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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:keenanpepper|keenanpepper]] and made on <tt>2011-10-28 04:09:09 UTC</tt>.<br>
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| : The original revision id was <tt>269487406</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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| In addition to names and cents values, the list below includes the factorization of each superparticular ratio as well as the largest prime involved. This is relevant when considering which intervals are characteristic of which [[harmonic limit]]s. [[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 |
| | | |
| | |} |
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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]].
| | === 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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|
| ||~ Ratio ||~ Cents Value ||~ Factorization ||~ Name(s) ||
| | === 5-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 ||
| | | [[5/4]] |
| || [[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 ||
| | | 386.314 |
| || [[16_15|16/15]] || 111.713 || 2<span style="vertical-align: super;">4</span>/(3*5) || minor diatonic semitone, 15th subharmonic ||
| | | 5/2<sup>2</sup> |
| || [[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| -2 0 1 }} |
| || [[81_80|81/80]] || 21.506 || 3<span style="vertical-align: super;">4</span>/(2<span style="vertical-align: super;">4</span>*5) || syntonic comma, Didymus comma ||
| | | Classic(al)/just major third, octave-reduced 5th harmonic |
| ||||||||~ 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 ||
| | | [[6/5]] |
| || [[15_14|15/14]] || 119.443 || (3*5)/(2*7) || septimal diatonic semitone ||
| | | 315.641 |
| || [[21_20|21/20]] || 84.467 || (3*7)/(2<span style="vertical-align: super;">2</span>*5) || minor semitone, large septimal chromatic semitone ||
| | | (2×3)/5 |
| || [[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| 1 1 -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 ||
| | | Classic(al)/just minor third |
| || [[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="vertical-align: super;">2</span>)/7<span style="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 || | | | [[10/9]] |
| || [[126_125|126/125]] || 13.795 || (2*3^2*7)/5^3 || starling comma, septimal semicomma ||
| | | 182.404 |
| || [[225_224|225/224]] || 7.7115 || (3^2*5^2)/(2^5*7) || marvel comma, septimal kleisma ||
| | | (2×5)/3<sup>2</sup> |
| || [[2401_2400|2401/2400]] || 0.72120 || 7^4/(2^5*3*5^2) || breedsma || | | | {{Monzo| 1 -2 1 }} |
| || [[4375_4374|4375/4374]] || 0.39576 || (5^4*7)/(2*3^7) || ragisma || | | | Classic(al) (whole) tone, classic major second, minor whole tone |
| ||||||||~ 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 || | | | [[16/15]] |
| || [[22_21|22/21]] || 80.537 || (2*11)/(3*7) || undecimal minor semitone ||
| | | 111.731 |
| || [[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) || | | | 2<sup>4</sup>/(3×5) |
| || [[45_44|45/44]] || 38.906 || (3<span style="vertical-align: super;">2</span>*5)/(2<span style="vertical-align: super;">2</span>*11) || 1/5-tone ||
| | | {{Monzo| 4 -1 -1 }} |
| || [[55_54|55/54]] || 31.767 || (5*11)/(2*3<span style="vertical-align: super;">3</span>) || || | | | Classic(al)/just diatonic semitone, 15th subharmonic |
| || [[56_55|56/55]] || 31.194 || (2<span style="vertical-align: super;">3</span>*7)/(5*11) || ||
| | | S4 |
| || [[99_98|99/98]] || 17.576 || (3<span style="vertical-align: super;">2</span>*11)/(2*7<span style="vertical-align: super;">2</span>) || ||
