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[[superparticular|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|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|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|comma]]s are superparticular ratios.
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]].


The list below is ordered by [[Harmonic_Limit|harmonic limit]], or the largest prime involved in the prime factorization. [[36/35|36/35]], for instance, is an interval of the [[7-limit|7-limit]], as it factors to (2<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>)/(5*7), while 37/36 would belong to the 37-limit.
[[Wikipedia: Størmer's theorem|Størmer's theorem]] states that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than [[2/1]], [[3/2]], [[4/3]], and [[9/8]]. {{OEIS| A002071 }} gives the number of superparticular ratios in each prime limit, {{OEIS| A145604 }} shows the increment from limit to limit, and {{OEIS| A117581 }} gives the largest numerator for each prime limit (with some exceptions, such as the 23-limit, where the largest value is smaller than that of a smaller prime limit, in this case the 19-limit).


[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. OEIS [http://oeis.org/A145604 A145604] gives the number of superparticular ratios in each prime 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).
== List of superparticular intervals ==
=== 2-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">Denoted by S-expressions, where s''k'' is defined as (''k''/(''k'' - 1))/((''k'' + 1)/''k''). See [[square superparticular]] for details.</ref>
|-
| [[2/1]]
| 1200.000
| 2/1
| {{Monzo| 1 }}
| Octave, duple, 2nd harmonic, diapason
|
|}
 
=== 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]]
| 701.955
| 3/2
| {{Monzo| -1 1 }}
| Perfect fifth, octave-reduced 3rd harmonic, diapente
|
|-
| [[4/3]]
| 498.045
| 2<sup>2</sup>/3
| {{Monzo| 2 -1 }}
| Perfect fourth, octave-reduced 3rd subharmonic, diatessaron
| S2
|-
| [[9/8]]
| 203.910
| 3<sup>2</sup>/2<sup>3</sup>
| {{monzo| -3 2 }}
| Pythagorean whole tone, Pythagorean major second, <br>major whole tone, octave-reduced 9th harmonic, harmonic ninth
| S3
|}
 
=== 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]]
| 386.314
| 5/2<sup>2</sup>
| {{Monzo| -2 0 1 }}
| Classic(al)/just major third, octave-reduced 5th harmonic
|
|-
| [[6/5]]
| 315.641
| (2×3)/5
| {{Monzo| 1 1 -1 }}
| Classic(al)/just minor third
|
|-
| [[10/9]]
| 182.404
| (2×5)/3<sup>2</sup>
| {{Monzo| 1 -2 1 }}
| Classic(al) (whole) tone, classic major second, minor whole tone
|
|-
| [[16/15]]
| 111.731
| 2<sup>4</sup>/(3×5)
| {{Monzo| 4 -1 -1 }}
| Classic(al)/just diatonic semitone, 15th subharmonic
| S4
|-
| [[25/24]]
| 70.672
| 5<sup>2</sup>/(2<sup>3</sup>×3)
| {{Monzo| -3 -1 2 }}
| Classic(al)/just chromatic semitone, chroma, Zarlinian semitone
| S5
|-
| [[81/80]]
| 21.506
| (3/2)<sup>4</sup>/5
| {{Monzo| -4 4 -1 }}
| Syntonic comma, Didymus comma
| S9
|}
 
=== 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]]
| 266.871
| 7/(2×3)
| {{Monzo| -1 -1 0 1 }}
| (Septimal) subminor third, septimal minor third
|
|-
| [[8/7]]
| 231.174
| 2<sup>3</sup>/7
| {{Monzo| 3 0 0 -1 }}
| (Septimal) supermajor second, septimal whole tone, <br>octave-reduced 7th subharmonic
|
|-
| [[15/14]]
| 119.443
| (3×5)/(2×7)
| {{Monzo| -1 1 1 -1 }}
| Septimal major semitone, septimal diatonic semitone
|
|-
| [[21/20]]
| 84.467
| (3×7)/(2<sup>2</sup>×5)
| {{Monzo| -2 1 -1 1 }}
| Septimal minor semitone, large septimal chroma
|
|-
| [[28/27]]
| 62.961
| (2<sup>2</sup>×7)/3<sup>3</sup>
| {{Monzo| 2 -3 0 1 }}
| Septimal 1/3-tone, small septimal chroma, <br>(septimal) subminor second, septimal minor second, <br>trienstonic comma
|
|-
| [[36/35]]
| 48.770
| (2×3)<sup>2</sup>/(5×7)
| {{Monzo| 2 2 -1 -1 }}
| Septimal 1/4-tone, mint comma
| S6
|-
| [[49/48]]
| 35.697
| 7<sup>2</sup>/(2<sup>4</sup>×3)
| {{Monzo| -4 -1 0 2 }}
| Large septimal diesis, large septimal 1/6-tone, slendro diesis, semaphoresma
| S7
|-
| [[50/49]]
| 34.976
| 2×(5/7)<sup>2</sup>
| {{Monzo| 1 0 2 -2 }}
| Small septimal diesis, small septimal 1/6-tone, septimal tritonic diesis, jubilisma
|
|-
| [[64/63]]
| 27.264
| 2<sup>6</sup>/(3<sup>2</sup>×7)
| {{Monzo| 6 -2 0 -1 }}
| Septimal comma, Archytas' comma
| S8
|-
| [[126/125]]
| 13.795
| (2×3<sup>2</sup>×7)/5<sup>3</sup>
| {{Monzo| 1 2 -3 1 }}
| Starling comma, septimal semicomma
|
|-
| [[225/224]]
| 7.7115
| (3×5)<sup>2</sup>/(2<sup>5</sup>×7)
| {{Monzo| -5 2 2 -1 }}
| Marvel comma, septimal kleisma
| S15
|-
| [[2401/2400]]
| 0.72120
| 7<sup>4</sup>/(2<sup>5</sup>×3×5<sup>2</sup>)
| {{Monzo| -5 -1 -2 4 }}
| Breedsma
| S49
|-
| [[4375/4374]]
| 0.39576
| (5<sup>4</sup>×7)/(2×3<sup>7</sup>)
| {{Monzo| -1 -7 4 1 }}
| Ragisma
|
|}
 
=== 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]]
| 165.004
| 11/(2×5)
| {{Monzo| -1 0 -1 0 1 }}
| Large undecimal neutral second, <br>undecimal submajor second, Ptolemy's second
|
|-
| [[12/11]]
| 150.637
| (2<sup>2</sup>×3)/11
| {{Monzo| 2 1 0 0 -1 }}
| Small undecimal neutral second
|
|-
| [[22/21]]
| 80.537
| (2×11)/(3×7)
| {{Monzo| 1 -1 0 -1 1 }}
| Undecimal minor semitone
|
|-
| [[33/32]]
| 53.273
| (3×11)/2<sup>5</sup>
| {{Monzo| -5 1 0 0 1 }}
| Undecimal 1/4-tone, undecimal diesis, <br>al-Farabi's 1/4-tone, octave-reduced 33rd harmonic
|
|-
| [[45/44]]
| 38.906
| (3/2)<sup>2</sup>×(5/11)
| {{monzo| -2 2 1 0 -1 }}
| Undecimal 1/5-tone, cake comma
|
|-
| [[55/54]]
| 31.767
| (5×11)/(2×3<sup>3</sup>)
| {{Monzo| -1 -3 1 0 1 }}
| Telepathma, eleventyfive comma, <br>undecimal diasecundal comma
|
|-
| [[56/55]]
| 31.194
| (2<sup>3</sup>×7)/(5×11)
| {{Monzo| 3 0 -1 1 -1 }}
| Undecimal tritonic comma, konbini comma
|
|-
| [[99/98]]
| 17.576
| (3/7)<sup>2</sup>×(11/2)
| {{Monzo| -1 2 0 -2 1 }}
| Mothwellsma, small undecimal comma
|
|-
| [[100/99]]
| 17.399
| ((2×5)/3)<sup>2</sup>/11
| {{monzo| 2 -2 2 0 -1 }}
| Ptolemisma, Ptolemy's comma
| S10
|-
| [[121/120]]
| 14.376
| 11<sup>2</sup>/(2<sup>3</sup>×3×5)
| {{Monzo| -3 -1 -1 0 2 }}
| Biyatisma, undecimal seconds comma
| S11
|-
| [[176/175]]
| 9.8646
| (2<sup>4</sup>×11)/(5<sup>2</sup>×7)
| {{Monzo| 4 0 -2 -1 1 }}
| Valinorsma
|
|-
| [[243/242]]
| 7.1391
| 3<sup>5</sup>/(2×11<sup>2</sup>)
| {{Monzo| -1 5 0 0 -2 }}
| Rastma, neutral thirds comma
|
|-
| [[385/384]]
| 4.5026
| (5×7×11)/(2<sup>7</sup>×3)
| {{Monzo| -7 -1 1 1 1 }}
| Keenanisma
|
|-
| [[441/440]]
| 3.9302
| (3×7)<sup>2</sup>/(2<sup>3</sup>×5×11)
| {{Monzo| -3 2 -1 2 -1 }}
| Werckisma, Werckmeister's undecimal septenarian schisma
| S21
|-
| [[540/539]]
| 3.2090
| (2/7)<sup>2</sup>×((3<sup>3</sup>×5)/11)
| {{Monzo| 2 3 1 -2 -1 }}
| Swetisma, Swets' comma
|
|-
| [[3025/3024]]
| 0.57240
| (5×11)<sup>2</sup>/(2<sup>4</sup>×3<sup>3</sup>×7)
| {{Monzo| -4 -3 2 -1 2 }}
| Lehmerisma
| S55
|-
| [[9801/9800]]
| 0.17665
| ((3<sup>2</sup>×11)/(5×7))<sup>2</sup>/2<sup>3</sup>
| {{Monzo| -3 4 -2 -2 2 }}
| Kalisma, Gauss comma
| S99
|}


See also: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]. Many of the names below come from [http://www.huygens-fokker.org/docs/intervals.html here].
