 0 0 -1}}
| {{Monzo| -2 0 0 1 1 0 0 -1 }}
| Small undevicesimal 1/9-tone
|  
|  
|-
|-
| [[96/95]]
| [[96/95]]
| 18.128
| 18.128
| (2<sup>5</sup>*3)/(5*19)
| (2<sup>5</sup>×3)/(5×19)
| {{Monzo|5 1 -1 0 0 0 0 -1}}
| {{Monzo| 5 1 -1 0 0 0 0 -1 }}
| 19th-partial chroma
|  
|  
|-
|-
| 133/132
| [[133/132]]
| 13.066
| 13.066
| (19*7)/(2<sup>2</sup>*3*11)
| (7×19)/(2<sup>2</sup>×3×11)
| {{Monzo|-2 -1 0 1 -1 0 0 1}}
| {{Monzo| -2 -1 0 1 -1 0 0 1 }}
| Minithirdma
|  
|  
|-
|-
| 153/152
| [[153/152]]
| 11.352
| 11.352
| (3<sup>2</sup>*17)/(2<sup>3</sup>*19)
| (3<sup>2</sup>×17)/(2<sup>3</sup>×19)
| {{Monzo|-3 2 0 0 0 0 1 -1}}
| {{Monzo| -3 2 0 0 0 0 1 -1 }}
| Ganassisma, Ganassi's comma
|  
|  
|-
|-
| 171/170
| [[171/170]]
| 10.154
| 10.154
| (3<sup>2</sup>*19)/(2*5*17)
| (3<sup>2</sup>×19)/(2×5×17)
| {{Monzo|-1 2 -1 0 0 0 -1 1}}
| {{Monzo| -1 2 -1 0 0 0 -1 1 }}
| 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
|  
|  
|-
|-
| 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
|  
|  
|-
|-
| 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]]
| 5.3516
| 5.3516
| (2<sup>2</sup>*3<sup>4</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 }}
|  
| Photisma
| S18
|-
|-
| 343/342
| [[343/342]]
| 5.0547
| 5.0547
| 7<sup>4</sup>/(2*3<sup>3</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, Dudon comma
| S19
|-
|-
| 400/399
| [[400/399]]
| 4.3335
| 4.3335
| (2<sup>4</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
|-
|-
| 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]]
| 3.501
| 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]]
| 3.378
| 3.3780
| (3<sup>3</sup>*19)/2<sup>9</sup>
| (3<sup>3</sup>×19)/2<sup>9</sup>
| {{Monzo|-9 3 0 0 0 0 0 1}}
| {{Monzo| -9 3 0 0 0 0 0 1 }}
| 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]]
| 1.4243
| 1.4243
| (2<sup>6</sup>*19)/(3<sup>5</sup>*5)
| (2<sup>6</sup>×19)/(3<sup>5</sup>×5)
| {{Monzo|6 -5 -1 0 0 0 0 1}}
| {{Monzo| 6 -5 -1 0 0 0 0 1 }}
| Password comma, Eratosthenes' comma
|  
|  
|-
|-
| 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]]
| 1.1985
| 1.1985
| 5*(17/(2*19))<sup>2</sup>
| 5×(17/(2×19))<sup>2</sup>
| {{Monzo|-2 0 1 0 0 0 2 -2}}
| {{Monzo| -2 0 1 0 0 0 2 -2 }}
| Aureusma
|  
|  
|-
|-
| 1521/1520
| [[1521/1520]]
| 1.1386
| 1.1386
| (3*13)<sup>2</sup>/(2<sup>4</sup>*5*19)
| (3×13)<sup>2</sup>/(2<sup>4</sup>×5×19)
| {{Monzo|-4 2 -1 0 0 2 0 -1}}
| {{Monzo| -4 2 -1 0 0 2 0 -1 }}
|  
| Pinkanberry
| 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]]
| 1.0016
| 1.0016
| (7*13*19)/(2<sup>6</sup>*3<sup>3</sup>)
| (7×13×19)/(2<sup>2</sup>×3)<sup>3</sup>
| {{Monzo|-6 -3 0 1 0 1 0 1}}
| {{Monzo| -6 -3 0 1 0 1 0 1 }}
| Ramanujanisma
|  
|  
|-
|-
! colspan="5" | 23-limit (incomplete)
| [[2376/2375]]
| 0.72879
| ((2×3)/5)<sup>3</sup>×(11/19)
| {{Monzo| 3 3 -3 0 1 0 0 -1 }}
| Trichthonisma
|
|-
|-
| [[23/22]]
| [[2432/2431]]
| 76.956
| 0.71200
| 23/(2*11)
| (2<sup>7</sup>×19)/(11×13×17)
| {{Monzo| 7 0 0 0 -1 -1 -1 1 }}
| Blumeyer comma
|  
|  
| greater vicesimotertial semitone
|-
|-
| [[24/23]]
| [[2926/2925]]
| 73.681
| 0.59177
| (2<sup>3</sup>*3)/23
| (2×7×11×19)/((3×5)<sup>2</sup>×13)
| {{Monzo| 1 -2 -2 1 1 -1 0 1 }}
| Neovulture comma, neovulturisma
|  
|  
| small vicesimotertial semitone
|-
|-
| [[46/45]]
| [[3136/3135]]
| 38.051
| 0.55214
| (2*23)/(3<sup>2</sup>*5)
| (2<sup>3</sup>×7)<sup>2</sup>/(3×5×11×19)
| {{Monzo| 6 -1 -1 2 -1 0 0 -1 }}
| Neomirkwai comma, neomirkwaisma
| S56
|-
| [[3250/3249]]
| 0.53277
| (2×5<sup>3</sup>×13)/(3×19)<sup>2</sup>
| {{Monzo| 1 -2 3 0 0 1 0 -2 }}
| Martebisma
|  
|  
|-
| [[4200/4199]]
| 0.41225
| (2<sup>3</sup>×3×5<sup>2</sup>×7)/(13×17×19)
| {{Monzo| 3 1 2 1 0 -1 -1 -1 }}
| Neosatanisma
|  
|  
|-
|-
| [[69/68]]
| [[5776/5775]]
| 25.274
| 0.29975
| (3*23)/(2<sup>2</sup>*17)
| (2<sup>2</sup>×19)<sup>2</sup>/(3×5<sup>2</sup>×7×11)
| {{Monzo| 4 -1 -2 -1 -1 0 0 2 }}
| Neovish comma, neovishma
| S76
|-
| [[5929/5928]]
| 0.29202
| (7×11)<sup>2</sup>/(2<sup>3</sup>×3×13×19)
| {{Monzo| -3 -1 0 2 2 -1 0 -1 }}
| Manzanisma
| S77
|-
| [[5985/5984]]
| 0.28929
| (3<sup>2</sup>×5×7×19)/(2<sup>5</sup>×11×17)
| {{Monzo| -5 2 1 1 -1 0 -1 1 }}
| Neogrendel comma, neogrendelisma
|  
|  
|-
| [[6175/6174]]
| 0.28038
| (5<sup>2</sup>×13×19)/(2×3<sup>2</sup>×7<sup>3</sup>)
| {{Monzo| -1 -2 2 -3 0 1 0 1 }}
| Neonewtisma
|  
|  
|-
|-
| [[70/69]]
| [[6860/6859]]
| 24.910
| 0.25238
| (2*5*7)/(3*23)
| (2<sup>2</sup>×5×7<sup>3</sup>)/19<sup>3</sup>
|  
| {{Monzo| 2 0 1 3 0 0 0 -3 }}
| Devicubisma
|  
|  
|-
|-
| [[92/91]]
| 10241/10240
| 18.921
| 0.16906
| (2<sup>2</sup>*23)/(7*13)
| (7<sup>2</sup>×11×19)/(2<sup>11</sup>×5)
| {{Monzo| -11 0 -1 2 1 0 0 1 }}
|  
|  
|  
|  
|-
|-
| 115/114
| 10830/10829
| 15.120
| 0.15986
| (5*23)/(2*3*19)
| (2×3×5×19<sup>2</sup>)/(7<sup>2</sup>×13×17)
| {{Monzo| 1 1 1 -2 0 -1 -1 2 }}
|  
|  
|  
|  
|-
|-
| 161/160
| [[12636/12635]]
| 10.7865
| 0.13701
| (7*23)/(2<sup>5</sup>*5)
| (2<sup>2</sup>×3<sup>5</sup>×13)/(5×7×19<sup>2</sup>)
|  
| {{Monzo| 2 5 -1 -1 0 1 0 -2 }}
| Padriellisma
|  
|  
|-
|-
| 162/161
| 13377/13376
| 10.720
| 0.12942
| (2*3<sup>4</sup>)/(7*23)
| (3×7<sup>3</sup>×13)/(2<sup>6</sup>×11×19)
| {{Monzo| -6 1 0 3 -1 1 0 -1 }}
|  
|  
|  
|  
|-
|-
| 208/207
| 14080/14079
| 8.343
| 0.12296
| (2<sup>4</sup>*13)/(23*9)
| (2<sup>8</sup>×5×11)/(3×13×19<sup>2</sup>)
| {{Monzo| 8 -1 1 0 1 -1 0 -2 }}
|  
|  
|  
|  
|-
|-
| 576/575
| 14365/14364
| 3.008
| 0.12052
| (2<sup>6</sup>*3<sup>2</sup>)/(23*25)
| (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 }}
|  
|  
|  
|  
|-
|-
! colspan="5" | 29-limit (incomplete)
| 23409/23408
| 0.073957
| ((3/2)<sup>2</sup>×17)<sup>2</sup>/(7×11×19)
| {{Monzo| -4 4 0 -1 -1 0 2 -1 }}
|
| S153
|-
|-
| [[29/28]]
| 27456/27455
| 60.751
| 0.063056
| 29/(2<sup>2</sup>*7)
| (2<sup>6</sup>×3×11×13)/(5×17<sup>2</sup>×19)
| {{Monzo| 6 1 -1 0 1 1 -2 -1 }}
|  
|  
|  
|  
|-
|-
| [[30/29]]
| 28900/28899
| 58.692
| 0.059905
| (2*3*5)/29
| ((2×5×17)/(3×13))<sup>2</sup>/19
| {{Monzo| 2 -2 2 0 0 -2 2 -1 }}
|  
|  
| S170
|-
| 43681/43680
| 0.039634
| (11×19)<sup>2</sup>/(2<sup>5</sup>×3×5×7×13)
| {{Monzo| -5 -1 -1 -1 2 -1 0 2 }}
|  
|  
| S209
|-
|-
| [[58/57]]
| 89376/89375
| 30.109
| 0.019370
| (2*29)/(3*19)
| (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 }}
|  
|  
|  
|  
|-
|-
| [[88/87]]
| 104976/104975
| 19.786
| 0.016492
| (2<sup>3</sup>*11)/(3*29)
| (2×3<sup>2</sup>)<sup>4</sup>/(5<sup>2</sup>×13×17×19)