| | |- |
| || [[100_99|100/99]] || 17.399 || (2<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">2</span>)/(3<span style="vertical-align: super;">2</span>*11) || Ptolemy's comma || | | | [[25/24]] |
| || [[121_120|121/120]] || 14.376 || 11^2/(2^3*3*5) || ||
| | | 70.672 |
| || [[176_175|176/175]] || 9.8646 || (2^4*11)/(5^2*7) || ||
| | | 5<sup>2</sup>/(2<sup>3</sup>×3) |
| || [[243_242|243/242]] || 7.1391 || 2^5/(2*11^2) || || | | | {{Monzo| -3 -1 2 }} |
| || [[385_384|385/384]] || 4.5026 || (5*7*11)/(2^7*3) || keenanisma || | | | Classic(al)/just chromatic semitone, chroma, Zarlinian semitone |
| || [[441_440|441/440]] || 3.9302 || (3^2*7^2)/(2^3*5*11) || ||
| | | S5 |
| || [[540_539|540/539]] || 3.2090 || (2^2*3^3*5)/(7^2*11) || || | | |- |
| || [[3025_3024|3025/3024]] || 0.57240 || (5^2*11^2)/(2^4*3^3*7) || ||
| | | [[81/80]] |
| || [[9801_9800|9801/9800]] || 0.17665 || (3^4*11^2)/(2^3*5^2*7^2) || || | | | 21.506 |
| ||||||||~ 13-limit (incomplete) || | | | (3/2)<sup>4</sup>/5 |
| || [[13_12|13/12]] || 138.573 || 13/(2<span style="vertical-align: super;">2</span>*3) || tridecimal 2/3-tone ||
| | | {{Monzo| -4 4 -1 }} |
| || [[14_13|14/13]] || 128.298 || (2*7)/13 || 2/3-tone, trienthird || | | | Syntonic comma, Didymus comma |
| || [[26_25|26/25]] || 67.900 || (2*13)/5<span style="vertical-align: super;">2</span> || tridecimal 1/3-tone ||
| | | S9 |
| || [[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 || | |
| || [[65_64|65/64]] || 26.841 || (5*13)/2<span style="vertical-align: super;">6</span> || 13th-partial chroma ||
| |
| || [[66_65|66/65]] || 26.432 || (2*3*11)/(5*13) || ||
| |
| || [[78_77|78/77]] || 22.339 || (2*3*13)/(7*11) || ||
| |
| || [[91_90|91/90]] || 19.130 || (7*13)/(2*3<span style="vertical-align: super;">2</span>*5) || ||
| |
| ||||||||~ 17-limit (incomplete) || | |
| || [[17_16|17/16]] || 104.955 || 17/2<span style="vertical-align: super;">4</span> || 17th harmonic (octave reduced) ||
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| || [[18_17|18/17]] || 98.955 || (2*3<span style="vertical-align: super;">2</span>)/17 || Arabic lute index finger ||
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| || [[34_33|34/33]] || 51.682 || (2*17)/(3*33) || || | |
| || [[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 ||
| |
| || [[52_51|52/51]] || 33.617 || (2<span style="vertical-align: super;">2</span>*13)/(3*17) || || | |
| || [[85_84|85/84]] || 20.488 || (5*17)/(2<span style="vertical-align: super;">2</span>*3*7) || ||
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| ||||||||~ 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>) || ||
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| || [[77_76|77/76]] || 22.631 || (7*11)/(2<span style="vertical-align: super;">2</span>*19) || ||
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| || [[96_95|96/95]] || 18.128 || (2<span style="vertical-align: super;">5</span>*3)/(5*19) || ||
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| ||||||||~ 23-limit (incomplete) ||
| |
| || [[23_22|23/22]] || 76.956 || 23/(2*11) || ||
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| || [[24_23|24/23]] || 73.681 || (2<span style="vertical-align: super;">3</span>*3)/23 || ||
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| || [[46_45|46/45]] || 38.051 || (2*23)/(3<span style="vertical-align: super;">2</span>*5) || ||
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| || [[69_68|69/68]] || 25.274 || (3*23)/(2<span style="vertical-align: super;">2</span>*17) || ||