=== 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]]
| 138.573
| 13/(2<sup>2</sup>×3)
| {{Monzo| -2 -1 0 0 0 1 }}
| Large tridecimal 2/3-tone, <br>tridecimal neutral second
|
|-
| [[14/13]]
| 128.298
| (2×7)/13
| {{Monzo| 1 0 0 1 0 -1 }}
| Small tridecimal 2/3-tone, trienthird
|
|-
| [[26/25]]
| 67.900
| (2×13)/5<sup>2</sup>
| {{Monzo| 1 0 -2 0 0 1 }}
| Large tridecimal 1/3-tone
|
|-
| [[27/26]]
| 65.337
| 3<sup>3</sup>/(2×13)
| {{Monzo| -1 3 0 0 0 -1 }}
| Small tridecimal 1/3-tone
|
|-
| [[40/39]]
| 43.831
| (2<sup>3</sup>×5)/(3×13)
| {{Monzo| 3 -1 1 0 0 -1 }}
| Tridecimal minor diesis
|
|-
| [[65/64]]
| 26.841
| (5×13)/2<sup>6</sup>
| {{Monzo| -6 0 1 0 0 1 }}
| Wilsorma, 13th-partial chroma
|
|-
| [[66/65]]
| 26.432
| (2×3×11)/(5×13)
| {{Monzo| 1 1 -1 0 1 -1 }}
| Winmeanma
|
|-
| [[78/77]]
| 22.339
| (2×3×13)/(7×11)
| {{Monzo| 1 1 0 -1 -1 1 }}
| Negustma
|  
|-
| [[91/90]]
| 19.130
| (7×13)/(2×3<sup>2</sup>×5)
| {{Monzo| -1 -2 -1 1 0 1 }}
| Biome comma, superleap comma
|
|-
| [[105/104]]
| 16.567
| (3×5×7)/(2<sup>3</sup>×13)
| {{Monzo| -3 1 1 1 0 -1 }}
| Animist comma, small tridecimal comma
|
|-
| [[144/143]]
| 12.064
| (2<sup>2</sup>×3)<sup>2</sup>/(11×13)
| {{Monzo| 4 2 0 0 -1 -1 }}
| Grossma
| S12
|-
| [[169/168]]
| 10.274
| 13<sup>2</sup>/(2<sup>3</sup>×3×7)
| {{Monzo| -3 -1 0 -1 0 2 }}
| Buzurgisma, dhanvantarisma
| S13
|-
| [[196/195]]
| 8.8554
| (2×7)<sup>2</sup>/(3×5×13)
| {{Monzo| 2 -1 -1 2 0 -1 }}
| Mynucuma
| S14
|-
| [[325/324]]
| 5.3351
| (5/(2×3<sup>2</sup>))<sup>2</sup>×13
| {{Monzo| -2 -4 2 0 0 1 }}
| Marveltwin comma
|
|-
| [[351/350]]
| 4.9393
| (3<sup>3</sup>×13)/(2×5<sup>2</sup>×7)
| {{Monzo| -1 3 -2 -1 0 1 }}
| Ratwolfsma
|
|-
| [[352/351]]
| 4.9253
| (2<sup>5</sup>×11)/(3<sup>3</sup>×13)
| {{Monzo| 5 -3 0 0 1 -1 }}
| Major minthma, major gentle comma
|
|-
| [[364/363]]
| 4.7627
| (2/11)<sup>2</sup>×((7×13)/3)
| {{Monzo| 2 -1 0 1 -2 1 }}
| Minor minthma, minor gentle comma
|
|-
| [[625/624]]
| 2.7722
| (5/2)<sup>4</sup>/(3×13)
| {{Monzo| -4 -1 4 0 0 -1 }}
| Tunbarsma
| S25
|-
| [[676/675]]
| 2.5629
| ((2×13)/5)<sup>2</sup>/3<sup>3</sup>
| {{Monzo| 2 -3 -2 0 0 2 }}
| Island comma
| S26
|-
| [[729/728]]
| 2.3764
| (3<sup>2</sup>/2)<sup>3</sup>/(7×13)
| {{Monzo| -3 6 0 -1 0 -1 }}
| Squbema
| S27
|-
| [[1001/1000]]
| 1.7304
| (7×11×13)/(2×5)<sup>3</sup>
| {{Monzo| -3 0 -3 1 1 1 }}
| Sinbadma
|
|-
| [[1716/1715]]
| 1.0092
| (2<sup>2</sup>×3×11×13)/(5×7<sup>3</sup>)
| {{Monzo| 2 1 -1 -3 1 1 }}
| Lummic comma
|
|-
| [[2080/2079]]
| 0.83252
| (2<sup>5</sup>×5×13)/(3<sup>3</sup>×7×11)
| {{Monzo| 5 -3 1 -1 -1 1 }}
| Ibnsinma
|
|-
| [[4096/4095]]
| 0.42272
| (2<sup>6</sup>/3)<sup>2</sup>/(5×7×13)
| {{Monzo| 12 -2 -1 -1 0 -1 }}
| Schismina, tridecimal schisma
| S64
|-
| [[4225/4224]]
| 0.40981
| (5×13)<sup>2</sup>/(2<sup>7</sup>×3×11)
| {{Monzo| -7 -1 2 0 -1 2 }}
| Leprechaun comma
| S65
|-
| [[6656/6655]]
| 0.26012
| (2<sup>3</sup>/11)<sup>3</sup>×(13/5)
| {{Monzo| 9 0 -1 0 -3 1 }}
| Jacobin comma
|
|-
| [[Harmonisma|10648/10647]]
| 0.16260
| (2×11)<sup>3</sup>/((3×13)<sup>2</sup>×7)
| {{Monzo| 3 -2 0 -1 3 -2 }}
| Harmonisma
|
|-
| [[Chalmersia|123201/123200]]
| 0.014052
| (3/2)<sup>6</sup>×(13/5)<sup>2</sup>/(7×11)
| {{Monzo| -6 6 -2 -1 -1 2 }}
| Chalmersia
| S351
|}


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


{| class="wikitable"
=== 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]]
| 93.603
| 19/(2×3<sup>2</sup>)
| {{Monzo| -1 -2 0 0 0 0 0 1 }}
| Large undevicesimal semitone
|
|-
|-
! | Ratio
| [[20/19]]
! | Cents
| 88.801
! | Factorization
| (2<sup>2</sup>×5)/19
! | [[monzo|Monzo]]
| {{Monzo| 2 0 1 0 0 0 0 -1 }}
! | Name(s)
| Small undevicesimal semitone
|  
|-
|-
! colspan="5" | 2-limit (complete)
| [[39/38]]
| 44.970
| (3×13)/(2×19)
| {{Monzo| -1 1 0 0 0 1 0 -1 }}
| Undevicesimal diesis, <br>undevicesimal 2/9-tone
|
|-
|-
| | [[2/1|2/1]]
| [[57/56]]
| | 1200.000
| 30.642
| | 2/1
| (3×19)/(2<sup>3</sup>×7)
| | | 1 &gt;
| {{Monzo| -3 1 0 -1 0 0 0 1 }}
| | (perfect) unison, unity, perfect prime, tonic, duple
| Hendrix comma
|  
|-
|-
! colspan="5" | 3-limit (complete)
| [[76/75]]
| 22.931
| (2<sup>2</sup>×19)/(3×5<sup>2</sup>)
| {{Monzo| 2 -1 -2 0 0 0 0 1 }}
| Large undevicesimal 1/9-tone
|
|-
|-
| | [[3/2|3/2]]
| [[77/76]]
| | 701.995
| 22.631
| | 3/2
| (7×11)/(2<sup>2</sup>×19)
| | | -1 1 &gt;
| {{Monzo| -2 0 0 1 1 0 0 -1 }}
| | [[perfect_fifth|perfect fifth]], 3rd harmonic (octave reduced), diapente
| Small undevicesimal 1/9-tone
|  
|-
|-
| | [[4/3|4/3]]
| [[96/95]]
| | 498.045
| 18.128
| | 2<span style="font-size: 70%; vertical-align: super;">2</span>/3
| (2<sup>5</sup>×3)/(5×19)
| | | 2 -1 &gt;
| {{Monzo| 5 1 -1 0 0 0 0 -1 }}
| | perfect fourth, 3rd subharmonic (octave reduced), diatessaron
| 19th-partial chroma
|  
|-
|-
| | [[9/8|9/8]]
| [[133/132]]
| | 203.910
| 13.066
| | 3<span style="font-size: 70%; vertical-align: super;">2</span>/2<span style="font-size: 70%; vertical-align: super;">3</span>
| (7×19)/(2<sup>2</sup>×3×11)
| | | -3 2 &gt;
| {{Monzo| -2 -1 0 1 -1 0 0 1 }}
| | (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced)
| Minithirdma
|  
|-
|-
! colspan="5" | 5-limit (complete)
| [[153/152]]
| 11.352
| (3<sup>2</sup>×17)/(2<sup>3</sup>×19)
| {{Monzo| -3 2 0 0 0 0 1 -1 }}
| Ganassisma, Ganassi's comma
|
|-
|-
| | [[5/4|5/4]]
| [[171/170]]
| | 386.314
| 10.154
| | 5/2<span style="font-size: 70%; vertical-align: super;">2</span>
| (3<sup>2</sup>×19)/(2×5×17)
| | | -2 0 1 &gt;
| {{Monzo| -1 2 -1 0 0 0 -1 1 }}
| | (classic) (5-limit) major third, 5th harmonic (octave reduced)
| Malcolmisma
|  
|-
|-
| | [[6/5|6/5]]
| [[190/189]]
| | 315.641
| 9.1358
| | (2*3)/5
| (2×5×19)/(3<sup>3</sup>×7)
| | | 1 1 -1 &gt;
| {{Monzo| 1 -3 1 -1 0 0 0 1 }}
| | (classic) (5-limit) minor third
| Cotylisma
|  
|-
|-
| | [[10/9|10/9]]
| [[209/208]]
| | 182.404
| 8.3033
| | (2*5)/3<span style="font-size: 70%; vertical-align: super;">2</span>
| (11×19)/(2<sup>4</sup>×13)
| | | 1 -2 1 &gt;
| {{Monzo| -4 0 0 0 1 -1 0 1 }}
| | classic (whole) tone, classic major second, minor whole tone
| Yama comma
|  
|-
|-
| | [[16/15|16/15]]
| [[210/209]]
| | 111.713
| 8.2637
| | 2<span style="font-size: 70%; vertical-align: super;">4</span>/(3*5)
| (2×3×5×7)/(11×19)
| | | 4 -1 -1 &gt;
| {{Monzo| 1 1 1 1 -1 0 0 -1 }}
| | minor diatonic semitone, 15th subharmonic
| Spleen comma
|  
|-
|-
| | [[25/24|25/24]]
| [[286/285]]
| | 70.672
| 6.0639
| | 5<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3)
| (2×11×13)/(3×5×19)
| | | -3 -1 2 &gt;
| {{Monzo| 1 -1 -1 0 1 1 0 -1 }}
| | chroma, (classic) chromatic semitone, Zarlinian semitone
| Chthonisma
|  
|-
|-
| | [[81/80|81/80]]
| [[324/323]]
| | 21.506
| 5.3516
| | (3/2)<span style="font-size: 70%; vertical-align: super;">4</span>/5
| (2×3<sup>2</sup>)<sup>2</sup>/(17×19)
| | | -4 4 -1 &gt;
| {{Monzo| 2 4 0 0 0 0 -1 -1 }}
| | syntonic comma, Didymus comma
| Photisma
| S18
|-
|-
! colspan="5" | 7-limit (complete)
| [[343/342]]
| 5.0547
| 7<sup>3</sup>/(2×3<sup>2</sup>×19)
| {{Monzo| -1 -2 0 3 0 0 0 -1 }}
| Nutrisma
|
|-
|-
| | [[7/6|7/6]]
| [[361/360]]
| | 266.871
| 4.8023
| | 7/(2*3)
| 19<sup>2</sup>/(2<sup>3</sup>×3<sup>2</sup>×5)
| | | -1 -1 0 1 &gt;
| {{Monzo| -3 -2 -1 0 0 0 0 2 }}
| | (septimal) subminor third, septimal minor third, augmented second
| Go comma, Dudon comma
| S19
|-
|-
| | [[8/7|8/7]]
| [[400/399]]
| | 231.174
| 4.3335
| | 2<span style="font-size: 70%; vertical-align: super;">3</span>/7
| (2<sup>2</sup>×5)<sup>2</sup>/(3×7×19)
| | | 3 0 0 -1 &gt;
| {{Monzo| 4 -1 2 -1 0 0 0 -1 }}
| | (septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic
| Devichroma
| S20
|-
|-
| | [[15/14|15/14]]
| [[456/455]]
| | 119.443
| 3.8007
| | (3*5)/(2*7)
| (2<sup>3</sup>×3×19)/(5×7×13)
| | | -1 1 1 -1 &gt;
| {{Monzo| 3 1 -1 -1 0 -1 0 1 }}
| | septimal diatonic semitone
| Abnobisma
|  
|-
|-
| | [[21/20|21/20]]
| [[476/475]]
| | 84.467
| 3.6409
| | (3*7)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*5)
| (2<sup>2</sup>×7×17)/(5<sup>2</sup>×19)
| | | -2 1 -1 1 &gt;
| {{Monzo| 2 0 -2 1 0 0 1 -1 }}
| | minor semitone, large septimal chromatic semitone
| Hedwigma
|  
|-
|-
| | [[28/27|28/27]]
| [[495/494]]
| | 62.961
| 3.5010
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*7)/3<span style="font-size: 70%; vertical-align: super;">3</span>
| (3<sup>2</sup>×5×11)/(2×13×19)
| | | 2 -3 0 1 &gt;
