List of superparticular intervals
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This is a list of superparticular intervals ordered by prime limit. It reaches to the 107-limit and is complete up to the 29-limit.
Størmer's theorem states that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. OEIS: A002071 gives the number of superparticular ratios in each prime limit, OEIS: A145604 shows the increment from limit to limit, and OEIS: A117581 gives the largest numerator for each prime limit (with some exceptions, such as the 23-limit, where the largest value is smaller than that of a smaller prime limit, in this case the 19-limit).
List of superparticular intervals
2-limit
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
2/1 | 1200.000 | 2/1 | [1⟩ | Octave, duple |
3-limit
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
3/2 | 701.955 | 3/2 | [-1 1⟩ | Perfect fifth, octave-reduced 3rd harmonic, diapente | |
4/3 | 498.045 | 22/3 | [2 -1⟩ | Perfect fourth, octave-reduced 3rd subharmonic, diatessaron | S2 |
9/8 | 203.910 | 32/23 | [-3 2⟩ | (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, octave-reduced 9th harmonic or harmonic ninth | S3 |
5-limit
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
5/4 | 386.314 | 5/22 | [-2 0 1⟩ | Classic(al)/just major third, octave-reduced 5th harmonic | |
6/5 | 315.641 | (2×3)/5 | [1 1 -1⟩ | Classic(al)/just minor third | |
10/9 | 182.404 | (2×5)/32 | [1 -2 1⟩ | Classic(al) (whole) tone, classic major second, minor whole tone | |
16/15 | 111.731 | 24/(3×5) | [4 -1 -1⟩ | Classic(al)/just diatonic semitone, 15th subharmonic | S4 |
25/24 | 70.672 | 52/(23×3) | [-3 -1 2⟩ | Classic(al)/just chromatic semitone, chroma, Zarlinian semitone | S5 |
81/80 | 21.506 | (3/2)4/5 | [-4 4 -1⟩ | Syntonic comma, Didymus comma | S9 |
7-limit
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
7/6 | 266.871 | 7/(2×3) | [-1 -1 0 1⟩ | (Septimal) subminor third, septimal minor third | |
8/7 | 231.174 | 23/7 | [3 0 0 -1⟩ | (Septimal) supermajor second, septimal whole tone, octave-reduced 7th subharmonic | |
15/14 | 119.443 | (3×5)/(2×7) | [-1 1 1 -1⟩ | Septimal major semitone, septimal diatonic semitone | |
21/20 | 84.467 | (3×7)/(22×5) | [-2 1 -1 1⟩ | Septimal minor semitone, large septimal chroma | |
28/27 | 62.961 | (22×7)/33 | [2 -3 0 1⟩ | Septimal 1/3-tone, small septimal chroma, (septimal) subminor second, septimal minor second, trienstonic comma | |
36/35 | 48.770 | (22×32)/(5×7) | [2 2 -1 -1⟩ | Septimal 1/4-tone, septimal diesis | S6 |
49/48 | 35.697 | 72/(24×3) | [-4 -1 0 2⟩ | Slendro diesis, large septimal diesis, large septimal 1/6-tone | S7 |
50/49 | 34.976 | 2×(5/7)2 | [1 0 2 -2⟩ | Jubilisma, tritonic diesis, small septimal diesis, small septimal 1/6-tone | |
64/63 | 27.264 | 26/(32×7) | [6 -2 0 -1⟩ | Septimal comma, Archytas' comma | S8 |
126/125 | 13.795 | (2×32×7)/53 | [1 2 -3 1⟩ | Starling comma, septimal semicomma | |
225/224 | 7.7115 | (3×5)2/(25×7) | [-5 2 2 -1⟩ | Marvel comma, septimal kleisma | S15 |
2401/2400 | 0.72120 | 74/(25×3×52) | [-5 -1 -2 4⟩ | Breedsma | S49 |
4375/4374 | 0.39576 | (54×7)/(2×37) | [-1 -7 4 1⟩ | Ragisma |
11-limit
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
11/10 | 165.004 | 11/(2×5) | [-1 0 -1 0 1⟩ | (Large) undecimal neutral second, undecimal submajor second, Ptolemy's second | |
12/11 | 150.637 | (22×3)/11 | [2 1 0 0 -1⟩ | (Small) undecimal neutral second | |
22/21 | 80.537 | (2×11)/(3×7) | [1 -1 0 -1 1⟩ | Undecimal minor semitone | |
33/32 | 53.273 | (3×11)/25 | [-5 1 0 0 1⟩ | Undecimal 1/4-tone, undecimal diesis, al-Farabi's 1/4-tone, octave-reduced 33rd harmonic | |