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| || [[70_69|70/69]] || 24.910 || (2*5*7)/(3*23) || ||
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| || [[92_91|92/91]] || 18.921 || (2<span style="vertical-align: super;">2</span>*23)/(7*13) || ||
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| ||||||||~ 29-limit (incomplete) ||
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| || [[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) || ||
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| || [[88_87|88/87]] || 19.786 || (2<span style="vertical-align: super;">3</span>*11)/(3*29) || ||
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| ||||||||~ 31-limit (incomplete) ||
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| || [[31_30|31/30]] || 56.767 || 31/(2*3*5) || ||
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| || [[32_31|32/31]] || 54.964 || 2<span style="vertical-align: super;">5</span>/31 || 31st subharmonic ||
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| || [[63_62|63/62]] || 27.700 || (3<span style="vertical-align: super;">2</span>*7)/(2*31) || ||
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| || [[93_92|93/92]] || 18.716 || (3*31)/(2<span style="vertical-align: super;">2</span>*23) || ||
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| ||||||||~ 37-limit (incomplete) ||
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| || [[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 || ||
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| || [[82_81|82/81]] || 21.242 || (2*41)/3<span style="vertical-align: super;">4</span> || ||
| |
| ||||||||~ 43-limit (incomplete) ||
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| || [[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>
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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;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>
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| <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 />
| |
| In addition to names and cents values, the list below includes the factorization of each superparticular ratio as well as the largest prime involved. This is relevant when considering which intervals are characteristic of which <a class="wiki_link" href="/harmonic%20limit">harmonic limit</a>s. <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 />
| |
| 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 />
| |
|
| |
|
| | === 7-limit === |
| | {| class="wikitable center-6" style="width:100%" |
| | ! width="10%" | [[Ratio]] |
| | ! width="10%" | [[Cent]]s |
| | ! width="15%" | Factorization |
| | ! width="15%" | [[Monzo]] |
| | ! width="45%" | Name(s) |
| | ! width="5%" | Meta<ref name="ssp"/> |
| | |- |
| | | [[7/6]] |
| | | 266.871 |
| | | 7/(2×3) |
| | | {{Monzo| -1 -1 0 1 }} |
| | | (Septimal) subminor third, septimal minor third |
| | | |
| | |- |
| | | [[8/7]] |
| | | 231.174 |
| | | 2<sup>3</sup>/7 |
| | | {{Monzo| 3 0 0 -1 }} |
| | | (Septimal) supermajor second, septimal whole tone, <br>octave-reduced 7th subharmonic |
| | | |
| | |- |
| | | [[15/14]] |
| | | 119.443 |
| | | (3×5)/(2×7) |
| | | {{Monzo| -1 1 1 -1 }} |
| | | Septimal major semitone, septimal diatonic semitone |
| | | |
| | |- |
| | | [[21/20]] |
| | | 84.467 |
| | | (3×7)/(2<sup>2</sup>×5) |
| | | {{Monzo| -2 1 -1 1 }} |
| | | Septimal minor semitone, large septimal chroma |
| | | |
| | |- |
| | | [[28/27]] |
| | | 62.961 |
| | | (2<sup>2</sup>×7)/3<sup>3</sup> |
| | | {{Monzo| 2 -3 0 1 }} |
