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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | This is a list of [[superparticular]] [[interval]]s ordered by [[prime limit]]. It reaches to the 127-limit and is complete up to the [[37-limit]]. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | |
| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-01-28 16:19:01 UTC</tt>.<br>
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| : The original revision id was <tt>538882498</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=<span style="color: #800080;">List of Superparticular Intervals</span>=
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| [[Superparticular]] numbers are ratios of the form (n+1)/n, or 1+1/n, where n is a whole number other than 1. They appear frequently in [[Just Intonation]] and [[OverToneSeries|Harmonic Series]] music. Adjacent tones in the harmonic series are separated by superparticular intervals: for instance, the 20th and 21st by the superparticular ratio [[21_20|21/20]]. As the overtones get closer together, the superparticular intervals get smaller and smaller. Thus, an examination of the superparticular intervals is an examination of some of the simplest small intervals in rational tuning systems. Indeed, many but not all common [[comma]]s are superparticular ratios. | | [[Wikipedia: Størmer's theorem|Størmer's theorem]] states that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than [[2/1]], [[3/2]], [[4/3]], and [[9/8]]. {{OEIS| A002071 }} gives the number of superparticular ratios in each prime limit, {{OEIS| A145604 }} shows the increment from limit to limit, and {{OEIS| A117581 }} gives the largest numerator for each prime limit (with some exceptions, such as the 23-limit, where the largest value is smaller than that of a smaller prime limit, in this case the 19-limit). |
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| The list below is ordered by [[harmonic limit]], or the largest prime involved in the prime factorization. [[36_35|36/35]], for instance, is an interval of the [[7-limit]], as it factors to (2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">2</span>)/(5*7), while 37/36 would belong to the 37-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 |
| | | |
| | |} |
|
| |
|
| [[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. | | === 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 |
| | |} |
|
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| See also: [[Gallery of Just Intervals]]. Many of the names below come from [[http://www.huygens-fokker.org/docs/intervals.html|here]].
| | === 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 |
| | |} |
|
| |
|
| ||~ Ratio ||~ Cents Value ||~ Factorization ||~ Name(s) ||
| | === 7-limit === |
| ||||||||~ 2-limit ||
| | {| class="wikitable center-6" style="width:100%" |
| || [[2_1|2/1]] || 1200.000 || 2/1 || (perfect) unison, unity, perfect prime, tonic, duple || | | ! width="10%" | [[Ratio]] |
| ||||||||~ 3-limit || | | ! width="10%" | [[Cent]]s |
| || [[3_2|3/2]] || 701.995 || 3/2 || [[perfect fifth]], 3rd harmonic (octave reduced), diapente ||
| | ! width="15%" | Factorization |
| || [[4_3|4/3]] || 498.045 || 2<span style="vertical-align: super;">2</span>/3 || perfect fourth, 3rd subharmonic (octave reduced), diatessaron ||
| | ! width="15%" | [[Monzo]] |
| || [[9_8|9/8]] || 203.910 || 3<span style="vertical-align: super;">2</span>/2<span style="vertical-align: super;">3</span> || (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced) ||
| | ! width="45%" | Name(s) |
| ||||||||~ 5-limit || | | ! width="5%" | Meta<ref name="ssp"/> |
| || [[5_4|5/4]] || 386.314 || 5/2<span style="vertical-align: super;">2</span> || (classic) (5-limit) major third, 5th harmonic (octave reduced) ||
| | |- |
| || [[6_5|6/5]] || 315.641 || (2*3)/5 || (classic) (5-limit) minor third || | | | [[7/6]] |
| || [[10_9|10/9]] || 182.404 || (2*5)/3<span style="vertical-align: super;">2</span> || classic (whole) tone, classic major second, minor whole tone ||
| | | 266.871 |
| || [[16_15|16/15]] || 111.713 || 2<span style="vertical-align: super;">4</span>/(3*5) || minor diatonic semitone, 15th subharmonic || | | | 7/(2×3) |
| || [[25_24|25/24]] || 70.672 || 5<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">3</span>*3) || chroma, (classic) chromatic semitone, Zarlinian semitone ||
| | | {{Monzo| -1 -1 0 1 }} |
| || [[81_80|81/80]] || 21.506 || <span style="line-height: 15.6000003814697px;">(</span>3<span style="line-height: 1.5;">/</span><span style="line-height: 15.6000003814697px;">2)</span><span style="line-height: 1.5; vertical-align: super;">4</span><span style="line-height: 15.6000003814697px;">/</span><span style="line-height: 1.5;">5</span> || syntonic comma, Didymus comma || | | | (Septimal) subminor third, septimal minor third |
| ||||||||~ 7-limit || | | | |
| || [[7_6|7/6]] || 266.871 || 7/(2*3) || (septimal) subminor third, septimal minor third, augmented second ||
| | |- |
| || [[8_7|8/7]] || 231.174 || 2<span style="vertical-align: super;">3</span>/7 || (septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic ||
| | | [[8/7]] |
| || [[15_14|15/14]] || 119.443 || (3*5)/(2*7) || septimal diatonic semitone || | | | 231.174 |
| || [[21_20|21/20]] || 84.467 || (3*7)/(2<span style="vertical-align: super;">2</span>*5) || minor semitone, large septimal chromatic semitone || | | | 2<sup>3</sup>/7 |
| || [[28_27|28/27]] || 62.961 || (2<span style="vertical-align: super;">2</span>*7)/3<span style="vertical-align: super;">3</span> || septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone ||
| | | {{Monzo| 3 0 0 -1 }} |
| || [[36_35|36/35]] || 48.770 || (2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">3</span>)/(5*7) || septimal quarter tone, septimal diesis ||
| | | (Septimal) supermajor second, septimal whole tone, <br>octave-reduced 7th subharmonic |
| || [[49_48|49/48]] || 35.697 || 7<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">4</span>*3) || large septimal diesis, slendro diesis, septimal 1/6-tone ||
| | | |
| || [[50_49|50/49]] || 34.976 || 2*(5<span style="line-height: 1.5;">/7)</span><span style="line-height: 1.5; vertical-align: super;">2</span> || septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma ||
| | |- |
| || [[64_63|64/63]] || 27.264 || 2<span style="vertical-align: super;">6</span>/(3<span style="vertical-align: super;">2</span>*7) || septimal comma, Archytas' comma ||
| | | [[15/14]] |
| || [[126_125|126/125]] || 13.795 || (2*3^2*7)/5^3 || starling comma, septimal semicomma ||
| | | 119.443 |
| || [[225_224|225/224]] || 7.7115 || (3*5)<span style="line-height: 1.5;">^2/(2^5*7)</span> || marvel comma, septimal kleisma ||
| | | (3×5)/(2×7) |
| || [[2401_2400|2401/2400]] || 0.72120 || 7^4/(2^5*3*5^2) || breedsma ||
| | | {{Monzo| -1 1 1 -1 }} |
| || [[4375_4374|4375/4374]] || 0.39576 || (5^4*7)/(2*3^7) || ragisma ||
| | | Septimal major semitone, septimal diatonic semitone |
| ||||||||~ 11-limit ||
| | | |
| || [[11_10|11/10]] || 165.004 || 11/(2*5) || (large) (undecimal) neutral second, 4/5-tone, Ptolemy's second ||
| | |- |
| || [[12_11|12/11]] || 150.637 || (2<span style="vertical-align: super;">2</span>*3)/11 || (small) (undecimal) neutral second, 3/4-tone ||
| | | [[21/20]] |
| || [[22_21|22/21]] || 80.537 || (2*11)/(3*7) || undecimal minor semitone ||
| | | 84.467 |
| || [[33_32|33/32]] || 53.273 || (3*11)/2<span style="vertical-align: super;">5</span> || unidecimal quarter tone, unidecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced) ||
| | | (3×7)/(2<sup>2</sup>×5) |
| || [[45_44|45/44]] || 38.906 || (3<span style="line-height: 15.6000003814697px;">/</span><span style="line-height: 1.5;">2)^</span><span style="line-height: 15.6000003814697px;">2*</span><span style="line-height: 1.5;">(</span><span style="line-height: 15.6000003814697px;">5/</span><span style="line-height: 1.5;">11)</span> || 1/5-tone ||
| | | {{Monzo| -2 1 -1 1 }} |
| || [[55_54|55/54]] || 31.767 || (5*11)/(2*3<span style="vertical-align: super;">3</span>) || ||
| | | Septimal minor semitone, large septimal chroma |
| || [[56_55|56/55]] || 31.194 || (2<span style="vertical-align: super;">3</span>*7)/(5*11) || ||
| | | |
| || [[99_98|99/98]] || 17.576 || (3<span style="line-height: 1.5;">/7)</span><span style="line-height: 1.5; vertical-align: super;">2</span><span style="line-height: 1.5;">*(11/2)</span> || small undecimal comma, mothwellsma ||
| | |- |
| || [[100_99|100/99]] || 17.399 || (2<span style="line-height: 1.5;">*5/3)</span><span style="line-height: 1.5; vertical-align: super;">2</span><span style="line-height: 1.5;">/11)</span> || Ptolemy's comma, ptolemisma ||
| | | [[28/27]] |
| || [[121_120|121/120]] || 14.376 || 11^2/(2^3*3*5) || undecimal seconds comma, biyatisma ||
| | | 62.961 |
| || [[176_175|176/175]] || 9.8646 || (2^4*11)/(5^2*7) || valinorsma ||
| | | (2<sup>2</sup>×7)/3<sup>3</sup> |
| || [[243_242|243/242]] || 7.1391 || 3^5/(2*11^2) || neutral third comma, rastma ||
| | | {{Monzo| 2 -3 0 1 }} |
| || [[385_384|385/384]] || 4.5026 || (5*7*11)/(2^7*3) || keenanisma ||
| | | Septimal 1/3-tone, small septimal chroma, <br>(septimal) subminor second, septimal minor second, <br>trienstonic comma |
| || [[441_440|441/440]] || 3.9302 || (3*7)^2/(2^3*5*11) || Werckmeister's undecimal septenarian schisma, werckisma ||
| | | |
| || [[540_539|540/539]] || 3.2090 || (2/7)^2*3^3*5/11 || Swets' comma, swetisma ||
| | |- |
| || [[3025_3024|3025/3024]] || 0.57240 || (5*11)^2/(2^4*3^3*7) || Lehmerisma ||
| | | [[36/35]] |
| || [[9801_9800|9801/9800]] || 0.17665 || <span style="line-height: 1.5;">[11/(5*7)]</span><span style="line-height: 15.6000003814697px;">^2*</span><span style="line-height: 1.5;">3^4/2^3</span> || Gauss comma, kalisma ||
| | | 48.770 |
| ||||||||~ 13-limit ||
| | | (2×3)<sup>2</sup>/(5×7) |
| || [[13_12|13/12]] || 138.573 || 13/(2<span style="vertical-align: super;">2</span>*3) || tridecimal 2/3-tone ||
| | | {{Monzo| 2 2 -1 -1 }} |
| || [[14_13|14/13]] || 128.298 || (2*7)/13 || 2/3-tone, trienthird ||
| | | Septimal 1/4-tone, mint comma |
| || [[26_25|26/25]] || 67.900 || (2*13)/5<span style="vertical-align: super;">2</span> || tridecimal 1/3-tone ||
| | | S6 |
| || [[27_26|27/26]] || 65.337 || 3<span style="vertical-align: super;">3</span>/(2*13) || tridecimal comma ||
| | |- |
| || [[40_39|40/39]] || 43.831 || (2<span style="vertical-align: super;">3</span>*5)/(3*13) || tridecimal minor diesis ||
| | | [[49/48]] |
| || [[65_64|65/64]] || 26.841 || (5*13)/2<span style="vertical-align: super;">6</span> || wilsorma, 13th-partial chroma ||
| | | 35.697 |
| || [[66_65|66/65]] || 26.432 || (2*3*11)/(5*13) || winmeanma ||
| | | 7<sup>2</sup>/(2<sup>4</sup>×3) |
| || [[78_77|78/77]] || 22.339 || (2*3*13)/(7*11) || negustma ||
| | | {{Monzo| -4 -1 0 2 }} |
| || [[91_90|91/90]] || 19.130 || (7*13)/(2*3<span style="vertical-align: super;">2</span>*5) || [[The Biosphere|Biome]] comma, superleap comma ||
| | | Large septimal diesis, large septimal 1/6-tone, slendro diesis, semaphoresma |
| || [[105_104|105/104]] || 16.567 || (3*5*7)/(2^3*13) || small tridecimal comma, animist comma ||
| | | S7 |
| || [[144_143|144/143]] || 12.064 || (<span style="line-height: 1.5;">2</span><span style="line-height: 1.5; vertical-align: super;">2</span><span style="line-height: 1.5;">*3)^2/(11*13)</span> || grossma ||
| | |- |
| || [[169_168|169/168]] || 10.274 || 13<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">3</span>*3*7) || buzurgisma, dhanvantarisma ||
| | | [[50/49]] |
| || [[196_195|196/195]] || 8.8554 || (2*7)^2/(3*5*13) || marveltwin comma ||
| | | 34.976 |
| || [[351_350|351/350]] || 4.9393 || (3/5)^2*13/(2*7) || ratwolfsma ||
| | | 2×(5/7)<sup>2</sup> |
| || [[352_351|352/351]] || 4.9253 || (<span style="line-height: 1.5;">2</span><span style="line-height: 1.5; vertical-align: super;">5</span><span style="line-height: 1.5;">*11)/(</span><span style="line-height: 15.6000003814697px;">3^</span>2<span style="line-height: 15.6000003814697px;">*13)</span> || minthma ||
| | | {{Monzo| 1 0 2 -2 }} |
| || [[364_363|364/363]] || 4.7627 || (2/11)^2*7*13/3 || gentle comma ||
| | | Small septimal diesis, small septimal 1/6-tone, septimal tritonic diesis, jubilisma |
| || [[625_624|625/624]] || 2.7722 || || tunbarsma ||
| | | |
| || [[676_675|676/675]] || 2.5629 || || island comma ||
| | |- |
| || [[729_728|729/728]] || 2.3764 || || squbema ||
| | | [[64/63]] |
| || [[1001_1000|1001/1000]] || 1.7304 || || sinbadma ||
| | | 27.264 |
| || [[1716_1715|1716/1715]] || 1.0092 || || lummic comma ||
| | | 2<sup>6</sup>/(3<sup>2</sup>×7) |
| || [[2080_2079|2080/2079]] || 0.83252 || || ibnsinma ||
| | | {{Monzo| 6 -2 0 -1 }} |
| || [[4096_4095|4096/4095]] || 0.42272 || || tridecimal schisma, Sagittal schismina ||
| | | Septimal comma, Archytas' comma |
| || [[4225_4224|4225/4224]] || 0.40981 || || leprechaun comma ||
| | | S8 |
| || [[6656_6655|6656/6655]] || 0.26012 || || jacobin comma ||
| | |- |
| || [[10648_10647|10648/10647]] || 0.16260 || || harmonisma ||
| | | [[126/125]] |
| || [[123201_123200|123201/123200]] || 0.014052 || || chalmersia ||