| {{Monzo| -1 2 1 0 1 -1 0 -1 }}
| | septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone
| Eulalisma
|  
|-
|-
| | [[36/35|36/35]]
| [[513/512]]
| | 48.770
| 3.3780
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">3</span>)/(5*7)
| (3<sup>3</sup>×19)/2<sup>9</sup>
| | | 2 2 -1 -1 &gt;
| {{Monzo| -9 3 0 0 0 0 0 1 }}
| | septimal quarter tone, septimal diesis
| Undevicesimal comma, undevicesimal schisma, <br>Boethius' comma, 513th harmonic
|  
|-
|-
| | [[49/48|49/48]]
| [[969/968]]
| | 35.697
| 1.7875
| | 7<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">4</span>*3)
| (3×17×19)/(2<sup>3</sup>×11<sup>2</sup>)
| | | -4 -1 0 2 &gt;
| {{Monzo| -3 1 0 0 -2 0 1 1 }}
| | large septimal diesis, slendro diesis, septimal 1/6-tone
| Kingfisher comma
|  
|-
|-
| | [[50/49|50/49]]
| [[1216/1215]]
| | 34.976
| 1.4243
| | 2*(5/7)<span style="font-size: 70%; vertical-align: super;">2</span>
| (2<sup>6</sup>×19)/(3<sup>5</sup>×5)
| | | 1 0 2 -2 &gt;
| {{Monzo| 6 -5 -1 0 0 0 0 1 }}
| | septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma
| Password comma, Eratosthenes' comma
|
|-
|-
| | [[64/63|64/63]]
| [[1331/1330]]
| | 27.264
| 1.3012
| | 2<span style="font-size: 70%; vertical-align: super;">6</span>/(3<span style="font-size: 70%; vertical-align: super;">2</span>*7)
| 11<sup>3</sup>/(2×5×7×19)
| | | 6 -2 0 -1 &gt;
| {{Monzo| -1 0 -1 -1 3 0 0 -1 }}
| | septimal comma, Archytas' comma
| Solvejgsma
|  
|-
|-
| | [[126/125|126/125]]
| [[1445/1444]]
| | 13.795
| 1.1985
| | (2*3<span style="font-size: 70%; vertical-align: super;">2</span>*7)/5<span style="font-size: 70%; vertical-align: super;">3</span>
| 5×(17/(2×19))<sup>2</sup>
| | | 1 2 -3 1 &gt;
| {{Monzo| -2 0 1 0 0 0 2 -2 }}
| | starling comma, septimal semicomma
| Aureusma
|  
|-
|-
| | [[225/224|225/224]]
| [[1521/1520]]
| | 7.7115
| 1.1386
| | (3*5)<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">5</span>*7)
| (3×13)<sup>2</sup>/(2<sup>4</sup>×5×19)
| | | -5 2 2 -1 &gt;
| {{Monzo| -4 2 -1 0 0 2 0 -1 }}
| | marvel comma, septimal kleisma
| Pinkanberry
| S39
|-
|-
| | [[2401/2400|2401/2400]]
| [[1540/1539]]
| | 0.72120
| 1.1245
| | 7<span style="font-size: 70%; vertical-align: super;">4</span>/(2<span style="font-size: 70%; vertical-align: super;">5</span>*3*5<span style="font-size: 70%; vertical-align: super;">2</span>)
| (2<sup>2</sup>×5×7×11)/(3<sup>4</sup>×19)
| | | -5 -1 -2 4 &gt;
| {{Monzo| 2 -4 1 1 1 0 0 -1 }}
| | breedsma
| Kevolisma
|  
|-
|-
| | [[4375/4374|4375/4374]]
| [[1729/1728]]
| | 0.39576
| 1.0016
| | (5<span style="font-size: 70%; vertical-align: super;">4</span>*7)/(2*3<span style="font-size: 70%; vertical-align: super;">7</span>)
| (7×13×19)/(2<sup>2</sup>×3)<sup>3</sup>
| | | -1 -7 4 1 &gt;
| {{Monzo| -6 -3 0 1 0 1 0 1 }}
| | ragisma
| Ramanujanisma
|  
|-
|-
! colspan="5" | 11-limit (complete)
| [[2376/2375]]
| 0.72879
| ((2×3)/5)<sup>3</sup>×(11/19)
| {{Monzo| 3 3 -3 0 1 0 0 -1 }}
| Trichthonisma
|
|-
|-
| | [[11/10|11/10]]
| [[2432/2431]]
| | 165.004
| 0.71200
| | 11/(2*5)
| (2<sup>7</sup>×19)/(11×13×17)
| | | -1 0 -1 0 1 &gt;
| {{Monzo| 7 0 0 0 -1 -1 -1 1 }}
| | (large) (undecimal) neutral second, 4/5-tone, Ptolemy's second
| Blumeyer comma
|  
|-
|-
| | [[12/11|12/11]]
| [[2926/2925]]
| | 150.637
| 0.59177
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*3)/11
| (2×7×11×19)/((3×5)<sup>2</sup>×13)
| | | 2 1 0 0 -1 &gt;
| {{Monzo| 1 -2 -2 1 1 -1 0 1 }}
| | (small) (undecimal) neutral second, 3/4-tone
| Neovulture comma, neovulturisma
|  
|-
|-
| | [[22/21|22/21]]
| [[3136/3135]]
| | 80.537
| 0.55214
| | (2*11)/(3*7)
| (2<sup>3</sup>×7)<sup>2</sup>/(3×5×11×19)
| | | 1 -1 0 -1 1 &gt;
| {{Monzo| 6 -1 -1 2 -1 0 0 -1 }}
| | undecimal minor semitone
| Neomirkwai comma, neomirkwaisma
| S56
|-
|-
| | [[33/32|33/32]]
| [[3250/3249]]
| | 53.273
| 0.53277
| | (3*11)/2<span style="font-size: 70%; vertical-align: super;">5</span>
| (2×5<sup>3</sup>×13)/(3×19)<sup>2</sup>
| | | -5 1 0 0 1 &gt;
| {{Monzo| 1 -2 3 0 0 1 0 -2 }}
| | undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced)
| Martebisma
|  
|-
|-
| | [[45/44|45/44]]
| [[4200/4199]]
| | 38.906
| 0.41225
| | (3/2)<span style="font-size: 70%; vertical-align: super;">2</span>*(5/11)
| (2<sup>3</sup>×3×5<sup>2</sup>×7)/(13×17×19)
| | | -2 2 1 0 -1 &gt;
| {{Monzo| 3 1 2 1 0 -1 -1 -1 }}
| | 1/5-tone
| Neosatanisma
|  
|-
|-
| | [[55/54|55/54]]
| [[5776/5775]]
| | 31.767
| 0.29975
| | (5*11)/(2*3<span style="font-size: 70%; vertical-align: super;">3</span>)
| (2<sup>2</sup>×19)<sup>2</sup>/(3×5<sup>2</sup>×7×11)
| | | -1 -3 1 0 1 &gt;
| {{Monzo| 4 -1 -2 -1 -1 0 0 2 }}
| | undecimal diasecundal comma, eleventyfive comma
| Neovish comma, neovishma
| S76
|-
|-
| | [[56/55|56/55]]
| [[5929/5928]]
| | 31.194
| 0.29202
| | (2<span style="font-size: 70%; vertical-align: super;">3</span>*7)/(5*11)
| (7×11)<sup>2</sup>/(2<sup>3</sup>×3×13×19)
| | | 3 0 -1 1 -1 &gt;
| {{Monzo| -3 -1 0 2 2 -1 0 -1 }}
| | undecimal tritonic comma, konbini comma
| Manzanisma
| S77
|-
|-
| | [[99/98|99/98]]
| [[5985/5984]]
| | 17.576
| 0.28929
| | (3/7)<span style="font-size: 70%; vertical-align: super;">2</span>*(11/2)
| (3<sup>2</sup>×5×7×19)/(2<sup>5</sup>×11×17)
| | | -1 2 0 -2 1 &gt;
| {{Monzo| -5 2 1 1 -1 0 -1 1 }}
| | small undecimal comma, mothwellsma
| Neogrendel comma, neogrendelisma
|
|-
|-
| | [[100/99|100/99]]
| [[6175/6174]]
| | 17.399
| 0.28038
| | (2*5/3)<span style="font-size: 70%; vertical-align: super;">2</span>/11)
| (5<sup>2</sup>×13×19)/(2×3<sup>2</sup>×7<sup>3</sup>)
| | | 2 -2 2 0 -1 &gt;
| {{Monzo| -1 -2 2 -3 0 1 0 1 }}
| | Ptolemy's comma, ptolemisma
| Neonewtisma
|  
|-
|-
| | [[121/120|121/120]]
| [[6860/6859]]
| | 14.376
| 0.25238
| | 11<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3*5)
| (2<sup>2</sup>×5×7<sup>3</sup>)/19<sup>3</sup>
| | | -3 -1 -1 0 2 &gt;
| {{Monzo| 2 0 1 3 0 0 0 -3 }}
| | undecimal seconds comma, biyatisma
| Devicubisma
|  
|-
|-
| | [[176/175|176/175]]
| 10241/10240
| | 9.8646
| 0.16906
| | (2<span style="font-size: 70%; vertical-align: super;">4</span>*11)/(5<span style="font-size: 70%; vertical-align: super;">2</span>*7)
| (7<sup>2</sup>×11×19)/(2<sup>11</sup>×5)
| | | 4 0 -2 -1 1 &gt;
| {{Monzo| -11 0 -1 2 1 0 0 1 }}
| | valinorsma
|  
|  
|-
|-
| | [[243/242|243/242]]
| 10830/10829
| | 7.1391
| 0.15986
| | 3<span style="font-size: 70%; vertical-align: super;">5</span>/(2*11<span style="font-size: 70%; vertical-align: super;">2</span>)
| (2×3×5×19<sup>2</sup>)/(7<sup>2</sup>×13×17)
| | | -1 5 0 0 -2 &gt;
| {{Monzo| 1 1 1 -2 0 -1 -1 2 }}
| | neutral third comma, rastma
|  
|  
|-
|-
| | [[385/384|385/384]]
| [[12636/12635]]
| | 4.5026
| 0.13701
| | (5*7*11)/(2<span style="font-size: 70%; vertical-align: super;">7</span>*3)
| (2<sup>2</sup>×3<sup>5</sup>×13)/(5×7×19<sup>2</sup>)
| | | -7 -1 1 1 1 &gt;
| {{Monzo| 2 5 -1 -1 0 1 0 -2 }}
| | keenanisma
| Padriellisma
|  
|-
|-
| | [[441/440|441/440]]
| 13377/13376
| | 3.9302
| 0.12942
| | (3*7)<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">3</span>*5*11)
| (3×7<sup>3</sup>×13)/(2<sup>6</sup>×11×19)
| | | -3 2 -1 2 -1 &gt;
| {{Monzo| -6 1 0 3 -1 1 0 -1 }}
| | Werckmeister's undecimal septenarian schisma, werckisma
|  
|  
|-
|-
| | [[540/539|540/539]]
| 14080/14079
| | 3.2090
| 0.12296
| | (2/7)<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">3</span>*5/11
| (2<sup>8</sup>×5×11)/(3×13×19<sup>2</sup>)
| | | 2 3 1 -2 -1 &gt;
| {{Monzo| 8 -1 1 0 1 -1 0 -2 }}
| | Swets' comma, swetisma
|  
|  
|-
|-
| | [[3025/3024|3025/3024]]
| 14365/14364
| | 0.57240
| 0.12052
| | (5*11)<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">4</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>*7)
| (5×13<sup>2</sup>×17)/(2<sup>2</sup>×3<sup>3</sup>×7×19)
| | | -4 -3 2 -1 2 &gt;
| {{Monzo| -2 -3 1 -1 0 2 1 -1 }}
| | Lehmerisma
|  
|  
|-
|-
| | [[9801/9800|9801/9800]]
| 23409/23408
| | 0.17665
| 0.073957
| | [11/(5*7)]<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">4</span>/2<span style="font-size: 70%; vertical-align: super;">3</span>
| ((3/2)<sup>2</sup>×17)<sup>2</sup>/(7×11×19)
| | | -3 4 -2 -2 2 &gt;
| {{Monzo| -4 4 0 -1 -1 0 2 -1 }}
| | Gauss comma, kalisma
|  
| S153
|-
|-
! colspan="5" | 13-limit (complete)
| 27456/27455
| 0.063056
| (2<sup>6</sup>×3×11×13)/(5×17<sup>2</sup>×19)
| {{Monzo| 6 1 -1 0 1 1 -2 -1 }}
|
|
|-
|-
| | [[13/12|13/12]]