| | | Septimal 1/3-tone, small septimal chroma, <br>(septimal) subminor second, septimal minor second, <br>trienstonic comma |
| | | |
| | |- |
| | | [[36/35]] |
| | | 48.770 |
| | | (2×3)<sup>2</sup>/(5×7) |
| | | {{Monzo| 2 2 -1 -1 }} |
| | | Septimal 1/4-tone, mint comma |
| | | S6 |
| | |- |
| | | [[49/48]] |
| | | 35.697 |
| | | 7<sup>2</sup>/(2<sup>4</sup>×3) |
| | | {{Monzo| -4 -1 0 2 }} |
| | | Large septimal diesis, large septimal 1/6-tone, slendro diesis, semaphoresma |
| | | S7 |
| | |- |
| | | [[50/49]] |
| | | 34.976 |
| | | 2×(5/7)<sup>2</sup> |
| | | {{Monzo| 1 0 2 -2 }} |
| | | Small septimal diesis, small septimal 1/6-tone, septimal tritonic diesis, jubilisma |
| | | |
| | |- |
| | | [[64/63]] |
| | | 27.264 |
| | | 2<sup>6</sup>/(3<sup>2</sup>×7) |
| | | {{Monzo| 6 -2 0 -1 }} |
| | | Septimal comma, Archytas' comma |
| | | S8 |
| | |- |
| | | [[126/125]] |
| | | 13.795 |
| | | (2×3<sup>2</sup>×7)/5<sup>3</sup> |
| | | {{Monzo| 1 2 -3 1 }} |
| | | Starling comma, septimal semicomma |
| | | |
| | |- |
| | | [[225/224]] |
| | | 7.7115 |
| | | (3×5)<sup>2</sup>/(2<sup>5</sup>×7) |
| | | {{Monzo| -5 2 2 -1 }} |
| | | Marvel comma, septimal kleisma |
| | | S15 |
| | |- |
| | | [[2401/2400]] |
| | | 0.72120 |
| | | 7<sup>4</sup>/(2<sup>5</sup>×3×5<sup>2</sup>) |
| | | {{Monzo| -5 -1 -2 4 }} |
| | | Breedsma |
| | | S49 |
| | |- |
| | | [[4375/4374]] |
| | | 0.39576 |
| | | (5<sup>4</sup>×7)/(2×3<sup>7</sup>) |
| | | {{Monzo| -1 -7 4 1 }} |
| | | Ragisma |
| | | |
| | |} |
|
| |
|
| <table class="wiki_table">
| | === 11-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>
| | | [[11/10]] |
| </tr>
| | | 165.004 |
| <tr>
| | | 11/(2×5) |
| <th colspan="4">2-limit<br />
| | | {{Monzo| -1 0 -1 0 1 }} |
| </th>
| | | Large undecimal neutral second, <br>undecimal submajor second, Ptolemy's second |
| </tr>
| | | |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/2_1">2/1</a><br />
| | | [[12/11]] |
| </td>
| | | 150.637 |
| <td>1200.000<br />
| | | (2<sup>2</sup>×3)/11 |
| </td>
| | | {{Monzo| 2 1 0 0 -1 }} |
| <td>2/1<br />
| | | Small undecimal neutral second |
| </td>
| | | |
| <td>(perfect) unison, unity, perfect prime, tonic, duple<br />
| | |- |
| </td>
| | | [[22/21]] |
| </tr>
| | | 80.537 |
| <tr>
| | | (2×11)/(3×7) |
| <th colspan="4">3-limit<br />
| | | {{Monzo| 1 -1 0 -1 1 }} |
| </th>
| | | Undecimal minor semitone |
| </tr>
| | | |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/3_2">3/2</a><br />
| | | [[33/32]] |
| </td>
| | | 53.273 |
| <td>701.995<br />
| | | (3×11)/2<sup>5</sup> |
| </td>
| | | {{Monzo| -5 1 0 0 1 }} |
| <td>3/2<br />
| | | Undecimal 1/4-tone, undecimal diesis, <br>al-Farabi's 1/4-tone, octave-reduced 33rd harmonic |
| </td>
| | | |
| <td><a class="wiki_link" href="/perfect%20fifth">perfect fifth</a>, 3rd harmonic (octave reduced), diapente<br />
| | |- |
| </td>
| | | [[45/44]] |
| </tr>
| | | 38.906 |
| <tr>
| | | (3/2)<sup>2</sup>×(5/11) |
| <td><a class="wiki_link" href="/4_3">4/3</a><br />
| | | {{monzo| -2 2 1 0 -1 }} |
| </td>
| | | Undecimal 1/5-tone, cake comma |
| <td>498.045<br />
| | | |
| </td>
| | |- |
| <td>2<span style="vertical-align: super;">2</span>/3<br />
| | | [[55/54]] |
| </td>
| | | 31.767 |
| <td>perfect fourth, 3rd subharmonic (octave reduced), diatessaron<br />
| | | (5×11)/(2×3<sup>3</sup>) |
| </td>
| | | {{Monzo| -1 -3 1 0 1 }} |
| </tr>
| | | Telepathma, eleventyfive comma, <br>undecimal diasecundal comma |
| <tr>
| | | |
| <td><a class="wiki_link" href="/9_8">9/8</a><br />
| | |- |
| </td>
| | | [[56/55]] |
| <td>203.910<br />
| | | 31.194 |
| </td>
| | | (2<sup>3</sup>×7)/(5×11) |