| | | 13.795 |
| ||||||||~ 17-limit (complete!) ||
| | | (2×3<sup>2</sup>×7)/5<sup>3</sup> |
| || [[17_16|17/16]] || 104.955 || 17/2<span style="vertical-align: super;">4</span> || 17th harmonic (octave reduced) ||
| | | {{Monzo| 1 2 -3 1 }} |
| || [[18_17|18/17]] || 98.955 || (2*3<span style="vertical-align: super;">2</span>)/17 || Arabic lute index finger ||
| | | Starling comma, septimal semicomma |
| || [[34_33|34/33]] || 51.682 || (2*17)/(3*11) || ||
| | | |
| || [[35_34|35/34]] || 50.184 || (5*7)/(2*17) || septendecimal 1/4-tone ||
| | |- |
| || [[51_50|51/50]] || 34.283 || (3*17)/(2*5<span style="vertical-align: super;">2</span>) || 17th-partial chroma ||
| | | [[225/224]] |
| || [[52_51|52/51]] || 33.617 || (2<span style="vertical-align: super;">2</span>*13)/(3*17) || ||
| | | 7.7115 |
| || [[85_84|85/84]] || 20.488 || (5*17)/(2<span style="vertical-align: super;">2</span>*3*7) || ||
| | | (3×5)<sup>2</sup>/(2<sup>5</sup>×7) |
| || 120/119 || 14.487 || (2<span style="vertical-align: super;">3</span>*3*5)/(7*17) || ||
| | | {{Monzo| -5 2 2 -1 }} |
| || 136/135 || 12.777 || (2/<span style="line-height: 1.5;">3)</span><span style="line-height: 1.5; vertical-align: super;">3</span><span style="line-height: 1.5;">*17/5</span> || ||
| | | Marvel comma, septimal kleisma |
| || 154/153 || 11.278 || (2*7*11)/(3<span style="vertical-align: super;">2</span>*17) || ||
| | | S15 |
| || 170/169 || 10.214 || (2*5*17)/13<span style="vertical-align: super;">2</span> || ||
| | |- |
| || 221/220 || 7.8514 || (13*17)/(2<span style="vertical-align: super;">2</span>*5*11) || ||
| | | [[2401/2400]] |
| || 256/255 || 6.7759 || (2^8)/(3*5*17) || 255th subharmonic ||
| | | 0.72120 |
| || 273/272 || 6.3532 || (3*7*13)/(2<span style="vertical-align: super;">4</span>*17) || ||
| | | 7<sup>4</sup>/(2<sup>5</sup>×3×5<sup>2</sup>) |
| || 289/288 || 6.0008 || (17<span style="line-height: 1.5;">/3)^</span><span style="line-height: 15.6000003814697px;">2</span><span style="line-height: 1.5;">/2</span><span style="line-height: 1.5; vertical-align: super;">5</span> || ||
| | | {{Monzo| -5 -1 -2 4 }} |
| || 375/374 || 4.6228 || (3*5<span style="vertical-align: super;">3</span>)/(2*11*17) || ||
| | | Breedsma |
| || 442/441 || 3.9213 || (2*13*17)/(3*7)<span style="vertical-align: super;">2</span> || ||
| | | S49 |
| || 561/560 || 3.0887 || (3*11*17)/(2<span style="vertical-align: super;">4</span>*5*7) || ||
| | |- |
| || 595/594 || 2.9121 || (5*7*17)/(2*3<span style="vertical-align: super;">3</span>*11) || ||
| | | [[4375/4374]] |
| || 715/714 || 2.4230 || (5*11*13)/(2*3*7*17) || ||
| | | 0.39576 |
| || 833/832 || 2.0796 || (7<span style="vertical-align: super;">2</span>*17)/(2<span style="vertical-align: super;">6</span>*13) || ||
| | | (5<sup>4</sup>×7)/(2×3<sup>7</sup>) |
| || 936/935 || 1.8506 || (2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">2</span>*13)/(5*11*17) || ||
| | | {{Monzo| -1 -7 4 1 }} |
| || 1089/1088 || 1.5905 || (3<span style="vertical-align: super;">2</span>*11<span style="vertical-align: super;">2</span>)/(2<span style="vertical-align: super;">6</span>*17) || ||
| | | Ragisma |
| || 1156/1155 || 1.4983 || (2<span style="vertical-align: super;">2</span>*17<span style="vertical-align: super;">2</span>)/(3*5*7*11) || ||
| | | |
| || 1225/1224 || 1.4138 || (5<span style="vertical-align: super;">2</span>*7<span style="vertical-align: super;">2</span>)/(2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">2</span>*17) || ||
| | |} |
| || 1275/1274 || 1.3584 || (3*5<span style="vertical-align: super;">2</span>*17)/(2*7<span style="vertical-align: super;">2</span>*13) || ||
| |
| || 1701/1700 || 1.0181 || (3<span style="vertical-align: super;">5</span>*7)/[(2*5)<span style="vertical-align: super;">2</span>*17] || ||
| |
| || 2058/2057 || 0.8414 || (2*3*7<span style="vertical-align: super;">3</span>)/(11<span style="vertical-align: super;">2</span>*17) || xenisma ||
| |
| || 2431/2430 || 0.7123 || (11*13*17)/(2*3<span style="vertical-align: super;">5</span>*5) || ||
| |
| || 2500/2499 || 0.6926 || (2<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">4</span>)/(3*7<span style="vertical-align: super;">2</span>*17) || ||
| |
| || 2601/2600 || 0.6657 || (3<span style="vertical-align: super;">2</span>*17<span style="vertical-align: super;">2</span>)/(2<span style="vertical-align: super;">3</span>*5<span style="vertical-align: super;">2</span>*13) || ||
| |
| || 4914/4913 || 0.3523 || (2*3<span style="vertical-align: super;">3</span>*7*13)/(17<span style="vertical-align: super;">3</span>) || ||
| |
| || 5832/5831 || 0.2969 || (2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">6</span>)/(7<span style="vertical-align: super;">3</span>*17) || ||
| |
| || 12376/12375 || 0.1399 || (2<span style="vertical-align: super;">3</span>*7*13*17)/(3<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">3</span>*11) || ||
| |
| || 14400/14399 || 0.1202 || (2<span style="vertical-align: super;">6</span>*3<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">2</span>)/(7*11<span style="vertical-align: super;">2</span>*17) || ||
| |
| || 28561/28560 || 0.0606 || (13<span style="vertical-align: super;">4</span>)/(2<span style="vertical-align: super;">4</span>*3*5*7*17) || ||
| |
| || 31213/31212 || 0.0555 || (7<span style="vertical-align: super;">4</span>*13)/(2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">3</span>*17<span style="vertical-align: super;">2</span>) || ||
| |
| || 37180/37179 || 0.0466 || (2<span style="vertical-align: super;">2</span>*5*11*13<span style="vertical-align: super;">2</span>)/(3<span style="vertical-align: super;">7</span>*17) || ||
| |
| || 194481/194480 || 0.0089 || (3<span style="vertical-align: super;">4</span>*7<span style="vertical-align: super;">4</span>)/(2<span style="vertical-align: super;">4</span>*5*11*13*17) || scintillisma ||
| |
| || 336141/336140 || 0.0052 || (3<span style="vertical-align: super;">2</span>*13<span style="vertical-align: super;">3</span>*17)/(2<span style="vertical-align: super;">2</span>*5*7<span style="vertical-align: super;">5</span>) || ||
| |
| ||||||||~ 19-limit (incomplete) ||
| |
| || [[19_18|19/18]] || 93.603 || 19/(2*3<span style="vertical-align: super;">2</span>) || undevicesimal semitone ||
| |
| || [[20_19|20/19]] || 88.801 || (2<span style="vertical-align: super;">2</span>*5)/19 || small undevicesimal semitone ||
| |
| || [[39_38|39/38]] || 44.970 || (3*13)/(2*19) || ||
| |
| || [[57_56|57/56]] || 30.642 || (3*19)/(2<span style="vertical-align: super;">3</span>*7) || ||
| |
| || [[76_75|76/75]] || 22.931 || (2<span style="vertical-align: super;">2</span>*19)/(3*5<span style="vertical-align: super;">2</span>) || ||
| |
| || [[77_76|77/76]] || 22.631 || (7*11)/(2<span style="vertical-align: super;">2</span>*19) || ||
| |
| || [[96_95|96/95]] || 18.128 || (2<span style="vertical-align: super;">5</span>*3)/(5*19) || ||
| |
| || 133/132 || 13.066 || (19*7)/(2<span style="vertical-align: super;">2</span>*3*11) || ||
| |
| || 153/152 || 11.352 || (3<span style="vertical-align: super;">2</span>*17)/(2<span style="vertical-align: super;">3</span>*19) || ||
| |
| || 171/170 || 10.154 || (3<span style="vertical-align: super;">2</span>*19)/(2*5*17) || ||
| |
| || 190/189 || 9.1358 || (2*5*19)/(3<span style="vertical-align: super;">3</span>*7) || ||
| |
| || 209/208 || 8.3033 || (11*19)/(2<span style="vertical-align: super;">4</span>*13) || ||
| |
| || 210/209 || 8.2637 || (2*3*5*7)/(11*19) || ||
| |
| || 286/285 || 6.0639 || (2*11*13)/(3*5*19) || ||
| |
| || 400/399 || 4.3335 || (2<span style="vertical-align: super;">4</span>*5<span style="vertical-align: super;">2</span>)/(3*7*19) || ||
| |
| || 456/455 || 3.8007 || (2<span style="vertical-align: super;">3</span>*3*19)/(5*7*13) || ||
| |
| || 476/475 || 3.6409 || (2<span style="vertical-align: super;">2</span>*7*17)/(5<span style="vertical-align: super;">2</span>*19) || ||
| |
| || 495/494 || 3.501 || (3<span style="vertical-align: super;">2</span>*5*11)/(2*13*19) || ||
| |
| || 513/512 || 3.378 || <span style="vertical-align: super;">(3^3*19)/2^9</span> || 513th harmonic ||
| |
| ||||||||~ 23-limit (incomplete) ||
| |
| || [[23_22|23/22]] || 76.956 || 23/(2*11) || ||
| |
| || [[24_23|24/23]] || 73.681 || (2<span style="vertical-align: super;">3</span>*3)/23 || ||
| |
| || [[46_45|46/45]] || 38.051 || (2*23)/(3<span style="vertical-align: super;">2</span>*5) || ||
| |
| || [[69_68|69/68]] || 25.274 || (3*23)/(2<span style="vertical-align: super;">2</span>*17) || ||
| |
| || [[70_69|70/69]] || 24.910 || (2*5*7)/(3*23) || ||
| |
| || [[92_91|92/91]] || 18.921 || (2<span style="vertical-align: super;">2</span>*23)/(7*13) || ||
| |
| || 115/114 || 15.120 || (5*23)/(2*3*19) || ||
| |
| || 161/160 || 10.7865 || (7*23)/(2^5*5) || ||
| |
| || 162/161 || 10.720 || (2*3^4)/(7*23) || ||
| |
| || 208/207 || 8.343 || (16*13)/(23*9) || ||
| |
| || 576/575 || 3.008 || (64*9)/(23*25) || ||
| |
| ||||||||~ 29-limit (incomplete) ||
| |
| || [[29_28|29/28]] || 60.751 || 29/(2<span style="vertical-align: super;">2</span>*7) || ||
| |
| || [[30_29|30/29]] || 58.692 || (2*3*5)/29 || ||
| |
| || [[58_57|58/57]] || 30.109 || (2*29)/(3*19) || ||
| |
| || [[88_87|88/87]] || 19.786 || (2<span style="vertical-align: super;">3</span>*11)/(3*29) || ||
| |
| ||||||||~ 31-limit (incomplete) ||
| |
| || [[31_30|31/30]] || 56.767 || 31/(2*3*5) || ||
| |
| || [[32_31|32/31]] || 54.964 || 2<span style="vertical-align: super;">5</span>/31 || 31st subharmonic ||
| |
| || [[63_62|63/62]] || 27.700 || (3<span style="vertical-align: super;">2</span>*7)/(2*31) || ||
| |
| || [[93_92|93/92]] || 18.716 || (3*31)/(2<span style="vertical-align: super;">2</span>*23) || ||
| |
| ||||||||~ 37-limit (incomplete) ||
| |
| || [[37_36|37/36]] || 47.434 || 37/(2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">2</span>) || ||
| |
| || [[38_37|38/37]] || 46.169 || (2*19)/37 || ||
| |
| || [[75_74|75/74]] || 23.238 || (3*5<span style="vertical-align: super;">2</span>)/(2*37) || ||
| |
| ||||||||~ 41-limit (incomplete) ||
| |
| || [[41_40|41/40]] || 42.749 || 41/(2<span style="vertical-align: super;">3</span>*5) || ||
| |
| || [[42_41|42/41]] || 41.719 || (2*3*7)/41 || ||
| |
| || [[82_81|82/81]] || 21.242 || (2*41)/3<span style="vertical-align: super;">4</span> || ||
| |
| ||||||||~ 43-limit (incomplete) ||
| |
| || [[43_42|43/42]] || 40.737 || 43/(2*3*7) || ||
| |
| || [[44_43|44/43]] || 39.800 || (2<span style="vertical-align: super;">2</span>*11)/43 || ||
| |
| || [[86_85|86/85]] || 20.249 || (2*43)/(5*17) || ||
| |
| || [[87_86|87/86]] || 20.014 || (3*29)/(2*43) || ||
| |
| ||||||||~ 47-limit (incomplete) ||
| |
| || [[47_46|47/46]] || 37.232 || 47/(2*23) || ||
| |
| || [[48_47|48/47]] || 36.448 || (2<span style="vertical-align: super;">4</span>*3)/47 || ||
| |
| || [[94_93|94/93]] || 18.516 || (2*47)/(3*31) || ||
| |
| || [[95_94|95/94]] || 18.320 || (5*19)/(2*47) || ||
| |
| ||||||||~ 53-limit (incomplete) ||
| |
| || [[53_52|53/52]] || 32.977 || 53/(2<span style="vertical-align: super;">2</span>*13) || ||
| |
| || [[54_53|54/53]] || 32.360 || (2*3<span style="vertical-align: super;">3</span>)/53 || ||
| |
| ||||||||~ 59-limit (incomplete) ||
| |
| || [[59_58|59/58]] || 29.594 || 59/(2*29) || ||
| |
| || [[60_59|60/59]] || 29.097 || (2<span style="vertical-align: super;">2</span>*3*5)/59 || ||
| |
| ||||||||~ 61-limit (incomplete) ||
| |
| || [[61_60|61/60]] || 28.616 || 61/(2<span style="vertical-align: super;">2</span>*3*5) || ||
| |
| || [[62_61|62/61]] || 28.151 || (2*31)/61 || ||
| |
| ||||||||~ 67-limit (incomplete) ||
| |
| || [[67_66|67/66]] || 26.034 || 67/(2*3*11) || ||
| |
| || [[68_67|68/67]] || 25.648 || (2<span style="vertical-align: super;">2</span>*17)/67 || ||
| |
| ||||||||~ 71-limit (incomplete) ||
| |
| || [[71_70|71/70]] || 24.557 || 71/(2*5*7) || ||
| |
| || [[72_71|72/71]] || 24.213 || (2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">2</span>)/71 || ||
| |
| ||||||||~ 73-limit (incomplete) ||
| |
| || [[73_72|73/72]] || 23.879 || 73/(2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">2</span>) || ||
| |
| || [[74_73|74/73]] || 23.555 || (2*37)/73 || ||
| |
| ||||||||~ 79-limit (incomplete) ||
| |
| || [[79_78|79/78]] || 22.054 || 79/(2*3*13) || ||
| |
| || [[80_79|80/79]] || 21.777 || (2<span style="vertical-align: super;">4</span>*5)/79 || ||
| |
| ||||||||~ 83-limit (incomplete) ||
| |
| || [[83_82|83/82]] || 20.985 || 83/(2*41) || ||
| |
| || [[84_83|84/83]] || 20.734 || (2<span style="vertical-align: super;">2</span>*3*7)/83 || ||
| |
| ||||||||~ 89-limit (incomplete) ||
| |
| || [[89_88|89/88]] || 19.562 || 89/(2<span style="vertical-align: super;">3</span>*11) || ||
| |
| || [[90_89|90/89]] || 19.344 || (2*3<span style="vertical-align: super;">2</span>*5)/89 || ||
| |
| ||||||||~ 97-limit (incomplete) ||
| |
| || [[97_96|97/96]] || 17.940 || 97/(2<span style="vertical-align: super;">5</span>*3) || ||
| |
| || [[98_97|98/97]] || 17.756 || (2*7<span style="vertical-align: super;">2</span>)/97 || ||
| |
| ||||||||~ 101-limit (incomplete) ||
| |