45/44 | 38.906 | (3/2)2×(5/11) | [-2 2 1 0 -1⟩ | Undecimal 1/5-tone | |
55/54 | 31.767 | (5×11)/(2×33) | [-1 -3 1 0 1⟩ | Telepathma, eleventyfive comma, undecimal diasecundal comma | |
56/55 | 31.194 | (23×7)/(5×11) | [3 0 -1 1 -1⟩ | Undecimal tritonic comma, konbini comma | |
99/98 | 17.576 | (3/7)2×(11/2) | [-1 2 0 -2 1⟩ | Mothwellsma, small undecimal comma | |
100/99 | 17.399 | (2×5/3)2/11) | [2 -2 2 0 -1⟩ | Ptolemisma, Ptolemy's comma | S10 |
121/120 | 14.376 | 112/(23×3×5) | [-3 -1 -1 0 2⟩ | Biyatisma, undecimal seconds comma | S11 |
176/175 | 9.8646 | (24×11)/(52×7) | [4 0 -2 -1 1⟩ | Valinorsma | |
243/242 | 7.1391 | 35/(2×112) | [-1 5 0 0 -2⟩ | Rastma, neutral thirds comma | |
385/384 | 4.5026 | (5×7×11)/(27×3) | [-7 -1 1 1 1⟩ | Keenanisma | |
441/440 | 3.9302 | (3×7)2/(23×5×11) | [-3 2 -1 2 -1⟩ | Werckisma, Werckmeister's undecimal septenarian schisma | S21 |
540/539 | 3.2090 | (2/7)2×33×5/11 | [2 3 1 -2 -1⟩ | Swetisma, Swets' comma | |
3025/3024 | 0.57240 | (5×11)2/(24×32×7) | [-4 -3 2 -1 2⟩ | Lehmerisma | S55 |
9801/9800 | 0.17665 | (11/(5×7))2×34/23 | [-3 4 -2 -2 2⟩ | Kalisma, Gauss comma | S99 |
13-limit
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
13/12 | 138.573 | 13/(22×3) | [-2 -1 0 0 0 1⟩ | (Large) tridecimal 2/3-tone, tridecimal neutral second | |
14/13 | 128.298 | (2×7)/13 | [1 0 0 1 0 -1⟩ | (Small) tridecimal 2/3-tone, trienthird | |
26/25 | 67.900 | (2×13)/52 | [1 0 -2 0 0 1⟩ | (Large) tridecimal 1/3-tone | |
27/26 | 65.337 | 33/(2×13) | [-1 3 0 0 0 -1⟩ | (Small) tridecimal 1/3-tone | |
40/39 | 43.831 | (23×5)/(3×13) | [3 -1 1 0 0 -1⟩ | Tridecimal minor diesis | |
65/64 | 26.841 | (5×13)/26 | [-6 0 1 0 0 1⟩ | Wilsorma, 13th-partial chroma | |
66/65 | 26.432 | (2×3×11)/(5×13) | [1 1 -1 0 1 -1⟩ | Winmeanma | |
78/77 | 22.339 | (2×3×13)/(7×11) | [1 1 0 -1 -1 1⟩ | Negustma | |
91/90 | 19.130 | (7×13)/(2×32×5) | [-1 -2 -1 1 0 1⟩ | Biome comma, superleap comma | |
105/104 | 16.567 | (3×5×7)/(23×13) | [-3 1 1 1 0 -1⟩ | Animist comma, small tridecimal comma | |
144/143 | 12.064 | (22×3)2/(11×13) | [4 2 0 0 -1 -1⟩ | Grossma | S12 |
169/168 | 10.274 | 132/(23×3×7) | [-3 -1 0 -1 0 2⟩ | Buzurgisma, dhanvantarisma | S13 |
196/195 | 8.8554 | (2×7)2/(3×5×13) | [2 -1 -1 2 0 -1⟩ | Mynucuma | S14 |
325/324 | 5.3351 | (52×13)/(22×34) | [-2 -4 2 0 0 1⟩ | Marveltwin comma | |
351/350 | 4.9393 | (3/5)2×13/(2×7) | [-1 3 -2 -1 0 1⟩ | Ratwolfsma | |
352/351 | 4.9253 | (25×11)/(32×13) | [5 -3 0 0 1 -1⟩ | Minthma | |
364/363 | 4.7627 | (2/11)2×7×13/3 | [2 -1 0 1 -2 1⟩ | Gentle comma | |
625/624 | 2.7722 | (5/2)4/(3×13) | [-4 -1 4 0 0 -1⟩ | Tunbarsma | S25 |
676/675 | 2.5629 | (2×13/5)2/33 | [2 -3 -2 0 0 2⟩ | Island comma | S26 |
729/728 | 2.3764 | (32/2)3/(7×13) | [-3 6 0 -1 0 -1⟩ | Squbema | S27 |
1001/1000 | 1.7304 | (7×11×13)/(2×5)3 | [-3 0 -3 1 1 1⟩ | Sinbadma | |
1716/1715 | 1.0092 | (22×3×11×13)/(5×73) | [2 1 -1 -3 1 1⟩ | Lummic comma | |
2080/2079 | 0.83252 | (25×5×13)/(33×7×11) | [5 -3 1 -1 -1 1⟩ | Ibnsinma | |
4096/4095 | 0.42272 | (26/3)2/(5×7×13) | [12 -2 -1 -1 0 -1⟩ | Schismina, tridecimal schisma | S65 |
4225/4224 | 0.40981 | (5×13)2/(27×3×11) | [-7 -1 2 0 -1 2⟩ | Leprechaun comma | S66 |
6656/6655 | 0.26012 | (23/11)3×13/5 | [9 0 -1 0 -3 1⟩ | Jacobin comma | |
10648/10647 | 0.16260 | (2×11)3/((3×13)2×7) | [3 -2 0 -1 3 -2⟩ | Harmonisma | |
123201/123200 | 0.014052 | (3/2)6×(13/5)2/(7×11) | [-6 6 -2 -1 -1 2⟩ | Chalmersia | S351 |
17-limit
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