| 28900/28899
| | 138.573
| 0.059905
| | 13/(2<span style="font-size: 70%; vertical-align: super;">2</span>*3)
| ((2×5×17)/(3×13))<sup>2</sup>/19
| | | -2 -1 0 0 0 1 &gt;
| {{Monzo| 2 -2 2 0 0 -2 2 -1 }}
| | tridecimal 2/3-tone
|  
| S170
|-
|-
| | [[14/13|14/13]]
| 43681/43680
| | 128.298
| 0.039634
| | (2*7)/13
| (11×19)<sup>2</sup>/(2<sup>5</sup>×3×5×7×13)
| | | 1 0 0 1 0 -1 &gt;
| {{Monzo| -5 -1 -1 -1 2 -1 0 2 }}
| | 2/3-tone, trienthird
|  
| S209
|-
|-
| | [[26/25|26/25]]
| 89376/89375
| | 67.900
| 0.019370
| | (2*13)/5<span style="font-size: 70%; vertical-align: super;">2</span>
| (2<sup>5</sup>×3×7<sup>2</sup>×19)/(5<sup>4</sup>×11×13)
| | | 1 0 -2 0 0 1 &gt;
| {{Monzo| 5 1 -4 2 -1 -1 0 1 }}
| | tridecimal 1/3-tone
|  
|  
|-
|-
| | [[27/26|27/26]]
| 104976/104975
| | 65.337
| 0.016492
| | 3<span style="font-size: 70%; vertical-align: super;">3</span>/(2*13)
| (2×3<sup>2</sup>)<sup>4</sup>/(5<sup>2</sup>×13×17×19)
| | | -1 3 0 0 0 -1 &gt;
| {{Monzo| 4 8 -2 0 0 -1 -1 -1 }}
| | tridecimal comma
|  
| S324
|-
|-
| | [[40/39|40/39]]
| [[Decimillisma|165376/165375]]
| | 43.831
| 0.010469
| | (2<span style="font-size: 70%; vertical-align: super;">3</span>*5)/(3*13)
| (2<sup>9</sup>×17×19)/((3×5)<sup>3</sup>×7<sup>2</sup>)
| | | 3 -1 1 0 0 -1 &gt;
| {{Monzo| 9 -3 -3 -2 0 0 1 1 }}
| | tridecimal minor diesis
| Decimillisma
|  
|-
|-
| | [[65/64|65/64]]
| 228096/228095
| | 26.841
| 0.0075900
| | (5*13)/2<span style="font-size: 70%; vertical-align: super;">6</span>
| ((2<sup>2</sup>×3)/7)<sup>4</sup>×(11/(5×19))
| | | -6 0 1 0 0 1 &gt;
| {{Monzo| 8 4 -1 -4 1 0 0 -1 }}
| | wilsorma, 13th-partial chroma
|  
|  
|-
|-
| | [[66/65|66/65]]
| 601426/601425
| | 26.432
| 0.0028786
| | (2*3*11)/(5*13)
| (2×7<sup>2</sup>×17×19<sup>2</sup>)/(3<sup>7</sup>×5<sup>2</sup>×11)
| | | 1 1 -1 0 1 -1 &gt;
| {{Monzo| 1 -7 -2 2 -1 0 1 2 }}
| | winmeanma
|  
|  
|-
|-
| | [[78/77|78/77]]
| [[Devicisma|633556/633555]]
| | 22.339
| 0.0027326
| | (2*3*13)/(7*11)
| (2<sup>2</sup>×7×11<sup>3</sup>×17)/(3<sup>3</sup>×5×13×19<sup>2</sup>)
| | | 1 1 0 -1 -1 1 &gt;
| {{Monzo| 2 -3 -1 1 3 -1 1 -2 }}
| | negustma
| Devicisma
|
|-
| 709632/709631
| 0.0024396
| (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 }}
|
|
|-
| 5909761/5909760
| 0.00029294
| (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 }}
|
|
|}
 
=== 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"/>
|-
|-
| | [[91/90|91/90]]
| [[23/22]]
| | 19.130
| 76.956
| | (7*13)/(2*3<span style="font-size: 70%; vertical-align: super;">2</span>*5)
| 23/(2×11)
| | | -1 -2 -1 1 0 1 &gt;
| {{Monzo| -1 0 0 0 -1 0 0 0 1 }}
| | [[The_Biosphere|Biome]] comma, superleap comma
| Large vicesimotertial semitone
|  
|-
|-
| | [[105/104|105/104]]
| [[24/23]]
| | 16.567
| 73.681
| | (3*5*7)/(2<span style="font-size: 70%; vertical-align: super;">3</span>*13)
| (2<sup>3</sup>×3)/23
| | | -3 1 1 1 0 -1 &gt;
| {{Monzo| 3 1 0 0 0 0 0 0 -1 }}
| | small tridecimal comma, animist comma
| Small vicesimotertial semitone
|  
|-
|-
| | [[144/143|144/143]]
| [[46/45]]
| | 12.064
| 38.051
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*3)<span style="font-size: 70%; vertical-align: super;">2</span>/(11*13)
| (2×23)/(3<sup>2</sup>×5)
| | | 4 2 0 0 -1 -1 &gt;
| {{Monzo| 1 -2 -1 0 0 0 0 0 1 }}
| | grossma
| Vicesimotertial 1/5-tone
|  
|-
|-
| | [[169/168|169/168]]
| [[69/68]]
| | 10.274
| 25.274
| | 13<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3*7)
| (3×23)/(2<sup>2</sup>×17)
| | | -3 -1 0 -1 0 2 &gt;
| {{Monzo| -2 1 0 0 0 0 -1 0 1 }}
| | buzurgisma, dhanvantarisma
| Large vicesimotertial 1/8-tone
|  
|-
|-
| | [[196/195|196/195]]
| [[70/69]]
| | 8.8554
| 24.910
| | (2*7)<span style="font-size: 70%; vertical-align: super;">2</span>/(3*5*13)
| (2×5×7)/(3×23)
| | | 2 -1 -1 2 0 -1 &gt;
| {{Monzo| 1 -1 1 1 0 0 0 0 -1 }}
| | marveltwin comma
| Small vicesimotertial 1/8-tone
|  
|-
|-
| | [[325/324|325/324]]
| [[92/91]]
| | 5.3351
| 18.921
| | (5<span style="font-size: 70%; vertical-align: super;">2</span>*13)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">4</span>)
| (2<sup>2</sup>×23)/(7×13)
| | | -2 -4 2 0 0 1 &gt;
| {{Monzo| 2 0 0 -1 0 -1 0 0 1 }}
| |  
| Undinisma
|  
|-
|-
| | [[351/350|351/350]]
| [[115/114]]
| | 4.9393
| 15.120
| | (3/5)<span style="font-size: 70%; vertical-align: super;">2</span>*13/(2*7)
| (5×23)/(2×3×19)
| | | -1 3 -2 -1 0 1 &gt;
| {{Monzo| -1 -1 1 0 0 0 0 -1 1 }}
| | ratwolfsma
| Yarmanisma
|  
|-
|-
| | [[352/351|352/351]]
| [[161/160]]
| | 4.9253
| 10.787
| | (2<span style="font-size: 70%; vertical-align: super;">5</span>*11)/(3<span style="font-size: 70%; vertical-align: super;">2</span>*13)
| (7×23)/(2<sup>5</sup>×5)
| | | 5 -3 0 0 1 -1 &gt;
| {{Monzo| -5 0 -1 1 0 0 0 0 1 }}
| | minthma
| Major kirnbergerisma
|  
|-
|-
| | [[364/363|364/363]]
| [[162/161]]
| | 4.7627
| 10.720
| | (2/11)<span style="font-size: 70%; vertical-align: super;">2</span>*7*13/3
| (2×3<sup>4</sup>)/(7×23)
| | | 2 -1 0 1 -2 1 &gt;
| {{Monzo| 1 4 0 -1 0 0 0 0 -1 }}
| | gentle comma
| Minor kirnbergerisma
|  
|-
|-
| | [[625/624|625/624]]
| [[208/207]]
| | 2.7722
| 8.3433
| |
| (2<sup>4</sup>×13)/(3<sup>2</sup>×23)
| | | -4 -1 4 0 0 -1 &gt;
| {{Monzo| 4 -2 0 0 0 1 0 0 -1 }}
| | tunbarsma
| Vicetone comma
|  
|-
|-
| | [[676/675|676/675]]
| [[231/230]]
| | 2.5629
| 7.5108
| |
| (3×7×11)/(2×5×23)
| | | 2 -3 -2 0 0 2 &gt;
| {{Monzo| -1 1 -1 1 1 0 0 0 -1 }}
| | island comma
| Major neutravicema
|  
|-
|-
| | [[729/728|729/728]]
| [[253/252]]
| | 2.3764
| 6.8564
| |
| (11×23)/((2×3)<sup>2</sup>×7)
| | | -3 6 0 -1 0 -1 &gt;
| {{Monzo| -2 -2 0 -1 1 0 0 0 1 }}
| | squbema
| Middle neutravicema
|  
|-
|-
| | [[1001/1000|1001/1000]]
| [[276/275]]
| | 1.7304
| 6.2840
| |
| (2<sup>2</sup>×3×23)/(5<sup>2</sup>×11)
| | | -3 0 -3 1 1 1 &gt;
| {{Monzo| 2 1 -2 0 -1 0 0 0 1 }}
| | sinbadma
| Minor neutravicema
|  
|-
|-
| | [[1716/1715|1716/1715]]
| [[300/299]]
| | 1.0092
| 5.7804
| |
| ((2×5)<sup>2</sup>×3)/(13×23)
| | | 2 1 -1 -3 1 1 &gt;
| {{Monzo| 2 1 2 0 0 -1 0 0 -1 }}
| | lummic comma
| Major naiadvicema
|  
|-
|-
| | [[2080/2079|2080/2079]]
| [[323/322]]
| | 0.83252
| 5.3682
| |
| (17×19)/(2×7×23)
| | | 5 -3 1 -1 -1 1 &gt;
| {{Monzo| -1 0 0 -1 0 0 1 1 -1 }}
| | ibnsinma
| Major semivicema
|  
|-
|-
| | [[4096/4095|4096/4095]]
| [[391/390]]
| | 0.42272
| 4.4334
| |
| (17×23)/(2×3×5×13)
| | | 12 -2 -1 -1 0 -1 &gt;
| {{Monzo| -1 -1 -1 0 0 -1 1 0 1 }}
| | tridecimal schisma, Sagittal schismina
| Minor naiadvicema
|  
|-
|-
| | [[4225/4224|4225/4224]]
| [[392/391]]
| | 0.40981
| 4.4221
| |
| (2<sup>3</sup>×7<sup>2</sup>)/(17×23)
| | | -7 -1 2 0 -1 2 &gt;
| {{Monzo| 3 0 0 2 0 0 -1 0 -1 }}
| | leprechaun comma
| Minor semivicema
|  
|-
|-
| | [[6656/6655|6656/6655]]
| [[460/459]]
| | 0.26012
| 3.7676
| |
| (2<sup>2</sup>×5×23)/(3<sup>3</sup>×17)
| | | 9 0 -1 0 -3 1 &gt;
| {{Monzo| 2 -3 1 0 0 0 -1 0 1 }}
| | jacobin comma
| Scanisma, vicewolf comma
|  
|-
|-
| | [[10648/10647|10648/10647]]
| [[484/483]]
| | 0.16260
| 3.5806
| |
| (2×11)<sup>2</sup>/(3×7×23)
| | | 3 -2 0 -1 3 -2 &gt;
| {{Monzo| 2 -1 0 -1 2 0 0 0 -1 }}
| | harmonisma
| Pittsburghisma
| S22
|-
|-
| | [[123201/123200|123201/123200]]
| [[507/506]]
| | 0.014052
| 3.4180
| |
| (3×13<sup>2</sup>)/(2×11×23)
| | | -6 6 -2 -1 -1 2 &gt;
| {{Monzo| -1 1 0 0 -1 2 0 0 -1 }}
| | chalmersia
| Laodicisma
|  
|-
|-
! colspan="5" | 17-limit (complete)
| [[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
|-
|-
| | [[17/16|17/16]]
| [[576/575]]
| | 104.955
| 3.0082
| | 17/2<span style="font-size: 70%; vertical-align: super;">4</span>
| ((2<sup>3</sup>×3)/5)<sup>2</sup>/23
| | | -4 0 0 0 0 0 1 &gt;
| {{Monzo| 6 2 -2 0 0 0 0 0 -1 }}
| | 17th harmonic (octave reduced)
| Worcester comma
| S24
|-
|-
| | [[18/17|18/17]]
| [[736/735]]
| | 98.955
| 2.3538
| | (2*3<span style="font-size: 70%; vertical-align: super;">2</span>)/17
| (2<sup>5</sup>×23)/(3×5×7<sup>2</sup>)
| | | 1 2 0 0 0 0 -1 &gt;
| {{Monzo| 5 -1 -1 -2 0 0 0 0 1 }}
| | Arabic lute index finger
| Harvardisma
|  
|-
|-
| | [[34/33|34/33]]
| [[760/759]]
| | 51.682
| 2.2794
| | (2*17)/(3*11)
| (2<sup>3</sup>×5×19)/(3×11×23)
| | | 1 -1 0 0 -1 0 1 &gt;
| {{Monzo| 3 -1 1 0 -1 0 0 1 -1 }}
| |  
| Squadronisma
|  
|-
|-
| | [[35/34|35/34]]
| [[875/874]]
| | 50.184
| 1.9797
| | (5*7)/(2*17)
| (5<sup>3</sup>×7)/(2×19×23)
| | | -1 0 1 1 0 0 -1 &gt;