| || [[101_100|101/100]] || 17.226 || 101/(2<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">2</span>) || ||</pre></div>
| |
| <h4>Original HTML content:</h4>
| |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>List of Superparticular Intervals</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="List of Superparticular Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #800080;">List of Superparticular Intervals</span></h1>
| |
| <br />
| |
| <a class="wiki_link" href="/Superparticular">Superparticular</a> 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 <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a> and <a class="wiki_link" href="/OverToneSeries">Harmonic Series</a> music. Adjacent tones in the harmonic series are separated by superparticular intervals: for instance, the 20th and 21st by the superparticular ratio <a class="wiki_link" href="/21_20">21/20</a>. 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 <a class="wiki_link" href="/comma">comma</a>s are superparticular ratios.<br />
| |
| <br />
| |
| The list below is ordered by <a class="wiki_link" href="/harmonic%20limit">harmonic limit</a>, or the largest prime involved in the prime factorization. <a class="wiki_link" href="/36_35">36/35</a>, for instance, is an interval of the <a class="wiki_link" href="/7-limit">7-limit</a>, as it factors to (2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">2</span>)/(5*7), while 37/36 would belong to the 37-limit.<br />
| |
| <br />
| |
| <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem" rel="nofollow">Størmer's theorem</a> 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.<br />
| |
| <br />
| |
| See also: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a>. Many of the names below come from <a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/intervals.html" rel="nofollow">here</a>.<br />
| |
| <br />
| |
|
| |
|
| | === 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 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | === 13-limit === |
| <tr>
| | {| class="wikitable center-6" style="width:100%" |
| <th>Ratio<br />
| | ! width="10%" | [[Ratio]] |
| </th>
| | ! width="10%" | [[Cent]]s |
| <th>Cents Value<br />
| | ! width="15%" | Factorization |
| </th>
| | ! width="15%" | [[Monzo]] |
| <th>Factorization<br />
| | ! width="45%" | Name(s) |
| </th>
| | ! width="5%" | Meta<ref name="ssp"/> |
| <th>Name(s)<br />
| | |- |
| </th>
| | | [[13/12]] |
| </tr>
| | | 138.573 |
| <tr>
| | | 13/(2<sup>2</sup>×3) |
| <th colspan="4">2-limit<br />
| | | {{Monzo| -2 -1 0 0 0 1 }} |
| </th>
| | | Large tridecimal 2/3-tone, <br>tridecimal neutral second |
| </tr>
| | | |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/2_1">2/1</a><br />
| | | [[14/13]] |
| </td>
| | | 128.298 |
| <td>1200.000<br />
| | | (2×7)/13 |
| </td>
| | | {{Monzo| 1 0 0 1 0 -1 }} |
| <td>2/1<br />
| | | Small tridecimal 2/3-tone, trienthird |
| </td>
| | | |
| <td>(perfect) unison, unity, perfect prime, tonic, duple<br />
| | |- |
| </td>
| | | [[26/25]] |
| </tr>
| | | 67.900 |
| <tr>
| | | (2×13)/5<sup>2</sup> |
| <th colspan="4">3-limit<br />
| | | {{Monzo| 1 0 -2 0 0 1 }} |
| </th>
| | | Large tridecimal 1/3-tone |
| </tr>
| | | |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/3_2">3/2</a><br />
| | | [[27/26]] |
| </td>
| | | 65.337 |
| <td>701.995<br />
| | | 3<sup>3</sup>/(2×13) |
| </td>
| | | {{Monzo| -1 3 0 0 0 -1 }} |
| <td>3/2<br />
| | | Small tridecimal 1/3-tone |
| </td>
| | | |
| <td><a class="wiki_link" href="/perfect%20fifth">perfect fifth</a>, 3rd harmonic (octave reduced), diapente<br />
| | |- |
| </td>
| | | [[40/39]] |
| </tr>
| | | 43.831 |
| <tr>
| | | (2<sup>3</sup>×5)/(3×13) |
| <td><a class="wiki_link" href="/4_3">4/3</a><br />
| | | {{Monzo| 3 -1 1 0 0 -1 }} |
| </td>
| | | Tridecimal minor diesis |
| <td>498.045<br />
| | | |
| </td>
| | |- |
| <td>2<span style="vertical-align: super;">2</span>/3<br />
| | | [[65/64]] |
| </td>
| | | 26.841 |
| <td>perfect fourth, 3rd subharmonic (octave reduced), diatessaron<br />
| | | (5×13)/2<sup>6</sup> |
| </td>
| | | {{Monzo| -6 0 1 0 0 1 }} |
| </tr>
| | | Wilsorma, 13th-partial chroma |
| <tr>
| | | |
| <td><a class="wiki_link" href="/9_8">9/8</a><br />
| | |- |
| </td>
| | | [[66/65]] |
| <td>203.910<br />
| | | 26.432 |
| </td>
| | | (2×3×11)/(5×13) |
| <td>3<span style="vertical-align: super;">2</span>/2<span style="vertical-align: super;">3</span><br />
| | | {{Monzo| 1 1 -1 0 1 -1 }} |
| </td>
| | | Winmeanma |
| <td>(Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced)<br />
| | | |
| </td>
| | |- |
| </tr>
| | | [[78/77]] |
| <tr>
| | | 22.339 |
| <th colspan="4">5-limit<br />
| | | (2×3×13)/(7×11) |
| </th>
| | | {{Monzo| 1 1 0 -1 -1 1 }} |
| </tr>
| | | Negustma |
| <tr>
| | | |
| <td><a class="wiki_link" href="/5_4">5/4</a><br />
| | |- |
| </td>
| | | [[91/90]] |
| <td>386.314<br />
| | | 19.130 |
| </td>
| | | (7×13)/(2×3<sup>2</sup>×5) |
| <td>5/2<span style="vertical-align: super;">2</span><br />
| | | {{Monzo| -1 -2 -1 1 0 1 }} |
| </td>
| | | Biome comma, superleap comma |
| <td>(classic) (5-limit) major third, 5th harmonic (octave reduced)<br />
| | | |
| </td>
| | |- |
| </tr>
| | | [[105/104]] |
| <tr>
| | | 16.567 |
| <td><a class="wiki_link" href="/6_5">6/5</a><br />
| | | (3×5×7)/(2<sup>3</sup>×13) |
| </td>
| | | {{Monzo| -3 1 1 1 0 -1 }} |
| <td>315.641<br />
| | | Animist comma, small tridecimal comma |
| </td>
| | | |
| <td>(2*3)/5<br />
| | |- |
| </td>
| | | [[144/143]] |
| <td>(classic) (5-limit) minor third<br />
| | | 12.064 |
| </td>
| | | (2<sup>2</sup>×3)<sup>2</sup>/(11×13) |
| </tr>
| | | {{Monzo| 4 2 0 0 -1 -1 }} |
| <tr>
| | | Grossma |
| <td><a class="wiki_link" href="/10_9">10/9</a><br />
| | | S12 |
| </td>
| | |- |
| <td>182.404<br />
| | | [[169/168]] |
| </td>
| | | 10.274 |
| <td>(2*5)/3<span style="vertical-align: super;">2</span><br />
| | | 13<sup>2</sup>/(2<sup>3</sup>×3×7) |
| </td>
| | | {{Monzo| -3 -1 0 -1 0 2 }} |
| <td>classic (whole) tone, classic major second, minor whole tone<br />
| | | Buzurgisma, dhanvantarisma |
| </td>
| | | S13 |
| </tr>
| | |- |
| <tr>
| | | [[196/195]] |
| <td><a class="wiki_link" href="/16_15">16/15</a><br />
| | | 8.8554 |
| </td>
| | | (2×7)<sup>2</sup>/(3×5×13) |
| <td>111.713<br />
| | | {{Monzo| 2 -1 -1 2 0 -1 }} |
| </td>
| | | Mynucuma |
| <td>2<span style="vertical-align: super;">4</span>/(3*5)<br />
| | | S14 |
| </td>
| | |- |
| <td>minor diatonic semitone, 15th subharmonic<br />
| | | [[325/324]] |
| </td>
| | | 5.3351 |
| </tr>
| | | (5/(2×3<sup>2</sup>))<sup>2</sup>×13 |
| <tr>
| | | {{Monzo| -2 -4 2 0 0 1 }} |
| <td><a class="wiki_link" href="/25_24">25/24</a><br />
| | | Marveltwin comma |
| </td>
| | | |
| <td>70.672<br />
| | |- |
| </td>
| | | [[351/350]] |
| <td>5<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">3</span>*3)<br />
| | | 4.9393 |
| </td>
| | | (3<sup>3</sup>×13)/(2×5<sup>2</sup>×7) |
| <td>chroma, (classic) chromatic semitone, Zarlinian semitone<br />
| | | {{Monzo| -1 3 -2 -1 0 1 }} |
| </td>
| | | Ratwolfsma |
| </tr>
| | | |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/81_80">81/80</a><br />
| | | [[352/351]] |
| </td>
| | | 4.9253 |
| <td>21.506<br />
| | | (2<sup>5</sup>×11)/(3<sup>3</sup>×13) |
| </td>
| | | {{Monzo| 5 -3 0 0 1 -1 }} |
| <td><span style="line-height: 15.6000003814697px;">(</span>3<span style="line-height: 1.5;">/</span><span style="line-height: 15.6000003814697px;">2)</span><span style="line-height: 1.5; vertical-align: super;">4</span><span style="line-height: 15.6000003814697px;">/</span><span style="line-height: 1.5;">5</span><br />
| | | Major minthma, major gentle comma |
| </td>
| | | |
| <td>syntonic comma, Didymus comma<br />
| | |- |
| </td>
| | | [[364/363]] |
| </tr>
| | | 4.7627 |
| <tr>
| | | (2/11)<sup>2</sup>×((7×13)/3) |
| <th colspan="4">7-limit<br />
| | | {{Monzo| 2 -1 0 1 -2 1 }} |
| </th>
| | | Minor minthma, minor gentle comma |
| </tr>
| | | |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/7_6">7/6</a><br />
| | | [[625/624]] |
| </td>
| | | 2.7722 |
| <td>266.871<br />
| | | (5/2)<sup>4</sup>/(3×13) |
| </td>
| | | {{Monzo| -4 -1 4 0 0 -1 }} |
| <td>7/(2*3)<br />
| | | Tunbarsma |
| </td>
| | | S25 |
| <td>(septimal) subminor third, septimal minor third, augmented second<br />
| | |- |
| </td>
| | | [[676/675]] |
| </tr>
| | | 2.5629 |
| <tr>
| | | ((2×13)/5)<sup>2</sup>/3<sup>3</sup> |
| <td><a class="wiki_link" href="/8_7">8/7</a><br />
| | | {{Monzo| 2 -3 -2 0 0 2 }} |
| </td>
| | | Island comma |
| <td>231.174<br />
| | | S26 |
| </td>
| | |- |
| <td>2<span style="vertical-align: super;">3</span>/7<br />
| | | [[729/728]] |
| </td>
| | | 2.3764 |
| <td>(septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic<br />
| | | (3<sup>2</sup>/2)<sup>3</sup>/(7×13) |
| </td>
| | | {{Monzo| -3 6 0 -1 0 -1 }} |
| </tr>
| | | Squbema |
| <tr>
| | | S27 |
| <td><a class="wiki_link" href="/15_14">15/14</a><br />
| | |- |
| </td>
| | | [[1001/1000]] |
| <td>119.443<br />
| | | 1.7304 |
| </td>
| | | (7×11×13)/(2×5)<sup>3</sup> |
| <td>(3*5)/(2*7)<br />
| | | {{Monzo| -3 0 -3 1 1 1 }} |
| </td>
| | | Sinbadma |
| <td>septimal diatonic semitone<br />
| | | |
| </td>
| | |- |
| </tr>
| | | [[1716/1715]] |
| <tr>
| | | 1.0092 |
| <td><a class="wiki_link" href="/21_20">21/20</a><br />
| | | (2<sup>2</sup>×3×11×13)/(5×7<sup>3</sup>) |
| </td>
| | | {{Monzo| 2 1 -1 -3 1 1 }} |
| <td>84.467<br />
| | | Lummic comma |
| </td>
| | | |
| <td>(3*7)/(2<span style="vertical-align: super;">2</span>*5)<br />
| | |- |
| </td>
| | | [[2080/2079]] |
| <td>minor semitone, large septimal chromatic semitone<br />
| | | 0.83252 |
| </td>
| | | (2<sup>5</sup>×5×13)/(3<sup>3</sup>×7×11) |
| </tr>
| | | {{Monzo| 5 -3 1 -1 -1 1 }} |
| <tr>
| | | Ibnsinma |
| <td><a class="wiki_link" href="/28_27">28/27</a><br />
| | | |
| </td>
| | |- |
| <td>62.961<br />
| | | [[4096/4095]] |
| </td>
| | | 0.42272 |
| <td>(2<span style="vertical-align: super;">2</span>*7)/3<span style="vertical-align: super;">3</span><br />
| | | (2<sup>6</sup>/3)<sup>2</sup>/(5×7×13) |
| </td>
| | | {{Monzo| 12 -2 -1 -1 0 -1 }} |
| <td>septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone<br />
| | | Schismina, tridecimal schisma |
| </td>
| | | S64 |
| </tr>
| | |- |
| <tr>
| | | [[4225/4224]] |
| <td><a class="wiki_link" href="/36_35">36/35</a><br />
| | | 0.40981 |
| </td>
| | | (5×13)<sup>2</sup>/(2<sup>7</sup>×3×11) |
| <td>48.770<br />
| | | {{Monzo| -7 -1 2 0 -1 2 }} |
| </td>
| | | Leprechaun comma |
| <td>(2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">3</span>)/(5*7)<br />
| | | S65 |
| </td>
| | |- |
| <td>septimal quarter tone, septimal diesis<br />
| | | [[6656/6655]] |
| </td>
| | | 0.26012 |
| </tr>
| | | (2<sup>3</sup>/11)<sup>3</sup>×(13/5) |
| <tr>
| | | {{Monzo| 9 0 -1 0 -3 1 }} |
| <td><a class="wiki_link" href="/49_48">49/48</a><br />
| | | Jacobin comma |
| </td>
| | | |
| <td>35.697<br />
| | |- |
| </td>
| | | [[Harmonisma|10648/10647]] |
| <td>7<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">4</span>*3)<br />
| | | 0.16260 |
| </td>
| | | (2×11)<sup>3</sup>/((3×13)<sup>2</sup>×7) |
| <td>large septimal diesis, slendro diesis, septimal 1/6-tone<br />
| | | {{Monzo| 3 -2 0 -1 3 -2 }} |
| </td>
| | | Harmonisma |
| </tr>
| | | |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/50_49">50/49</a><br />
| | | [[Chalmersia|123201/123200]] |
| </td>
| | | 0.014052 |
| <td>34.976<br />
| | | (3/2)<sup>6</sup>×(13/5)<sup>2</sup>/(7×11) |
| </td>
| | | {{Monzo| -6 6 -2 -1 -1 2 }} |
| <td>2*(5<span style="line-height: 1.5;">/7)</span><span style="line-height: 1.5; vertical-align: super;">2</span><br />
| | | Chalmersia |
| </td>
| | | S351 |
| <td>septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma<br />
| | |} |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/64_63">64/63</a><br />
| |
| </td>
| |
| <td>27.264<br />
| |
| </td>
| |
| <td>2<span style="vertical-align: super;">6</span>/(3<span style="vertical-align: super;">2</span>*7)<br />
| |
| </td>
| |
| <td>septimal comma, Archytas' comma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/126_125">126/125</a><br />
| |
| </td>
| |
| <td>13.795<br />
| |
| </td>
| |
| <td>(2*3^2*7)/5^3<br />
| |
| </td>
| |
| <td>starling comma, septimal semicomma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/225_224">225/224</a><br />
| |
| </td>
| |
| <td>7.7115<br />
| |
| </td>
| |
| <td>(3*5)<span style="line-height: 1.5;">^2/(2^5*7)</span><br />
| |
| </td>
| |
| <td>marvel comma, septimal kleisma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/2401_2400">2401/2400</a><br />
| |
| </td>
| |
| <td>0.72120<br />
| |
| </td>
| |
| <td>7^4/(2^5*3*5^2)<br />
| |
| </td>
| |
| <td>breedsma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/4375_4374">4375/4374</a><br />
| |
| </td>
| |
| <td>0.39576<br />
| |
| </td>
| |
| <td>(5^4*7)/(2*3^7)<br />
| |
| </td>
| |
| <td>ragisma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">11-limit<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/11_10">11/10</a><br />
| |
| </td>
| |
| <td>165.004<br />
| |
| </td>
| |