17/16 | 104.955 | 17/24 | [-4 0 0 0 0 0 1⟩ | Large septendecimal semitone, octave-reduced 17th harmonic | |
18/17 | 98.955 | (2×32)/17 | [1 2 0 0 0 0 -1⟩ | Small septendecimal semitone, Arabic lute index finger | |
34/33 | 51.682 | (2×17)/(3×11) | [1 -1 0 0 -1 0 1⟩ | Large septendecimal 1/4-tone | |
35/34 | 50.184 | (5×7)/(2×17) | [-1 0 1 1 0 0 -1⟩ | Small septendecimal 1/4-tone | |
51/50 | 34.283 | (3×17)/(2×52) | [-1 1 -2 0 0 0 1⟩ | Large septendecimal 1/6-tone | |
52/51 | 33.617 | (22×13)/(3×17) | [2 -1 0 0 0 1 -1⟩ | Small septendecimal 1/6-tone | |
85/84 | 20.488 | (5×17)/(22×3×7) | [-2 -1 1 -1 0 0 1⟩ | Monk comma | |
120/119 | 14.487 | (23×3×5)/(7×17) | [3 1 1 -1 0 0 -1⟩ | Lynchisma | |
136/135 | 12.777 | (2/3)3×17/5 | [3 -3 -1 0 0 0 1⟩ | Diatonisma, septendecimal major second comma | |
154/153 | 11.278 | (2×7×11)/(32×17) | [1 -2 0 1 1 0 -1⟩ | Augustma | |
170/169 | 10.214 | (2×5×17)/132 | [1 0 1 0 0 -2 1⟩ | Major naiadma | |
221/220 | 7.8514 | (13×17)/(22×5×11) | [-2 0 -1 0 -1 1 1⟩ | Minor naiadma | |
256/255 | 6.7759 | 28/(3×5×17) | [8 -1 -1 0 0 0 -1⟩ | Diasemisma, septendecimal kleisma, octave-reduced 255th subharmonic | S16 |
273/272 | 6.3532 | (3×7×13)/(24×17) | [-4 1 0 1 0 1 -1⟩ | Tannisma, prototannisma | |
289/288 | 6.0008 | (17/3)2/25 | [-5 -2 0 0 0 0 2⟩ | Semitonisma | S17 |
375/374 | 4.6228 | (3×53)/(2×11×17) | [-1 1 3 0 -1 0 -1⟩ | Ursulisma | |
442/441 | 3.9213 | (2×13×17)/(3×7)2 | [1 -2 0 -2 0 1 1⟩ | Seminaiadma | |
561/560 | 3.0887 | (3×11×17)/(24×5×7) | [-4 1 -1 -1 1 0 1⟩ | Monardisma, tsaharuk comma | |
595/594 | 2.9121 | (5×7×17)/(2×33×11) | [-1 -3 1 1 -1 0 1⟩ | Dakotisma | |
715/714 | 2.4230 | (5×11×13)/(2×3×7×17) | [-1 -1 1 -1 1 1 -1⟩ | September comma, septembrisma | |
833/832 | 2.0796 | (72×17)/(26×13) | [-6 0 0 2 0 -1 1⟩ | Horizma, horizon comma | |
936/935 | 1.8506 | (23×32×13)/(5×11×17) | [3 2 -1 0 -1 1 -1⟩ | Ainisma, ainic comma | |
1089/1088 | 1.5905 | (3×11)2/(26×17) | [-6 2 0 0 2 0 -1⟩ | Twosquare comma | S33 |
1156/1155 | 1.4983 | (2×17)2/(3×5×7×11) | [2 -1 -1 -1 -1 0 2⟩ | Quadrantonisma | S34 |
1225/1224 | 1.4138 | (5×7)2/(23×32×17) | [-3 -2 2 2 0 0 -1⟩ | Noellisma | S35 |
1275/1274 | 1.3584 | (3×52×17)/(2×72×13) | [-1 1 2 -2 0 -1 1⟩ | Cimbrisma | |
1701/1700 | 1.0181 | (35×7)/((2×5)2×17) | [-2 5 -2 1 0 0 -1⟩ | Palingenetic comma, palingenesis | |
2058/2057 | 0.84143 | (2×3×73)/(112×17) | [1 1 0 3 -2 0 -1⟩ | Xenisma | |
2431/2430 | 0.71230 | (11×13×17)/(2×35×5) | [-1 -5 -1 0 1 1 1⟩ | Heptacircle comma | |
2500/2499 | 0.69263 | (2×52)2/(3×72×17) | [2 -1 4 -2 0 0 -1⟩ | Sperasma | S50 |
2601/2600 | 0.66573 | (3×17)2/(23×52×13) | [-3 2 -2 0 0 -1 2⟩ | Sextantonisma | S51 |
4914/4913 | 0.35234 | (2×33×7×13)/173 | [1 3 0 1 0 1 -3⟩ | Baladisma | |
5832/5831 | 0.29688 | (2×32)3/(73×17) | [3 6 0 -3 0 0 -1⟩ | Chlorisma | |
12376/12375 | 0.13989 | (23×7×13×17)/(32×53×11) | [3 -2 -3 1 -1 1 1⟩ | Flashma | |
14400/14399 | 0.12023 | (23×3×5)2/(7×112×17) | [6 2 2 -1 -2 0 -1⟩ | Sparkisma | S120 |
28561/28560 | 0.060616 | 134/(24×3×5×7×17) | [-4 -1 -1 -1 0 4 -1⟩ | Neuseisma | S169 |
31213/31212 | 0.055466 | (74×13)/(22×33×172) | [-2 -3 0 4 0 1 -2⟩ | ||
37180/37179 | 0.046564 | (22×5×11×132)/(37×17) | [2 -7 1 0 1 2 -1⟩ | ||
194481/194480 | 0.008902 | (3×7)4/(24×5×11×13×17) | [-4 4 -1 4 -1 -1 -1⟩ | Scintillisma | S441 |
336141/336140 | 0.005150 | (32×133×17)/(22×5×75) | [-2 2 -1 -5 0 3 1⟩ |
19-limit
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
19/18 | 93.603 | 19/(2×32) | [-1 -2 0 0 0 0 0 1⟩ | Large undevicesimal semitone | |
20/19 | 88.801 | (22×5)/19 | [2 0 1 0 0 0 0 -1⟩ | Small undevicesimal semitone | |