| {{Monzo| 4 8 -2 0 0 -1 -1 -1 }}
|  
|  
| S324
|-
| [[Decimillisma|165376/165375]]
| 0.010469
| (2<sup>9</sup>×17×19)/((3×5)<sup>3</sup>×7<sup>2</sup>)
| {{Monzo| 9 -3 -3 -2 0 0 1 1 }}
| Decimillisma
|  
|  
|-
|-
! colspan="5" | 31-limit (incomplete)
| 228096/228095
| 0.0075900
| ((2<sup>2</sup>×3)/7)<sup>4</sup>×(11/(5×19))
| {{Monzo| 8 4 -1 -4 1 0 0 -1 }}
|
|
|-
|-
| [[31/30]]
| 601426/601425
| 56.767
| 0.0028786
| 31/(2*3*5)
| (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 }}
|  
|  
|  
|  
|-
|-
| [[32/31]]
| [[Devicisma|633556/633555]]
| 54.964
| 0.0027326
| 2<sup>5</sup>/31
| (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 }}
| Devicisma
|  
|  
| 31st subharmonic
|-
|-
| [[63/62]]
| 709632/709631
| 27.700
| 0.0024396
| (3<sup>2</sup>*7)/(2*31)
| (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 }}
|  
|  
|  
|  
|-
|-
| [[93/92]]
| 5909761/5909760
| 18.716
| 0.00029294
| (3*31)/(2<sup>2</sup>*23)
| (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 }}
|  
|  
| S2431
|-
| <font style="font-size:0.88em">[[11859211/11859210]]</font>
| 0.00014598
| (19/(3×11))<sup>4</sup>×((7×13)/(2×5))
| {{Monzo| -1 -4 -1 1 -4 1 0 4 }}
| Tredekisma
|  
|  
|}
=== 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"/>
|-
|-
! colspan="5" | 37-limit (incomplete)
| [[23/22]]
| 76.956
| 23/(2×11)
| {{Monzo| -1 0 0 0 -1 0 0 0 1 }}
| Large vicesimotertial semitone
|
|-
|-
| [[37/36]]
| [[24/23]]
| 47.434
| 73.681
| 37/(2<sup>2</sup>*3<sup>2</sup>)
| (2<sup>3</sup>×3)/23
| {{Monzo| 3 1 0 0 0 0 0 0 -1 }}
| Small vicesimotertial semitone
|  
|  
|-
| [[46/45]]
| 38.051
| (2×23)/(3<sup>2</sup>×5)
| {{Monzo| 1 -2 -1 0 0 0 0 0 1 }}
| Vicesimotertial 1/5-tone
|  
|  
|-
|-
| [[38/37]]
| [[69/68]]
| 46.169
| 25.274
| (2*19)/37
| (3×23)/(2<sup>2</sup>×17)
| {{Monzo| -2 1 0 0 0 0 -1 0 1 }}
| Large vicesimotertial 1/8-tone
|  
|  
|-
| [[70/69]]
| 24.910
| (2×5×7)/(3×23)
| {{Monzo| 1 -1 1 1 0 0 0 0 -1 }}
| Small vicesimotertial 1/8-tone
|
|-
| [[92/91]]
| 18.921
| (2<sup>2</sup>×23)/(7×13)
| {{Monzo| 2 0 0 -1 0 -1 0 0 1 }}
| Undinisma
|  
|  
|-
|-
| [[75/74]]
| [[115/114]]
| 23.238
| 15.120
| (3*5<sup>2</sup>)/(2*37)
| (5×23)/(2×3×19)
| {{Monzo| -1 -1 1 0 0 0 0 -1 1 }}
| Yarmanisma
|  
|  
|-
| [[161/160]]
| 10.787
| (7×23)/(2<sup>5</sup>×5)
| {{Monzo| -5 0 -1 1 0 0 0 0 1 }}
| Major kirnbergerisma
|  
|  
|-
|-
! colspan="5" | 41-limit (incomplete)
| [[162/161]]
| 10.720
| (2×3<sup>4</sup>)/(7×23)
| {{Monzo| 1 4 0 -1 0 0 0 0 -1 }}
| Minor kirnbergerisma
|
|-
|-
| [[41/40]]
| [[208/207]]
| 42.749
| 8.3433
| 41/(2<sup>3</sup>*5)
| (2<sup>4</sup>×13)/(3<sup>2</sup>×23)
| {{Monzo| 4 -2 0 0 0 1 0 0 -1 }}
| Vicetone comma
|  
|  
|-
| [[231/230]]
| 7.5108
| (3×7×11)/(2×5×23)
| {{Monzo| -1 1 -1 1 1 0 0 0 -1 }}
| Major neutravicema
|  
|  
|-
|-
| [[42/41]]
| [[253/252]]
| 41.719
| 6.8564
| (2*3*7)/41
| (11×23)/((2×3)<sup>2</sup>×7)
| {{Monzo| -2 -2 0 -1 1 0 0 0 1 }}
| Middle neutravicema
|  
|  
|-
| [[276/275]]
| 6.2840
| (2<sup>2</sup>×3×23)/(5<sup>2</sup>×11)
| {{Monzo| 2 1 -2 0 -1 0 0 0 1 }}
| Minor neutravicema
|  
|  
|-
|-
| [[82/81]]
| [[300/299]]
| 21.242
| 5.7804
| (2*41)/3<sup>4</sup>
| ((2×5)<sup>2</sup>×3)/(13×23)
| {{Monzo| 2 1 2 0 0 -1 0 0 -1 }}
| Major naiadvicema
|  
|  
|-
| [[323/322]]
| 5.3682
| (17×19)/(2×7×23)
| {{Monzo| -1 0 0 -1 0 0 1 1 -1 }}
| Major semivicema
|  
|  
|-
|-
! colspan="5" | 43-limit (incomplete)
| [[391/390]]
| 4.4334
| (17×23)/(2×3×5×13)
| {{Monzo| -1 -1 -1 0 0 -1 1 0 1 }}
| Minor naiadvicema
|
|-
|-
| [[43/42]]
| [[392/391]]
| 40.737
| 4.4221
| 43/(2*3*7)
| (2<sup>3</sup>×7<sup>2</sup>)/(17×23)
| {{Monzo| 3 0 0 2 0 0 -1 0 -1 }}
| Minor semivicema
|  
|  
|-
| [[460/459]]
| 3.7676
| (2<sup>2</sup>×5×23)/(3<sup>3</sup>×17)
| {{Monzo| 2 -3 1 0 0 0 -1 0 1 }}
| Scanisma, vicewolf comma
|  
|  
|-
|-
| [[44/43]]
| [[484/483]]
| 39.800
| 3.5806
| (2<sup>2</sup>*11)/43
| (2×11)<sup>2</sup>/(3×7×23)
| {{Monzo| 2 -1 0 -1 2 0 0 0 -1 }}
| Pittsburghisma
| S22
|-
| [[507/506]]
| 3.4180
| (3×13<sup>2</sup>)/(2×11×23)
| {{Monzo| -1 1 0 0 -1 2 0 0 -1 }}
| Laodicisma
|  
|  
|-
| [[529/528]]
| 3.2758
| 23<sup>2</sup>/(2<sup>4</sup>×3×11)
| {{Monzo| -4 -1 0 0 -1 0 0 0 2 }}
| Preziosisma
| S23
|-
| [[576/575]]
| 3.0082
| ((2<sup>3</sup>×3)/5)<sup>2</sup>/23
| {{Monzo| 6 2 -2 0 0 0 0 0 -1 }}
| Worcester comma
| S24
|-
| [[736/735]]
| 2.3538
| (2<sup>5</sup>×23)/(3×5×7<sup>2</sup>)
| {{Monzo| 5 -1 -1 -2 0 0 0 0 1 }}
| Harvardisma
|  
|  
|-
|-
| [[86/85]]
| [[760/759]]
| 20.249
| 2.2794
| (2*43)/(5*17)
| (2<sup>3</sup>×5×19)/(3×11×23)
| {{Monzo| 3 -1 1 0 -1 0 0 1 -1 }}
| Squadronisma
|  
|  
|-
| [[875/874]]
| 1.9797
| (5<sup>3</sup>×7)/(2×19×23)
| {{Monzo| -1 0 3 1 0 0 0 -1 -1 }}
| Nymphisma
|  
|  
|-
|-
| [[87/86]]
| [[897/896]]
| 20.014
| 1.9311
| (3*29)/(2*43)
| (3×13×23)/(2<sup>7</sup>×7)
| {{Monzo| -7 1 0 -1 0 1 0 0 1 }}
| Lysistratisma
|  
|  
|-
| [[1105/1104]]
| 1.5674
| (5×13×17)/(2<sup>4</sup>×3×23)
| {{Monzo| -4 -1 1 0 0 1 1 0 -1 }}
| Fragarisma
|  
|  
|-
|-
! colspan="5" | 47-limit (incomplete)
| [[1197/1196]]
| 1.4469
| (3<sup>2</sup>×7×19)/(2<sup>2</sup>×13×23)
| {{Monzo| -2 2 0 1 0 -1 0 1 -1 }}
| Rodessisma
|
|-
|-
| [[47/46]]
| [[1288/1287]]
| 37.232
| 1.3446
| 47/(2*23)
| (2<sup>3</sup>×7×23)/(3<sup>2</sup>×11×13)
| {{Monzo| 3 -2 0 1 -1 -1 0 0 1 }}
| Santisma, triaphonisma
|  
|  
|-
| [[1496/1495]]
| 1.1576
| (2<sup>3</sup>×11×17)/(5×13×23)
| {{Monzo| 3 0 -1 0 1 -1 1 0 -1 }}
| Turkisma
|  
|  
|-
|-
| [[48/47]]
| [[1863/1862]]
| 36.448
| 0.92952
| (2<sup>4</sup>*3)/47
| (3<sup>4</sup>×23)/(2×7<sup>2</sup>×19)
| {{Monzo| -1 4 0 -2 0 0 0 -1 1 }}
| Antinousisma
|  
|  
|-
| [[2024/2023]]
| 0.85556
| (2<sup>3</sup>×11×23)/(7×17<sup>2</sup>)
| {{Monzo| 3 0 0 -1 1 0 -2 0 1 }}
| Artifisma, insincere comma
|  
|  
|-
|-
| [[94/93]]
| [[2025/2024]]
| 18.516
| 0.85514
| (2*47)/(3*31)
| (3<sup>2</sup>×5)<sup>2</sup>/(2<sup>3</sup>×11×23)
| {{Monzo| -3 4 2 0 -1 0 0 0 -1 }}
| Cupcake comma, cupcakesma
| S45
|-
| [[2185/2184]]
| 0.79251
| (5×19×23)/(2<sup>3</sup>×3×7×13)
| {{Monzo| -3 -1 1 -1 0 -1 0 1 1 }}
| Guangdongisma
|  
|  
|-
| [[2300/2299]]
| 0.75287
| ((2×5)/11)<sup>2</sup>×(23/19)
| {{Monzo| 2 0 2 0 -2 0 0 -1 1 }}
| Travellisma
|  
|  
|-
|-
| [[95/94]]
| [[2646/2645]]
| 18.320
| 0.65441
| (5*19)/(2*47)
| (2×3<sup>3</sup>×7<sup>2</sup>)/(5×23<sup>2</sup>)
| {{Monzo| 1 3 -1 2 0 0 0 0 -2 }}
| Biyativice comma, biyativicema
|  
|  
|-
| [[2737/2736]]
| 0.63265
| (7×17×23)/(2<sup>4</sup>×3<sup>2</sup>×19)