| {{Monzo| -1 0 3 1 0 0 0 -1 -1 }}
| | septendecimal 1/4-tone
| Nymphisma
|  
|-
|-
| | [[51/50|51/50]]
| [[897/896]]
| | 34.283
| 1.9311
| | (3*17)/(2*5<span style="font-size: 70%; vertical-align: super;">2</span>)
| (3×13×23)/(2<sup>7</sup>×7)
| | | -1 1 -2 0 0 0 1 &gt;
| {{Monzo| -7 1 0 -1 0 1 0 0 1 }}
| | 17th-partial chroma
| Lysistratisma
|  
|-
|-
| | [[52/51|52/51]]
| [[1105/1104]]
| | 33.617
| 1.5674
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*13)/(3*17)
| (5×13×17)/(2<sup>4</sup>×3×23)
| | | 2 -1 0 0 0 1 -1 &gt;
| {{Monzo| -4 -1 1 0 0 1 1 0 -1 }}
| |  
| Fragarisma
|  
|-
|-
| | [[85/84|85/84]]
| [[1197/1196]]
| | 20.488
| 1.4469
| | (5*17)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*3*7)
| (3<sup>2</sup>×7×19)/(2<sup>2</sup>×13×23)
| | | -2 -1 1 -1 0 0 1 &gt;
| {{Monzo| -2 2 0 1 0 -1 0 1 -1 }}
| |  
| Rodessisma
|  
|-
|-
| | 120/119
| [[1288/1287]]
| | 14.487
| 1.3446
| | (2<span style="font-size: 70%; vertical-align: super;">3</span>*3*5)/(7*17)
| (2<sup>3</sup>×7×23)/(3<sup>2</sup>×11×13)
| | | 3 1 1 -1 0 0 -1 &gt;
| {{Monzo| 3 -2 0 1 -1 -1 0 0 1 }}
| |  
| Santisma, triaphonisma
|  
|-
|-
| | 136/135
| [[1496/1495]]
| | 12.777
| 1.1576
| | (2/3)<span style="font-size: 70%; vertical-align: super;">3</span>*17/5
| (2<sup>3</sup>×11×17)/(5×13×23)
| | | 3 -3 -1 0 0 0 1 &gt;
| {{Monzo| 3 0 -1 0 1 -1 1 0 -1 }}
| |  
| Turkisma
|  
|-
|-
| | 154/153
| [[1863/1862]]
| | 11.278
| 0.92952
| | (2*7*11)/(3<span style="font-size: 70%; vertical-align: super;">2</span>*17)
| (3<sup>4</sup>×23)/(2×7<sup>2</sup>×19)
| | | 1 -2 0 1 1 0 -1 &gt;
| {{Monzo| -1 4 0 -2 0 0 0 -1 1 }}
| |  
| Antinousisma
|  
|-
|-
| | 170/169
| [[2024/2023]]
| | 10.214
| 0.85556
| | (2*5*17)/13<span style="font-size: 70%; vertical-align: super;">2</span>
| (2<sup>3</sup>×11×23)/(7×17<sup>2</sup>)
| | | 1 0 1 0 0 -2 1 &gt;
| {{Monzo| 3 0 0 -1 1 0 -2 0 1 }}
| |  
| Artifisma, insincere comma
|  
|-
|-
| | 221/220
| [[2025/2024]]
| | 7.8514
| 0.85514
| | (13*17)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*5*11)
| (3<sup>2</sup>×5)<sup>2</sup>/(2<sup>3</sup>×11×23)
| | | -2 0 -1 0 -1 1 1 &gt;
| {{Monzo| -3 4 2 0 -1 0 0 0 -1 }}
| |  
| Cupcake comma, cupcakesma
| S45
|-
|-
| | 256/255
| [[2185/2184]]
| | 6.7759
| 0.79251
| | (2<span style="font-size: 70%; vertical-align: super;">8</span>)/(3*5*17)
| (5×19×23)/(2<sup>3</sup>×3×7×13)
| | | 8 -1 -1 0 0 0 -1 &gt;
| {{Monzo| -3 -1 1 -1 0 -1 0 1 1 }}
| | 255th subharmonic
| Guangdongisma
|  
|-
|-
| | 273/272
| [[2300/2299]]
| | 6.3532
| 0.75287
| | (3*7*13)/(2<span style="font-size: 70%; vertical-align: super;">4</span>*17)
| ((2×5)/11)<sup>2</sup>×(23/19)
| | | -4 1 0 1 0 1 -1 &gt;
| {{Monzo| 2 0 2 0 -2 0 0 -1 1 }}
| |  
| Travellisma
|  
|-
|-
| | 289/288
| [[2646/2645]]
| | 6.0008
| 0.65441
| | (17/3)<span style="font-size: 70%; vertical-align: super;">2</span>/2<span style="font-size: 70%; vertical-align: super;">5</span>
| (2×3<sup>3</sup>×7<sup>2</sup>)/(5×23<sup>2</sup>)
| | | -5 -2 0 0 0 0 2 &gt;
| {{Monzo| 1 3 -1 2 0 0 0 0 -2 }}
| |  
| Biyativice comma, biyativicema
|  
|-
|-
| | 375/374
| [[2737/2736]]
| | 4.6228
| 0.63265
| | (3*5<span style="font-size: 70%; vertical-align: super;">3</span>)/(2*11*17)
| (7×17×23)/(2<sup>4</sup>×3<sup>2</sup>×19)
| | | -1 1 3 0 -1 0 -1 &gt;
| {{Monzo| -4 -2 0 1 0 0 1 -1 1 }}
| |  
| Kotkisma
|  
|-
|-
| | 442/441
| [[3060/3059]]
| | 3.9213
| 0.56586
| | (2*13*17)/(3*7)<span style="font-size: 70%; vertical-align: super;">2</span>
| ((2×3)<sup>2</sup>×5×17)/(7×19×23)
| | | 1 -2 0 -2 0 1 1 &gt;
| {{Monzo| 2 2 1 -1 0 0 1 -1 -1 }}
| |  
| Vicious comma, viciousma
|  
|-
|-
| | 561/560
| [[3381/3380]]
| | 3.0887
| 0.51212
| | (3*11*17)/(2<span style="font-size: 70%; vertical-align: super;">4</span>*5*7)
| (3×7<sup>2</sup>×23)/(2<sup>2</sup>×5×13<sup>2</sup>)
| | | -4 1 -1 -1 1 0 1 &gt;
| {{Monzo| -2 1 -1 2 0 -2 0 0 1 }}
| |  
| Mikkolisma
|  
|-
|-
| | 595/594
| [[3520/3519]]
| | 2.9121
| 0.49190
| | (5*7*17)/(2*3<span style="font-size: 70%; vertical-align: super;">3</span>*11)
| (2<sup>6</sup>×5×11)/(3<sup>2</sup>×17×23)
| | | -1 -3 1 1 -1 0 1 &gt;
| {{Monzo| 6 -2 1 0 1 0 -1 0 -1 }}
| |  
| Vicedim comma, vicedimma
|  
|-
|-
| | 715/714
| [[3888/3887]]
| | 2.4230
| 0.44533
| | (5*11*13)/(2*3*7*17)
| (2<sup>4</sup>×3<sup>5</sup>)/(13<sup>2</sup>×23)
| | | -1 -1 1 -1 1 1 -1 &gt;
| {{Monzo| 4 5 0 0 0 -2 0 0 -1 }}
| |  
| Shoalma, vicetride comma
|  
|-
|-
| | 833/832
| [[4693/4692]]
| | 2.0796
| 0.36893
| | (7<span style="font-size: 70%; vertical-align: super;">2</span>*17)/(2<span style="font-size: 70%; vertical-align: super;">6</span>*13)
| (13×19<sup>2</sup>)/(2<sup>2</sup>×3×17×23)
| | | -6 0 0 2 0 -1 1 &gt;
| {{Monzo| -2 -1 0 0 0 1 -1 2 -1 }}
| |  
| Viceaug comma, viceaugma
|  
|-
|-
| | 936/935
| [[4761/4760]]
| | 1.8506
| 0.36367
| | (2<span style="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>*13)/(5*11*17)
| (3×23)<sup>2</sup>/(2<sup>3</sup>×5×7×17)
| | | 3 2 -1 0 -1 1 -1 &gt;
| {{Monzo| -3 2 -1 -1 0 0 -1 0 2 }}
| |  
| Demiquartervice comma
| S69
|-
|-
| | 1089/1088
| [[5083/5082]]
| | 1.5905
| 0.34063
| | (3<span style="font-size: 70%; vertical-align: super;">2</span>*11<span style="font-size: 70%; vertical-align: super;">2</span>)/(2<span style="font-size: 70%; vertical-align: super;">6</span>*17)
| (13×17×23)/(2×3×7×11<sup>2</sup>)
| | | -6 2 0 0 2 0 -1 &gt;
| {{Monzo| -1 -1 0 -1 -2 1 1 0 1 }}
| | twosquare comma
| Broadviewsma
|  
|-
|-
| | 1156/1155
| [[7866/7865]]
| | 1.4983
| 0.22010
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*17<span style="font-size: 70%; vertical-align: super;">2</span>)/(3*5*7*11)
| (2×3<sup>2</sup>×19×23)/(5×11<sup>2</sup>×13)
| | | 2 -1 -1 -1 -1 0 2 &gt;
| {{Monzo| 1 2 -1 0 -2 -1 0 1 1 }}
| |  
|  
|  
|-
|-
| | 1225/1224
| [[8281/8280]]
| | 1.4138
| 0.20907
| | (5<span style="font-size: 70%; vertical-align: super;">2</span>*7<span style="font-size: 70%; vertical-align: super;">2</span>)/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>*17)
| (7×13)<sup>2</sup>/(2<sup>3</sup>×3<sup>2</sup>×5×23)
| | | -3 -2 2 2 0 0 -1 &gt;
| {{Monzo| -3 -2 -1 2 0 2 0 0 -1 }}
| |  
|  
| S91
|-
|-
| | 1275/1274
| [[8625/8624]]
| | 1.3584
| 0.20073
| | (3*5<span style="font-size: 70%; vertical-align: super;">2</span>*17)/(2*7<span style="font-size: 70%; vertical-align: super;">2</span>*13)
| (3×5<sup>3</sup>×23)/(2<sup>4</sup>×7<sup>2</sup>×11)
| | | -1 1 2 -2 0 -1 1 &gt;
| {{Monzo| -4 1 3 -2 -1 0 0 0 1 }}
| |  
| Beerglass comma
|  
|-
|-
| | 1701/1700
| [[10626/10625]]
| | 1.0181
| 0.16293
| | (3<span style="font-size: 70%; vertical-align: super;">5</span>*7)/[(2*5)<span style="font-size: 70%; vertical-align: super;">2</span>*17]
| (2×3×7×11×23)/(5<sup>4</sup>×17)
| | | -2 5 -2 1 0 0 -1 &gt;
| {{Monzo| 1 1 -4 1 1 0 -1 0 1 }}
| |  
| Demiglace comma
|  
|-
|-
| | 2058/2057
| 11271/11270
| | 0.8414
| 0.15361
| | (2*3*7<span style="font-size: 70%; vertical-align: super;">3</span>)/(11<span style="font-size: 70%; vertical-align: super;">2</span>*17)
| (3×13×17<sup>2</sup>)/(2×5×7<sup>2</sup>×23)
| | | 1 1 0 3 -2 0 -1 &gt;
| {{Monzo| -1 1 -1 -2 0 1 2 0 -1 }}
| | xenisma
|  
|  
|-
|-
| | 2431/2430
| 11662/11661
| | 0.7123
| 0.14846
| | (11*13*17)/(2*3<span style="font-size: 70%; vertical-align: super;">5</span>*5)
| (2×7<sup>3</sup>×17)/(3×13<sup>2</sup>×23)
| | | -1 -5 -1 0 1 1 1 &gt;
| {{Monzo| 1 -1 0 3 0 -2 1 0 -1 }}
| |  
|  
|  
|-
|-
| | 2500/2499
| [[Vicetertisma|12168/12167]]
| | 0.6926
| 0.14228
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*5<span style="font-size: 70%; vertical-align: super;">4</span>)/(3*7<span style="font-size: 70%; vertical-align: super;">2</span>*17)
| (2/23)<sup>3</sup>×(3×13)<sup>2</sup>
| | | 2 -1 4 -2 0 0 -1 &gt;
| {{Monzo| 3 2 0 0 0 2 0 0 -3 }}
| |  
| Vicetertisma
|  
|-
|-
| | 2601/2600
| 16929/16928
| | 0.6657
| 0.10227
| | (3<span style="font-size: 70%; vertical-align: super;">2</span>*17<span style="font-size: 70%; vertical-align: super;">2</span>)/(2<span style="font-size: 70%; vertical-align: super;">3</span>*5<span style="font-size: 70%; vertical-align: super;">2</span>*13)
| (3<sup>4</sup>×11×19)/(2<sup>5</sup>×23<sup>2</sup>)
| | | -3 2 -2 0 0 -1 2 &gt;
| {{Monzo| -5 4 0 0 1 0 0 1 -2 }}
| |  
|  
|  
|-
|-
| | 4914/4913
| 19551/19550
| | 0.3523
| 0.088552