| <td>3<span style="vertical-align: super;">2</span>/2<span style="vertical-align: super;">3</span><br />
| | | {{Monzo| 3 0 -1 1 -1 }} |
| </td>
| | | Undecimal tritonic comma, konbini comma |
| <td>(Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced)<br />
| | | |
| </td>
| | |- |
| </tr>
| | | [[99/98]] |
| <tr>
| | | 17.576 |
| <th colspan="4">5-limit<br />
| | | (3/7)<sup>2</sup>×(11/2) |
| </th>
| | | {{Monzo| -1 2 0 -2 1 }} |
| </tr>
| | | Mothwellsma, small undecimal comma |
| <tr>
| | | |
| <td><a class="wiki_link" href="/5_4">5/4</a><br />
| | |- |
| </td>
| | | [[100/99]] |
| <td>386.314<br />
| | | 17.399 |
| </td>
| | | ((2×5)/3)<sup>2</sup>/11 |
| <td>5/2<span style="vertical-align: super;">2</span><br />
| | | {{monzo| 2 -2 2 0 -1 }} |
| </td>
| | | Ptolemisma, Ptolemy's comma |
| <td>(classic) (5-limit) major third, 5th harmonic (octave reduced)<br />
| | | S10 |
| </td>
| | |- |
| </tr>
| | | [[121/120]] |
| <tr>
| | | 14.376 |
| <td><a class="wiki_link" href="/6_5">6/5</a><br />
| | | 11<sup>2</sup>/(2<sup>3</sup>×3×5) |
| </td>
| | | {{Monzo| -3 -1 -1 0 2 }} |
| <td>315.641<br />
| | | Biyatisma, undecimal seconds comma |
| </td>
| | | S11 |
| <td>(2*3)/5<br />
| | |- |
| </td>
| | | [[176/175]] |
| <td>(classic) (5-limit) minor third<br />
| | | 9.8646 |
| </td>
| | | (2<sup>4</sup>×11)/(5<sup>2</sup>×7) |
| </tr>
| | | {{Monzo| 4 0 -2 -1 1 }} |
| <tr>
| | | Valinorsma |
| <td><a class="wiki_link" href="/10_9">10/9</a><br />
| | | |
| </td>
| | |- |
| <td>182.404<br />
| | | [[243/242]] |
| </td>
| | | 7.1391 |
| <td>(2*5)/3<span style="vertical-align: super;">2</span><br />
| | | 3<sup>5</sup>/(2×11<sup>2</sup>) |
| </td>
| | | {{Monzo| -1 5 0 0 -2 }} |
| <td>classic (whole) tone, classic major second, minor whole tone<br />
| | | Rastma, neutral thirds comma |
| </td>
| | | |
| </tr>
| | |- |
| <tr>
| | | [[385/384]] |
| <td><a class="wiki_link" href="/16_15">16/15</a><br />
| | | 4.5026 |
| </td>
| | | (5×7×11)/(2<sup>7</sup>×3) |
| <td>111.713<br />
| | | {{Monzo| -7 -1 1 1 1 }} |
| </td>
| | | Keenanisma |
| <td>2<span style="vertical-align: super;">4</span>/(3*5)<br />
| | | |
| </td>
| | |- |
| <td>minor diatonic semitone, 15th subharmonic<br />
| | | [[441/440]] |
| </td>
| | | 3.9302 |
| </tr>
| | | (3×7)<sup>2</sup>/(2<sup>3</sup>×5×11) |
| <tr>
| | | {{Monzo| -3 2 -1 2 -1 }} |
| <td><a class="wiki_link" href="/25_24">25/24</a><br />
| | | Werckisma, Werckmeister's undecimal septenarian schisma |
| </td>
| | | S21 |
| <td>70.672<br />
| | |- |
| </td>
| | | [[540/539]] |
| <td>5<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">3</span>*3)<br />
| | | 3.2090 |
| </td>
| | | (2/7)<sup>2</sup>×((3<sup>3</sup>×5)/11) |
| <td>chroma, (classic) chromatic semitone, Zarlinian semitone<br />
| | | {{Monzo| 2 3 1 -2 -1 }} |
| </td>
| | | Swetisma, Swets' comma |
| </tr>
| | | |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/81_80">81/80</a><br />
| | | [[3025/3024]] |
| </td>
| | | 0.57240 |
| <td>21.506<br />
| | | (5×11)<sup>2</sup>/(2<sup>4</sup>×3<sup>3</sup>×7) |
| </td>
| | | {{Monzo| -4 -3 2 -1 2 }} |
| <td>3<span style="vertical-align: super;">4</span>/(2<span style="vertical-align: super;">4</span>*5)<br />
| | | Lehmerisma |
| </td>
| | | S55 |
| <td>syntonic comma, Didymus comma<br />
| | |- |
| </td>
| | | [[9801/9800]] |
| </tr>
| | | 0.17665 |
| <tr>
| | | ((3<sup>2</sup>×11)/(5×7))<sup>2</sup>/2<sup>3</sup> |
| <th colspan="4">7-limit<br />
| | | {{Monzo| -3 4 -2 -2 2 }} |
| </th>
| | | Kalisma, Gauss comma |
| </tr>
| | | S99 |
| <tr>
| | |} |
| <td><a class="wiki_link" href="/7_6">7/6</a><br />
| |
| </td>
| |