39/38 | 44.970 | (3×13)/(2×19) | [-1 1 0 0 0 1 0 -1⟩ | Undevicesimal 2/9-tone | |
57/56 | 30.642 | (3×19)/(23×7) | [-3 1 0 -1 0 0 0 1⟩ | Hendrix comma | |
76/75 | 22.931 | (22×19)/(3×52) | [2 -1 -2 0 0 0 0 1⟩ | Large undevicesimal 1/9-tone | |
77/76 | 22.631 | (7×11)/(22×19) | [-2 0 0 1 1 0 0 -1⟩ | Small undevicesimal 1/9-tone | |
96/95 | 18.128 | (25×3)/(5×19) | [5 1 -1 0 0 0 0 -1⟩ | 19th-partial chroma | |
133/132 | 13.066 | (7×19)/(22×3×11) | [-2 -1 0 1 -1 0 0 1⟩ | Minithirdma | |
153/152 | 11.352 | (32×17)/(23×19) | [-3 2 0 0 0 0 1 -1⟩ | Ganassisma, Ganassi's comma | |
171/170 | 10.154 | (32×19)/(2×5×17) | [-1 2 -1 0 0 0 -1 1⟩ | Malcolmisma | |
190/189 | 9.1358 | (2×5×19)/(33×7) | [1 -3 1 -1 0 0 0 1⟩ | Cotylisma | |
209/208 | 8.3033 | (11×19)/(24×13) | [-4 0 0 0 1 -1 0 1⟩ | Yama comma | |
210/209 | 8.2637 | (2×3×5×7)/(11×19) | [1 1 1 1 -1 0 0 -1⟩ | Spleen comma | |
286/285 | 6.0639 | (2×11×13)/(3×5×19) | [1 -1 -1 0 1 1 0 -1⟩ | Chthonisma | |
324/323 | 5.3516 | (2×32)2/(17×19) | [2 4 0 0 0 0 -1 -1⟩ | Photisma | S18 |
343/342 | 5.0547 | 73/(2×32×19) | [-1 -2 0 3 0 0 0 -1⟩ | Nutrisma | |
361/360 | 4.8023 | 192/(23×32×5) | [-3 -2 -1 0 0 0 0 2⟩ | Go comma, Dudon comma | S19 |
400/399 | 4.3335 | (22×5)2/(3×7×19) | [4 -1 2 -1 0 0 0 -1⟩ | Devichroma | S20 |
456/455 | 3.8007 | (23×3×19)/(5×7×13) | [3 1 -1 -1 0 -1 0 1⟩ | Abnobisma | |
476/475 | 3.6409 | (22×7×17)/(52×19) | [2 0 -2 1 0 0 1 -1⟩ | Hedwigma | |
495/494 | 3.5010 | (32×5×11)/(2×13×19) | [-1 2 1 0 1 -1 0 -1⟩ | Eulalisma | |
513/512 | 3.3780 | (33×19)/29 | [-9 3 0 0 0 0 0 1⟩ | Undevicesimal comma, undevicesimal schisma, Boethius' comma, 513th harmonic | |
969/968 | 1.7875 | (3×17×19)/(23×112) | [-3 1 0 0 -2 0 1 1⟩ | ||
1216/1215 | 1.4243 | (26×19)/(35×5) | [6 -5 -1 0 0 0 0 1⟩ | Password comma, Eratosthenes' comma | |
1331/1330 | 1.3012 | 113/(2×5×7×19) | [-1 0 -1 -1 3 0 0 -1⟩ | ||
1445/1444 | 1.1985 | 5×(17/(2×19))2 | [-2 0 1 0 0 0 2 -2⟩ | Aureusma | |
1521/1520 | 1.1386 | (3×13)2/(24×5×19) | [-4 2 -1 0 0 2 0 -1⟩ | Pinkanberry | S39 |
1540/1539 | 1.1245 | (22×5×7×11)/(34×19) | [2 -4 1 1 1 0 0 -1⟩ | ||
1729/1728 | 1.0016 | (7×13×19)/(22×3)3 | [-6 -3 0 1 0 1 0 1⟩ | Ramanujanisma | |
2376/2375 | 0.7288 | (23×33×11)/(53×19) | [3 3 -3 0 1 0 0 -1⟩ | ||
2432/2431 | 0.7120 | (27×19)/(11×13×17) | [7 0 0 0 -1 -1 -1 1⟩ | Blumeyer comma | |
2926/2925 | 0.5918 | (2×7×11×19)/(32×52×13) | [1 -2 -2 1 1 -1 0 1⟩ | ||
3136/3135 | 0.5521 | (23×7)2/(3×5×11×19) | [6 -1 -1 2 -1 0 0 -1⟩ | S56 | |
3250/3249 | 0.5328 | (2×53×13)/(3×19)2 | [1 -2 3 0 0 1 0 -2⟩ | ||
4200/4199 | 0.4123 | (23×3×52×7)/(13×17×19) | [3 1 2 1 0 -1 -1 -1⟩ | ||
5776/5775 | 0.2998 | (22×19)2/(3×52×7×11) | [4 -1 -2 -1 -1 0 0 2⟩ | S76 | |
5929/5928 | 0.2920 | (7×11)2/(23×3×13×19) | [-3 -1 0 2 2 -1 0 -1⟩ | S77 | |
5985/5984 | 0.2893 | (32×5×7×19)/(25×11×17) | [-5 2 1 1 -1 0 -1 1⟩ | ||
6175/6174 | 0.2804 | (52×13×19)/(2×32×73) | [-1 -2 2 -3 0 1 0 1⟩ | ||
6860/6859 | 0.2524 | (22×5×73)/193 | [2 0 1 3 0 0 0 -3⟩ | ||
10241/10240 | 0.1691 | (72×11×19)/(211×5) | [-11 0 -1 2 1 0 0 1⟩ | ||
10830/10829 | 0.1599 | (2×3×5×192)/(72×13×17) | [1 1 1 -2 0 -1 -1 2⟩ | ||
12636/12635 | 0.1370 | (22×35×13)/(5×7×192) | [2 5 -1 -1 0 1 0 -2⟩ | ||
13377/13376 | 0.1294 | (3×73×13)/(26×11×19) | [-6 1 0 3 -1 1 0 -1⟩ | ||
14080/14079 | 0.1230 | (28×5×11)/(3×13×192) | [8 -1 1 0 1 -1 0 -2⟩ | ||
14365/14364 | 0.1205 | (5×132×17)/(22×33×7×19) | [-2 -3 1 -1 0 2 1 -1⟩ | ||
23409/23408 | 0.07396 | (32×17)2/(24×7×11×19) | [-4 4 0 -1 -1 0 1 -1⟩ | S153 | |
27456/27455 | 0.06306 | (26×3×11)/(5×172×19) | [6 1 -1 0 1 0 -2 -1⟩ | ||