| | (2*3<span style="font-size: 70%; vertical-align: super;">3</span>*7*13)/(17<span style="font-size: 70%; vertical-align: super;">3</span>)
| (3×7<sup>3</sup>×19)/(2×5<sup>2</sup>×17×23)
| | | 1 3 0 1 0 1 -3 &gt;
| {{Monzo| -1 1 -2 3 0 0 -1 1 -1 }}
| |  
|  
|  
|-
|-
| | 5832/5831
| 21505/21504
| | 0.2969
| 0.080506
| | (2<span style="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">6</span>)/(7<span style="font-size: 70%; vertical-align: super;">3</span>*17)
| (5×11×17×23)/(2<sup>10</sup>×3×7)
| | | 3 6 0 -3 0 0 -1 &gt;
| {{Monzo| -10 -1 1 -1 1 0 1 0 1 }}
| |  
|  
|  
|-
|-
| | 12376/12375
| 21736/21735
| | 0.1399
| 0.079650
| | (2<span style="font-size: 70%; vertical-align: super;">3</span>*7*13*17)/(3<span style="font-size: 70%; vertical-align: super;">2</span>*5<span style="font-size: 70%; vertical-align: super;">3</span>*11)
| (2<sup>3</sup>×11×13×19)/(3<sup>3</sup>×5×7×23)
| | | 3 -2 -3 1 -1 1 1 &gt;
| {{Monzo| 3 -3 -1 -1 1 1 0 1 -1 }}
| |  
|  
|  
|-
|-
| | 14400/14399
| 23276/23275
| | 0.1202
| 0.074380
| | (2<span style="font-size: 70%; vertical-align: super;">6</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>*5<span style="font-size: 70%; vertical-align: super;">2</span>)/(7*11<span style="font-size: 70%; vertical-align: super;">2</span>*17)
| ((2×23)/(5×7))<sup>2</sup>×(11/19)
| | | 6 2 2 -1 -2 0 -1 &gt;
| {{Monzo| 2 0 -2 -2 1 0 0 -1 2 }}
| |  
|  
|  
|-
|-
| | 28561/28560
| [[Joshuavoisma|25025/25024]]
| | 0.0606
| 0.069182
| | (13<span style="font-size: 70%; vertical-align: super;">4</span>)/(2<span style="font-size: 70%; vertical-align: super;">4</span>*3*5*7*17)
| (5<sup>2</sup>×7×11×13)/(2<sup>6</sup>×17×23)
| | | -4 -1 -1 -1 0 4 -1 &gt;
| {{Monzo| -6 0 2 1 1 1 -1 0 -1 }}
| |  
| Joshuavoisma
|  
|-
|-
| | 31213/31212
| [[Diarithmedia|25921/25920]]
| | 0.0555
| 0.066790
| | (7<span style="font-size: 70%; vertical-align: super;">4</span>*13)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">3</span>*17<span style="font-size: 70%; vertical-align: super;">2</span>)
| (7×23)<sup>2</sup>/(2<sup>6</sup>×3<sup>4</sup>×5)
| | | -2 -3 0 4 0 1 -2 &gt;
| {{Monzo| -6 -4 -1 2 0 0 0 0 2 }}
| |  
| Diarithmedia
| S161
|-
|-
| | 37180/37179
| 43264/43263
| | 0.0466
| 0.040016
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*5*11*13<span style="font-size: 70%; vertical-align: super;">2</span>)/(3<span style="font-size: 70%; vertical-align: super;">7</span>*17)
| (2<sup>4</sup>×13)<sup>2</sup>/(3<sup>2</sup>×11×19×23)
| | | 2 -7 1 0 1 2 -1 &gt;
| {{Monzo| 8 -2 0 0 -1 2 0 -1 -1 }}
| |  
|  
| S208
|-
|-
| | 194481/194480
| 52326/52325
| | 0.0089
| 0.033086
| | (3<span style="font-size: 70%; vertical-align: super;">4</span>*7<span style="font-size: 70%; vertical-align: super;">4</span>)/(2<span style="font-size: 70%; vertical-align: super;">4</span>*5*11*13*17)
| (2×3<sup>4</sup>×17×19)/(5<sup>2</sup>×7×13×23)
| | | -4 4 -1 4 -1 -1 -1&gt;
| {{Monzo| 1 4 -2 -1 0 -1 1 1 -1 }}
| | scintillisma
|  
|  
|-
|-
| | 336141/336140
| 71875/71874
| | 0.0052
| 0.024087
| | (3<span style="font-size: 70%; vertical-align: super;">2</span>*13<span style="font-size: 70%; vertical-align: super;">3</span>*17)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*5*7<span style="font-size: 70%; vertical-align: super;">5</span>)
| (5<sup>5</sup>×23)/(2×(3×11)<sup>3</sup>)
| | | -2 2 -1 -5 0 3 1 &gt;
| {{Monzo| -1 -3 5 0 -3 0 0 0 1 }}
| |  
|  
|  
|-
|-
! colspan="5" | 19-limit (incomplete)
| 75141/75140
| 0.023040
| (3<sup>3</sup>×11<sup>2</sup>×23)/(2<sup>2</sup>×5×13×17<sup>2</sup>)
| {{Monzo| -2 3 -1 0 2 -1 -2 0 1 }}
|
|
|-
|-
| | [[19/18|19/18]]
| 76545/76544
| | 93.603
| 0.022617
| | 19/(2*3<span style="font-size: 70%; vertical-align: super;">2</span>)
| (3<sup>7</sup>×5×7)/(2<sup>8</sup>×13×23)
| | | -1 -2 0 0 0 0 0 1 &gt;
| {{Monzo| -8 7 1 1 0 -1 0 0 -1 }}
| | undevicesimal semitone
|  
|  
|-
|-
| | [[20/19|20/19]]
| 104329/104328
| | 88.801
| 0.016594
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*5)/19
| (17×19)<sup>2</sup>/(2<sup>3</sup>×3<sup>4</sup>×7×23)
| | | 2 0 1 0 0 0 0 -1 &gt;
| {{Monzo| -3 -4 0 -1 0 0 2 2 -1 }}
| | small undevicesimal semitone
|  
| S323
|-
|-
| | [[39/38|39/38]]
| 122452/122451
| | 44.970
| 0.014138
| | (3*13)/(2*19)
| (2<sup>2</sup>×11<sup>3</sup>×23)/(3×7<sup>4</sup>×17)
| | | -1 1 0 0 0 1 0 -1 &gt;
| {{Monzo| 2 -1 0 -4 3 0 -1 0 1 }}
| |  
|  
|  
|-
|-
| | [[57/56|57/56]]
| 126225/126224
| | 30.642
| 0.013716
| | (3*19)/(2<span style="font-size: 70%; vertical-align: super;">3</span>*7)
| (3<sup>3</sup>×5<sup>2</sup>×11×17)/(2<sup>4</sup>×7<sup>3</sup>×23)
| | | -3 1 0 -1 0 0 0 1 &gt;
| {{Monzo| -4 3 2 -3 1 0 1 0 -1 }}
| |  
|  
|  
|-
|-
| | [[76/75|76/75]]
| 152881/152880
| | 22.931
| 0.011324
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*19)/(3*5<span style="font-size: 70%; vertical-align: super;">2</span>)
| (17×23)<sup>2</sup>/(2<sup>4</sup>×3×5×7<sup>2</sup>×13)
| | | 2 -1 -2 0 0 0 0 1 &gt;
| {{Monzo| -4 -1 -1 -2 0 -1 2 0 2 }}
| |  
|  
| S391
|-
|-
| | [[77/76|77/76]]
| 202125/202124
| | 22.631
| 0.0085652
| | (7*11)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*19)
| (3×5<sup>3</sup>×7<sup>2</sup>×11)/(2<sup>2</sup>×13<sup>3</sup>×23)
| | | -2 0 0 1 1 0 0 -1 &gt;
| {{Monzo| -2 1 3 2 1 -3 0 0 -1 }}
| |  
|  
|  
|-
|-
| | [[96/95|96/95]]
| 264385/264384
| | 18.128
| 0.0065482
| | (2<span style="font-size: 70%; vertical-align: super;">5</span>*3)/(5*19)
| (5×11<sup>2</sup>×19×23)/(2<sup>6</sup>×3<sup>5</sup>×17)
| | | 5 1 -1 0 0 0 0 -1 &gt;
| {{Monzo| -6 -5 1 0 2 0 -1 1 1 }}
| |  
|  
|  
|-
|-
| | 133/132
| 282625/282624
| | 13.066
| 0.0061256
| | (19*7)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*3*11)
| (5<sup>3</sup>×7×17×19)/(2<sup>12</sup>×3×23)
| | | -2 -1 0 1 -1 0 0 1 &gt;
| {{Monzo| -12 -1 3 1 0 0 1 1 -1 }}
| |  
|  
|  
|-
|-
| | 153/152
| 328510/328509
| | 11.352
| 0.0052700
| | (3<span style="font-size: 70%; vertical-align: super;">2</span>*17)/(2<span style="font-size: 70%; vertical-align: super;">3</span>*19)
| (2×5×7×13×19<sup>2</sup>)/(3×23)<sup>3</sup>
| | | -3 2 0 0 0 0 1 -1 &gt;
| {{Monzo| 1 -3 1 1 0 1 0 2 -3 }}
| |  
|  
|  
|-
|-
| | 171/170
| 2023425/2023424
| | 10.154
| 0.00085560
| | (3<span style="font-size: 70%; vertical-align: super;">2</span>*19)/(2*5*17)
| ((3×5×23)<sup>2</sup>×17)/(2<sup>13</sup>×13×19)
| | | -1 2 -1 0 0 0 -1 1 &gt;
| {{Monzo| -13 2 2 0 0 -1 1 -1 2 }}
| |  
|  
|  
|-
|-
| | 190/189
| 4096576/4096575
| | 9.1358
| 0.00042261
| | (2*5*19)/(3<span style="font-size: 70%; vertical-align: super;">3</span>*7)
| ((2<sup>3</sup>×11×23)/(3<sup>2</sup>×5×17))<sup>2</sup>/7
| | | 1 -3 1 -1 0 0 0 1 &gt;
| {{Monzo| 6 -4 -2 -1 2 0 -2 0 2 }}
| |  
|  
| S2024
|-
|-
| | 209/208
| 5142501/5142500
| | 8.3033
| 0.00033665
| | (11*19)/(2<span style="font-size: 70%; vertical-align: super;">4</span>*13)
| 3<sup>3</sup>×((7×13)/(2×5<sup>2</sup>×11))<sup>2</sup>×(23/17)
| | | -4 0 0 0 1 -1 0 1 &gt;
| {{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"/>
|-
|-
| | 210/209
| [[41/40]]
| | 8.2637
| 42.749
| | (2*3*5*7)/(11*19)
| 41/(2<sup>3</sup>×5)
| | | 1 1 1 1 -1 0 0 -1 &gt;
| 2.5.41 {{monzo| -3 -1 1 }}
| |  
| Large quadracesimoprimal 1/5-tone
|  
|-
|-
| | 286/285
| [[42/41]]
| | 6.0639
| 41.719
| | (2*11*13)/(3*5*19)
| (2×3×7)/41
| | | 1 -1 -1 0 1 1 0 -1 &gt;
| 2.3.7.41 {{monzo| 1 1 1 -1 }}
| |  
| Small quadracesimoprimal 1/5-tone
|  
|-
|-
| | 324/323
| [[82/81]]
| | 5.3516
| 21.242
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">4</span>)/(17*19)
| (2×41)/3<sup>4</sup>
| | | 2 4 0 0 0 0 -1 -1 &gt;
| 2.3.41 {{monzo| 1 -4 1 }}
| |  
| 41st-partial chroma
|  
|-
|-
| | 343/342
| [[124/123]]
| | 5.0547
| 14.018
| | 7<span style="font-size: 70%; vertical-align: super;">4</span>/(2*3<span style="font-size: 70%; vertical-align: super;">3</span>*19)
| (2<sup>2</sup>×31)/(3×41)
| | | -1 -2 0 3 0 0 0 -1 &gt;
| 2.3.31.41 {{monzo| 2 -1 1 -1 }}
| |  
|  
|  
|-
|-
| | 361/360
| [[165/164]]
| | 4.8023
| 10.524
| | 19<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>*5)
| (3×5×11)/(2<sup>2</sup>×41)
| | | -3 -2 -1 0 0 0 0 2 &gt;
| 2.3.5.11.41 {{monzo| -2 1 1 1 -1 }}
| |  
|  
|  
|-
|-
| | 400/399
| [[205/204]]
| | 4.3335
| 8.4657
| | (2<span style="font-size: 70%; vertical-align: super;">4</span>*5<span style="font-size: 70%; vertical-align: super;">2</span>)/(3*7*19)
| (5×41)/(2<sup>2</sup>×3×17)
| | | 4 -1 2 -1 0 0 0 -1 &gt;