| {{Monzo| -4 -2 0 1 0 0 1 -1 1 }}
| Kotkisma
|  
|  
|-
|-
! colspan="5" | 53-limit (incomplete)
| [[3060/3059]]
| 0.56586
| ((2×3)<sup>2</sup>×5×17)/(7×19×23)
| {{Monzo| 2 2 1 -1 0 0 1 -1 -1 }}
| Vicious comma, viciousma
|
|-
|-
| [[53/52]]
| [[3381/3380]]
| 32.977
| 0.51212
| 53/(2<sup>2</sup>*13)
| (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 }}
| Mikkolisma
|  
|  
|-
| [[3520/3519]]
| 0.49190
| (2<sup>6</sup>×5×11)/(3<sup>2</sup>×17×23)
| {{Monzo| 6 -2 1 0 1 0 -1 0 -1 }}
| Vicedim comma, vicedimma
|  
|  
|-
|-
| [[54/53]]
| [[3888/3887]]
| 32.360
| 0.44533
| (2*3<sup>3</sup>)/53
| (2<sup>4</sup>×3<sup>5</sup>)/(13<sup>2</sup>×23)
| {{Monzo| 4 5 0 0 0 -2 0 0 -1 }}
| Shoalma, vicetride comma
|  
|  
|-
| [[4693/4692]]
| 0.36893
| (13×19<sup>2</sup>)/(2<sup>2</sup>×3×17×23)
| {{Monzo| -2 -1 0 0 0 1 -1 2 -1 }}
| Viceaug comma, viceaugma
|  
|  
|-
|-
! colspan="5" | 59-limit (incomplete)
| [[4761/4760]]
| 0.36367
| (3×23)<sup>2</sup>/(2<sup>3</sup>×5×7×17)
| {{Monzo| -3 2 -1 -1 0 0 -1 0 2 }}
| Demiquartervice comma
| S69
|-
| [[5083/5082]]
| 0.34063
| (13×17×23)/(2×3×7×11<sup>2</sup>)
| {{Monzo| -1 -1 0 -1 -2 1 1 0 1 }}
| Broadviewsma
|
|-
|-
| [[59/58]]
| [[7866/7865]]
| 29.594
| 0.22010
| 59/(2*29)
| (2×3<sup>2</sup>×19×23)/(5×11<sup>2</sup>×13)
| {{Monzo| 1 2 -1 0 -2 -1 0 1 1 }}
|  
|  
|  
|  
|-
|-
| [[60/59]]
| [[8281/8280]]
| 29.097
| 0.20907
| (2<sup>2</sup>*3*5)/59
| (7×13)<sup>2</sup>/(2<sup>3</sup>×3<sup>2</sup>×5×23)
| {{Monzo| -3 -2 -1 2 0 2 0 0 -1 }}
|  
|  
| S91
|-
| [[8625/8624]]
| 0.20073
| (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 }}
| Beerglass comma
|  
|  
|-
|-
! colspan="5" | 61-limit (incomplete)
| [[10626/10625]]
| 0.16293
| (2×3×7×11×23)/(5<sup>4</sup>×17)
| {{Monzo| 1 1 -4 1 1 0 -1 0 1 }}
| Demiglace comma
|
|-
|-
| [[61/60]]
| 11271/11270
| 28.616
| 0.15361
| 61/(2<sup>2</sup>*3*5)
| (3×13×17<sup>2</sup>)/(2×5×7<sup>2</sup>×23)
| {{Monzo| -1 1 -1 -2 0 1 2 0 -1 }}
|  
|  
|  
|  
|-
|-
| [[62/61]]
| 11662/11661
| 28.151
| 0.14846
| (2*31)/61
| (2×7<sup>3</sup>×17)/(3×13<sup>2</sup>×23)
| {{Monzo| 1 -1 0 3 0 -2 1 0 -1 }}
|  
|  
|  
|  
|-
|-
! colspan="5" | 67-limit (incomplete)
| [[Vicetertisma|12168/12167]]
| 0.14228
| (2/23)<sup>3</sup>×(3×13)<sup>2</sup>
| {{Monzo| 3 2 0 0 0 2 0 0 -3 }}
| Vicetertisma
|
|-
|-
| [[67/66]]
| 16929/16928
| 26.034
| 0.10227
| 67/(2*3*11)
| (3<sup>4</sup>×11×19)/(2<sup>5</sup>×23<sup>2</sup>)
| {{Monzo| -5 4 0 0 1 0 0 1 -2 }}
|  
|  
|  
|  
|-
|-
| [[68/67]]
| 19551/19550
| 25.648
| 0.088552
| (2<sup>2</sup>*17)/67
| (3×7<sup>3</sup>×19)/(2×5<sup>2</sup>×17×23)
| {{Monzo| -1 1 -2 3 0 0 -1 1 -1 }}
|  
|  
|  
|  
|-
|-
! colspan="5" | 71-limit (incomplete)
| 21505/21504
| 0.080506
| (5×11×17×23)/(2<sup>10</sup>×3×7)
| {{Monzo| -10 -1 1 -1 1 0 1 0 1 }}
|
|
|-
|-
| [[71/70]]
| 21736/21735
| 24.557
| 0.079650
| 71/(2*5*7)
| (2<sup>3</sup>×11×13×19)/(3<sup>3</sup>×5×7×23)
| {{Monzo| 3 -3 -1 -1 1 1 0 1 -1 }}
|  
|  
|  
|  
|-
|-
| [[72/71]]
| 23276/23275
| 24.213
| 0.074380
| (2<sup>3</sup>*3<sup>2</sup>)/71
| ((2×23)/(5×7))<sup>2</sup>×(11/19)
| {{Monzo| 2 0 -2 -2 1 0 0 -1 2 }}
|
|  
|  
|-
| [[Joshuavoisma|25025/25024]]
| 0.069182
| (5<sup>2</sup>×7×11×13)/(2<sup>6</sup>×17×23)
| {{Monzo| -6 0 2 1 1 1 -1 0 -1 }}
| Joshuavoisma
|  
|  
|-
|-
! colspan="5" | 73-limit (incomplete)
| [[Diarithmedia|25921/25920]]
| 0.066790
| (7×23)<sup>2</sup>/(2<sup>6</sup>×3<sup>4</sup>×5)
| {{Monzo| -6 -4 -1 2 0 0 0 0 2 }}
| Diarithmedia
| S161
|-
|-
| [[73/72]]
| 43264/43263
| 23.879
| 0.040016
| 73/(2<sup>3</sup>*3<sup>2</sup>)
| (2<sup>4</sup>×13)<sup>2</sup>/(3<sup>2</sup>×11×19×23)
| {{Monzo| 8 -2 0 0 -1 2 0 -1 -1 }}
|
| S208
|-
| 52326/52325
| 0.033086
| (2×3<sup>4</sup>×17×19)/(5<sup>2</sup>×7×13×23)
| {{Monzo| 1 4 -2 -1 0 -1 1 1 -1 }}
|  
|  
|  
|  
|-
|-
| [[74/73]]
| 71875/71874
| 23.555
| 0.024087
| (2*37)/73
| (5<sup>5</sup>×23)/(2×(3×11)<sup>3</sup>)
| {{Monzo| -1 -3 5 0 -3 0 0 0 1 }}
|  
|  
|  
|  
|-
|-
! colspan="5" | 79-limit (incomplete)
| 75141/75140
|-
| 0.023040
| [[79/78]]
| (3<sup>3</sup>×11<sup>2</sup>×23)/(2<sup>2</sup>×5×13×17<sup>2</sup>)
| 22.054
| {{Monzo| -2 3 -1 0 2 -1 -2 0 1 }}
| 79/(2*3*13)
|  
|  
|  
|  
|-
|-
| [[80/79]]
| 76545/76544
| 21.777
| 0.022617
| (2<sup>4</sup>*5)/79
| (3<sup>7</sup>×5×7)/(2<sup>8</sup>×13×23)
| {{Monzo| -8 7 1 1 0 -1 0 0 -1 }}
|  
|  
|  
|  
|-
|-
! colspan="5" | 83-limit (incomplete)
| 104329/104328
| 0.016594
| (17×19)<sup>2</sup>/(2<sup>3</sup>×3<sup>4</sup>×7×23)
| {{Monzo| -3 -4 0 -1 0 0 2 2 -1 }}
|
| S323
|-
|-
| [[83/82]]
| 122452/122451
| 20.985
| 0.014138
| 83/(2*41)
| (2<sup>2</sup>×11<sup>3</sup>×23)/(3×7<sup>4</sup>×17)
| {{Monzo| 2 -1 0 -4 3 0 -1 0 1 }}
|  
|  
|  
|  
|-
|-
| [[84/83]]
| 126225/126224
| 20.734
| 0.013716
| (2<sup>2</sup>*3*7)/83
| (3<sup>3</sup>×5<sup>2</sup>×11×17)/(2<sup>4</sup>×7<sup>3</sup>×23)
| {{Monzo| -4 3 2 -3 1 0 1 0 -1 }}
|  
|  
|  
|  
|-
|-
! colspan="5" | 89-limit (incomplete)
| 152881/152880
| 0.011324
| (17×23)<sup>2</sup>/(2<sup>4</sup>×3×5×7<sup>2</sup>×13)
| {{Monzo| -4 -1 -1 -2 0 -1 2 0 2 }}
|
| S391
|-
|-
| [[89/88]]
| 202125/202124
| 19.562
| 0.0085652
| 89/(2<sup>3</sup>*11)
| (3×5<sup>3</sup>×7<sup>2</sup>×11)/(2<sup>2</sup>×13<sup>3</sup>×23)
| {{Monzo| -2 1 3 2 1 -3 0 0 -1 }}
|  
|  
|  
|  
|-
|-
| [[90/89]]
| 264385/264384
| 19.344
| 0.0065482
| (2*3<sup>2</sup>*5)/89
| (5×11<sup>2</sup>×19×23)/(2<sup>6</sup>×3<sup>5</sup>×17)
| {{Monzo| -6 -5 1 0 2 0 -1 1 1 }}
|  
|  
|  
|  
|-
|-
! colspan="5" | 97-limit (incomplete)
| 282625/282624
| 0.0061256
| (5<sup>3</sup>×7×17×19)/(2<sup>12</sup>×3×23)
| {{Monzo| -12 -1 3 1 0 0 1 1 -1 }}
|
|
|-
|-
| [[97/96]]
| 328510/328509
| 17.940
| 0.0052700
| 97/(2<sup>5</sup>*3)
| (2×5×7×13×19<sup>2</sup>)/(3×23)<sup>3</sup>
| {{Monzo| 1 -3 1 1 0 1 0 2 -3 }}
|  
|  
|  
|  
|-
|-
| [[98/97]]
| 2023425/2023424
| 17.756
| 0.00085560
| (2*7<sup>2</sup>)/97
| ((3×5×23)<sup>2</sup>×17)/(2<sup>13</sup>×13×19)
| {{Monzo| -13 2 2 0 0 -1 1 -1 2 }}
|  
|  
|  
|  
|-
|-
! colspan="5" | 101-limit (incomplete)
| 4096576/4096575
|-
| 0.00042261
| [[101/100]]
| ((2<sup>3</sup>×11×23)/(3<sup>2</sup>×5×17))<sup>2</sup>/7
| 17.226
| {{Monzo| 6 -4 -2 -1 2 0 -2 0 2 }}
| 101/(2<sup>2</sup>*5<sup>2</sup>)
|  
|  
|  
| S2024
|-
|-
| [[102/101]]
| 5142501/5142500
| 17.057
| 0.00033665
| (2*3*17)/101
| 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 }}
|  
|  
|  
|  
|}
|}