| <td>11/(2*5)<br />
| |
| </td>
| |
| <td>(large) (undecimal) neutral second, 4/5-tone, Ptolemy's second<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/12_11">12/11</a><br />
| |
| </td>
| |
| <td>150.637<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">2</span>*3)/11<br />
| |
| </td>
| |
| <td>(small) (undecimal) neutral second, 3/4-tone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/22_21">22/21</a><br />
| |
| </td>
| |
| <td>80.537<br />
| |
| </td>
| |
| <td>(2*11)/(3*7)<br />
| |
| </td>
| |
| <td>undecimal minor semitone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/33_32">33/32</a><br />
| |
| </td>
| |
| <td>53.273<br />
| |
| </td>
| |
| <td>(3*11)/2<span style="vertical-align: super;">5</span><br />
| |
| </td>
| |
| <td>unidecimal quarter tone, unidecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/45_44">45/44</a><br />
| |
| </td>
| |
| <td>38.906<br />
| |
| </td>
| |
| <td>(3<span style="line-height: 15.6000003814697px;">/</span><span style="line-height: 1.5;">2)^</span><span style="line-height: 15.6000003814697px;">2*</span><span style="line-height: 1.5;">(</span><span style="line-height: 15.6000003814697px;">5/</span><span style="line-height: 1.5;">11)</span><br />
| |
| </td>
| |
| <td>1/5-tone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/55_54">55/54</a><br />
| |
| </td>
| |
| <td>31.767<br />
| |
| </td>
| |
| <td>(5*11)/(2*3<span style="vertical-align: super;">3</span>)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/56_55">56/55</a><br />
| |
| </td>
| |
| <td>31.194<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">3</span>*7)/(5*11)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/99_98">99/98</a><br />
| |
| </td>
| |
| <td>17.576<br />
| |
| </td>
| |
| <td>(3<span style="line-height: 1.5;">/7)</span><span style="line-height: 1.5; vertical-align: super;">2</span><span style="line-height: 1.5;">*(11/2)</span><br />
| |
| </td>
| |
| <td>small undecimal comma, mothwellsma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/100_99">100/99</a><br />
| |
| </td>
| |
| <td>17.399<br />
| |
| </td>
| |
| <td>(2<span style="line-height: 1.5;">*5/3)</span><span style="line-height: 1.5; vertical-align: super;">2</span><span style="line-height: 1.5;">/11)</span><br />
| |
| </td>
| |
| <td>Ptolemy's comma, ptolemisma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/121_120">121/120</a><br />
| |
| </td>
| |
| <td>14.376<br />
| |
| </td>
| |
| <td>11^2/(2^3*3*5)<br />
| |
| </td>
| |
| <td>undecimal seconds comma, biyatisma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/176_175">176/175</a><br />
| |
| </td>
| |
| <td>9.8646<br />
| |
| </td>
| |
| <td>(2^4*11)/(5^2*7)<br />
| |
| </td>
| |
| <td>valinorsma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/243_242">243/242</a><br />
| |
| </td>
| |
| <td>7.1391<br />
| |
| </td>
| |
| <td>3^5/(2*11^2)<br />
| |
| </td>
| |
| <td>neutral third comma, rastma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/385_384">385/384</a><br />
| |
| </td>
| |
| <td>4.5026<br />
| |
| </td>
| |
| <td>(5*7*11)/(2^7*3)<br />
| |
| </td>
| |
| <td>keenanisma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/441_440">441/440</a><br />
| |
| </td>
| |
| <td>3.9302<br />
| |
| </td>
| |
| <td>(3*7)^2/(2^3*5*11)<br />
| |
| </td>
| |
| <td>Werckmeister's undecimal septenarian schisma, werckisma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/540_539">540/539</a><br />
| |
| </td>
| |
| <td>3.2090<br />
| |
| </td>
| |
| <td>(2/7)^2*3^3*5/11<br />
| |
| </td>
| |
| <td>Swets' comma, swetisma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/3025_3024">3025/3024</a><br />
| |
| </td>
| |
| <td>0.57240<br />
| |
| </td>
| |
| <td>(5*11)^2/(2^4*3^3*7)<br />
| |
| </td>
| |
| <td>Lehmerisma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/9801_9800">9801/9800</a><br />
| |
| </td>
| |
| <td>0.17665<br />
| |
| </td>
| |
| <td><span style="line-height: 1.5;">[11/(5*7)]</span><span style="line-height: 15.6000003814697px;">^2*</span><span style="line-height: 1.5;">3^4/2^3</span><br />
| |
| </td>
| |
| <td>Gauss comma, kalisma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">13-limit<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/13_12">13/12</a><br />
| |
| </td>
| |
| <td>138.573<br />
| |
| </td>
| |
| <td>13/(2<span style="vertical-align: super;">2</span>*3)<br />
| |
| </td>
| |
| <td>tridecimal 2/3-tone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/14_13">14/13</a><br />
| |
| </td>
| |
| <td>128.298<br />
| |
| </td>
| |
| <td>(2*7)/13<br />
| |
| </td>
| |
| <td>2/3-tone, trienthird<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/26_25">26/25</a><br />
| |
| </td>
| |
| <td>67.900<br />
| |
| </td>
| |
| <td>(2*13)/5<span style="vertical-align: super;">2</span><br />
| |
| </td>
| |
| <td>tridecimal 1/3-tone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/27_26">27/26</a><br />
| |
| </td>
| |
| <td>65.337<br />
| |
| </td>
| |
| <td>3<span style="vertical-align: super;">3</span>/(2*13)<br />
| |
| </td>
| |
| <td>tridecimal comma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/40_39">40/39</a><br />
| |
| </td>
| |
| <td>43.831<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">3</span>*5)/(3*13)<br />
| |
| </td>
| |
| <td>tridecimal minor diesis<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/65_64">65/64</a><br />
| |
| </td>
| |
| <td>26.841<br />
| |
| </td>
| |
| <td>(5*13)/2<span style="vertical-align: super;">6</span><br />
| |
| </td>
| |
| <td>wilsorma, 13th-partial chroma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/66_65">66/65</a><br />
| |
| </td>
| |
| <td>26.432<br />
| |
| </td>
| |
| <td>(2*3*11)/(5*13)<br />
| |
| </td>
| |
| <td>winmeanma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/78_77">78/77</a><br />
| |
| </td>
| |
| <td>22.339<br />
| |
| </td>
| |
| <td>(2*3*13)/(7*11)<br />
| |
| </td>
| |
| <td>negustma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/91_90">91/90</a><br />
| |
| </td>
| |
| <td>19.130<br />
| |
| </td>
| |
| <td>(7*13)/(2*3<span style="vertical-align: super;">2</span>*5)<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/The%20Biosphere">Biome</a> comma, superleap comma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/105_104">105/104</a><br />
| |
| </td>
| |
| <td>16.567<br />
| |
| </td>
| |
| <td>(3*5*7)/(2^3*13)<br />
| |
| </td>
| |
| <td>small tridecimal comma, animist comma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/144_143">144/143</a><br />
| |
| </td>
| |
| <td>12.064<br />
| |
| </td>
| |
| <td>(<span style="line-height: 1.5;">2</span><span style="line-height: 1.5; vertical-align: super;">2</span><span style="line-height: 1.5;">*3)^2/(11*13)</span><br />
| |
| </td>
| |
| <td>grossma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/169_168">169/168</a><br />
| |
| </td>
| |
| <td>10.274<br />
| |
| </td>
| |
| <td>13<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">3</span>*3*7)<br />
| |
| </td>
| |
| <td>buzurgisma, dhanvantarisma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/196_195">196/195</a><br />
| |
| </td>
| |
| <td>8.8554<br />
| |
| </td>
| |
| <td>(2*7)^2/(3*5*13)<br />
| |
| </td>
| |
| <td>marveltwin comma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/351_350">351/350</a><br />
| |
| </td>
| |
| <td>4.9393<br />
| |
| </td>
| |
| <td>(3/5)^2*13/(2*7)<br />
| |
| </td>
| |
| <td>ratwolfsma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/352_351">352/351</a><br />
| |
| </td>
| |
| <td>4.9253<br />
| |
| </td>
| |
| <td>(<span style="line-height: 1.5;">2</span><span style="line-height: 1.5; vertical-align: super;">5</span><span style="line-height: 1.5;">*11)/(</span><span style="line-height: 15.6000003814697px;">3^</span>2<span style="line-height: 15.6000003814697px;">*13)</span><br />
| |
| </td>
| |
| <td>minthma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/364_363">364/363</a><br />
| |
| </td>
| |
| <td>4.7627<br />
| |
| </td>
| |
| <td>(2/11)^2*7*13/3<br />
| |
| </td>
| |
| <td>gentle comma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/625_624">625/624</a><br />
| |
| </td>
| |
| <td>2.7722<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>tunbarsma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/676_675">676/675</a><br />
| |
| </td>
| |
| <td>2.5629<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>island comma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/729_728">729/728</a><br />
| |
| </td>
| |
| <td>2.3764<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>squbema<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/1001_1000">1001/1000</a><br />
| |
| </td>
| |
| <td>1.7304<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>sinbadma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/1716_1715">1716/1715</a><br />
| |
| </td>
| |
| <td>1.0092<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>lummic comma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/2080_2079">2080/2079</a><br />
| |
| </td>
| |
| <td>0.83252<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>ibnsinma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/4096_4095">4096/4095</a><br />
| |
| </td>
| |
| <td>0.42272<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>tridecimal schisma, Sagittal schismina<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/4225_4224">4225/4224</a><br />
| |
| </td>
| |
| <td>0.40981<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>leprechaun comma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/6656_6655">6656/6655</a><br />
| |
| </td>
| |
| <td>0.26012<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>jacobin comma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/10648_10647">10648/10647</a><br />
| |
| </td>
| |
| <td>0.16260<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>harmonisma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/123201_123200">123201/123200</a><br />
| |
| </td>
| |
| <td>0.014052<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>chalmersia<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">17-limit (complete!)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/17_16">17/16</a><br />
| |
| </td>
| |
| <td>104.955<br />
| |
| </td>
| |
| <td>17/2<span style="vertical-align: super;">4</span><br />
| |
| </td>
| |
| <td>17th harmonic (octave reduced)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/18_17">18/17</a><br />
| |
| </td>
| |
| <td>98.955<br />
| |
| </td>
| |
| <td>(2*3<span style="vertical-align: super;">2</span>)/17<br />
| |
| </td>
| |
| <td>Arabic lute index finger<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/34_33">34/33</a><br />
| |
| </td>
| |
| <td>51.682<br />
| |
| </td>
| |
| <td>(2*17)/(3*11)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/35_34">35/34</a><br />
| |
| </td>
| |
| <td>50.184<br />
| |
| </td>
| |
| <td>(5*7)/(2*17)<br />
| |
| </td>
| |
| <td>septendecimal 1/4-tone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/51_50">51/50</a><br />
| |
| </td>
| |
| <td>34.283<br />
| |
| </td>
| |
| <td>(3*17)/(2*5<span style="vertical-align: super;">2</span>)<br />
| |
| </td>
| |
| <td>17th-partial chroma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/52_51">52/51</a><br />
| |
| </td>
| |
| <td>33.617<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">2</span>*13)/(3*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/85_84">85/84</a><br />
| |
| </td>
| |
| <td>20.488<br />
| |
| </td>
| |
| <td>(5*17)/(2<span style="vertical-align: super;">2</span>*3*7)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>120/119<br />
| |
| </td>
| |
| <td>14.487<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">3</span>*3*5)/(7*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>136/135<br />
| |
| </td>
| |
| <td>12.777<br />
| |
| </td>
| |
| <td>(2/<span style="line-height: 1.5;">3)</span><span style="line-height: 1.5; vertical-align: super;">3</span><span style="line-height: 1.5;">*17/5</span><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>154/153<br />
| |
| </td>
| |
| <td>11.278<br />
| |
| </td>
| |
| <td>(2*7*11)/(3<span style="vertical-align: super;">2</span>*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>170/169<br />
| |
| </td>
| |
| <td>10.214<br />
| |
| </td>
| |
| <td>(2*5*17)/13<span style="vertical-align: super;">2</span><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>221/220<br />
| |
| </td>
| |
| <td>7.8514<br />
| |
| </td>
| |
| <td>(13*17)/(2<span style="vertical-align: super;">2</span>*5*11)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>256/255<br />
| |
| </td>
| |
| <td>6.7759<br />
| |
| </td>
| |
| <td>(2^8)/(3*5*17)<br />
| |
| </td>
| |
| <td>255th subharmonic<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>273/272<br />
| |
| </td>
| |
| <td>6.3532<br />
| |
| </td>
| |
| <td>(3*7*13)/(2<span style="vertical-align: super;">4</span>*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>289/288<br />
| |
| </td>
| |
| <td>6.0008<br />
| |
| </td>
| |