28900/28899 | 0.05991 | (2×5×17)2/(32×132×19) | [2 -2 2 0 0 -2 2 -1⟩ | S170 | |
43681/43680 | 0.03963 | (11×19)2/(25×3×5×7×13) | [-5 -1 -1 -1 2 -1 0 2⟩ | S209 | |
89376/89375 | 0.01937 | (25×3×72×19)/(54×11×13) | [5 1 -4 2 -1 -1 0 1⟩ | ||
104976/104975 | 0.01649 | (2×32)4/(52×13×17×19) | [4 8 -2 0 0 0 -1 -1 -1⟩ | S324 | |
165376/165375 | 0.01047 | (29×17×19)/(33×53×72) | [9 -3 -3 -2 0 0 1 1⟩ | Decimillisma | |
228096/228095 | 0.007590 | (28×34×11)/(5×74×19) | [8 4 -1 -4 1 0 0 -1⟩ | ||
601426/601425 | 0.002879 | (2×72×17×192)/(37×52×11) | [1 -7 -2 2 -1 0 1 2⟩ | ||
633556/633555 | 0.002733 | (22×7×113×17)/(33×5×13×192) | [2 -3 -1 1 3 -1 1 -2⟩ | Devicisma | |
709632/709631 | 0.002440 | (210×32×7×11)/(133×17×19) | [10 2 0 1 1 -3 -1 -1⟩ | ||
5909761/5909760 | 0.0002929 | (11×13×17)2/(28×35×5×19) | [-8 -5 -1 0 2 2 2 -1⟩ | S2431 | |
11859211/11859210 | 0.0001460 | (7×13×194)/(2×34×5×114) | [-1 -4 -1 1 -4 1 0 4⟩ |
23-limit
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
23/22 | 76.956 | 23/(2×11) | [-1 0 0 0 -1 0 0 0 1⟩ | Greater vicesimotertial semitone | |
24/23 | 73.681 | (23×3)/23 | [3 1 0 0 0 0 0 0 -1⟩ | Small vicesimotertial semitone | |
46/45 | 38.051 | (2×23)/(32×5) | [1 -2 -1 0 0 0 0 0 1⟩ | Vicesimotertial 1/5-tone | |
69/68 | 25.274 | (3×23)/(22×17) | [-2 1 0 0 0 0 -1 0 1⟩ | Large vicesimotertial 1/8-tone | |
70/69 | 24.910 | (2×5×7)/(3×23) | [1 -1 1 1 0 0 0 0 -1⟩ | Small vicesimotertial 1/8-tone | |
92/91 | 18.921 | (22×23)/(7×13) | [2 0 0 -1 0 -1 0 0 1⟩ | ||
115/114 | 15.120 | (5×23)/(2×3×19) | [-1 -1 1 0 0 0 0 -1 1⟩ | ||
161/160 | 10.787 | (7×23)/(25×5) | [-5 0 -1 1 0 0 0 0 1⟩ | Major kirnbergerisma | |
162/161 | 10.720 | (2×34)/(7×23) | [1 4 0 -1 0 0 0 0 -1⟩ | Minor kirnbergerisma | |
208/207 | 8.3433 | (24×13)/(32×23) | [4 -2 0 0 0 1 0 0 -1⟩ | ||
231/230 | 7.5108 | (3×7×11)/(2×5×23) | [-1 1 -1 1 1 0 0 0 -1⟩ | ||
253/252 | 6.8564 | (11×23)/((2×3)2×7) | [-2 -2 0 -1 1 0 0 0 1⟩ | ||
276/275 | 6.2840 | (22×3×23)/(52×11) | [2 1 -2 0 -1 0 0 0 1⟩ | ||
300/299 | 5.7804 | ((2×5)2×3)/(13×23) | [2 1 2 0 0 -1 0 0 -1⟩ | ||
323/322 | 5.3682 | (17×19)/(2×7×23) | [-1 0 0 -1 0 0 1 1 -1⟩ | ||
391/390 | 4.4334 | (17×23)/(2×3×5×13) | [-1 -1 -1 0 0 -1 1 0 1⟩ | ||
392/391 | 4.4221 | (23×72)/(17×23) | [3 0 0 2 0 0 -1 0 -1⟩ | ||
460/459 | 3.7676 | (22×5×23)/(33×17) | [2 -3 1 0 0 0 -1 0 1⟩ | ||
484/483 | 3.5806 | (2×11)2/(3×7×23) | [2 -1 0 -1 2 0 0 0 -1⟩ | S22 | |
507/506 | 3.4180 | (3×132)/(2×11×23) | [-1 1 0 0 -1 2 0 0 -1⟩ | ||
529/528 | 3.2758 | 232/(24×3×11) | [-4 -1 0 0 -1 0 0 0 2⟩ | S23 | |
576/575 | 3.0082 | (23×3)2/(23×52) | [6 2 -2 0 0 0 0 0 -1⟩ | Worcester comma | S24 |
736/735 | 2.3538 | (25×23)/(3×5×72) | [5 -1 -1 -2 0 0 0 0 1⟩ | ||
760/759 | 2.2794 | (23×5×19)/(3×11×23) | [3 -1 1 0 -1 0 0 1 -1⟩ | ||
875/874 | 1.9797 | (53×7)/(2×19×23) | [-1 0 3 1 0 0 0 -1 -1⟩ | ||
897/896 | 1.9311 | (3×13×23)/(27×7) | [-7 1 0 -1 0 1 0 0 1⟩ | ||
1105/1104 | 1.5674 | (5×13×17)/(24×3×23) | [-4 -1 1 0 0 1 1 0 -1⟩ | ||
1197/1196 | 1.4469 | (32×17×19)/(22×13×23) | [-2 2 0 0 0 -1 1 1 -1⟩ | ||
1288/1287 | 1.3446 | (23×7×23)/(32×11×13) | [3 -2 0 1 -1 -1 0 0 1⟩ | ||
1496/1495 | 1.1576 | (23×11×17)/(5×13×23) | [3 0 -1 0 1 -1 1 0 -1⟩ | ||
1863/1862 | 0.92952 | (34×23)/(2×72×19) | [-1 4 0 -2 0 0 0 -1 1⟩ | ||
2024/2023 | 0.85556 | (23×11×23)/(7×172) | [3 0 0 -1 1 0 -2 0 1⟩ | ||
2025/2024 | 0.85514 | (32×5)2/(23×11×23) | [-3 4 2 0 -1 0 0 0 -1⟩ | S45 | |
2185/2184 | 0.79251 | (5×19×23)/(23×3×7×13) | [-3 -1 1 -1 0 -1 0 1 1⟩ | ||
2300/2299 | 0.75287 | (22×52×23)/(112×19) | [2 0 2 0 -2 0 0 -1 1⟩ | ||
2646/2645 | 0.65441 | (2×33×72)/(5×232) | [1 3 -1 2 0 0 0 0 -2⟩ | ||