| <td>266.871<br />
| |
| </td>
| |
| <td>7/(2*3)<br />
| |
| </td>
| |
| <td>(septimal) subminor third, septimal minor third, augmented second<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/8_7">8/7</a><br />
| |
| </td>
| |
| <td>231.174<br />
| |
| </td>
| |
| <td>2<span style="vertical-align: super;">3</span>/7<br />
| |
| </td>
| |
| <td>(septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/15_14">15/14</a><br />
| |
| </td>
| |
| <td>119.443<br />
| |
| </td>
| |
| <td>(3*5)/(2*7)<br />
| |
| </td>
| |
| <td>septimal diatonic semitone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/21_20">21/20</a><br />
| |
| </td>
| |
| <td>84.467<br />
| |
| </td>
| |
| <td>(3*7)/(2<span style="vertical-align: super;">2</span>*5)<br />
| |
| </td>
| |
| <td>minor semitone, large septimal chromatic semitone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/28_27">28/27</a><br />
| |
| </td>
| |
| <td>62.961<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">2</span>*7)/3<span style="vertical-align: super;">3</span><br />
| |
| </td>
| |
| <td>septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/36_35">36/35</a><br />
| |
| </td>
| |
| <td>48.770<br />
| |
| </td>
| |
| <td>(2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">3</span>)/(5*7)<br />
| |
| </td>
| |
| <td>septimal quarter tone, septimal diesis<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/49_48">49/48</a><br />
| |
| </td>
| |
| <td>35.697<br />
| |
| </td>
| |
| <td>7<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">4</span>*3)<br />
| |
| </td>
| |
| <td>large septimal diesis, slendro diesis, septimal 1/6-tone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/50_49">50/49</a><br />
| |
| </td>
| |
| <td>34.976<br />
| |
| </td>
| |
| <td>(2*5<span style="vertical-align: super;">2</span>)/7<span style="vertical-align: super;">2</span><br />
| |
| </td>
| |
| <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>(3^2*5^2)/(2^5*7)<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="vertical-align: super;">2</span>*5)/(2<span style="vertical-align: super;">2</span>*11)<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="vertical-align: super;">2</span>*11)/(2*7<span style="vertical-align: super;">2</span>)<br />
| |
| </td>
| |
| <td><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="vertical-align: super;">2</span>*5<span style="vertical-align: super;">2</span>)/(3<span style="vertical-align: super;">2</span>*11)<br />
| |
| </td>
| |
| <td>Ptolemy's comma<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><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><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/243_242">243/242</a><br />
| |
| </td>
| |
| <td>7.1391<br />
| |
| </td>
| |
| <td>2^5/(2*11^2)<br />
| |
| </td>
| |
| <td><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>(3^2*7^2)/(2^3*5*11)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/540_539">540/539</a><br />
| |
| </td>
| |
| <td>3.2090<br />
| |
| </td>
| |
| <td>(2^2*3^3*5)/(7^2*11)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/3025_3024">3025/3024</a><br />
| |
| </td>
| |
| <td>0.57240<br />
| |
| </td>
| |
| <td>(5^2*11^2)/(2^4*3^3*7)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/9801_9800">9801/9800</a><br />
| |
| </td>
| |
| <td>0.17665<br />
| |
| </td>
| |
| <td>(3^4*11^2)/(2^3*5^2*7^2)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">13-limit (incomplete)<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>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><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><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><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <th colspan="4">17-limit (incomplete)<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*33)<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>