| <td>(17<span style="line-height: 1.5;">/3)^</span><span style="line-height: 15.6000003814697px;">2</span><span style="line-height: 1.5;">/2</span><span style="line-height: 1.5; vertical-align: super;">5</span><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>375/374<br />
| |
| </td>
| |
| <td>4.6228<br />
| |
| </td>
| |
| <td>(3*5<span style="vertical-align: super;">3</span>)/(2*11*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>442/441<br />
| |
| </td>
| |
| <td>3.9213<br />
| |
| </td>
| |
| <td>(2*13*17)/(3*7)<span style="vertical-align: super;">2</span><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>561/560<br />
| |
| </td>
| |
| <td>3.0887<br />
| |
| </td>
| |
| <td>(3*11*17)/(2<span style="vertical-align: super;">4</span>*5*7)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>595/594<br />
| |
| </td>
| |
| <td>2.9121<br />
| |
| </td>
| |
| <td>(5*7*17)/(2*3<span style="vertical-align: super;">3</span>*11)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>715/714<br />
| |
| </td>
| |
| <td>2.4230<br />
| |
| </td>
| |
| <td>(5*11*13)/(2*3*7*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>833/832<br />
| |
| </td>
| |
| <td>2.0796<br />
| |
| </td>
| |
| <td>(7<span style="vertical-align: super;">2</span>*17)/(2<span style="vertical-align: super;">6</span>*13)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>936/935<br />
| |
| </td>
| |
| <td>1.8506<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">2</span>*13)/(5*11*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1089/1088<br />
| |
| </td>
| |
| <td>1.5905<br />
| |
| </td>
| |
| <td>(3<span style="vertical-align: super;">2</span>*11<span style="vertical-align: super;">2</span>)/(2<span style="vertical-align: super;">6</span>*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1156/1155<br />
| |
| </td>
| |
| <td>1.4983<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">2</span>*17<span style="vertical-align: super;">2</span>)/(3*5*7*11)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1225/1224<br />
| |
| </td>
| |
| <td>1.4138<br />
| |
| </td>
| |
| <td>(5<span style="vertical-align: super;">2</span>*7<span style="vertical-align: super;">2</span>)/(2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">2</span>*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1275/1274<br />
| |
| </td>
| |
| <td>1.3584<br />
| |
| </td>
| |
| <td>(3*5<span style="vertical-align: super;">2</span>*17)/(2*7<span style="vertical-align: super;">2</span>*13)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1701/1700<br />
| |
| </td>
| |
| <td>1.0181<br />
| |
| </td>
| |
| <td>(3<span style="vertical-align: super;">5</span>*7)/[(2*5)<span style="vertical-align: super;">2</span>*17]<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2058/2057<br />
| |
| </td>
| |
| <td>0.8414<br />
| |
| </td>
| |
| <td>(2*3*7<span style="vertical-align: super;">3</span>)/(11<span style="vertical-align: super;">2</span>*17)<br />
| |
| </td>
| |
| <td>xenisma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2431/2430<br />
| |
| </td>
| |
| <td>0.7123<br />
| |
| </td>
| |
| <td>(11*13*17)/(2*3<span style="vertical-align: super;">5</span>*5)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2500/2499<br />
| |
| </td>
| |
| <td>0.6926<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">4</span>)/(3*7<span style="vertical-align: super;">2</span>*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2601/2600<br />
| |
| </td>
| |
| <td>0.6657<br />
| |
| </td>
| |
| <td>(3<span style="vertical-align: super;">2</span>*17<span style="vertical-align: super;">2</span>)/(2<span style="vertical-align: super;">3</span>*5<span style="vertical-align: super;">2</span>*13)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4914/4913<br />
| |
| </td>
| |
| <td>0.3523<br />
| |
| </td>
| |
| <td>(2*3<span style="vertical-align: super;">3</span>*7*13)/(17<span style="vertical-align: super;">3</span>)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5832/5831<br />
| |
| </td>
| |
| <td>0.2969<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">6</span>)/(7<span style="vertical-align: super;">3</span>*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12376/12375<br />
| |
| </td>
| |
| <td>0.1399<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">3</span>*7*13*17)/(3<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">3</span>*11)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14400/14399<br />
| |
| </td>
| |
| <td>0.1202<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">6</span>*3<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">2</span>)/(7*11<span style="vertical-align: super;">2</span>*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>28561/28560<br />
| |
| </td>
| |
| <td>0.0606<br />
| |
| </td>
| |
| <td>(13<span style="vertical-align: super;">4</span>)/(2<span style="vertical-align: super;">4</span>*3*5*7*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31213/31212<br />
| |
| </td>
| |
| <td>0.0555<br />
| |
| </td>
| |
| <td>(7<span style="vertical-align: super;">4</span>*13)/(2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">3</span>*17<span style="vertical-align: super;">2</span>)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37180/37179<br />
| |
| </td>
| |
| <td>0.0466<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">2</span>*5*11*13<span style="vertical-align: super;">2</span>)/(3<span style="vertical-align: super;">7</span>*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>194481/194480<br />
| |
| </td>
| |
| <td>0.0089<br />
| |
| </td>
| |
| <td>(3<span style="vertical-align: super;">4</span>*7<span style="vertical-align: super;">4</span>)/(2<span style="vertical-align: super;">4</span>*5*11*13*17)<br />
| |
| </td>
| |
| <td>scintillisma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>336141/336140<br />
| |
| </td>
| |
| <td>0.0052<br />
| |
| </td>
| |
| <td>(3<span style="vertical-align: super;">2</span>*13<span style="vertical-align: super;">3</span>*17)/(2<span style="vertical-align: super;">2</span>*5*7<span style="vertical-align: super;">5</span>)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">19-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/19_18">19/18</a><br />
| |
| </td>
| |
| <td>93.603<br />
| |
| </td>
| |
| <td>19/(2*3<span style="vertical-align: super;">2</span>)<br />
| |
| </td>
| |
| <td>undevicesimal semitone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/20_19">20/19</a><br />
| |
| </td>
| |
| <td>88.801<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">2</span>*5)/19<br />
| |
| </td>
| |
| <td>small undevicesimal semitone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/39_38">39/38</a><br />
| |
| </td>
| |
| <td>44.970<br />
| |
| </td>
| |
| <td>(3*13)/(2*19)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/57_56">57/56</a><br />
| |
| </td>
| |
| <td>30.642<br />
| |
| </td>
| |
| <td>(3*19)/(2<span style="vertical-align: super;">3</span>*7)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/76_75">76/75</a><br />
| |
| </td>
| |
| <td>22.931<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">2</span>*19)/(3*5<span style="vertical-align: super;">2</span>)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/77_76">77/76</a><br />
| |
| </td>
| |
| <td>22.631<br />
| |
| </td>
| |
| <td>(7*11)/(2<span style="vertical-align: super;">2</span>*19)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/96_95">96/95</a><br />
| |
| </td>
| |
| <td>18.128<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">5</span>*3)/(5*19)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>133/132<br />
| |
| </td>
| |
| <td>13.066<br />
| |
| </td>
| |
| <td>(19*7)/(2<span style="vertical-align: super;">2</span>*3*11)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>153/152<br />
| |
| </td>
| |
| <td>11.352<br />
| |
| </td>
| |
| <td>(3<span style="vertical-align: super;">2</span>*17)/(2<span style="vertical-align: super;">3</span>*19)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>171/170<br />
| |
| </td>
| |
| <td>10.154<br />
| |
| </td>
| |
| <td>(3<span style="vertical-align: super;">2</span>*19)/(2*5*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>190/189<br />
| |
| </td>
| |
| <td>9.1358<br />
| |
| </td>
| |
| <td>(2*5*19)/(3<span style="vertical-align: super;">3</span>*7)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>209/208<br />
| |
| </td>
| |
| <td>8.3033<br />
| |
| </td>
| |
| <td>(11*19)/(2<span style="vertical-align: super;">4</span>*13)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>210/209<br />
| |
| </td>
| |
| <td>8.2637<br />
| |
| </td>
| |
| <td>(2*3*5*7)/(11*19)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>286/285<br />
| |
| </td>
| |
| <td>6.0639<br />
| |
| </td>
| |
| <td>(2*11*13)/(3*5*19)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>400/399<br />
| |
| </td>
| |
| <td>4.3335<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">4</span>*5<span style="vertical-align: super;">2</span>)/(3*7*19)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>456/455<br />
| |
| </td>
| |
| <td>3.8007<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">3</span>*3*19)/(5*7*13)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>476/475<br />
| |
| </td>
| |
| <td>3.6409<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">2</span>*7*17)/(5<span style="vertical-align: super;">2</span>*19)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>495/494<br />
| |
| </td>
| |
| <td>3.501<br />
| |
| </td>
| |
| <td>(3<span style="vertical-align: super;">2</span>*5*11)/(2*13*19)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>513/512<br />
| |
| </td>
| |
| <td>3.378<br />
| |
| </td>
| |
| <td><span style="vertical-align: super;">(3^3*19)/2^9</span><br />
| |
| </td>
| |
| <td>513th harmonic<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">23-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/23_22">23/22</a><br />
| |
| </td>
| |
| <td>76.956<br />
| |
| </td>
| |
| <td>23/(2*11)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/24_23">24/23</a><br />
| |
| </td>
| |
| <td>73.681<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">3</span>*3)/23<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/46_45">46/45</a><br />
| |
| </td>
| |
| <td>38.051<br />
| |
| </td>
| |
| <td>(2*23)/(3<span style="vertical-align: super;">2</span>*5)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/69_68">69/68</a><br />
| |
| </td>
| |
| <td>25.274<br />
| |
| </td>
| |
| <td>(3*23)/(2<span style="vertical-align: super;">2</span>*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/70_69">70/69</a><br />
| |
| </td>
| |
| <td>24.910<br />
| |
| </td>
| |
| <td>(2*5*7)/(3*23)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/92_91">92/91</a><br />
| |
| </td>
| |
| <td>18.921<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">2</span>*23)/(7*13)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>115/114<br />
| |
| </td>
| |
| <td>15.120<br />
| |
| </td>
| |
| <td>(5*23)/(2*3*19)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>161/160<br />
| |
| </td>
| |
| <td>10.7865<br />
| |
| </td>
| |
| <td>(7*23)/(2^5*5)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>162/161<br />
| |
| </td>
| |
| <td>10.720<br />
| |
| </td>
| |
| <td>(2*3^4)/(7*23)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>208/207<br />
| |
| </td>
| |
| <td>8.343<br />
| |
| </td>
| |
| <td>(16*13)/(23*9)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>576/575<br />
| |
| </td>
| |
| <td>3.008<br />
| |
| </td>
| |
| <td>(64*9)/(23*25)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">29-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/29_28">29/28</a><br />
| |
| </td>
| |
| <td>60.751<br />
| |
| </td>
| |
| <td>29/(2<span style="vertical-align: super;">2</span>*7)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/30_29">30/29</a><br />
| |
| </td>
| |
| <td>58.692<br />
| |
| </td>
| |
| <td>(2*3*5)/29<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/58_57">58/57</a><br />
| |
| </td>
| |
| <td>30.109<br />
| |
| </td>
| |
| <td>(2*29)/(3*19)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/88_87">88/87</a><br />
| |
| </td>
| |
| <td>19.786<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">3</span>*11)/(3*29)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">31-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/31_30">31/30</a><br />
| |
| </td>
| |
| <td>56.767<br />
| |
| </td>
| |
| <td>31/(2*3*5)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/32_31">32/31</a><br />
| |
| </td>
| |
| <td>54.964<br />
| |
| </td>
| |
| <td>2<span style="vertical-align: super;">5</span>/31<br />
| |
| </td>
| |
| <td>31st subharmonic<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/63_62">63/62</a><br />
| |
| </td>
| |
| <td>27.700<br />
| |
| </td>
| |
| <td>(3<span style="vertical-align: super;">2</span>*7)/(2*31)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/93_92">93/92</a><br />
| |
| </td>
| |
| <td>18.716<br />
| |
| </td>
| |