2737/2736 | 0.63265 | (7×17×23)/(24×32×19) | [-4 -2 0 1 0 0 1 -1 1⟩ | ||
3060/3059 | 0.56586 | (22×32×5×17)/(7×19×23) | [2 2 1 -1 0 0 1 -1 -1⟩ | ||
3381/3380 | 0.51212 | (3×72×23)/(22×5×132) | [-2 1 -1 2 0 -2 0 0 1⟩ | ||
3520/3519 | 0.49190 | (26×5×11)/(32×17×23) | [6 -2 1 0 1 0 -1 0 -1⟩ | ||
3888/3887 | 0.44533 | (24×35)/(132×23) | [4 5 0 0 0 -2 0 0 -1⟩ | ||
4693/4692 | 0.36893 | (13×192)/(22×3×17×23) | [-2 -1 0 0 0 1 -1 2 -1⟩ | ||
4761/4760 | 0.36367 | (3×23)2/(23×5×7×17) | [-3 2 -1 -1 0 0 -1 0 2⟩ | S69 | |
5083/5082 | 0.34063 | (13×17×23)/(2×3×7×112) | [-1 -1 0 -1 -2 1 1 0 1⟩ | ||
7866/7865 | 0.22010 | (2×32×19×23)/(5×112×13) | [1 2 -1 0 -2 -1 0 1 1⟩ | ||
8281/8280 | 0.20907 | (7×13)2/(23×32×5×23) | [-3 -2 -1 2 0 2 0 0 -1⟩ | S91 | |
8625/8624 | 0.20073 | (3×53×23)/(24×72×11) | [-4 1 3 -2 -1 0 0 0 1⟩ | ||
10626/10625 | 0.16293 | (2×3×7×11×23)/(54×17) | [1 1 -4 1 1 0 -1 0 1⟩ | ||
11271/11270 | 0.15361 | (3×13×172)/(2×5×72×23) | [-1 1 -1 -2 0 1 2 0 -1⟩ | ||
11662/11661 | 0.14846 | (2×73×17)/(3×132×23) | [1 0 0 3 0 -2 1 0 -1⟩ | ||
12168/12167 | 0.14228 | (23×32×132)/233 | [3 2 0 0 0 2 0 0 -3⟩ | ||
16929/16928 | 0.10227 | (34×11×19)/(25×232) | [-5 4 0 0 1 0 0 1 -2⟩ | ||
19551/19550 | 0.088552 | (3×73×19)/(2×52×17×23) | [-1 1 -2 3 0 0 -1 1 -1⟩ | ||
21505/21504 | 0.080506 | (5×11×17×23)/(210×3×7) | [-10 -1 1 -1 1 0 1 0 1⟩ | ||
21736/21735 | 0.079650 | (23×11×13×19)/(33×5×7×23) | [3 -3 -1 -1 1 1 0 1 -1⟩ | ||
23276/23275 | 0.074380 | (22×11×232)/(52×72×19) | [2 0 -2 -2 1 0 0 -1 2⟩ | ||
25025/25024 | 0.069182 | (52×7×11×13)/(26×17×23) | [-6 0 2 1 1 1 -1 0 -1⟩ | ||
25921/25920 | 0.066790 | (7×23)2/(26×34×5) | [-6 -4 -1 2 0 0 0 0 2⟩ | S161 | |
43264/43263 | 0.040016 | (24×13)2/(32×11×19×23) | [8 -2 0 0 -1 2 0 -1 -1⟩ | S208 | |
52326/52325 | 0.033086 | (2×34×17×19)/(52×7×13×23) | [1 4 -2 -1 0 -1 1 1 -1⟩ | ||
71875/71874 | 0.024087 | (55×23)/(2×33×113) | [-1 -3 5 0 -3 0 0 0 1⟩ | ||
75141/75140 | 0.023040 | (33×112×23)/(22×5×13×172) | [-2 3 -1 0 2 -1 -2 0 1⟩ | ||
76545/76544 | 0.022617 | (37×5×7)/(28×13×23) | [-8 7 1 1 0 -1 0 0 -1⟩ | ||
104329/104328 | 0.016594 | (17×19)2/(23×34×7×23) | [-3 -4 0 -1 -1 0 2 2 -1⟩ | S323 | |
122452/122451 | 0.014138 | (22×113×23)/(3×74×17) | [2 -1 0 -4 3 0 -1 0 1⟩ | ||
126225/126224 | 0.013716 | (33×52×11×17)/(24×73×23) | [-4 3 2 -3 1 0 1 0 -1⟩ | ||
152881/152880 | 0.011324 | (17×23)2/(24×3×5×72×13) | [-4 -1 -1 -2 0 -1 2 0 2⟩ | S391 | |
202125/202124 | 0.0085652 | (3×53×72×11)/(22×133×23) | [-2 1 3 2 1 -3 0 0 -1⟩ | ||
264385/264384 | 0.0065482 | (5×112×19×23)/(26×35×17) | [-6 -5 1 0 2 0 -1 1 1⟩ | ||
282625/282624 | 0.0061256 | (53×7×17×19)/(212×3×23) | [-12 -1 3 1 0 0 1 1 -1⟩ | ||
328510/328509 | 0.0052700 | (2×5×7×13×192)/(3×23)3 | [1 -3 1 1 0 1 0 0 -3⟩ | ||
2023425/2023424 | 0.00085560 | (32×52×17×232)/(213×13×19) | [-13 2 2 0 0 -1 1 -1 2⟩ | ||
4096576/4096575 | 0.00042261 | (23×11×23)2/(34×52×7×172) | [6 -4 -2 -1 2 0 -2 0 2⟩ | S2024 | |
5142501/5142500 | 0.00033665 | (33×72×132×23)/(22×54×112×17) | [-2 3 -4 2 -2 2 -1 0 1⟩ |
29-limit
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
29/28 | 60.751 | 29/(22×7) | 2.7.29 [-2 -1 1⟩ | Large vicesimononal 1/4-tone | |
30/29 | 58.692 | (2×3×5)/29 | 2.3.5.29 [1 1 1 -1⟩ | Small vicesimononal 1/4-tone | |
58/57 | 30.109 | (2×29)/(3×19) | 2.3.19.29 [1 -1 -1 1⟩ | ||
88/87 | 19.786 | (23×11)/(3×29) | 2.3.11.29 [3 -1 1 -1⟩ | ||
116/115 | 14.989 | (22×29)/(5×23) | 2.5.23.29 [2 -1 -1 1⟩ | ||
117/116 | 14.860 | (33×13)/(22×29) | 2.3.13.29 [-2 3 1 -1⟩ | ||
145/144 | 11.981 | (5×29)/(22×3)2 | 2.3.5.29 [-4 -2 1 1⟩ | 29th-partial chroma | |