[[Category:Interval list]]
=== Higher-limit ===
[[Category:Superparticular]]
See:
* [[List of superparticular intervals/29-limit]]
* [[List of superparticular intervals/31-limit]]
* [[List of superparticular intervals/37-limit]]
* [[List of superparticular intervals/41-limit]]
* [[List of superparticular intervals/43-limit]]
* [[List of superparticular intervals/47-limit]]
* [[List of superparticular intervals/53-limit]]
* [[List of superparticular intervals/59-limit]]
* [[List of superparticular intervals/61-limit]]
* [[List of superparticular intervals/67-limit]]
* [[List of superparticular intervals/71-limit]]
* [[List of superparticular intervals/73-limit]]
* [[List of superparticular intervals/79-limit]]
* [[List of superparticular intervals/83-limit]]
* [[List of superparticular intervals/89-limit]]
* [[List of superparticular intervals/97-limit]]
* [[List of superparticular intervals/101-limit]]
* [[List of superparticular intervals/103-limit]]
* [[List of superparticular intervals/107-limit]]
* [[List of superparticular intervals/109-limit]]
* [[List of superparticular intervals/113-limit]]
* [[List of superparticular intervals/127-limit]]
 
== See also ==
* [[Gallery of just intervals]]
 
== Notes ==
<references/>
 
== External links ==
* [http://www.huygens-fokker.org/docs/intervals.html ''List of intervals''] on the Huygens-Fokker Foundation website
 