| |
| <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>
| |
| <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>
| |
| <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>
| | === 13-limit === |
| | {| class="wikitable center-6" style="width:100%" |
| | ! width="10%" | [[Ratio]] |
| | ! width="10%" | [[Cent]]s |
| | ! width="15%" | Factorization |
| | ! width="15%" | [[Monzo]] |
| | ! width="45%" | Name(s) |
| | ! width="5%" | Meta<ref name="ssp"/> |
| | |- |
| | | [[13/12]] |
| | | 138.573 |
| | | 13/(2<sup>2</sup>×3) |
| | | {{Monzo| -2 -1 0 0 0 1 }} |
| | | Large tridecimal 2/3-tone, <br>tridecimal neutral second |
| | | |
| | |- |
| | | [[14/13]] |
| | | 128.298 |
| | | (2×7)/13 |
| | | {{Monzo| 1 0 0 1 0 -1 }} |
| | | Small tridecimal 2/3-tone, trienthird |
| | | |
| | |- |
| | | [[26/25]] |
| | | 67.900 |
| | | (2×13)/5<sup>2</sup> |
| | | {{Monzo| 1 0 -2 0 0 1 }} |
| | | Large tridecimal 1/3-tone |
| | | |
| | |- |
| | | [[27/26]] |
| | | 65.337 |
| | | 3<sup>3</sup>/(2×13) |
| | | {{Monzo| -1 3 0 0 0 -1 }} |
| | | Small tridecimal 1/3-tone |
| | | |
| | |- |
| | | [[40/39]] |
| | | 43.831 |
| | | (2<sup>3</sup>×5)/(3×13) |
| | | {{Monzo| 3 -1 1 0 0 -1 }} |
| | | Tridecimal minor diesis |
| | | |
| | |- |
| | | [[65/64]] |
| | | 26.841 |
| | | (5×13)/2<sup>6</sup> |
| | | {{Monzo| -6 0 1 0 0 1 }} |
| | | Wilsorma, 13th-partial chroma |
| | | |
| | |- |
| | | [[66/65]] |
| | | 26.432 |
| | | (2×3×11)/(5×13) |
| | | {{Monzo| 1 1 -1 0 1 -1 }} |
| | | Winmeanma |
| | | |
| | |- |
| | | [[78/77]] |
| | | 22.339 |
| | | (2×3×13)/(7×11) |
| | | {{Monzo| 1 1 0 -1 -1 1 }} |
| | | Negustma |
| | | |
| | |- |
| | | [[91/90]] |
| | | 19.130 |
| | | (7×13)/(2×3<sup>2</sup>×5) |
| | | {{Monzo| -1 -2 -1 1 0 1 }} |
| | | Biome comma, superleap comma |
| | | |
| | |- |
| | | [[105/104]] |
| | | 16.567 |
| | | (3×5×7)/(2<sup>3</sup>×13) |
| | | {{Monzo| -3 1 1 1 0 -1 }} |
| | | Animist comma, small tridecimal comma |
| | | |
| | |- |
| | | [[144/143]] |
| | | 12.064 |
| | | (2<sup>2</sup>×3)<sup>2</sup>/(11×13) |
| | | {{Monzo| 4 2 0 0 -1 -1 }} |
| | | Grossma |
| | | S12 |
| | |- |
| | | [[169/168]] |
| | | 10.274 |
| | | 13<sup>2</sup>/(2<sup>3</sup>×3×7) |
| | | {{Monzo| -3 -1 0 -1 0 2 }} |
| | | Buzurgisma, dhanvantarisma |
| | | S13 |
| | |- |
| | | [[196/195]] |
| | | 8.8554 |
| | | (2×7)<sup>2</sup>/(3×5×13) |
| | | {{Monzo| 2 -1 -1 2 0 -1 }} |
| | | Mynucuma |
| | | S14 |
| | |- |
| | | [[325/324]] |
| | | 5.3351 |
| | | (5/(2×3<sup>2</sup>))<sup>2</sup>×13 |
| | | {{Monzo| -2 -4 2 0 0 1 }} |
| | | Marveltwin comma |
| | | |
| | |- |
| | | [[351/350]] |
| | | 4.9393 |
| | | (3<sup>3</sup>×13)/(2×5<sup>2</sup>×7) |
| | | {{Monzo| -1 3 -2 -1 0 1 }} |
| | | Ratwolfsma |
| | | |
| | |- |
| | | [[352/351]] |
| | | 4.9253 |
| | | (2<sup>5</sup>×11)/(3<sup>3</sup>×13) |
| | | {{Monzo| 5 -3 0 0 1 -1 }} |
| | | Major minthma, major gentle comma |
| | | |
| | |- |
| | | [[364/363]] |
| | | 4.7627 |
| | | (2/11)<sup>2</sup>×((7×13)/3) |
| | | {{Monzo| 2 -1 0 1 -2 1 }} |
| | | Minor minthma, minor gentle comma |
| | | |
| | |- |
| | | [[625/624]] |
| | | 2.7722 |
| | | (5/2)<sup>4</sup>/(3×13) |
| | | {{Monzo| -4 -1 4 0 0 -1 }} |
| | | Tunbarsma |
| | | S25 |
| | |- |
| | | [[676/675]] |
| | | 2.5629 |
| | | ((2×13)/5)<sup>2</sup>/3<sup>3</sup> |
| | | {{Monzo| 2 -3 -2 0 0 2 }} |