175/174 | 9.9211 | (52×7)/(2×3×29) | 2.3.5.7.29 [-1 -1 2 1 -1⟩ | ||
204/203 | 8.5073 | (22×3×17)/(7×29) | 2.3.7.17.29 [2 1 -1 1 -1⟩ | ||
232/231 | 7.4783 | (23×29)/(3×7×11) | 2.3.7.11.29 [3 -1 -1 -1 1⟩ | ||
261/260 | 6.6458 | (32×29)/(22×5×13) | 2.3.5.13.29 [-2 2 -1 -1 1⟩ | ||
290/289 | 5.9801 | (2×5×29)/172 | 2.5.17.29 [1 1 -2 1⟩ | ||
320/319 | 5.4186 | (26×5)/(11×29) | 2.5.11.29 [6 1 -1 -1⟩ | ||
378/377 | 4.5861 | (2×33×7)/(13×29) | 2.3.7.13.29 [1 3 1 -1 -1⟩ | ||
406/405 | 4.2694 | (2×7×29)/(34×5) | 2.3.5.7.29 [1 -4 -1 1 1⟩ | ||
494/493 | 3.5081 | (2×13×19)/(17×29) | 2.13.17.19.29 [1 1 -1 1 -1⟩ | ||
551/550 | 3.1448 | (19×29)/(2×52×11) | 2.5.11.19.29 [-1 -2 -1 1 1⟩ | ||
552/551 | 3.1391 | (23×3×23)/(19×29) | 2.3.19.23.29 [3 1 -1 1 -1⟩ | Marmosarubra | |
609/608 | 2.8451 | (3×7×19)/(25×29) | 2.3.7.19.29 [-5 1 1 1 -1⟩ | ||
638/637 | 2.7157 | (2×11×29)/(72×13) | 2.7.11.13.29 [1 -2 1 -1 1⟩ | ||
726/725 | 2.3863 | (2×3×112)/(52×29) | 2.3.5.11.29 [1 1 -2 2 -2⟩ | ||
783/782 | 2.2124 | 2.3.17.23.29 [-1 3 -1 -1 1⟩ | |||
784/783 | 2.2096 | (22×7)2/(33×29) | 2.3.7.29 [4 -3 2 -1⟩ | S28 | |
841/840 | 2.0598 | 292/(23×3×5×7) | 2.3.5.7.29 [-3 -1 -1 -1 2⟩ | S29 | |
1015/1014 | 1.7065 | 2.3.5.7.13.29 [-1 -1 1 1 -2 1⟩ | |||
1045/1044 | 1.6575 | 2.3.5.11.19.29 [-2 -2 1 1 1 -1⟩ | |||
1276/1275 | 1.3573 | 2.3.5.11.17.29 [2 -1 -2 1 -1 1⟩ | |||
1450/1449 | 1.1944 | 2.3.5.7.23.29 [1 -2 2 -1 -1 1⟩ | |||
1596/1595 | 1.0851 | 2.3.5.7.11.19.29 [2 1 -1 1 -1 1 -1⟩ | |||
1625/1624 | 1.0657 | 2.5.7.13.29 [-3 3 -1 1 -1⟩ | |||
1683/1682 | 1.0290 | 2.3.11.17.29 [-1 2 1 1 -2⟩ | |||
2001/2000 | 0.86540 | 2.3.5.23.29 [-4 1 -3 1 1⟩ | |||
2002/2001 | 0.86497 | 2.3.7.11.13.23.29 [1 -1 1 1 1 -1 -1⟩ | |||
2176/2175 | 0.79579 | 2.3.5.17.29 [7 -1 -2 1 -1⟩ | |||
2205/2204 | 0.78532 | 2.3.5.7.19.29 [-2 2 1 2 -1 -1⟩ | |||
2262/2261 | 0.76552 | 2.3.7.13.17.19.29 [1 1 -1 1 -1 -1 1⟩ | |||
2465/2464 | 0.70247 | 2.5.7.11.17.29 [-5 1 -1 -1 1 1⟩} | |||
2640/2639 | 0.65589 | 2.3.5.7.11.13.29 [4 1 1 -1 1 -1 -1⟩ | |||
2755/2754 | 0.62851 | 2.3.5.17.19.29 [-1 -4 1 -1 1 1⟩ | |||
2784/2783 | 0.62196 | 2.3.11.23.29 [5 1 -2 -1 1⟩ | |||
3249/3248 | 0.53293 | 2.3.7.19.29 [-4 2 -1 2 -1⟩ | S57 | ||
3451/3450 | 0.50173 | 2.3.5.7.17.23.29 [-1 -1 -2 1 1 -1 1⟩ | |||
3510/3509 | 0.49330 | 2.3.5.11.13.29 [1 3 1 -2 1 -1⟩ | |||
4641/4640 | 0.37307 | 2.3.5.7.13.17.29 [-5 1 -1 1 1 1 -1⟩ | |||
4785/4784 | 0.36184 | 2.3.5.11.13.23.29 [-4 1 1 1 -1 -1 1⟩ | |||
4901/4900 | 0.35328 | 2.5.7.13.29 [-2 -2 -2 2 1⟩ | |||
5104/5103 | 0.33922 | 2.3.7.11.29 [4 -6 -1 1 1⟩ | |||
5888/5887 | 0.29405 | 2.7.23.29 [8 -1 1 -2⟩ | |||
5916/5915 | 0.29266 | 2.3.5.7.13.17.29 [2 1 -1 -1 -2 1 1⟩ | |||
6670/6669 | 0.25957 | 2.3.5.13.19.23.29 [1 -3 1 -1 -1 1 1⟩ | |||
7106/7105 | 0.24365 | 2.5.7.11.17.19.29 [1 -1 -2 1 1 1 -1⟩ | |||
7425/7424 | 0.23318 | 2.3.5.11.29 [-8 3 2 1 -1⟩ | |||
7889/7888 | 0.21946 | 2.7.17.23.29 [-4 3 -1 1 -1⟩ | |||
8671/8670 | 0.19967 | 2.3.5.13.17.23.29 [-1 -1 -1 1 -2 1 1⟩ | |||
9802/9801 | 0.17663 | 2.3.11.13.29 [1 -4 -2 2 1⟩ | |||
10557/10556 | 0.16400 | 2.3.7.13.17.23.29 [-2 3 -1 -1 1 1 -1⟩ | |||
11340/11339 | 0.15267 | 2.3.5.7.17.23.29 [2 4 1 1 -1 -1 -1⟩ | |||
12006/12005 | 0.14420 | 2.3.5.7.23.29 [1 2 -1 -4 1 1⟩ | |||
12673/12672 | 0.13661 | 2.3.11.19.23.29 [-7 -2 -1 1 1 1⟩ | |||
13225/13224 | 0.13091 | 2.3.5.19.23.29 [-3 -1 2 -1 2 -1⟩ | S115 | ||
13311/13310 | 0.13007 | 2.3.5.11.17.29 [-1 3 -1 -3 1 1⟩ | |||
13312/13311 | 0.13006 | 2.3.13.17.29 [10 -3 1 -1 -1⟩ | |||
13456/13455 | 0.12866 | 2.3.5.13.23.29 [4 -2 -1 -1 -1 2⟩ | S116 | ||