[[Category:Lists of intervals]]
[[Category:Superparticular ratios|*]]

Latest revision as of 08:38, 28 March 2026

This is a list of superparticular intervals ordered by prime limit. It reaches to the 127-limit and is complete up to the 37-limit.

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

List of superparticular intervals

2-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
2/1 1200.000 2/1 [1⟩ Octave, duple, 2nd harmonic, diapason

3-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
3/2 701.955 3/2 [-1 1⟩ Perfect fifth, octave-reduced 3rd harmonic, diapente
4/3 498.045 22/3 [2 -1⟩ Perfect fourth, octave-reduced 3rd subharmonic, diatessaron S2
9/8 203.910 32/23 [-3 2⟩ Pythagorean whole tone, Pythagorean major second,
major whole tone, octave-reduced 9th harmonic, harmonic ninth 		S3

5-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
5/4 386.314 5/22 [-2 0 1⟩ Classic(al)/just major third, octave-reduced 5th harmonic
6/5 315.641 (2×3)/5 [1 1 -1⟩ Classic(al)/just minor third
10/9 182.404 (2×5)/32 [1 -2 1⟩ Classic(al) (whole) tone, classic major second, minor whole tone
16/15 111.731 24/(3×5) [4 -1 -1⟩ Classic(al)/just diatonic semitone, 15th subharmonic S4
25/24 70.672 52/(23×3) [-3 -1 2⟩ Classic(al)/just chromatic semitone, chroma, Zarlinian semitone S5
81/80 21.506 (3/2)4/5 [-4 4 -1⟩ Syntonic comma, Didymus comma S9

7-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
7/6 266.871 7/(2×3) [-1 -1 0 1⟩ (Septimal) subminor third, septimal minor third
8/7 231.174 23/7 [3 0 0 -1⟩ (Septimal) supermajor second, septimal whole tone,
octave-reduced 7th subharmonic
15/14 119.443 (3×5)/(2×7) [-1 1 1 -1⟩ Septimal major semitone, septimal diatonic semitone
21/20 84.467 (3×7)/(22×5) [-2 1 -1 1⟩ Septimal minor semitone, large septimal chroma
28/27 62.961 (22×7)/33 [2 -3 0 1⟩ Septimal 1/3-tone, small septimal chroma,
(septimal) subminor second, septimal minor second,
trienstonic comma
36/35 48.770 (2×3)2/(5×7) [2 2 -1 -1⟩ Septimal 1/4-tone, mint comma S6
49/48 35.697 72/(24×3) [-4 -1 0 2⟩ Large septimal diesis, large septimal 1/6-tone, slendro diesis, semaphoresma S7
50/49 34.976 2×(5/7)2 [1 0 2 -2⟩ Small septimal diesis, small septimal 1/6-tone, septimal tritonic diesis, jubilisma
64/63 27.264 26/(32×7) [6 -2 0 -1⟩ Septimal comma, Archytas' comma S8
126/125 13.795 (2×32×7)/53 [1 2 -3 1⟩ Starling comma, septimal semicomma
225/224 7.7115 (3×5)2/(25×7) [-5 2 2 -1⟩ Marvel comma, septimal kleisma S15
2401/2400 0.72120 74/(25×3×52) [-5 -1 -2 4⟩ Breedsma S49
4375/4374 0.39576 (54×7)/(2×37) [-1 -7 4 1⟩ Ragisma

11-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
11/10 165.004 11/(2×5) [-1 0 -1 0 1⟩ Large undecimal neutral second,
undecimal submajor second, Ptolemy's second
12/11 150.637 (22×3)/11 [2 1 0 0 -1⟩ Small undecimal neutral second
22/21 80.537 (2×11)/(3×7) [1 -1 0 -1 1⟩ Undecimal minor semitone
33/32 53.273 (3×11)/25 [-5 1 0 0 1⟩ Undecimal 1/4-tone, undecimal diesis,
al-Farabi's 1/4-tone, octave-reduced 33rd harmonic
45/44 38.906 (3/2)2×(5/11) [-2 2 1 0 -1⟩ Undecimal 1/5-tone, cake comma
55/54 31.767 (5×11)/(2×33) [-1 -3 1 0 1⟩ Telepathma, eleventyfive comma,
undecimal diasecundal comma
56/55 31.194 (23×7)/(5×11) [3 0 -1 1 -1⟩ Undecimal tritonic comma, konbini comma
99/98 17.576 (3/7)2×(11/2) [-1 2 0 -2 1⟩ Mothwellsma, small undecimal comma
100/99 17.399 ((2×5)/3)2/11 [2 -2 2 0 -1⟩ Ptolemisma, Ptolemy's comma S10
121/120 14.376 112/(23×3×5) [-3 -1 -1 0 2⟩ Biyatisma, undecimal seconds comma S11
176/175 9.8646 (24×11)/(52×7) [4 0 -2 -1 1⟩ Valinorsma
243/242 7.1391 35/(2×112) [-1 5 0 0 -2⟩ Rastma, neutral thirds comma
385/384 4.5026 (5×7×11)/(27×3) [-7 -1 1 1 1⟩ Keenanisma
441/440 3.9302 (3×7)2/(23×5×11) [-3 2 -1 2 -1⟩ Werckisma, Werckmeister's undecimal septenarian schisma S21
540/539 3.2090 (2/7)2×((33×5)/11) [2 3 1 -2 -1⟩ Swetisma, Swets' comma
3025/3024 0.57240 (5×11)2/(24×33×7) [-4 -3 2 -1 2⟩ Lehmerisma S55
9801/9800 0.17665 ((32×11)/(5×7))2/23 [-3 4 -2 -2 2⟩ Kalisma, Gauss comma S99