| | | Island comma |
| | | S26 |
| | |- |
| | | [[729/728]] |
| | | 2.3764 |
| | | (3<sup>2</sup>/2)<sup>3</sup>/(7×13) |
| | | {{Monzo| -3 6 0 -1 0 -1 }} |
| | | Squbema |
| | | S27 |
| | |- |
| | | [[1001/1000]] |
| | | 1.7304 |
| | | (7×11×13)/(2×5)<sup>3</sup> |
| | | {{Monzo| -3 0 -3 1 1 1 }} |
| | | Sinbadma |
| | | |
| | |- |
| | | [[1716/1715]] |
| | | 1.0092 |
| | | (2<sup>2</sup>×3×11×13)/(5×7<sup>3</sup>) |
| | | {{Monzo| 2 1 -1 -3 1 1 }} |
| | | Lummic comma |
| | | |
| | |- |
| | | [[2080/2079]] |
| | | 0.83252 |
| | | (2<sup>5</sup>×5×13)/(3<sup>3</sup>×7×11) |
| | | {{Monzo| 5 -3 1 -1 -1 1 }} |
| | | Ibnsinma, sinaisma |
| | | |
| | |- |
| | | [[4096/4095]] |
| | | 0.42272 |
| | | (2<sup>6</sup>/3)<sup>2</sup>/(5×7×13) |
| | | {{Monzo| 12 -2 -1 -1 0 -1 }} |
| | | Minisma |
| | | S64 |
| | |- |
| | | [[4225/4224]] |
| | | 0.40981 |
| | | (5×13)<sup>2</sup>/(2<sup>7</sup>×3×11) |
| | | {{Monzo| -7 -1 2 0 -1 2 }} |
| | | Leprechaun comma |
| | | S65 |
| | |- |
| | | [[6656/6655]] |
| | | 0.26012 |
| | | (2<sup>3</sup>/11)<sup>3</sup>×(13/5) |
| | | {{Monzo| 9 0 -1 0 -3 1 }} |
| | | Jacobin comma |
| | | |
| | |- |
| | | [[Harmonisma|10648/10647]] |
| | | 0.16260 |
| | | (2×11)<sup>3</sup>/((3×13)<sup>2</sup>×7) |
| | | {{Monzo| 3 -2 0 -1 3 -2 }} |
| | | Harmonisma |
| | | |
| | |- |
| | | [[Chalmersia|123201/123200]] |
| | | 0.014052 |
| | | (3/2)<sup>6</sup>×(13/5)<sup>2</sup>/(7×11) |
| | | {{Monzo| -6 6 -2 -1 -1 2 }} |
| | | Chalmersia |
| | | S351 |
| | |} |
| | |
| | === 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 }} |
| | | Tredekisma |
| | | |
| | |} |
| | |
| | === 23-limit === |
| | {| class="wikitable center-6" style="width:100%" |
| | ! width="10%" | [[Ratio]] |
| | ! width="10%" | [[Cent]]s |
| | ! width="15%" | Factorization |
| | ! width="15%" | [[Monzo]] |
| | ! width="45%" | Name(s) |
| | ! width="5%" | Meta<ref name="ssp"/> |
| | |- |
| | | [[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 }} |
| | | |
| | | |
| | |} |
| | |
| | === Higher-limit === |
| | See: |
| | * [[List of superparticular intervals/29-limit]] |
| | * [[List of superparticular intervals/31-limit]] |
| | * [[List of superparticular intervals/37-limit]] |
| | * [[List of superparticular intervals/41-limit]] |
| | * [[List of superparticular intervals/43-limit]] |
| | * [[List of superparticular intervals/47-limit]] |
| | * [[List of superparticular intervals/53-limit]] |
| | * [[List of superparticular intervals/59-limit]] |
| | * [[List of superparticular intervals/61-limit]] |
| | * [[List of superparticular intervals/67-limit]] |
| | * [[List of superparticular intervals/71-limit]] |
| | * [[List of superparticular intervals/73-limit]] |
| | * [[List of superparticular intervals/79-limit]] |
| | * [[List of superparticular intervals/83-limit]] |
| | * [[List of superparticular intervals/89-limit]] |
| | * [[List of superparticular intervals/97-limit]] |
| | * [[List of superparticular intervals/101-limit]] |
| | * [[List of superparticular intervals/103-limit]] |
| | * [[List of superparticular intervals/107-limit]] |
| | * [[List of superparticular intervals/109-limit]] |
| | * [[List of superparticular intervals/113-limit]] |
| | * [[List of superparticular intervals/127-limit]] |
| | |
| | == See also == |
| | * [[Gallery of just intervals]] |
| | |
| | == Notes == |
| | <references/> |
| | |
| | == External links == |
| | * [http://www.huygens-fokker.org/docs/intervals.html ''List of intervals''] on the Huygens-Fokker Foundation website |
| | |
| | [[Category:Lists of intervals]] |
| | [[Category:Superparticular ratios|*]] |