| <td>(3*31)/(2<span style="vertical-align: super;">2</span>*23)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">37-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/37_36">37/36</a><br />
| |
| </td>
| |
| <td>47.434<br />
| |
| </td>
| |
| <td>37/(2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">2</span>)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/38_37">38/37</a><br />
| |
| </td>
| |
| <td>46.169<br />
| |
| </td>
| |
| <td>(2*19)/37<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/75_74">75/74</a><br />
| |
| </td>
| |
| <td>23.238<br />
| |
| </td>
| |
| <td>(3*5<span style="vertical-align: super;">2</span>)/(2*37)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">41-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/41_40">41/40</a><br />
| |
| </td>
| |
| <td>42.749<br />
| |
| </td>
| |
| <td>41/(2<span style="vertical-align: super;">3</span>*5)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/42_41">42/41</a><br />
| |
| </td>
| |
| <td>41.719<br />
| |
| </td>
| |
| <td>(2*3*7)/41<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/82_81">82/81</a><br />
| |
| </td>
| |
| <td>21.242<br />
| |
| </td>
| |
| <td>(2*41)/3<span style="vertical-align: super;">4</span><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">43-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/43_42">43/42</a><br />
| |
| </td>
| |
| <td>40.737<br />
| |
| </td>
| |
| <td>43/(2*3*7)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/44_43">44/43</a><br />
| |
| </td>
| |
| <td>39.800<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">2</span>*11)/43<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/86_85">86/85</a><br />
| |
| </td>
| |
| <td>20.249<br />
| |
| </td>
| |
| <td>(2*43)/(5*17)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/87_86">87/86</a><br />
| |
| </td>
| |
| <td>20.014<br />
| |
| </td>
| |
| <td>(3*29)/(2*43)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">47-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/47_46">47/46</a><br />
| |
| </td>
| |
| <td>37.232<br />
| |
| </td>
| |
| <td>47/(2*23)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/48_47">48/47</a><br />
| |
| </td>
| |
| <td>36.448<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">4</span>*3)/47<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/94_93">94/93</a><br />
| |
| </td>
| |
| <td>18.516<br />
| |
| </td>
| |
| <td>(2*47)/(3*31)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/95_94">95/94</a><br />
| |
| </td>
| |
| <td>18.320<br />
| |
| </td>
| |
| <td>(5*19)/(2*47)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">53-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/53_52">53/52</a><br />
| |
| </td>
| |
| <td>32.977<br />
| |
| </td>
| |
| <td>53/(2<span style="vertical-align: super;">2</span>*13)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/54_53">54/53</a><br />
| |
| </td>
| |
| <td>32.360<br />
| |
| </td>
| |
| <td>(2*3<span style="vertical-align: super;">3</span>)/53<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">59-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/59_58">59/58</a><br />
| |
| </td>
| |
| <td>29.594<br />
| |
| </td>
| |
| <td>59/(2*29)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/60_59">60/59</a><br />
| |
| </td>
| |
| <td>29.097<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">2</span>*3*5)/59<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">61-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/61_60">61/60</a><br />
| |
| </td>
| |
| <td>28.616<br />
| |
| </td>
| |
| <td>61/(2<span style="vertical-align: super;">2</span>*3*5)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/62_61">62/61</a><br />
| |
| </td>
| |
| <td>28.151<br />
| |
| </td>
| |
| <td>(2*31)/61<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">67-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/67_66">67/66</a><br />
| |
| </td>
| |
| <td>26.034<br />
| |
| </td>
| |
| <td>67/(2*3*11)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/68_67">68/67</a><br />
| |
| </td>
| |
| <td>25.648<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">2</span>*17)/67<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">71-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/71_70">71/70</a><br />
| |
| </td>
| |
| <td>24.557<br />
| |
| </td>
| |
| <td>71/(2*5*7)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/72_71">72/71</a><br />
| |
| </td>
| |
| <td>24.213<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">2</span>)/71<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">73-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/73_72">73/72</a><br />
| |
| </td>
| |
| <td>23.879<br />
| |
| </td>
| |
| <td>73/(2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">2</span>)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/74_73">74/73</a><br />
| |
| </td>
| |
| <td>23.555<br />
| |
| </td>
| |
| <td>(2*37)/73<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">79-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/79_78">79/78</a><br />
| |
| </td>
| |
| <td>22.054<br />
| |
| </td>
| |
| <td>79/(2*3*13)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/80_79">80/79</a><br />
| |
| </td>
| |
| <td>21.777<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">4</span>*5)/79<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">83-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/83_82">83/82</a><br />
| |
| </td>
| |
| <td>20.985<br />
| |
| </td>
| |
| <td>83/(2*41)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/84_83">84/83</a><br />
| |
| </td>
| |
| <td>20.734<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">2</span>*3*7)/83<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">89-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/89_88">89/88</a><br />
| |
| </td>
| |
| <td>19.562<br />
| |
| </td>
| |
| <td>89/(2<span style="vertical-align: super;">3</span>*11)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/90_89">90/89</a><br />
| |
| </td>
| |
| <td>19.344<br />
| |
| </td>
| |
| <td>(2*3<span style="vertical-align: super;">2</span>*5)/89<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">97-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/97_96">97/96</a><br />
| |
| </td>
| |
| <td>17.940<br />
| |
| </td>
| |
| <td>97/(2<span style="vertical-align: super;">5</span>*3)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/98_97">98/97</a><br />
| |
| </td>
| |
| <td>17.756<br />
| |
| </td>
| |
| <td>(2*7<span style="vertical-align: super;">2</span>)/97<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">101-limit (incomplete)<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/101_100">101/100</a><br />
| |
| </td>
| |
| <td>17.226<br />
| |
| </td>
| |
| <td>101/(2<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">2</span>)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | === 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 |
| | | |
| | |} |
| | |
| | === 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 |
| | | |
| | |- |
| | | [[20/19]] |
| | | 88.801 |
| | | (2<sup>2</sup>×5)/19 |
| | | {{Monzo| 2 0 1 0 0 0 0 -1 }} |
| | | Small undevicesimal semitone |
| | | |
| | |- |
| | | [[39/38]] |
| | | 44.970 |
| | | (3×13)/(2×19) |
| | | {{Monzo| -1 1 0 0 0 1 0 -1 }} |
| | | Undevicesimal diesis, <br>undevicesimal 2/9-tone |
| | | |
| | |- |
| | | [[57/56]] |
| | | 30.642 |
| | | (3×19)/(2<sup>3</sup>×7) |
| | | {{Monzo| -3 1 0 -1 0 0 0 1 }} |
| | | Hendrix comma |
| | | |
| | |- |
| | | [[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 |
| | | |
| | |- |
| | | [[77/76]] |
| | | 22.631 |
| | | (7×11)/(2<sup>2</sup>×19) |
| | | {{Monzo| -2 0 0 1 1 0 0 -1 }} |
| | | Small undevicesimal 1/9-tone |
| | | |
| | |- |
| | | [[96/95]] |
| | | 18.128 |
| | | (2<sup>5</sup>×3)/(5×19) |
| | | {{Monzo| 5 1 -1 0 0 0 0 -1 }} |
| | | 19th-partial chroma |
| | | |
| | |- |
| | | [[133/132]] |
| | | 13.066 |
| | | (7×19)/(2<sup>2</sup>×3×11) |
| | | {{Monzo| -2 -1 0 1 -1 0 0 1 }} |
| | | Minithirdma |
| | | |
| | |- |
| | | [[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 |
| | | |
| | |- |
| | | [[171/170]] |
| | | 10.154 |
| | | (3<sup>2</sup>×19)/(2×5×17) |
| | | {{Monzo| -1 2 -1 0 0 0 -1 1 }} |
| | | Malcolmisma |
| | | |
| | |- |
| | | [[190/189]] |
| | | 9.1358 |
| | | (2×5×19)/(3<sup>3</sup>×7) |
| | | {{Monzo| 1 -3 1 -1 0 0 0 1 }} |
| | | Cotylisma |
| | | |
| | |- |
| | | [[209/208]] |
| | | 8.3033 |
| | | (11×19)/(2<sup>4</sup>×13) |
| | | {{Monzo| -4 0 0 0 1 -1 0 1 }} |
| | | Yama comma |
| | | |
| | |- |
| | | [[210/209]] |
| | | 8.2637 |
| | | (2×3×5×7)/(11×19) |
| | | {{Monzo| 1 1 1 1 -1 0 0 -1 }} |
| | | Spleen comma |
| | | |
| | |- |
| | | [[286/285]] |
| | | 6.0639 |
| | | (2×11×13)/(3×5×19) |
| | | {{Monzo| 1 -1 -1 0 1 1 0 -1 }} |
| | | Chthonisma |
| | | |
| | |- |
| | | [[324/323]] |
| | | 5.3516 |
| | | (2×3<sup>2</sup>)<sup>2</sup>/(17×19) |
| | | {{Monzo| 2 4 0 0 0 0 -1 -1 }} |
| | | Photisma |
| | | S18 |
| | |- |
| | | [[343/342]] |
| | | 5.0547 |
| | | 7<sup>3</sup>/(2×3<sup>2</sup>×19) |
| | | {{Monzo| -1 -2 0 3 0 0 0 -1 }} |
| | | Nutrisma |
| | | |
| | |- |
| | | [[361/360]] |
| | | 4.8023 |
| | | 19<sup>2</sup>/(2<sup>3</sup>×3<sup>2</sup>×5) |
| | | {{Monzo| -3 -2 -1 0 0 0 0 2 }} |
| | | Go comma, Dudon comma |
| | | S19 |
| | |- |
| | | [[400/399]] |
| | | 4.3335 |
| | | (2<sup>2</sup>×5)<sup>2</sup>/(3×7×19) |
| | | {{Monzo| 4 -1 2 -1 0 0 0 -1 }} |
| | | Devichroma |
| | | S20 |
| | |- |
| | | [[456/455]] |
| | | 3.8007 |
| | | (2<sup>3</sup>×3×19)/(5×7×13) |
| | | {{Monzo| 3 1 -1 -1 0 -1 0 1 }} |
| | | Abnobisma |
| | | |
| | |- |
| | | [[476/475]] |
| | | 3.6409 |
| | | (2<sup>2</sup>×7×17)/(5<sup>2</sup>×19) |
| | | {{Monzo| 2 0 -2 1 0 0 1 -1 }} |
| | | Hedwigma |
| | | |
| | |- |
| | | [[495/494]] |
| | | 3.5010 |
| | | (3<sup>2</sup>×5×11)/(2×13×19) |
| | | {{Monzo| -1 2 1 0 1 -1 0 -1 }} |
| | | Eulalisma |
| | | |
| | |- |
| | | [[513/512]] |
| | | 3.3780 |
| | | (3<sup>3</sup>×19)/2<sup>9</sup> |
| | | {{Monzo| -9 3 0 0 0 0 0 1 }} |
| | | Undevicesimal comma, undevicesimal schisma, <br>Boethius' comma, 513th harmonic |
| | | |
| | |- |
| | | [[969/968]] |
| | | 1.7875 |
| | | (3×17×19)/(2<sup>3</sup>×11<sup>2</sup>) |
| | | {{Monzo| -3 1 0 0 -2 0 1 1 }} |
| | | Kingfisher comma |
| | | |
| | |- |
| | | [[1216/1215]] |
| | | 1.4243 |
| | | (2<sup>6</sup>×19)/(3<sup>5</sup>×5) |
| | | {{Monzo| 6 -5 -1 0 0 0 0 1 }} |
| | | Password comma, Eratosthenes' comma |
| | | |
| | |- |
| | | [[1331/1330]] |
| | | 1.3012 |
| | | 11<sup>3</sup>/(2×5×7×19) |
| | | {{Monzo| -1 0 -1 -1 3 0 0 -1 }} |
| | | Solvejgsma |
| | | |
| | |- |
| | | [[1445/1444]] |
| | | 1.1985 |
| | | 5×(17/(2×19))<sup>2</sup> |
| | | {{Monzo| -2 0 1 0 0 0 2 -2 }} |
| | | Aureusma |
| | | |
| | |- |
| | | [[1521/1520]] |
| | | 1.1386 |
| | | (3×13)<sup>2</sup>/(2<sup>4</sup>×5×19) |
| | | {{Monzo| -4 2 -1 0 0 2 0 -1 }} |
| | | Pinkanberry |
| | | S39 |
| | |- |
| | | [[1540/1539]] |
| | | 1.1245 |
| | | (2<sup>2</sup>×5×7×11)/(3<sup>4</sup>×19) |
| | | {{Monzo| 2 -4 1 1 1 0 0 -1 }} |
| | | Kevolisma |
| | | |
| | |- |
| | | [[1729/1728]] |
| | | 1.0016 |
| | | (7×13×19)/(2<sup>2</sup>×3)<sup>3</sup> |
| | | {{Monzo| -6 -3 0 1 0 1 0 1 }} |
| | | Ramanujanisma |
| | | |
| | |- |
| | | [[2376/2375]] |
| | | 0.72879 |
| | | ((2×3)/5)<sup>3</sup>×(11/19) |
| | | {{Monzo| 3 3 -3 0 1 0 0 -1 }} |
| | | Trichthonisma |
| | | |
| | |- |
| | | [[2432/2431]] |
| | | 0.71200 |
| | | (2<sup>7</sup>×19)/(11×13×17) |
| | | {{Monzo| 7 0 0 0 -1 -1 -1 1 }} |
| | | Blumeyer comma |
| | | |
| | |- |
| | | [[2926/2925]] |
| | | 0.59177 |
| | | (2×7×11×19)/((3×5)<sup>2</sup>×13) |
| | | {{Monzo| 1 -2 -2 1 1 -1 0 1 }} |
| | | Neovulture comma, neovulturisma |
| | | |
| | |- |
| | | [[3136/3135]] |
| | | 0.55214 |
| | | (2<sup>3</sup>×7)<sup>2</sup>/(3×5×11×19) |
| | | {{Monzo| 6 -1 -1 2 -1 0 0 -1 }} |
| | | Neomirkwai comma, neomirkwaisma |
| | | S56 |
| | |- |
| | | [[3250/3249]] |
| | | 0.53277 |
| | | (2×5<sup>3</sup>×13)/(3×19)<sup>2</sup> |
| | | {{Monzo| 1 -2 3 0 0 1 0 -2 }} |
| | | Martebisma |
| | | |
| | |- |
| | | [[4200/4199]] |
| | | 0.41225 |
| | | (2<sup>3</sup>×3×5<sup>2</sup>×7)/(13×17×19) |
| | | {{Monzo| 3 1 2 1 0 -1 -1 -1 }} |
| | | Neosatanisma |
| | | |
| | |- |
| | | [[5776/5775]] |
| | | 0.29975 |
| | | (2<sup>2</sup>×19)<sup>2</sup>/(3×5<sup>2</sup>×7×11) |
| | | {{Monzo| 4 -1 -2 -1 -1 0 0 2 }} |
| | | Neovish comma, neovishma |
| | | S76 |
| | |- |
| | | [[5929/5928]] |
| | | 0.29202 |
| | | (7×11)<sup>2</sup>/(2<sup>3</sup>×3×13×19) |
| | | {{Monzo| -3 -1 0 2 2 -1 0 -1 }} |
| | | Manzanisma |
| | | S77 |
| | |- |
| | | [[5985/5984]] |
| | | 0.28929 |
| | | (3<sup>2</sup>×5×7×19)/(2<sup>5</sup>×11×17) |
| | | {{Monzo| -5 2 1 1 -1 0 -1 1 }} |
| | | Neogrendel comma, neogrendelisma |
| | | |
| | |- |
| | | [[6175/6174]] |
| | | 0.28038 |
| | | (5<sup>2</sup>×13×19)/(2×3<sup>2</sup>×7<sup>3</sup>) |
| | | {{Monzo| -1 -2 2 -3 0 1 0 1 }} |
| | | Neonewtisma |
| | | |
| | |- |
| | | [[6860/6859]] |
| | | 0.25238 |
| | | (2<sup>2</sup>×5×7<sup>3</sup>)/19<sup>3</sup> |
| | | {{Monzo| 2 0 1 3 0 0 0 -3 }} |
| | | Devicubisma |
| | | |
| | |- |
| | | 10241/10240 |