13-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
13/12 138.573 13/(22×3) [-2 -1 0 0 0 1⟩ Large tridecimal 2/3-tone,
tridecimal neutral second
14/13 128.298 (2×7)/13 [1 0 0 1 0 -1⟩ Small tridecimal 2/3-tone, trienthird
26/25 67.900 (2×13)/52 [1 0 -2 0 0 1⟩ Large tridecimal 1/3-tone
27/26 65.337 33/(2×13) [-1 3 0 0 0 -1⟩ Small tridecimal 1/3-tone
40/39 43.831 (23×5)/(3×13) [3 -1 1 0 0 -1⟩ Tridecimal minor diesis
65/64 26.841 (5×13)/26 [-6 0 1 0 0 1⟩ Wilsorma, 13th-partial chroma
66/65 26.432 (2×3×11)/(5×13) [1 1 -1 0 1 -1⟩ Winmeanma
78/77 22.339 (2×3×13)/(7×11) [1 1 0 -1 -1 1⟩ Negustma
91/90 19.130 (7×13)/(2×32×5) [-1 -2 -1 1 0 1⟩ Biome comma, superleap comma
105/104 16.567 (3×5×7)/(23×13) [-3 1 1 1 0 -1⟩ Animist comma, small tridecimal comma
144/143 12.064 (22×3)2/(11×13) [4 2 0 0 -1 -1⟩ Grossma S12
169/168 10.274 132/(23×3×7) [-3 -1 0 -1 0 2⟩ Buzurgisma, dhanvantarisma S13
196/195 8.8554 (2×7)2/(3×5×13) [2 -1 -1 2 0 -1⟩ Mynucuma S14
325/324 5.3351 (5/(2×32))2×13 [-2 -4 2 0 0 1⟩ Marveltwin comma
351/350 4.9393 (33×13)/(2×52×7) [-1 3 -2 -1 0 1⟩ Ratwolfsma
352/351 4.9253 (25×11)/(33×13) [5 -3 0 0 1 -1⟩ Major minthma, major gentle comma
364/363 4.7627 (2/11)2×((7×13)/3) [2 -1 0 1 -2 1⟩ Minor minthma, minor gentle comma
625/624 2.7722 (5/2)4/(3×13) [-4 -1 4 0 0 -1⟩ Tunbarsma S25
676/675 2.5629 ((2×13)/5)2/33 [2 -3 -2 0 0 2⟩ Island comma S26
729/728 2.3764 (32/2)3/(7×13) [-3 6 0 -1 0 -1⟩ Squbema S27
1001/1000 1.7304 (7×11×13)/(2×5)3 [-3 0 -3 1 1 1⟩ Sinbadma
1716/1715 1.0092 (22×3×11×13)/(5×73) [2 1 -1 -3 1 1⟩ Lummic comma
2080/2079 0.83252 (25×5×13)/(33×7×11) [5 -3 1 -1 -1 1⟩ Ibnsinma, sinaisma
4096/4095 0.42272 (26/3)2/(5×7×13) [12 -2 -1 -1 0 -1⟩ Minisma S64
4225/4224 0.40981 (5×13)2/(27×3×11) [-7 -1 2 0 -1 2⟩ Leprechaun comma S65
6656/6655 0.26012 (23/11)3×(13/5) [9 0 -1 0 -3 1⟩ Jacobin comma
10648/10647 0.16260 (2×11)3/((3×13)2×7) [3 -2 0 -1 3 -2⟩ Harmonisma
123201/123200 0.014052 (3/2)6×(13/5)2/(7×11) [-6 6 -2 -1 -1 2⟩ Chalmersia S351

17-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
17/16 104.955 17/24 [-4 0 0 0 0 0 1⟩ Large septendecimal semitone,
octave-reduced 17th harmonic
18/17 98.955 (2×32)/17 [1 2 0 0 0 0 -1⟩ Small septendecimal semitone,
Arabic lute index finger
34/33 51.682 (2×17)/(3×11) [1 -1 0 0 -1 0 1⟩ Large septendecimal 1/4-tone
35/34 50.184 (5×7)/(2×17) [-1 0 1 1 0 0 -1⟩ Small septendecimal 1/4-tone
51/50 34.283 (3×17)/(2×52) [-1 1 -2 0 0 0 1⟩ Large septendecimal 1/6-tone
52/51 33.617 (22×13)/(3×17) [2 -1 0 0 0 1 -1⟩ Small septendecimal 1/6-tone
85/84 20.488 (5×17)/(22×3×7) [-2 -1 1 -1 0 0 1⟩ Monk comma
120/119 14.487 (23×3×5)/(7×17) [3 1 1 -1 0 0 -1⟩ Lynchisma
136/135 12.777 (2/3)3×(17/5) [3 -3 -1 0 0 0 1⟩ Diatisma, septendecimal major second comma
154/153 11.278 (2×7×11)/(32×17) [1 -2 0 1 1 0 -1⟩ Augustma
170/169 10.214 (2×5×17)/132 [1 0 1 0 0 -2 1⟩ Major naiadma
221/220 7.8514 (13×17)/(22×5×11) [-2 0 -1 0 -1 1 1⟩ Minor naiadma
256/255 6.7759 28/(3×5×17) [8 -1 -1 0 0 0 -1⟩ Charisma, charic comma,
septendecimal kleisma 		S16
273/272 6.3532 (3×7×13)/(24×17) [-4 1 0 1 0 1 -1⟩ Tannisma, prototannisma
289/288 6.0008 (17/3)2/25 [-5 -2 0 0 0 0 2⟩ Semitonisma S17
375/374 4.6228 (3×53)/(2×11×17) [-1 1 3 0 -1 0 -1⟩ Ursulisma
442/441 3.9213 (2×13×17)/(3×7)2 [1 -2 0 -2 0 1 1⟩ Seminaiadma
561/560 3.0887 (3×11×17)/(24×5×7) [-4 1 -1 -1 1 0 1⟩ Monardisma, tsaharuk comma
595/594 2.9121 (5×7×17)/(2×33×11) [-1 -3 1 1 -1 0 1⟩ Dakotisma
715/714 2.4230 (5×11×13)/(2×3×7×17) [-1 -1 1 -1 1 1 -1⟩ September comma, septembrisma
833/832 2.0796 (72×17)/(26×13) [-6 0 0 2 0 -1 1⟩ Horizma, horizon comma
936/935 1.8506 (23×32×13)/(5×11×17) [3 2 -1 0 -1 1 -1⟩ Ainisma, ainic comma
1089/1088 1.5905 (3×11)2/(26×17) [-6 2 0 0 2 0 -1⟩ Twosquare comma S33
1156/1155 1.4983 (2×17)2/(3×5×7×11) [2 -1 -1 -1 -1 0 2⟩ Quadrantonisma S34
1225/1224 1.4138 (5×7)2/(23×32×17) [-3 -2 2 2 0 0 -1⟩ Noellisma S35
1275/1274 1.3584 (3×52×17)/(2×72×13) [-1 1 2 -2 0 -1 1⟩ Cimbrisma
1701/1700 1.0181 (35×7)/((2×5)2×17) [-2 5 -2 1 0 0 -1⟩ Palingenetic comma, palingenesis
2058/2057 0.84143 (2×3×73)/(112×17) [1 1 0 3 -2 0 -1⟩ Xenisma
2431/2430 0.71230 (11×13×17)/(2×35×5) [-1 -5 -1 0 1 1 1⟩ Heptacircle comma
2500/2499 0.69263 (2×52)2/(3×72×17) [2 -1 4 -2 0 0 -1⟩ Sperasma S50
2601/2600 0.66573 (3×17)2/(23×52×13) [-3 2 -2 0 0 -1 2⟩ Sextantonisma S51
4914/4913 0.35234 (2×33×7×13)/173 [1 3 0 1 0 1 -3⟩ Baladisma
5832/5831 0.29688 (2×32)3/(73×17) [3 6 0 -3 0 0 -1⟩ Chlorisma
12376/12375 0.13989 (23×7×13×17)/(32×53×11) [3 -2 -3 1 -1 1 1⟩ Flashma
14400/14399 0.12023 (23×3×5)2/(7×112×17) [6 2 2 -1 -2 0 -1⟩ Sparkisma S120
28561/28560 0.060616 (13/2)4/(3×5×7×17) [-4 -1 -1 -1 0 4 -1⟩ Pisanoisma S169
31213/31212 0.055466 (74×13)/(22×33×172) [-2 -3 0 4 0 1 -2⟩ E-shaped comma
37180/37179 0.046564 (22×5×11×132)/(37×17) [2 -7 1 0 1 2 -1⟩ Lateral comma
194481/194480 0.0089018 (3×7)4/(24×5×11×13×17) [-4 4 -1 4 -1 -1 -1⟩ Scintillisma S441
336141/336140 0.0051503 (32×133×17)/(22×5×75) [-2 2 -1 -5 0 3 1⟩ Aksial comma