| 2.3.5.17.41 {{monzo| -2 -1 1 -1 1 }}
| |  
|  
|  
|-
|-
| | 456/455
| [[246/245]]
| | 3.8007
| 7.0519
| | (2<span style="font-size: 70%; vertical-align: super;">3</span>*3*19)/(5*7*13)
| (2×3×41)/(5×7<sup>2</sup>)
| | | 3 1 -1 -1 0 -1 0 1 &gt;
| 2.3.5.7.41 {{monzo| 1 1 -1 -2 1 }}
| |  
|  
|  
|-
|-
| | 476/475
| [[247/246]]
| | 3.6409
| 7.0233
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*7*17)/(5<span style="font-size: 70%; vertical-align: super;">2</span>*19)
| (13×19)/(2×3×41)
| | | 2 0 -2 1 0 0 1 -1 &gt;
| 2.3.13.19.41 {{monzo| -1 -1 1 1 -1 }}
| |  
|  
|  
|-
|-
| | 495/494
| [[287/286]]
| | 3.501
| 6.0427
| | (3<span style="font-size: 70%; vertical-align: super;">2</span>*5*11)/(2*13*19)
| (7×41)/(2×11×13)
| | | -1 2 1 0 1 -1 0 -1 &gt;
| 2.7.11.13.41 {{monzo| -1 1 -1 -1 1 }}
| |  
|  
|  
|-
|-
| | 513/512
| [[288/287]]
| | 3.378
| 6.0217
| | (3<span style="font-size: 70%; vertical-align: super;">3</span>*19)/2<span style="font-size: 70%; vertical-align: super;">9</span>
| (2<sup>5</sup>×3<sup>2</sup>)/(7×41)
| | | -9 3 0 0 0 0 0 1 &gt;
| 2.3.7.41 {{monzo| 5 2 -1 -1 }}
| | 513th harmonic
|  
|  
|-
|-
! colspan="5" | 23-limit (incomplete)
| [[369/368]]
| 4.6981
| (3<sup>2</sup>×41)/(2<sup>4</sup>×23)
| 2.3.23.41 {{monzo| -4 2 -1 1 }}
|
|
|-
|-
| | [[23/22|23/22]]
| [[370/369]]
| | 76.956
| 4.6853
| | 23/(2*11)
| (2×5×37)/(3<sup>2</sup>×41)
| |  
| 2.3.5.37.41 {{monzo| 1 -2 1 1 -1 }}
| |  
|  
|  
|-
|-
| | [[24/23|24/23]]
| [[451/450]]
| | 73.681
| 3.8429
| | (2<span style="font-size: 70%; vertical-align: super;">3</span>*3)/23
| (11×41)/(2×(3×5)<sup>2</sup>)
| |  
| 2.3.5.11.41 {{monzo| -1 -2 -2 1 1 }}
| |  
|  
|  
|-
|-
| | [[46/45|46/45]]
| [[493/492]]
| | 38.051
| 3.5152
| | (2*23)/(3<span style="font-size: 70%; vertical-align: super;">2</span>*5)
| (17×29)/(2<sup>2</sup>×3×41)
| |  
| 2.3.17.29.41 {{monzo| -2 -1 1 1 -1 }}
| |  
|  
|  
|-
|-
| | [[69/68|69/68]]
| [[533/532]]
| | 25.274
| 3.2511
| | (3*23)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*17)
| (13×41)/(2<sup>2</sup>×7×19)
| |  
| 2.7.13.19.41 {{monzo| -2 -1 1 -1 1 }}
| |  
|  
|  
|-
|-
| | [[70/69|70/69]]
| [[575/574]]
| | 24.910
| 3.0135
| | (2*5*7)/(3*23)
| (5<sup>2</sup>×23)/(2×7×41)
| |  
| 2.5.7.23.41 {{monzo| -1 2 -1 1 -1 }}
| |  
| Renatisma
|  
|-
|-
| | [[92/91|92/91]]
| [[616/615]]
| | 18.921
| 2.8127
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*23)/(7*13)
| (2<sup>3</sup>×7×11)/(3×5×41)
| |  
| 2.3.5.7.11.41 {{monzo| 3 -1 -1 1 1 -1 }}
| |  
| Ellisma
|  
|-
|-
| | 115/114
| [[697/696]]
| | 15.120
| 2.4856
| | (5*23)/(2*3*19)
| (17×41)/(2<sup>3</sup>×3×29)
| |  
| 2.3.17.29.41 {{monzo| -3 -1 1 -1 1 }}
| |  
|  
|  
|-
|-
| | 161/160
| [[780/779]]
| | 10.7865
| 2.2210
| | (7*23)/(2<span style="font-size: 70%; vertical-align: super;">5</span>*5)
| (2<sup>2</sup>×3×5×13)/(19×41)
| |  
| 2.3.5.13.19.41 {{monzo| 2 1 1 1 -1 -1 }}
| |  
| Wiesentisma
|  
|-
|-
| | 162/161
| [[820/819]]
| | 10.720
| 2.1125
| | (2*3<span style="font-size: 70%; vertical-align: super;">4</span>)/(7*23)
| (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 }}
| |  
|  
|  
|-
|-
| | 208/207
| [[1025/1024]]
| | 8.343
| 1.6898
| | (2<span style="font-size: 70%; vertical-align: super;">4</span>*13)/(23*9)
| (5<sup>2</sup>×41)/2<sup>10</sup>
| |  
| 2.5.41 {{monzo| -10 2 1 }}
| |  
| Kilobytisma
|  
|-
|-
| | 576/575
| [[1026/1025]]
| | 3.008
| 1.6882
| | (2<span style="font-size: 70%; vertical-align: super;">6</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>)/(23*25)
| (2×3<sup>3</sup>×19)/(5<sup>2</sup>×41)
| |  
| 2.3.5.19.41 {{monzo| 1 3 -2 1 -1 }}
| |  
| Ingridisma
|  
|-
|-
! colspan="5" | 29-limit (incomplete)
| [[1148/1147]]
| 1.5087
| (2<sup>2</sup>×7×41)/(31×37)
| 2.7.31.37.41 {{monzo| 2 1 -1 -1 1 }}
|
|
|-
|-
| | [[29/28|29/28]]
| [[1189/1188]]
| | 60.751
| 1.4567
| | 29/(2<span style="font-size: 70%; vertical-align: super;">2</span>*7)
| (29×41)/(2<sup>2</sup>×3<sup>3</sup>×11)
| |  
| 2.3.11.29.41 {{monzo| -2 -3 -1 1 1 }}
| |  
|  
|  
|-
|-
| | [[30/29|30/29]]
| [[1190/1189]]
| | 58.692
| 1.4554
| | (2*3*5)/29
| (2×5×7×17)/(29×41)
| |  
| 2.5.7.17.29.41 {{monzo| 1 1 1 1 -1 -1 }}
| |  
| Pelagisma
|  
|-
|-
| | [[58/57|58/57]]
| [[1312/1311]]
| | 30.109
| 1.3200
| | (2*29)/(3*19)
| (2<sup>5</sup>×41)/(3×19×23)
| |  
| 2.3.19.23.41 {{monzo| 5 -1 -1 -1 1 }}
| |  
|  
|  
|-
|-
| | [[88/87|88/87]]
| [[1353/1352]]
| | 19.786
| 1.2800
| | (2<span style="font-size: 70%; vertical-align: super;">3</span>*11)/(3*29)
| (3×11×41)/(2<sup>3</sup>×13<sup>2</sup>)
| |  
| 2.3.11.13.41 {{monzo| -3 1 1 -2 1 }}
| |  
|  
|  
|-
|-
! colspan="5" | 31-limit (incomplete)
| [[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 }}
|
|
|-
|-
| | [[31/30|31/30]]
| [[1518/1517]]
| | 56.767
| 1.1408
| | 31/(2*3*5)
| (2×3×11×23)/(37×41)
| |  
| 2.3.11.23.37.41 {{monzo| 1 1 1 1 -1 -1 }}
| |  
| Rovaniemisma
|  
|-
|-
| | [[32/31|32/31]]
| [[1600/1599]]
| | 54.964
| 1.0824
| | 2<span style="font-size: 70%; vertical-align: super;">5</span>/31
| (2<sup>3</sup>×5)<sup>2</sup>/(3×13×41)
| |  
| 2.3.5.13.41 {{monzo| 6 -1 2 -1 -1 }}
| | 31st subharmonic
|
| S40
|-
|-
| | [[63/62|63/62]]
| [[1681/1680]]
| | 27.700
| 1.0302
| | (3<span style="font-size: 70%; vertical-align: super;">2</span>*7)/(2*31)
| 41<sup>2</sup>/(2<sup>4</sup>×3×5×7)
| |  
| 2.3.5.7.41 {{monzo| -4 -1 -1 -1 2 }}
| |  
|
| S41
|-
|-
| | [[93/92|93/92]]
| [[1682/1681]]
| | 18.716
| 1.0296
| | (3*31)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*23)
| (2×29<sup>2</sup>)/41<sup>2</sup>
| |  
| 2.29.41 {{monzo| 1 2 -2 }}
| |  
| Shaftesburisma
|  
|-
|-
! colspan="5" | 37-limit (incomplete)
| [[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 }}
|
|
|-
|-
| | [[37/36|37/36]]
| [[1886/1885]]
| | 47.434
| 0.91818
| | 37/(2<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>)
| (2×23×41)/(5×13×29)
| |  
| 2.5.13.23.29.41 {{monzo| 1 -1 -1 1 -1 1 }}
| |  
|  
|  
|-
|-
| | [[38/37|38/37]]
| [[1887/1886]]
| | 46.169
| 0.91770
| | (2*19)/37
| (3×17×37)/(2×23×41)
| |  
| 2.3.17.23.37.41 {{monzo| -1 1 1 -1 1 -1 }}
| |  
|  
|  
|-
|-
| | [[75/74|75/74]]
| [[2091/2090]]
| | 23.238
| 0.82814
| | (3*5<span style="font-size: 70%; vertical-align: super;">2</span>)/(2*37)
| (3×17×41)/(2×5×11×19)
| |  
| 2.3.5.11.17.19.41 {{monzo| -1 1 -1 -1 1 -1 1 }}
| |  
|  
|  
|-
|-
! colspan="5" | 41-limit (incomplete)
| [[2255/2254]]
| 0.76790
| (5×11×41)/(2×7<sup>2</sup>×23)
| 2.5.7.11.23.41 {{monzo| -1 1 -2 1 -1 1 }}
| Qinghaisma
|
|-
|-
| | [[41/40|41/40]]
| [[2296/2295]]
| | 42.749
| 0.75419
| | 41/(2<span style="font-size: 70%; vertical-align: super;">3</span>*5)
| (2<sup>3</sup>×7×41)/(3<sup>3</sup>×5×17)
| |  
| 2.3.5.7.17.41 {{monzo| 3 -3 -1 1 -1 1 }}
| |  
|  
|  
|-
|-
| | [[42/41|42/41]]
| [[2542/2541]]
| | 41.719
| 0.68119
| | (2*3*7)/41
| (2×31×41)/(3×7×11<sup>2</sup>)
| |  
| 2.3.7.11.31.41 {{monzo| 1 -1 -1 -2 1 1 }}
| |  
|  
|  
|-
|-
| | [[82/81|82/81]]
| [[2584/2583]]
| | 21.242
| 0.67011
| | (2*41)/3<span style="font-size: 70%; vertical-align: super;">4</span>
| (2<sup>3</sup>×17×19)/(3<sup>2</sup>×7×41)
| |  
| 2.3.7.17.19.41 {{monzo| 3 -2 -1 1 1 -1 }}
| |  
|  
|  
|-
|-
! colspan="5" | 43-limit (incomplete)
| [[2625/2624]]
| 0.65964
| (3×5<sup>3</sup>×7)/(2<sup>6</sup>×41)
| 2.3.5.7.41 {{monzo| -6 1 3 1 -1 }}
|
|
|-
|-
| | [[43/42|43/42]]
| [[2665/2664]]
| | 40.737
| 0.64974
| | 43/(2*3*7)
| (5×13×41)/(2<sup>3</sup>×3<sup>2</sup>×37)
| |  
| 2.3.5.13.37.41 {{monzo| -3 -2 1 1 -1 1 }}
| |  
|  
|  
|-
|-
| | [[44/43|44/43]]
| [[2871/2870]]
| | 39.800
| 0.60311
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*11)/43
| (3<sup>2</sup>×11×29)/(2×5×7×41)
| |  
| 2.3.5.7.11.29.41 {{monzo| -1 2 -1 -1 1 1 -1 }}
| |  
| Schoberisma
|  
|-
|-
| | [[86/85|86/85]]
| [[3690/3689]]
| | 20.249
| 0.46923
| | (2*43)/(5*17)
| (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 }}
| |  
|  
|  
|-
|-
| | [[87/86|87/86]]
| [[3773/3772]]
| | 20.014
| 0.45891
| | (3*29)/(2*43)
| (7<sup>3</sup>×11)/(2<sup>2</sup>×23×41)
| |  
| 2.7.11.23.41 {{monzo| -2 3 1 -1 -1 }}
| |  
| Smithsonianisma
|  
|-
|-
! colspan="5" | 47-limit (incomplete)
| [[4060/4059]]
| 0.42646
| (2<sup>2</sup>×5×7×29)/(3<sup>2</sup>×11×41)
| 2.3.5.7.11.29.41 {{monzo| 2 -2 1 1 -1 1 -1 }}
| Deipylosisma
|
|-
|-
| | [[47/46|47/46]]
| [[4264/4263]]
| | 37.232