| | | 0.16906 |
| | | (7<sup>2</sup>×11×19)/(2<sup>11</sup>×5) |
| | | {{Monzo| -11 0 -1 2 1 0 0 1 }} |
| | | |
| | | |
| | |- |
| | | 10830/10829 |
| | | 0.15986 |
| | | (2×3×5×19<sup>2</sup>)/(7<sup>2</sup>×13×17) |
| | | {{Monzo| 1 1 1 -2 0 -1 -1 2 }} |
| | | |
| | | |
| | |- |
| | | [[12636/12635]] |
| | | 0.13701 |
| | | (2<sup>2</sup>×3<sup>5</sup>×13)/(5×7×19<sup>2</sup>) |
| | | {{Monzo| 2 5 -1 -1 0 1 0 -2 }} |
| | | Padriellisma |
| | | |
| | |- |
| | | 13377/13376 |
| | | 0.12942 |
| | | (3×7<sup>3</sup>×13)/(2<sup>6</sup>×11×19) |
| | | {{Monzo| -6 1 0 3 -1 1 0 -1 }} |
| | | |
| | | |
| | |- |
| | | 14080/14079 |
| | | 0.12296 |
| | | (2<sup>8</sup>×5×11)/(3×13×19<sup>2</sup>) |
| | | {{Monzo| 8 -1 1 0 1 -1 0 -2 }} |
| | | |
| | | |
| | |- |
| | | 14365/14364 |
| | | 0.12052 |
| | | (5×13<sup>2</sup>×17)/(2<sup>2</sup>×3<sup>3</sup>×7×19) |
| | | {{Monzo| -2 -3 1 -1 0 2 1 -1 }} |
| | | |
| | | |
| | |- |
| | | 23409/23408 |
| | | 0.073957 |
| | | ((3/2)<sup>2</sup>×17)<sup>2</sup>/(7×11×19) |
| | | {{Monzo| -4 4 0 -1 -1 0 2 -1 }} |
| | | |
| | | S153 |
| | |- |
| | | 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 }} |
| | | |
| | | |
| | |- |
| | | 28900/28899 |
| | | 0.059905 |
| | | ((2×5×17)/(3×13))<sup>2</sup>/19 |
| | | {{Monzo| 2 -2 2 0 0 -2 2 -1 }} |
| | | |
| | | S170 |
| | |- |
| | | 43681/43680 |
| | | 0.039634 |
| | | (11×19)<sup>2</sup>/(2<sup>5</sup>×3×5×7×13) |
| | | {{Monzo| -5 -1 -1 -1 2 -1 0 2 }} |
| | | |
| | | S209 |
| | |- |
| | | 89376/89375 |
| | | 0.019370 |
| | | (2<sup>5</sup>×3×7<sup>2</sup>×19)/(5<sup>4</sup>×11×13) |
| | | {{Monzo| 5 1 -4 2 -1 -1 0 1 }} |
| | | |
| | | |
| | |- |
| | | 104976/104975 |
| | | 0.016492 |
| | | (2×3<sup>2</sup>)<sup>4</sup>/(5<sup>2</sup>×13×17×19) |
| | | {{Monzo| 4 8 -2 0 0 -1 -1 -1 }} |
| | | |
| | | S324 |
| | |- |
| | | [[Decimillisma|165376/165375]] |
| | | 0.010469 |
| | | (2<sup>9</sup>×17×19)/((3×5)<sup>3</sup>×7<sup>2</sup>) |
| | | {{Monzo| 9 -3 -3 -2 0 0 1 1 }} |
| | | Decimillisma |
| | | |
| | |- |
| | | 228096/228095 |
| | | 0.0075900 |
| | | ((2<sup>2</sup>×3)/7)<sup>4</sup>×(11/(5×19)) |
| | | {{Monzo| 8 4 -1 -4 1 0 0 -1 }} |
| | | |
| | | |
| | |- |
| | | 601426/601425 |
| | | 0.0028786 |
| | | (2×7<sup>2</sup>×17×19<sup>2</sup>)/(3<sup>7</sup>×5<sup>2</sup>×11) |
| | | {{Monzo| 1 -7 -2 2 -1 0 1 2 }} |
| | | |
| | | |
| | |- |
| | | [[Devicisma|633556/633555]] |
| | | 0.0027326 |
| | | (2<sup>2</sup>×7×11<sup>3</sup>×17)/(3<sup>3</sup>×5×13×19<sup>2</sup>) |
| | | {{Monzo| 2 -3 -1 1 3 -1 1 -2 }} |
| | | Devicisma |
| | | |
| | |- |
| | | 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"/> |
| | |- |
| | | [[23/22]] |
| | | 76.956 |
| | | 23/(2×11) |
| | | {{Monzo| -1 0 0 0 -1 0 0 0 1 }} |
| | | Large vicesimotertial semitone |
| | | |
| | |- |
| | | [[24/23]] |
| | | 73.681 |
| | | (2<sup>3</sup>×3)/23 |
| | | {{Monzo| 3 1 0 0 0 0 0 0 -1 }} |
| | | Small vicesimotertial semitone |
| | | |
| | |- |
| | | [[46/45]] |
| | | 38.051 |
| | | (2×23)/(3<sup>2</sup>×5) |
| | | {{Monzo| 1 -2 -1 0 0 0 0 0 1 }} |
| | | Vicesimotertial 1/5-tone |
| | | |
| | |- |
| | | [[69/68]] |
| | | 25.274 |
| | | (3×23)/(2<sup>2</sup>×17) |
| | | {{Monzo| -2 1 0 0 0 0 -1 0 1 }} |
| | | Large vicesimotertial 1/8-tone |
| | | |
| | |- |
| | | [[70/69]] |
| | | 24.910 |
| | | (2×5×7)/(3×23) |
| | | {{Monzo| 1 -1 1 1 0 0 0 0 -1 }} |
| | | Small vicesimotertial 1/8-tone |
| | | |
| | |- |
| | | [[92/91]] |
| | | 18.921 |
| | | (2<sup>2</sup>×23)/(7×13) |
| | | {{Monzo| 2 0 0 -1 0 -1 0 0 1 }} |
| | | Undinisma |
| | | |
| | |- |
| | | [[115/114]] |
| | | 15.120 |
| | | (5×23)/(2×3×19) |
| | | {{Monzo| -1 -1 1 0 0 0 0 -1 1 }} |
| | | Yarmanisma |
| | | |
| | |- |
| | | [[161/160]] |
| | | 10.787 |
| | | (7×23)/(2<sup>5</sup>×5) |
| | | {{Monzo| -5 0 -1 1 0 0 0 0 1 }} |
| | | Major kirnbergerisma |
| | | |
| | |- |
| | | [[162/161]] |
| | | 10.720 |
| | | (2×3<sup>4</sup>)/(7×23) |
| | | {{Monzo| 1 4 0 -1 0 0 0 0 -1 }} |
| | | Minor kirnbergerisma |
| | | |
| | |- |
| | | [[208/207]] |
| | | 8.3433 |
| | | (2<sup>4</sup>×13)/(3<sup>2</sup>×23) |
| | | {{Monzo| 4 -2 0 0 0 1 0 0 -1 }} |
| | | Vicetone comma |
| | | |
| | |- |
| | | [[231/230]] |
| | | 7.5108 |
| | | (3×7×11)/(2×5×23) |
| | | {{Monzo| -1 1 -1 1 1 0 0 0 -1 }} |
| | | Major neutravicema |
| | | |
| | |- |
| | | [[253/252]] |
| | | 6.8564 |
| | | (11×23)/((2×3)<sup>2</sup>×7) |
| | | {{Monzo| -2 -2 0 -1 1 0 0 0 1 }} |
| | | Middle neutravicema |
| | | |
| | |- |
| | | [[276/275]] |
| | | 6.2840 |
| | | (2<sup>2</sup>×3×23)/(5<sup>2</sup>×11) |
| | | {{Monzo| 2 1 -2 0 -1 0 0 0 1 }} |
| | | Minor neutravicema |
| | | |
| | |- |
| | | [[300/299]] |
| | | 5.7804 |
| | | ((2×5)<sup>2</sup>×3)/(13×23) |
| | | {{Monzo| 2 1 2 0 0 -1 0 0 -1 }} |
| | | Major naiadvicema |
| | | |
| | |- |
| | | [[323/322]] |
| | | 5.3682 |
| | | (17×19)/(2×7×23) |
| | | {{Monzo| -1 0 0 -1 0 0 1 1 -1 }} |
| | | Major semivicema |
| | | |
| | |- |
| | | [[391/390]] |
| | | 4.4334 |
| | | (17×23)/(2×3×5×13) |
| | | {{Monzo| -1 -1 -1 0 0 -1 1 0 1 }} |
| | | Minor naiadvicema |
| | | |
| | |- |
| | | [[392/391]] |
| | | 4.4221 |
| | | (2<sup>3</sup>×7<sup>2</sup>)/(17×23) |
| | | {{Monzo| 3 0 0 2 0 0 -1 0 -1 }} |
| | | Minor semivicema |
| | | |
| | |- |
| | | [[460/459]] |
| | | 3.7676 |
| | | (2<sup>2</sup>×5×23)/(3<sup>3</sup>×17) |
| | | {{Monzo| 2 -3 1 0 0 0 -1 0 1 }} |
| | | Scanisma, vicewolf comma |
| | | |
| | |- |
| | | [[484/483]] |
| | | 3.5806 |
| | | (2×11)<sup>2</sup>/(3×7×23) |
| | | {{Monzo| 2 -1 0 -1 2 0 0 0 -1 }} |
| | | Pittsburghisma |
| | | S22 |
| | |- |
| | | [[507/506]] |
| | | 3.4180 |
| | | (3×13<sup>2</sup>)/(2×11×23) |
| | | {{Monzo| -1 1 0 0 -1 2 0 0 -1 }} |
| | | Laodicisma |
| | | |
| | |- |
| | | [[529/528]] |
| | | 3.2758 |
| | | 23<sup>2</sup>/(2<sup>4</sup>×3×11) |
| | | {{Monzo| -4 -1 0 0 -1 0 0 0 2 }} |
| | | Preziosisma |
| | | S23 |
| | |- |
| | | [[576/575]] |
| | | 3.0082 |
| | | ((2<sup>3</sup>×3)/5)<sup>2</sup>/23 |
| | | {{Monzo| 6 2 -2 0 0 0 0 0 -1 }} |
| | | Worcester comma |
| | | S24 |
| | |- |
| | | [[736/735]] |
| | | 2.3538 |
| | | (2<sup>5</sup>×23)/(3×5×7<sup>2</sup>) |
| | | {{Monzo| 5 -1 -1 -2 0 0 0 0 1 }} |
| | | Harvardisma |
| | | |
| | |- |
| | | [[760/759]] |
| | | 2.2794 |
| | | (2<sup>3</sup>×5×19)/(3×11×23) |
| | | {{Monzo| 3 -1 1 0 -1 0 0 1 -1 }} |
| | | Squadronisma |
| | | |
| | |- |
| | | [[875/874]] |
| | | 1.9797 |
| | | (5<sup>3</sup>×7)/(2×19×23) |
| | | {{Monzo| -1 0 3 1 0 0 0 -1 -1 }} |
| | | Nymphisma |
| | | |
| | |- |
| | | [[897/896]] |
| | | 1.9311 |
| | | (3×13×23)/(2<sup>7</sup>×7) |
| | | {{Monzo| -7 1 0 -1 0 1 0 0 1 }} |
| | | Lysistratisma |
| | | |
| | |- |
| | | [[1105/1104]] |
| | | 1.5674 |
| | | (5×13×17)/(2<sup>4</sup>×3×23) |
| | | {{Monzo| -4 -1 1 0 0 1 1 0 -1 }} |
| | | Fragarisma |
| | | |
| | |- |
| | | [[1197/1196]] |
| | | 1.4469 |
| | | (3<sup>2</sup>×7×19)/(2<sup>2</sup>×13×23) |
| | | {{Monzo| -2 2 0 1 0 -1 0 1 -1 }} |
| | | Rodessisma |
| | | |
| | |- |
| | | [[1288/1287]] |
| | | 1.3446 |
| | | (2<sup>3</sup>×7×23)/(3<sup>2</sup>×11×13) |
| | | {{Monzo| 3 -2 0 1 -1 -1 0 0 1 }} |
| | | Santisma, triaphonisma |
| | | |
| | |- |
| | | [[1496/1495]] |
| | | 1.1576 |
| | | (2<sup>3</sup>×11×17)/(5×13×23) |
| | | {{Monzo| 3 0 -1 0 1 -1 1 0 -1 }} |
| | | Turkisma |
| | | |
| | |- |
| | | [[1863/1862]] |
| | | 0.92952 |
| | | (3<sup>4</sup>×23)/(2×7<sup>2</sup>×19) |
| | | {{Monzo| -1 4 0 -2 0 0 0 -1 1 }} |
| | | Antinousisma |
| | | |
| | |- |
| | | [[2024/2023]] |
| | | 0.85556 |
| | | (2<sup>3</sup>×11×23)/(7×17<sup>2</sup>) |
| | | {{Monzo| 3 0 0 -1 1 0 -2 0 1 }} |
| | | Artifisma, insincere comma |
| | | |
| | |- |
| | | [[2025/2024]] |
| | | 0.85514 |
| | | (3<sup>2</sup>×5)<sup>2</sup>/(2<sup>3</sup>×11×23) |
| | | {{Monzo| -3 4 2 0 -1 0 0 0 -1 }} |
| | | Cupcake comma, cupcakesma |
| | | S45 |
| | |- |
| | | [[2185/2184]] |
| | | 0.79251 |
| | | (5×19×23)/(2<sup>3</sup>×3×7×13) |
| | | {{Monzo| -3 -1 1 -1 0 -1 0 1 1 }} |
| | | Guangdongisma |
| | | |
| | |- |
| | | [[2300/2299]] |
| | | 0.75287 |
| | | ((2×5)/11)<sup>2</sup>×(23/19) |
| | | {{Monzo| 2 0 2 0 -2 0 0 -1 1 }} |
| | | Travellisma |
| | | |
| | |- |
| | | [[2646/2645]] |
| | | 0.65441 |
| | | (2×3<sup>3</sup>×7<sup>2</sup>)/(5×23<sup>2</sup>) |
| | | {{Monzo| 1 3 -1 2 0 0 0 0 -2 }} |
| | | Biyativice comma, biyativicema |
| | | |
| | |- |
| | | [[2737/2736]] |
| | | 0.63265 |
| | | (7×17×23)/(2<sup>4</sup>×3<sup>2</sup>×19) |
| | | {{Monzo| -4 -2 0 1 0 0 1 -1 1 }} |
| | | Kotkisma |
| | | |
| | |- |
| | | [[3060/3059]] |
| | | 0.56586 |
| | | ((2×3)<sup>2</sup>×5×17)/(7×19×23) |
| | | {{Monzo| 2 2 1 -1 0 0 1 -1 -1 }} |
| | | Vicious comma, viciousma |
| | | |
| | |- |
| | | [[3381/3380]] |
| | | 0.51212 |
| | | (3×7<sup>2</sup>×23)/(2<sup>2</sup>×5×13<sup>2</sup>) |
| | | {{Monzo| -2 1 -1 2 0 -2 0 0 1 }} |
| | | Mikkolisma |
| | | |
| | |- |
| | | [[3520/3519]] |
| | | 0.49190 |
| | | (2<sup>6</sup>×5×11)/(3<sup>2</sup>×17×23) |
| | | {{Monzo| 6 -2 1 0 1 0 -1 0 -1 }} |
| | | Vicedim comma, vicedimma |
| | | |
| | |- |
| | | [[3888/3887]] |
| | | 0.44533 |
| | | (2<sup>4</sup>×3<sup>5</sup>)/(13<sup>2</sup>×23) |
| | | {{Monzo| 4 5 0 0 0 -2 0 0 -1 }} |
| | | Shoalma, vicetride comma |
| | | |
| | |- |
| | | [[4693/4692]] |
| | | 0.36893 |
| | | (13×19<sup>2</sup>)/(2<sup>2</sup>×3×17×23) |
| | | {{Monzo| -2 -1 0 0 0 1 -1 2 -1 }} |
| | | Viceaug comma, viceaugma |
| | | |
| | |- |
| | | [[4761/4760]] |
| | | 0.36367 |
| | | (3×23)<sup>2</sup>/(2<sup>3</sup>×5×7×17) |
| | | {{Monzo| -3 2 -1 -1 0 0 -1 0 2 }} |
| | | Demiquartervice comma |
| | | S69 |
| | |- |
| | | [[5083/5082]] |
| | | 0.34063 |
| | | (13×17×23)/(2×3×7×11<sup>2</sup>) |
| | | {{Monzo| -1 -1 0 -1 -2 1 1 0 1 }} |
| | | Broadviewsma |
| | | |
| | |- |
| | | [[7866/7865]] |
| | | 0.22010 |
| | | (2×3<sup>2</sup>×19×23)/(5×11<sup>2</sup>×13) |
| | | {{Monzo| 1 2 -1 0 -2 -1 0 1 1 }} |
| | | |
| | | |
| | |- |
| | | [[8281/8280]] |
| | | 0.20907 |
| | | (7×13)<sup>2</sup>/(2<sup>3</sup>×3<sup>2</sup>×5×23) |
| | | {{Monzo| -3 -2 -1 2 0 2 0 0 -1 }} |
| | | |
| | | S91 |
| | |- |
| | | [[8625/8624]] |
| | | 0.20073 |
| | | (3×5<sup>3</sup>×23)/(2<sup>4</sup>×7<sup>2</sup>×11) |
| | | {{Monzo| -4 1 3 -2 -1 0 0 0 1 }} |
| | | Beerglass comma |
| | | |
| | |- |
| | | [[10626/10625]] |
| | | 0.16293 |
| | | (2×3×7×11×23)/(5<sup>4</sup>×17) |
| | | {{Monzo| 1 1 -4 1 1 0 -1 0 1 }} |
| | | Demiglace comma |
| | | |
| | |- |
| | | 11271/11270 |
| | | 0.15361 |
| | | (3×13×17<sup>2</sup>)/(2×5×7<sup>2</sup>×23) |
| | | {{Monzo| -1 1 -1 -2 0 1 2 0 -1 }} |
| | | |
| | | |
| | |- |
| | | 11662/11661 |
| | | 0.14846 |
| | | (2×7<sup>3</sup>×17)/(3×13<sup>2</sup>×23) |
| | | {{Monzo| 1 -1 0 3 0 -2 1 0 -1 }} |
| | | |
| | | |
| | |- |
| | | [[Vicetertisma|12168/12167]] |
| | | 0.14228 |
| | | (2/23)<sup>3</sup>×(3×13)<sup>2</sup> |
| | | {{Monzo| 3 2 0 0 0 2 0 0 -3 }} |
| | | Vicetertisma |
| | | |
| | |- |
| | | 16929/16928 |
| | | 0.10227 |
| | | (3<sup>4</sup>×11×19)/(2<sup>5</sup>×23<sup>2</sup>) |
| | | {{Monzo| -5 4 0 0 1 0 0 1 -2 }} |
| | | |
| | | |
| | |- |
| | | 19551/19550 |
| | | 0.088552 |
| | | (3×7<sup>3</sup>×19)/(2×5<sup>2</sup>×17×23) |
| | | {{Monzo| -1 1 -2 3 0 0 -1 1 -1 }} |
| | | |
| | | |
| | |- |
| | | 21505/21504 |
| | | 0.080506 |
| | | (5×11×17×23)/(2<sup>10</sup>×3×7) |
| | | {{Monzo| -10 -1 1 -1 1 0 1 0 1 }} |
| | | |
| | | |
| | |- |
| | | 21736/21735 |
| | | 0.079650 |
| | | (2<sup>3</sup>×11×13×19)/(3<sup>3</sup>×5×7×23) |
| | | {{Monzo| 3 -3 -1 -1 1 1 0 1 -1 }} |
| | | |
| | | |
| | |- |
| | | 23276/23275 |
| | | 0.074380 |
| | | ((2×23)/(5×7))<sup>2</sup>×(11/19) |
| | | {{Monzo| 2 0 -2 -2 1 0 0 -1 2 }} |
| | | |
| | | |
| | |- |
| | | [[Joshuavoisma|25025/25024]] |
| | | 0.069182 |
| | | (5<sup>2</sup>×7×11×13)/(2<sup>6</sup>×17×23) |
| | | {{Monzo| -6 0 2 1 1 1 -1 0 -1 }} |
| | | Joshuavoisma |
| | | |
| | |- |
| | | [[Diarithmedia|25921/25920]] |
| | | 0.066790 |
| | | (7×23)<sup>2</sup>/(2<sup>6</sup>×3<sup>4</sup>×5) |
| | | {{Monzo| -6 -4 -1 2 0 0 0 0 2 }} |
| | | Diarithmedia |
| | | S161 |
| | |- |
| | | 43264/43263 |
| | | 0.040016 |
| | | (2<sup>4</sup>×13)<sup>2</sup>/(3<sup>2</sup>×11×19×23) |
| | | {{Monzo| 8 -2 0 0 -1 2 0 -1 -1 }} |
| | | |
| | | S208 |
| | |- |
| | | 52326/52325 |
| | | 0.033086 |
| | | (2×3<sup>4</sup>×17×19)/(5<sup>2</sup>×7×13×23) |
| | | {{Monzo| 1 4 -2 -1 0 -1 1 1 -1 }} |
| | | |
| | | |
| | |- |
| | | 71875/71874 |
| | | 0.024087 |
| | | (5<sup>5</sup>×23)/(2×(3×11)<sup>3</sup>) |
| | | {{Monzo| -1 -3 5 0 -3 0 0 0 1 }} |
| | | |
| | | |
| | |- |
| | | 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 }} |
| | | |
| | | |
| | |- |
| | | 76545/76544 |
| | | 0.022617 |
| | | (3<sup>7</sup>×5×7)/(2<sup>8</sup>×13×23) |
| | | {{Monzo| -8 7 1 1 0 -1 0 0 -1 }} |
| | | |
| | | |
| | |- |
| | | 104329/104328 |
| | | 0.016594 |
| | | (17×19)<sup>2</sup>/(2<sup>3</sup>×3<sup>4</sup>×7×23) |
| | | {{Monzo| -3 -4 0 -1 0 0 2 2 -1 }} |
| | | |
| | | S323 |
| | |- |
| | | 122452/122451 |
| | | 0.014138 |
| | | (2<sup>2</sup>×11<sup>3</sup>×23)/(3×7<sup>4</sup>×17) |
| | | {{Monzo| 2 -1 0 -4 3 0 -1 0 1 }} |
| | | |
| | | |
| | |- |