19-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
19/18 93.603 19/(2×32) [-1 -2 0 0 0 0 0 1⟩ Large undevicesimal semitone
20/19 88.801 (22×5)/19 [2 0 1 0 0 0 0 -1⟩ Small undevicesimal semitone
39/38 44.970 (3×13)/(2×19) [-1 1 0 0 0 1 0 -1⟩ Undevicesimal diesis,
undevicesimal 2/9-tone
57/56 30.642 (3×19)/(23×7) [-3 1 0 -1 0 0 0 1⟩ Hendrix comma
76/75 22.931 (22×19)/(3×52) [2 -1 -2 0 0 0 0 1⟩ Large undevicesimal 1/9-tone
77/76 22.631 (7×11)/(22×19) [-2 0 0 1 1 0 0 -1⟩ Small undevicesimal 1/9-tone
96/95 18.128 (25×3)/(5×19) [5 1 -1 0 0 0 0 -1⟩ 19th-partial chroma
133/132 13.066 (7×19)/(22×3×11) [-2 -1 0 1 -1 0 0 1⟩ Minithirdma
153/152 11.352 (32×17)/(23×19) [-3 2 0 0 0 0 1 -1⟩ Ganassisma, Ganassi's comma
171/170 10.154 (32×19)/(2×5×17) [-1 2 -1 0 0 0 -1 1⟩ Malcolmisma
190/189 9.1358 (2×5×19)/(33×7) [1 -3 1 -1 0 0 0 1⟩ Cotylisma
209/208 8.3033 (11×19)/(24×13) [-4 0 0 0 1 -1 0 1⟩ Yama comma
210/209 8.2637 (2×3×5×7)/(11×19) [1 1 1 1 -1 0 0 -1⟩ Spleen comma
286/285 6.0639 (2×11×13)/(3×5×19) [1 -1 -1 0 1 1 0 -1⟩ Chthonisma
324/323 5.3516 (2×32)2/(17×19) [2 4 0 0 0 0 -1 -1⟩ Photisma S18
343/342 5.0547 73/(2×32×19) [-1 -2 0 3 0 0 0 -1⟩ Nutrisma
361/360 4.8023 192/(23×32×5) [-3 -2 -1 0 0 0 0 2⟩ Go comma, Dudon comma S19
400/399 4.3335 (22×5)2/(3×7×19) [4 -1 2 -1 0 0 0 -1⟩ Devichroma S20
456/455 3.8007 (23×3×19)/(5×7×13) [3 1 -1 -1 0 -1 0 1⟩ Abnobisma
476/475 3.6409 (22×7×17)/(52×19) [2 0 -2 1 0 0 1 -1⟩ Hedwigma
495/494 3.5010 (32×5×11)/(2×13×19) [-1 2 1 0 1 -1 0 -1⟩ Eulalisma
513/512 3.3780 (33×19)/29 [-9 3 0 0 0 0 0 1⟩ Undevicesimal comma, undevicesimal schisma,
Boethius' comma, 513th harmonic
969/968 1.7875 (3×17×19)/(23×112) [-3 1 0 0 -2 0 1 1⟩ Kingfisher comma
1216/1215 1.4243 (26×19)/(35×5) [6 -5 -1 0 0 0 0 1⟩ Password comma, Eratosthenes' comma
1331/1330 1.3012 113/(2×5×7×19) [-1 0 -1 -1 3 0 0 -1⟩ Solvejgsma
1445/1444 1.1985 5×(17/(2×19))2 [-2 0 1 0 0 0 2 -2⟩ Aureusma
1521/1520 1.1386 (3×13)2/(24×5×19) [-4 2 -1 0 0 2 0 -1⟩ Pinkanberry S39
1540/1539 1.1245 (22×5×7×11)/(34×19) [2 -4 1 1 1 0 0 -1⟩ Kevolisma
1729/1728 1.0016 (7×13×19)/(22×3)3 [-6 -3 0 1 0 1 0 1⟩ Ramanujanisma
2376/2375 0.72879 ((2×3)/5)3×(11/19) [3 3 -3 0 1 0 0 -1⟩ Trichthonisma
2432/2431 0.71200 (27×19)/(11×13×17) [7 0 0 0 -1 -1 -1 1⟩ Blumeyer comma
2926/2925 0.59177 (2×7×11×19)/((3×5)2×13) [1 -2 -2 1 1 -1 0 1⟩ Neovulture comma, neovulturisma
3136/3135 0.55214 (23×7)2/(3×5×11×19) [6 -1 -1 2 -1 0 0 -1⟩ Neomirkwai comma, neomirkwaisma S56
3250/3249 0.53277 (2×53×13)/(3×19)2 [1 -2 3 0 0 1 0 -2⟩ Martebisma
4200/4199 0.41225 (23×3×52×7)/(13×17×19) [3 1 2 1 0 -1 -1 -1⟩ Neosatanisma
5776/5775 0.29975 (22×19)2/(3×52×7×11) [4 -1 -2 -1 -1 0 0 2⟩ Neovish comma, neovishma S76
5929/5928 0.29202 (7×11)2/(23×3×13×19) [-3 -1 0 2 2 -1 0 -1⟩ Manzanisma S77
5985/5984 0.28929 (32×5×7×19)/(25×11×17) [-5 2 1 1 -1 0 -1 1⟩ Neogrendel comma, neogrendelisma
6175/6174 0.28038 (52×13×19)/(2×32×73) [-1 -2 2 -3 0 1 0 1⟩ Neonewtisma
6860/6859 0.25238 (22×5×73)/193 [2 0 1 3 0 0 0 -3⟩ Devicubisma
10241/10240 0.16906 (72×11×19)/(211×5) [-11 0 -1 2 1 0 0 1⟩
10830/10829 0.15986 (2×3×5×192)/(72×13×17) [1 1 1 -2 0 -1 -1 2⟩
12636/12635 0.13701 (22×35×13)/(5×7×192) [2 5 -1 -1 0 1 0 -2⟩ Padriellisma
13377/13376 0.12942 (3×73×13)/(26×11×19) [-6 1 0 3 -1 1 0 -1⟩
14080/14079 0.12296 (28×5×11)/(3×13×192) [8 -1 1 0 1 -1 0 -2⟩
14365/14364 0.12052 (5×132×17)/(22×33×7×19) [-2 -3 1 -1 0 2 1 -1⟩
23409/23408 0.073957 ((3/2)2×17)2/(7×11×19) [-4 4 0 -1 -1 0 2 -1⟩ S153
27456/27455 0.063056 (26×3×11×13)/(5×172×19) [6 1 -1 0 1 1 -2 -1⟩
28900/28899 0.059905 ((2×5×17)/(3×13))2/19 [2 -2 2 0 0 -2 2 -1⟩ S170
43681/43680 0.039634 (11×19)2/(25×3×5×7×13) [-5 -1 -1 -1 2 -1 0 2⟩ S209
89376/89375 0.019370 (25×3×72×19)/(54×11×13) [5 1 -4 2 -1 -1 0 1⟩
104976/104975 0.016492 (2×32)4/(52×13×17×19) [4 8 -2 0 0 -1 -1 -1⟩ S324
165376/165375 0.010469 (29×17×19)/((3×5)3×72) [9 -3 -3 -2 0 0 1 1⟩ Decimillisma
228096/228095 0.0075900 ((22×3)/7)4×(11/(5×19)) [8 4 -1 -4 1 0 0 -1⟩
601426/601425 0.0028786 (2×72×17×192)/(37×52×11) [1 -7 -2 2 -1 0 1 2⟩
633556/633555 0.0027326 (22×7×113×17)/(33×5×13×192) [2 -3 -1 1 3 -1 1 -2⟩ Devicisma
709632/709631 0.0024396 (210×32×7×11)/(133×17×19) [10 2 0 1 1 -3 -1 -1⟩
5909761/5909760 0.00029294 (11×13×17)2/(28×35×5×19) [-8 -5 -1 0 2 2 2 -1⟩ S2431
11859211/11859210 0.00014598 (19/(3×11))4×((7×13)/(2×5)) [-1 -4 -1 1 -4 1 0 4⟩ Tredekisma