| 0.40606
| | 47/(2*23)
| (2<sup>3</sup>×13×41)/(3×7<sup>2</sup>×29)
| |  
| 2.3.7.13.29.41 {{monzo| 3 -1 -2 1 -1 1 }}
| |  
|  
|  
|-
|-
| | [[48/47|48/47]]
| [[4551/4550]]
| | 36.448
| 0.38045
| | (2<span style="font-size: 70%; vertical-align: super;">4</span>*3)/47
| (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 }}
| |  
|  
|  
|-
|-
| | [[94/93|94/93]]
| [[4675/4674]]
| | 18.516
| 0.37036
| | (2*47)/(3*31)
| (5<sup>2</sup>×11×17)/(2×3×19×41)
| |  
| 2.3.5.11.17.19.41 {{monzo| -1 -1 2 1 1 -1 -1 }}
| |  
| Ohbokisma
|  
|-
|-
| | [[95/94|95/94]]
| [[4921/4920]]
| | 18.320
| 0.35184
| | (5*19)/(2*47)
| (7×19×37)/(2<sup>3</sup>×3×5×41)
| |  
| 2.3.5.7.19.37.41 {{monzo| -3 -1 -1 1 1 1 -1 }}
| |  
| Volontisma
|  
|-
|-
! colspan="5" | 53-limit (incomplete)
| [[4961/4960]]
| 0.34900
| (11<sup>2</sup>×41)/(2<sup>5</sup>×5×31)
| 2.5.11.31.41 {{monzo| -5 -1 2 -1 1 }}
|
|
|-
|-
| | [[53/52|53/52]]
| [[5084/5083]]
| | 32.977
| 0.34056
| | 53/(2<span style="font-size: 70%; vertical-align: super;">2</span>*13)
| (2<sup>2</sup>×31×41)/(13×17×23)
| |  
| 2.13.17.23.31.41 {{monzo| 2 -1 -1 -1 1 1 }}
| |  
|  
|  
|-
|-
| | [[54/53|54/53]]
| [[5577/5576]]
| | 32.360
| 0.31045
| | (2*3<span style="font-size: 70%; vertical-align: super;">3</span>)/53
| (3×11×13<sup>2</sup>)/(2<sup>3</sup>×17×41)
| |  
| 2.3.11.13.17.41 {{monzo| -3 1 1 2 -1 -1 }}
| |  
| Priestlisma
|  
|-
|-
! colspan="5" | 59-limit (incomplete)
| [[6069/6068]]
| 0.28528
| (3×7×17<sup>2</sup>)/(2<sup>2</sup>×37×41)
| 2.3.7.17.37.41 {{monzo| -2 1 1 2 -1 -1 }}
| Cevolanisma
|
|-
|-
| | [[59/58|59/58]]
| [[6273/6272]]
| | 29.594
| 0.27600
| | 59/(2*29)
| (3<sup>2</sup>×17×41)/(2<sup>7</sup>×7<sup>2</sup>)
| |  
| 2.3.7.17.41 {{monzo| -7 2 -2 1 1 }}
| |  
|  
|  
|-
|-
| | [[60/59|60/59]]
| [[6561/6560]]
| | 29.097
| 0.26389
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*3*5)/59
| 3<sup>8</sup>/(2<sup>5</sup>×5×41)
| |  
| 2.3.5.41 {{monzo| -5 8 -1 -1 }}
| |  
|  
| S81
|-
|-
! colspan="5" | 61-limit (incomplete)
| [[6601/6600]]
| 0.26229
| (7×23×41)/(2<sup>3</sup>×3×5<sup>2</sup>×11)
| 2.3.5.7.11.23.41 {{monzo| -3 -1 -2 1 -1 1 1 }}
|
|
|-
|-
| | [[61/60|61/60]]
| [[6930/6929]]
| | 28.616
| 0.24984
| | 61/(2<span style="font-size: 70%; vertical-align: super;">2</span>*3*5)
| (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
|  
|-
|-
| | [[62/61|62/61]]
| [[7176/7175]]
| | 28.151
| 0.24127
| | (2*31)/61
| (2<sup>3</sup>×3×13×23)/(5<sup>2</sup>×7×41)
| |  
| 2.3.5.7.13.23.41 {{monzo| 3 1 -2 -1 1 1 -1 }}
| |  
| Kunijisma
|  
|-
|-
! colspan="5" | 67-limit (incomplete)
| [[7216/7215]]
| 0.23993
| (2<sup>4</sup>×11×41)/(3×5×13×37)
| 2.3.5.11.13.37.41 {{monzo| 4 -1 -1 1 -1 -1 1 }}
|
|
|-
|-
| | [[67/66|67/66]]
| [[7750/7749]]
| | 26.034
| 0.22340
| | 67/(2*3*11)
| (2×5<sup>3</sup>×31)/(3<sup>3</sup>×7×41)
| |  
| 2.3.5.7.31.41 {{monzo| 1 -3 3 -1 1 -1 }}
| |  
|  
|  
|-
|-
| | [[68/67|68/67]]
| [[8569/8568]]
| | 25.648
| 0.20205
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*17)/67
| (11×19×41)/(2<sup>3</sup>×3<sup>2</sup>×7×17)
| |  
| 2.3.7.11.17.19.41 {{monzo| -3 -2 -1 1 -1 1 1 }}
| |  
| Mamelisma
|  
|-
|-
! colspan="5" | 71-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 }}
|
|
|-
|-
| | [[71/70|71/70]]
| [[9472/9471]]
| | 24.557
| 0.18278
| | 71/(2*5*7)
| (2<sup>8</sup>×37)/(3×7×11×41)
| |  
| 2.3.7.11.37.41 {{monzo| 8 -1 -1 -1 1 -1 }}
| |  
| Brugesisma
|  
|-
|-
| | [[72/71|72/71]]
| 10045/10044
| | 24.213
| 0.17236
| | (2<span style="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>)/71
| (5×7<sup>2</sup>×41)/(2<sup>2</sup>×3<sup>4</sup>×31)
| |  
| 2.3.5.7.31.41 {{monzo| -2 -4 1 2 -1 1 }}
| |  
|  
|  
|-
|-
! colspan="5" | 73-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
|
|-
|-
| | [[73/72|73/72]]
| 10660/10659
| | 23.879
| 0.16241
| | 73/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>)
| (2<sup>2</sup>×5×13×41)/(3×11×17×19)
| |  
| 2.3.5.11.13.17.19.41 {{monzo| 2 -1 1 -1 1 -1 -1 1 }}
| |  
|  
|  
|-
|-
| | [[74/73|74/73]]
| [[11440/11439]]
| | 23.555
| 0.15134
| | (2*37)/73
| (2<sup>4</sup>×5×11×13)/(3<sup>2</sup>×31×41)
| |  
| 2.3.5.11.13.31.41 {{monzo| 4 -2 1 1 1 -1 -1 }}
| |  
| Massironisma
|  
|-
|-
! colspan="5" | 79-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 }}
|
|
|-
|-
| | [[79/78|79/78]]
| 14145/14144
| | 22.054
| 0.12240
| | 79/(2*3*13)
| (3×5×23×41)/(2<sup>6</sup>×13×17)
| |  
| 2.3.5.13.17.23.41 {{monzo| -6 1 1 -1 -1 1 1 }}
| |  
|  
|  
|-
|-
| | [[80/79|80/79]]
| 14801/14800
| | 21.777
| 0.11697
| | (2<span style="font-size: 70%; vertical-align: super;">4</span>*5)/79
| (19<sup>2</sup>×41)/(2<sup>4</sup>×5<sup>2</sup>×37)
| |  
| 2.5.19.37.41 {{monzo| -4 -2 2 -1 1 }}
| |  
|  
|  
|-
|-
! colspan="5" | 83-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
|-
|-
| | [[83/82|83/82]]
| 15457/15456
| | 20.985
| 0.11201
| | 83/(2*41)
| (13×29×41)/(2<sup>5</sup>×3×7×23)
| |  
| 2.3.7.13.23.29.41 {{monzo| -5 -1 -1 1 -1 1 1 }}
| |  
|  
|  
|-
|-
| | [[84/83|84/83]]
| 16400/16399
| | 20.734
| 0.10557
| | (2<span style="font-size: 70%; vertical-align: super;">2</span>*3*7)/83
| (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 }}
| |  
|  
|  
|-
|-
! colspan="5" | 89-limit (incomplete)
| 16524/16523
| 0.10477
| (2<sup>2</sup>×3<sup>5</sup>×17)/(13×31×41)
| 2.3.13.17.31.41 {{monzo| 2 5 -1 1 -1 -1 }}
|
|
|-
|-
| | [[89/88|89/88]]
| 16606/16605
| | 19.562
| 0.10426
| | 89/(2<span style="font-size: 70%; vertical-align: super;">3</span>*11)
| (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 }}
| |  
|  
|  
|-
|-
| | [[90/89|90/89]]
| 17425/17424
| | 19.344
| 0.099356
| | (2*3<span style="font-size: 70%; vertical-align: super;">2</span>*5)/89
| (5<sup>2</sup>×17×41)/(2<sup>2</sup>×3×11)<sup>2</sup>
| |  
| 2.3.5.11.17.41 {{monzo| -4 -2 2 -2 1 1 }}
| |  
|  
|  
|-
|-
! colspan="5" | 97-limit (incomplete)
| [[17836/17835]]
| 0.097067
| (2<sup>2</sup>×7<sup>3</sup>×13)/(3×5×29×41)
| 2.3.5.7.13.29.41 {{monzo| 2 -1 -1 3 1 -1 -1 }}
| Canupisma
|
|-
|-
| | [[97/96|97/96]]
| 17918/17917
| | 17.940
| 0.096623
| | 97/(2<span style="font-size: 70%; vertical-align: super;">5</span>*3)
| (2×17<sup>2</sup>×31)/(19×23×41)
| |  
| 2.17.19.23.31.41 {{monzo| 1 2 -1 -1 1 -1 }}
| |  
|  
|  
|-
|-
| | [[98/97|98/97]]
| 19721/19720
| | 17.756
| 0.087789
| | (2*7<span style="font-size: 70%; vertical-align: super;">2</span>)/97
| (13×37×41)/(2<sup>3</sup>×5×17×29)
| |  
| 2.5.13.17.29.37.41 {{monzo| -3 -1 1 -1 -1 1 1 }}
| |  
|  
|  
|-
|-
! colspan="5" | 101-limit (incomplete)
| 19845/19844
| 0.087240
| (3<sup>4</sup>×5×7<sup>2</sup>)/((2×11)<sup>2</sup>×41)
| 2.3.5.7.11.41 {{monzo| -2 4 1 2 -2 -1 }}
|
|
|-
|-
| | [[101/100|101/100]]
| [[76384/76383]]
| | 17.226
| 0.022665
| | 101/(2<span style="font-size: 70%; vertical-align: super;">2</span>*5<span style="font-size: 70%; vertical-align: super;">2</span>)
| (2<sup>5</sup>×7×11×31)/(3<sup>4</sup>×23×41)
| |  
| 2.3.7.11.23.31.41 {{monzo| 5 -4 1 1 -1 1 -1 }}
| |  
| Vernonisma
|  
|-
|-
| | [[102/101|102/101]]
| [[Mebisma|1048576/1048575]]
| | 17.057
| 0.0016510
| | (2*3*17)/101
| 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
|}
|}
[[Category:interval_list]]
 
[[Category:superparticular]]
=== 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"/>
|-
| [[43/42]]
| 40.737
| 43/(2×3×7)
| 2.3.7.43 {{monzo| -1 -1 -1 1 }}
| Large quadracesimotertial 1/5-tone
|
|-
| [[44/43]]
| 39.800
| (2<sup>2</sup>×11)/43
| 2.11.43 {{monzo| 2 1 -1 }}
| Small quadracesimotertial 1/5-tone
|
|-
| [[86/85]]
| 20.249
| (2×43)/(5×17)
| 2.5.17.43 {{monzo| 1 -1 -1 1 }}
| Large quadracesimotertial 1/10-tone
|
|-
| [[87/86]]
| 20.014
| (3×29)/(2×43)
| 2.3.29.43 {{monzo| -1 1 1 -1 }}
| Small quadracesimotertial 1/10-tone
|
|-
| [[129/128]]
| 13.473
| (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 }}
|
|
|}
 
=== 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 }}
|
|
|-
| [[128/127]]
| 13.578
| 2<sup>7</sup>/127
| 2.127 {{monzo| 7 -1 }}
|
|
|-
| [[381/380]]
| 4.5499
| (3×127)/(2<sup>2</sup>×5×19)
| 2.3.5.19.127 {{monzo| -2 1 -1 -1 1 }}
| Five feet comma
|
|-
| 500000/499999
| 0.0034625
| (2<sup>5</sup>×5<sup>6</sup>)/(31×127<sup>2</sup>)
| 2.5.31.127 {{monzo| 5 6 -1 -2 }}
|
|
|}
 
== 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|*]]
Retrieved from "https://en.xen.wiki/w/List_of_superparticular_intervals"