| | | 126225/126224 |
| | | 0.013716 |
| | | (3<sup>3</sup>×5<sup>2</sup>×11×17)/(2<sup>4</sup>×7<sup>3</sup>×23) |
| | | {{Monzo| -4 3 2 -3 1 0 1 0 -1 }} |
| | | |
| | | |
| | |- |
| | | 152881/152880 |
| | | 0.011324 |
| | | (17×23)<sup>2</sup>/(2<sup>4</sup>×3×5×7<sup>2</sup>×13) |
| | | {{Monzo| -4 -1 -1 -2 0 -1 2 0 2 }} |
| | | |
| | | S391 |
| | |- |
| | | 202125/202124 |
| | | 0.0085652 |
| | | (3×5<sup>3</sup>×7<sup>2</sup>×11)/(2<sup>2</sup>×13<sup>3</sup>×23) |
| | | {{Monzo| -2 1 3 2 1 -3 0 0 -1 }} |
| | | |
| | | |
| | |- |
| | | 264385/264384 |
| | | 0.0065482 |
| | | (5×11<sup>2</sup>×19×23)/(2<sup>6</sup>×3<sup>5</sup>×17) |
| | | {{Monzo| -6 -5 1 0 2 0 -1 1 1 }} |
| | | |
| | | |
| | |- |
| | | 282625/282624 |
| | | 0.0061256 |
| | | (5<sup>3</sup>×7×17×19)/(2<sup>12</sup>×3×23) |
| | | {{Monzo| -12 -1 3 1 0 0 1 1 -1 }} |
| | | |
| | | |
| | |- |
| | | 328510/328509 |
| | | 0.0052700 |
| | | (2×5×7×13×19<sup>2</sup>)/(3×23)<sup>3</sup> |
| | | {{Monzo| 1 -3 1 1 0 1 0 2 -3 }} |
| | | |
| | | |
| | |- |
| | | 2023425/2023424 |
| | | 0.00085560 |
| | | ((3×5×23)<sup>2</sup>×17)/(2<sup>13</sup>×13×19) |
| | | {{Monzo| -13 2 2 0 0 -1 1 -1 2 }} |
| | | |
| | | |
| | |- |
| | | 4096576/4096575 |
| | | 0.00042261 |
| | | ((2<sup>3</sup>×11×23)/(3<sup>2</sup>×5×17))<sup>2</sup>/7 |
| | | {{Monzo| 6 -4 -2 -1 2 0 -2 0 2 }} |
| | | |
| | | S2024 |
| | |- |
| | | 5142501/5142500 |
| | | 0.00033665 |
| | | 3<sup>3</sup>×((7×13)/(2×5<sup>2</sup>×11))<sup>2</sup>×(23/17) |
| | | {{Monzo| -2 3 -4 2 -2 2 -1 0 1 }} |
| | | |
| | | |
| | |} |
| | |
| | === 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"/> |
| | |- |
| | | [[41/40]] |
| | | 42.749 |
| | | 41/(2<sup>3</sup>×5) |
| | | 2.5.41 {{monzo| -3 -1 1 }} |
| | | Large quadracesimoprimal 1/5-tone |
| | | |
| | |- |
| | | [[42/41]] |
| | | 41.719 |
| | | (2×3×7)/41 |
| | | 2.3.7.41 {{monzo| 1 1 1 -1 }} |
| | | Small quadracesimoprimal 1/5-tone |
| | | |
| | |- |
| | | [[82/81]] |
| | | 21.242 |
| | | (2×41)/3<sup>4</sup> |
| | | 2.3.41 {{monzo| 1 -4 1 }} |
| | | 41st-partial chroma |
| | | |
| | |- |
| | | [[124/123]] |
| | | 14.018 |
| | | (2<sup>2</sup>×31)/(3×41) |
| | | 2.3.31.41 {{monzo| 2 -1 1 -1 }} |
| | | |
| | | |
| | |- |
| | | [[165/164]] |
| | | 10.524 |
| | | (3×5×11)/(2<sup>2</sup>×41) |
| | | 2.3.5.11.41 {{monzo| -2 1 1 1 -1 }} |
| | | |
| | | |
| | |- |
| | | [[205/204]] |
| | | 8.4657 |
| | | (5×41)/(2<sup>2</sup>×3×17) |
| | | 2.3.5.17.41 {{monzo| -2 -1 1 -1 1 }} |
| | | |
| | | |
| | |- |
| | | [[246/245]] |
| | | 7.0519 |
| | | (2×3×41)/(5×7<sup>2</sup>) |
| | | 2.3.5.7.41 {{monzo| 1 1 -1 -2 1 }} |
| | | |
| | | |
| | |- |
| | | [[247/246]] |
| | | 7.0233 |
| | | (13×19)/(2×3×41) |
| | | 2.3.13.19.41 {{monzo| -1 -1 1 1 -1 }} |
| | | |
| | | |
| | |- |
| | | [[287/286]] |
| | | 6.0427 |
| | | (7×41)/(2×11×13) |
| | | 2.7.11.13.41 {{monzo| -1 1 -1 -1 1 }} |
| | | |
| | | |
| | |- |
| | | [[288/287]] |
| | | 6.0217 |
| | | (2<sup>5</sup>×3<sup>2</sup>)/(7×41) |
| | | 2.3.7.41 {{monzo| 5 2 -1 -1 }} |
| | | |
| | | |
| | |- |
| | | [[369/368]] |
| | | 4.6981 |
| | | (3<sup>2</sup>×41)/(2<sup>4</sup>×23) |
| | | 2.3.23.41 {{monzo| -4 2 -1 1 }} |
| | | |
| | | |
| | |- |
| | | [[370/369]] |
| | | 4.6853 |
| | | (2×5×37)/(3<sup>2</sup>×41) |
| | | 2.3.5.37.41 {{monzo| 1 -2 1 1 -1 }} |
| | | |
| | | |
| | |- |
| | | [[451/450]] |
| | | 3.8429 |
| | | (11×41)/(2×(3×5)<sup>2</sup>) |
| | | 2.3.5.11.41 {{monzo| -1 -2 -2 1 1 }} |
| | | |
| | | |
| | |- |
| | | [[493/492]] |
| | | 3.5152 |
| | | (17×29)/(2<sup>2</sup>×3×41) |
| | | 2.3.17.29.41 {{monzo| -2 -1 1 1 -1 }} |
| | | |
| | | |
| | |- |
| | | [[533/532]] |
| | | 3.2511 |
| | | (13×41)/(2<sup>2</sup>×7×19) |
| | | 2.7.13.19.41 {{monzo| -2 -1 1 -1 1 }} |
| | | |
| | | |
| | |- |
| | | [[575/574]] |
| | | 3.0135 |
| | | (5<sup>2</sup>×23)/(2×7×41) |
| | | 2.5.7.23.41 {{monzo| -1 2 -1 1 -1 }} |
| | | Renatisma |
| | | |
| | |- |
| | | [[616/615]] |
| | | 2.8127 |
| | | (2<sup>3</sup>×7×11)/(3×5×41) |
| | | 2.3.5.7.11.41 {{monzo| 3 -1 -1 1 1 -1 }} |
| | | Ellisma |
| | | |
| | |- |
| | | [[697/696]] |
| | | 2.4856 |
| | | (17×41)/(2<sup>3</sup>×3×29) |
| | | 2.3.17.29.41 {{monzo| -3 -1 1 -1 1 }} |
| | | |
| | | |
| | |- |
| | | [[780/779]] |
| | | 2.2210 |
| | | (2<sup>2</sup>×3×5×13)/(19×41) |
| | | 2.3.5.13.19.41 {{monzo| 2 1 1 1 -1 -1 }} |
| | | Wiesentisma |
| | | |
| | |- |
| | | [[820/819]] |
| | | 2.1125 |
| | | (2<sup>2</sup>×5×41)/(3<sup>2</sup>×7×13) |
| | | 2.3.5.7.13.41 {{monzo| 2 -2 1 -1 -1 1 }} |
| | | |
| | | |
| | |- |
| | | [[1025/1024]] |
| | | 1.6898 |
| | | (5<sup>2</sup>×41)/2<sup>10</sup> |
| | | 2.5.41 {{monzo| -10 2 1 }} |
| | | Kilobytisma |
| | | |
| | |- |
| | | [[1026/1025]] |
| | | 1.6882 |
| | | (2×3<sup>3</sup>×19)/(5<sup>2</sup>×41) |
| | | 2.3.5.19.41 {{monzo| 1 3 -2 1 -1 }} |
| | | Ingridisma |
| | | |
| | |- |
| | | [[1148/1147]] |
| | | 1.5087 |
| | | (2<sup>2</sup>×7×41)/(31×37) |
| | | 2.7.31.37.41 {{monzo| 2 1 -1 -1 1 }} |
| | | |
| | | |
| | |- |
| | | [[1189/1188]] |
| | | 1.4567 |
| | | (29×41)/(2<sup>2</sup>×3<sup>3</sup>×11) |
| | | 2.3.11.29.41 {{monzo| -2 -3 -1 1 1 }} |
| | | |
| | | |
| | |- |
| | | [[1190/1189]] |
| | | 1.4554 |
| | | (2×5×7×17)/(29×41) |
| | | 2.5.7.17.29.41 {{monzo| 1 1 1 1 -1 -1 }} |
| | | Pelagisma |
| | | |
| | |- |
| | | [[1312/1311]] |
| | | 1.3200 |
| | | (2<sup>5</sup>×41)/(3×19×23) |
| | | 2.3.19.23.41 {{monzo| 5 -1 -1 -1 1 }} |
| | | |
| | | |
| | |- |
| | | [[1353/1352]] |
| | | 1.2800 |
| | | (3×11×41)/(2<sup>3</sup>×13<sup>2</sup>) |
| | | 2.3.11.13.41 {{monzo| -3 1 1 -2 1 }} |
| | | |
| | | |
| | |- |
| | | [[1395/1394]] |
| | | 1.2415 |
| | | (3<sup>2</sup>×5×31)/(2×17×41) |
| | | 2.3.5.17.31.41 {{monzo| -1 2 1 -1 1 -1 }} |
| | | |
| | | |
| | |- |
| | | [[1518/1517]] |
| | | 1.1408 |
| | | (2×3×11×23)/(37×41) |
| | | 2.3.11.23.37.41 {{monzo| 1 1 1 1 -1 -1 }} |
| | | Rovaniemisma |
| | | |
| | |- |
| | | [[1600/1599]] |
| | | 1.0824 |
| | | (2<sup>3</sup>×5)<sup>2</sup>/(3×13×41) |
| | | 2.3.5.13.41 {{monzo| 6 -1 2 -1 -1 }} |
| | | |
| | | S40 |
| | |- |
| | | [[1681/1680]] |
| | | 1.0302 |
| | | 41<sup>2</sup>/(2<sup>4</sup>×3×5×7) |
| | | 2.3.5.7.41 {{monzo| -4 -1 -1 -1 2 }} |
| | | |
| | | S41 |
| | |- |
| | | [[1682/1681]] |
| | | 1.0296 |
| | | (2×29<sup>2</sup>)/41<sup>2</sup> |
| | | 2.29.41 {{monzo| 1 2 -2 }} |
| | | Shaftesburisma |
| | | |
| | |- |
| | | [[1805/1804]] |
| | | 0.95940 |
| | | (5×19<sup>2</sup>)/(2<sup>2</sup>×11×41) |
| | | 2.5.11.19.41 {{monzo| -2 1 -1 2 -1 }} |
| | | |
| | | |
| | |- |
| | | [[1886/1885]] |
| | | 0.91818 |
| | | (2×23×41)/(5×13×29) |
| | | 2.5.13.23.29.41 {{monzo| 1 -1 -1 1 -1 1 }} |
| | | |
| | | |
| | |- |
| | | [[1887/1886]] |
| | | 0.91770 |
| | | (3×17×37)/(2×23×41) |
| | | 2.3.17.23.37.41 {{monzo| -1 1 1 -1 1 -1 }} |
| | | |
| | | |
| | |- |
| | | [[2091/2090]] |
| | | 0.82814 |
| | | (3×17×41)/(2×5×11×19) |
| | | 2.3.5.11.17.19.41 {{monzo| -1 1 -1 -1 1 -1 1 }} |
| | | |
| | | |
| | |- |
| | | [[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 |
| | | |
| | |- |
| | | [[2296/2295]] |
| | | 0.75419 |
| | | (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 }} |
| | | |
| | | |
| | |- |
| | | [[2542/2541]] |
| | | 0.68119 |
| | | (2×31×41)/(3×7×11<sup>2</sup>) |
| | | 2.3.7.11.31.41 {{monzo| 1 -1 -1 -2 1 1 }} |
| | | |
| | | |
| | |- |
| | | [[2584/2583]] |
| | | 0.67011 |
| | | (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 }} |
| | | |
| | | |
| | |- |
| | | [[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 }} |
| | | |
| | | |
| | |- |
| | | [[2665/2664]] |
| | | 0.64974 |
| | | (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 }} |
| | | |
| | | |
| | |- |
| | | [[2871/2870]] |
| | | 0.60311 |
| | | (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 |
| | | |
| | |- |
| | | [[3690/3689]] |
| | | 0.46923 |
| | | (2×3<sup>2</sup>×5×41)/(7×17×31) |
| | | 2.3.5.7.17.31.41 {{monzo| 1 2 1 -1 -1 -1 1 }} |
| | | |
| | | |
| | |- |
| | | [[3773/3772]] |
| | | 0.45891 |
| | | (7<sup>3</sup>×11)/(2<sup>2</sup>×23×41) |
| | | 2.7.11.23.41 {{monzo| -2 3 1 -1 -1 }} |
| | | Smithsonianisma |
| | | |
| | |- |
| | | [[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 |
| | | |
| | |- |
| | | [[4264/4263]] |
| | | 0.40606 |
| | | (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 }} |
| | | |
| | | |
| | |- |
| | | [[4551/4550]] |
| | | 0.38045 |
| | | (3×37×41)/(2×5<sup>2</sup>×7×13) |
| | | 2.3.5.7.13.37.41 {{monzo| -1 1 -2 -1 -1 1 1 }} |
| | | |
| | | |
| | |- |
| | | [[4675/4674]] |
| | | 0.37036 |
| | | (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 |
| | | |
| | |- |
| | | [[4921/4920]] |
| | | 0.35184 |
| | | (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 |
| | | |
| | |- |
| | | [[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 }} |
| | | |
| | | |
| | |- |
| | | [[5084/5083]] |
| | | 0.34056 |
| | | (2<sup>2</sup>×31×41)/(13×17×23) |
| | | 2.13.17.23.31.41 {{monzo| 2 -1 -1 -1 1 1 }} |
| | | |
| | | |
| | |- |
| | | [[5577/5576]] |
| | | 0.31045 |
| | | (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 |
| | | |
| | |- |
| | | [[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 |
| | | |
| | |- |
| | | [[6273/6272]] |
| | | 0.27600 |
| | | (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 }} |
| | | |
| | | |
| | |- |
| | | [[6561/6560]] |
| | | 0.26389 |
| | | 3<sup>8</sup>/(2<sup>5</sup>×5×41) |
| | | 2.3.5.41 {{monzo| -5 8 -1 -1 }} |
| | | |
| | | S81 |
| | |- |
| | | [[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 }} |
| | | |
| | | |
| | |- |
| | | [[6930/6929]] |
| | | 0.24984 |
| | | (2×3<sup>2</sup>×5×7×11)/(13<sup>2</sup>×41) |
| | | 2.3.5.7.11.13.41 {{monzo| 1 2 1 1 1 -2 -1 }} |
| | | Bedanisma |
| | | |
| | |- |
| | | [[7176/7175]] |
| | | 0.24127 |
| | | (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 |
| | | |
| | |- |
| | | [[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 }} |
| | | |
| | | |
| | |- |
| | | [[7750/7749]] |
| | | 0.22340 |
| | | (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 }} |
| | | |
| | | |
| | |- |
| | | [[8569/8568]] |
| | | 0.20205 |
| | | (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 |
| | | |
| | |- |
| | | [[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 }} |
| | | |
| | | |
| | |- |
| | | [[9472/9471]] |
| | | 0.18278 |
| | | (2<sup>8</sup>×37)/(3×7×11×41) |
| | | 2.3.7.11.37.41 {{monzo| 8 -1 -1 -1 1 -1 }} |
| | | Brugesisma |
| | | |
| | |- |
| | | 10045/10044 |
| | | 0.17236 |
| | | (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 }} |
| | | |
| | | |
| | |- |
| | | [[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 |
| | | |
| | |- |
| | | 10660/10659 |
| | | 0.16241 |
| | | (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 }} |
| | | |
| | | |
| | |- |
| | | [[11440/11439]] |
| | | 0.15134 |
| | | (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 |
| | | |
| | |- |
| | | 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 }} |
| | | |
| | | |
| | |- |
| | | 14145/14144 |
| | | 0.12240 |
| | | (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 }} |
| | | |
| | | |
| | |- |
| | | 14801/14800 |
| | | 0.11697 |
| | | (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 }} |
| | | |
| | | |
| | |- |
| | | [[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 |
| | |- |
| | | 15457/15456 |
| | | 0.11201 |
| | | (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 }} |
| | | |
| | | |
| | |- |
| | | 16400/16399 |
| | | 0.10557 |
| | | (2<sup>4</sup>×5<sup>2</sup>×41)/(23<sup>2</sup>×31) |
| | | 2.5.23.31.41 {{monzo| 4 2 -2 -1 1 }} |
| | | |
| | | |
| | |- |
| | | 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 }} |
| | | |
| | | |
| | |- |
| | | 16606/16605 |
| | | 0.10426 |
| | | (2×19<sup>2</sup>×23)/(3<sup>4</sup>×5×41) |
| | | 2.3.5.19.23.41 {{monzo| 1 -4 -1 2 1 -1 }} |
| | | |
| | | |
| | |- |
| | | 17425/17424 |
| | | 0.099356 |
| | | (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 }} |
| | | |
| | | |
| | |- |
| | | [[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 |
| | | |
| | |- |
| | | 17918/17917 |
| | | 0.096623 |
| | | (2×17<sup>2</sup>×31)/(19×23×41) |
| | | 2.17.19.23.31.41 {{monzo| 1 2 -1 -1 1 -1 }} |
| | | |
| | | |
| | |- |
| | | 19721/19720 |
| | | 0.087789 |
| | | (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 }} |
| | | |
| | | |
| | |- |
| | | 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 }} |
| | | |
| | | |
| | |- |
| | | [[76384/76383]] |
| | | 0.022665 |
| | | (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 |
| | | |
| | |- |
| | | [[Mebisma|1048576/1048575]] |
| | | 0.0016510 |
| | | 2<sup>20</sup>/(3×5<sup>2</sup>×11×31×41) |
| | | 2.3.5.11.31.41 {{monzo| 20 -1 -2 -1 -1 -1 }} |
| | | Mebisma |
| | | S1024 |
| | |} |
| | |
| | === 43-limit (incomplete) === |
| | {| class="wikitable center-6" style="width:100%" |
| | ! width="10%" | [[Ratio]] |
| | ! width="10%" | [[Cent]]s |
| | ! width="15%" | Factorization |
| | ! width="15%" | [[Monzo]] |
| | ! width="45%" | Name(s) |
| | ! width="5%" | Meta<ref name="ssp"/> |
| | |- |
| | | [[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|*]] |