23-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
23/22 76.956 23/(2×11) [-1 0 0 0 -1 0 0 0 1⟩ Large vicesimotertial semitone
24/23 73.681 (23×3)/23 [3 1 0 0 0 0 0 0 -1⟩ Small vicesimotertial semitone
46/45 38.051 (2×23)/(32×5) [1 -2 -1 0 0 0 0 0 1⟩ Vicesimotertial 1/5-tone
69/68 25.274 (3×23)/(22×17) [-2 1 0 0 0 0 -1 0 1⟩ Large vicesimotertial 1/8-tone
70/69 24.910 (2×5×7)/(3×23) [1 -1 1 1 0 0 0 0 -1⟩ Small vicesimotertial 1/8-tone
92/91 18.921 (22×23)/(7×13) [2 0 0 -1 0 -1 0 0 1⟩ Undinisma
115/114 15.120 (5×23)/(2×3×19) [-1 -1 1 0 0 0 0 -1 1⟩ Yarmanisma
161/160 10.787 (7×23)/(25×5) [-5 0 -1 1 0 0 0 0 1⟩ Major kirnbergerisma
162/161 10.720 (2×34)/(7×23) [1 4 0 -1 0 0 0 0 -1⟩ Minor kirnbergerisma
208/207 8.3433 (24×13)/(32×23) [4 -2 0 0 0 1 0 0 -1⟩ Vicetone comma
231/230 7.5108 (3×7×11)/(2×5×23) [-1 1 -1 1 1 0 0 0 -1⟩ Major neutravicema
253/252 6.8564 (11×23)/((2×3)2×7) [-2 -2 0 -1 1 0 0 0 1⟩ Middle neutravicema
276/275 6.2840 (22×3×23)/(52×11) [2 1 -2 0 -1 0 0 0 1⟩ Minor neutravicema
300/299 5.7804 ((2×5)2×3)/(13×23) [2 1 2 0 0 -1 0 0 -1⟩ Major naiadvicema
323/322 5.3682 (17×19)/(2×7×23) [-1 0 0 -1 0 0 1 1 -1⟩ Major semivicema
391/390 4.4334 (17×23)/(2×3×5×13) [-1 -1 -1 0 0 -1 1 0 1⟩ Minor naiadvicema
392/391 4.4221 (23×72)/(17×23) [3 0 0 2 0 0 -1 0 -1⟩ Minor semivicema
460/459 3.7676 (22×5×23)/(33×17) [2 -3 1 0 0 0 -1 0 1⟩ Scanisma, vicewolf comma
484/483 3.5806 (2×11)2/(3×7×23) [2 -1 0 -1 2 0 0 0 -1⟩ Pittsburghisma S22
507/506 3.4180 (3×132)/(2×11×23) [-1 1 0 0 -1 2 0 0 -1⟩ Laodicisma
529/528 3.2758 232/(24×3×11) [-4 -1 0 0 -1 0 0 0 2⟩ Preziosisma S23
576/575 3.0082 ((23×3)/5)2/23 [6 2 -2 0 0 0 0 0 -1⟩ Worcester comma S24
736/735 2.3538 (25×23)/(3×5×72) [5 -1 -1 -2 0 0 0 0 1⟩ Harvardisma
760/759 2.2794 (23×5×19)/(3×11×23) [3 -1 1 0 -1 0 0 1 -1⟩ Squadronisma
875/874 1.9797 (53×7)/(2×19×23) [-1 0 3 1 0 0 0 -1 -1⟩ Nymphisma
897/896 1.9311 (3×13×23)/(27×7) [-7 1 0 -1 0 1 0 0 1⟩ Lysistratisma
1105/1104 1.5674 (5×13×17)/(24×3×23) [-4 -1 1 0 0 1 1 0 -1⟩ Fragarisma
1197/1196 1.4469 (32×7×19)/(22×13×23) [-2 2 0 1 0 -1 0 1 -1⟩ Rodessisma
1288/1287 1.3446 (23×7×23)/(32×11×13) [3 -2 0 1 -1 -1 0 0 1⟩ Santisma, triaphonisma
1496/1495 1.1576 (23×11×17)/(5×13×23) [3 0 -1 0 1 -1 1 0 -1⟩ Turkisma
1863/1862 0.92952 (34×23)/(2×72×19) [-1 4 0 -2 0 0 0 -1 1⟩ Antinousisma
2024/2023 0.85556 (23×11×23)/(7×172) [3 0 0 -1 1 0 -2 0 1⟩ Artifisma, insincere comma
2025/2024 0.85514 (32×5)2/(23×11×23) [-3 4 2 0 -1 0 0 0 -1⟩ Cupcake comma, cupcakesma S45
2185/2184 0.79251 (5×19×23)/(23×3×7×13) [-3 -1 1 -1 0 -1 0 1 1⟩ Guangdongisma
2300/2299 0.75287 ((2×5)/11)2×(23/19) [2 0 2 0 -2 0 0 -1 1⟩ Travellisma
2646/2645 0.65441 (2×33×72)/(5×232) [1 3 -1 2 0 0 0 0 -2⟩ Biyativice comma, biyativicema
2737/2736 0.63265 (7×17×23)/(24×32×19) [-4 -2 0 1 0 0 1 -1 1⟩ Kotkisma
3060/3059 0.56586 ((2×3)2×5×17)/(7×19×23) [2 2 1 -1 0 0 1 -1 -1⟩ Vicious comma, viciousma
3381/3380 0.51212 (3×72×23)/(22×5×132) [-2 1 -1 2 0 -2 0 0 1⟩ Mikkolisma
3520/3519 0.49190 (26×5×11)/(32×17×23) [6 -2 1 0 1 0 -1 0 -1⟩ Vicedim comma, vicedimma
3888/3887 0.44533 (24×35)/(132×23) [4 5 0 0 0 -2 0 0 -1⟩ Shoalma, vicetride comma
4693/4692 0.36893 (13×192)/(22×3×17×23) [-2 -1 0 0 0 1 -1 2 -1⟩ Viceaug comma, viceaugma
4761/4760 0.36367 (3×23)2/(23×5×7×17) [-3 2 -1 -1 0 0 -1 0 2⟩ Demiquartervice comma S69
5083/5082 0.34063 (13×17×23)/(2×3×7×112) [-1 -1 0 -1 -2 1 1 0 1⟩ Broadviewsma
7866/7865 0.22010 (2×32×19×23)/(5×112×13) [1 2 -1 0 -2 -1 0 1 1⟩
8281/8280 0.20907 (7×13)2/(23×32×5×23) [-3 -2 -1 2 0 2 0 0 -1⟩ S91
8625/8624 0.20073 (3×53×23)/(24×72×11) [-4 1 3 -2 -1 0 0 0 1⟩ Beerglass comma
10626/10625 0.16293 (2×3×7×11×23)/(54×17) [1 1 -4 1 1 0 -1 0 1⟩ Demiglace comma
11271/11270 0.15361 (3×13×172)/(2×5×72×23) [-1 1 -1 -2 0 1 2 0 -1⟩
11662/11661 0.14846 (2×73×17)/(3×132×23) [1 -1 0 3 0 -2 1 0 -1⟩
12168/12167 0.14228 (2/23)3×(3×13)2 [3 2 0 0 0 2 0 0 -3⟩ Vicetertisma
16929/16928 0.10227 (34×11×19)/(25×232) [-5 4 0 0 1 0 0 1 -2⟩
19551/19550 0.088552 (3×73×19)/(2×52×17×23) [-1 1 -2 3 0 0 -1 1 -1⟩
21505/21504 0.080506 (5×11×17×23)/(210×3×7) [-10 -1 1 -1 1 0 1 0 1⟩
21736/21735 0.079650 (23×11×13×19)/(33×5×7×23) [3 -3 -1 -1 1 1 0 1 -1⟩
23276/23275 0.074380 ((2×23)/(5×7))2×(11/19) [2 0 -2 -2 1 0 0 -1 2⟩
25025/25024 0.069182 (52×7×11×13)/(26×17×23) [-6 0 2 1 1 1 -1 0 -1⟩ Joshuavoisma
25921/25920 0.066790 (7×23)2/(26×34×5) [-6 -4 -1 2 0 0 0 0 2⟩ Diarithmedia S161
43264/43263 0.040016 (24×13)2/(32×11×19×23) [8 -2 0 0 -1 2 0 -1 -1⟩ S208
52326/52325 0.033086 (2×34×17×19)/(52×7×13×23) [1 4 -2 -1 0 -1 1 1 -1⟩
71875/71874 0.024087 (55×23)/(2×(3×11)3) [-1 -3 5 0 -3 0 0 0 1⟩
75141/75140 0.023040 (33×112×23)/(22×5×13×172) [-2 3 -1 0 2 -1 -2 0 1⟩
76545/76544 0.022617 (37×5×7)/(28×13×23) [-8 7 1 1 0 -1 0 0 -1⟩
104329/104328 0.016594 (17×19)2/(23×34×7×23) [-3 -4 0 -1 0 0 2 2 -1⟩ S323
122452/122451 0.014138 (22×113×23)/(3×74×17) [2 -1 0 -4 3 0 -1 0 1⟩
126225/126224 0.013716 (33×52×11×17)/(24×73×23) [-4 3 2 -3 1 0 1 0 -1⟩
152881/152880 0.011324 (17×23)2/(24×3×5×72×13) [-4 -1 -1 -2 0 -1 2 0 2⟩ S391
202125/202124 0.0085652 (3×53×72×11)/(22×133×23) [-2 1 3 2 1 -3 0 0 -1⟩
264385/264384 0.0065482 (5×112×19×23)/(26×35×17) [-6 -5 1 0 2 0 -1 1 1⟩
282625/282624 0.0061256 (53×7×17×19)/(212×3×23) [-12 -1 3 1 0 0 1 1 -1⟩
328510/328509 0.0052700 (2×5×7×13×192)/(3×23)3 [1 -3 1 1 0 1 0 2 -3⟩
2023425/2023424 0.00085560 ((3×5×23)2×17)/(213×13×19) [-13 2 2 0 0 -1 1 -1 2⟩
4096576/4096575 0.00042261 ((23×11×23)/(32×5×17))2/7 [6 -4 -2 -1 2 0 -2 0 2⟩ S2024
5142501/5142500 0.00033665 33×((7×13)/(2×52×11))2×(23/17) [-2 3 -4 2 -2 2 -1 0 1⟩

Higher-limit

See:

See also

Notes

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Denoted by S-expressions, where sk is defined as (k/(k - 1))/((k + 1)/k). See square superparticular for details.

External links

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