19228/19227 | 0.090039 | 2.3.11.13.17.19.23.29 [2 -1 1 -1 -1 1 1 -1⟩ | |||
20736/20735 | 0.083491 | 2.3.5.11.13.29 [8 4 -1 -1 -1 -1⟩ | S144 | ||
23751/23750 | 0.072893 | 2.3.5.7.13.19.29 [-1 2 -4 1 1 -1 1⟩ | |||
24795/24794 | 0.069823 | 2.3.5.7.11.19.23.29 [-1 2 1 -2 -1 1 -1 1⟩ | |||
25840/25839 | 0.067000 | 2.3.5.11.17.19.29 [4 -4 1 -1 1 1 -1⟩ | |||
27000/26999 | 0.064121 | 2.3.5.7.19.29 [3 3 3 -2 -1 -1⟩ | |||
30625/30624 | 0.056531 | 2.3.5.7.11.20 [-5 -1 4 2 -1 -1⟩ | S175 | ||
30856/30855 | 0.056108 | 2.3.5.7.11.17.19.29 [3 -1 -1 1 -2 -1 1 1⟩ | |||
35322/35321 | 0.049014 | 2.3.7.11.13.19.29 [1 1 1 -1 -2 -1 2⟩ | |||
47125/47124 | 0.036737 | 2.3.5.7.11.13.17.29 [-2 -2 3 -1 -1 1 -1 1⟩ | |||
53361/53360 | 0.032444 | 2.3.5.7.11.23.29 [-4 2 -1 2 2 -1 -1⟩ | S231 | ||
72501/72500 | 0.023879 | 2.3.5.11.13.29 [-2 1 -4 1 3 -1⟩ | |||
83521/83520 | 0.020728 | 2.3.5.17.29 [-6 -2 -1 4 -1⟩ | S289 | ||
87465/87464 | 0.019794 | 2.3.5.7.13.17.29 [-3 1 1 3 -1 1 -2⟩ | |||
136851/136850 | 0.012651 | 2.3.5.7.11.13.17.23.29 [-1 1 -2 -1 2 1 -1 -1 1⟩ | |||
158950/158949 | 0.010892 | 2.3.5.7.11.17.29 [1 -3 2 -1 1 2 -2⟩ | |||
166635/166634 | 0.010389 | 2.3.5.7.13.17.23.29 [-1 2 1 1 -2 -1 2 -1⟩ | |||
168751/168750 | 0.010259 | 2.3.5.11.23.29 [-1 -3 -5 1 2 1⟩ | |||
176001/176000 | 0.0098365 | 2.3.5.7.11.17.29 [-7 1 -3 1 -1 2 1⟩ | |||
176176/176175 | 0.0098268 | 2.3.5.7.11.13.29 [4 -5 -2 1 2 1 -1⟩ | |||
184093/184092 | 0.0094042 | 2.3.7.13.17.23.29 [-2 -1 2 1 2 -2 -1⟩ | |||
240787/240786 | 0.0071899 | 2.3.7.13.19.23.29 [-1 -3 -3 -1 2 1 1⟩ | |||
244036/244035 | 0.0070942 | 2.3.5.11.13.17.19.29 [2 -2 -1 -1 2 -1 2 -1⟩ | S494 | ||
303601/303600 | 0.0057023 | 2.3.5.11.19.23.29 [-4 -1 -2 -1 2 -1 2⟩ | S551 | ||
410670/410669 | 0.0042156 | 2.3.5.7.13.17.29 [1 5 1 -2 2 -2 -1⟩ | |||
418761/418760 | 0.0041342 | 2.3.5.7.17.19.23.29 [-3 2 -1 1 2 -2 1 -1⟩ | |||
613089/613088 | 0.0028238 | 2.3.7.17.23.29 [-5 6 -2 -1 -1 2⟩ | S783 | ||
949026/949025 | 0.0018242 | 2.3.5.7.11.13.17.23.29 [1 1 -2 -1 -1 1 -1 3 -1⟩ | |||
1163800/1163799 | 0.0014876 | 2.3.5.7.11.13.23.29 [3 -2 2 -3 1 -1 2 -1⟩ | |||
1235169/1235168 | 0.0014016 | 2.3.11.13.17.23.29 [-5 5 -3 1 1 1 -1⟩ | |||
1243840/1243839 | 0.0013918 | 2.3.5.13.17.23.29 [6 -1 1 2 -1 1 -3⟩ | |||
1625625/1625624 | 0.0010650 | 2.3.5.7.11.13.17.29 [-3 2 4 -2 -1 -1 2 -1⟩ | S1275 | ||
1852201/1852200 | 0.00093469 | 2.3.5.7.13.17.29 [-3 -3 -2 -3 1 3 1⟩ | |||
2697696/2697695 | 0.00064175 | 2.3.5.7.11.13.17.19.29 [5 2 -1 -3 -2 -1 1 1 1⟩ | |||
4004001/4004000 | 0.00043238 | 2.3.5.7.11.13.23.29 [-5 2 -3 -1 -1 -1 2 2⟩ | S2001 | ||
4090625/4090624 | 0.00042322 | 2.5.7.11.17.19.29 [-8 5 1 1 1 -1 -2⟩ | |||
8268800/8268799 | 0.00020937 | 2.5.7.11.17.19.23.29 [10 2 -2 -1 1 1 -2 -1⟩ | |||
10556001/10556000 | 0.00016400 | 2.3.5.7.13.19.29 [-5 4 -3 -1 -1 4 -1⟩ | S3249 | ||
18085705/18085704 | 9.5724×10-5 | 2.3.5.7.11.13.17.23.29 [-3 -1 1 -3 1 -3 1 1 2⟩ | |||
96059601/96059600 | 1.8022×10-5 | 2.3.5.7.11.13.29 [-4 8 -2 -2 4 -2 -1⟩ | S9801 | ||
177182721/177182720 | 9.7709×10-6 | 2.3.5.11.13.17.29 [-11 6 -1 -3 -1 2 2⟩ | S13311 |
31-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
31/30 | 56.767 | 31/(2×3×5) | 2.3.5.31 [-1 -1 -1 1⟩ | Large tricesimoprimal 1/4-tone | |
32/31 | 54.964 | 25/31 | 2.31 [5 -1⟩ | Small tricesimoprimal 1/4-tone, octave-reduced 31st subharmonic | |
63/62 | 27.700 | (32×7)/(2×31) | 2.3.7.31 [-1 2 1 -1⟩ | tricesimoprimal 1/8-tone | |
93/92 | 18.716 | (3×31)/(22×23) | 2.3.23.31 [-2 1 -1 1⟩ | ||
125/124 | 13.906 | 53/(22×31) | 2.5.31 [-2 3 -1⟩ | Twizzler | |
155/154 | 11.205 | (5×31)/(2×7×11) | 2.5.7.11.31 [-1 1 -1 -1 1⟩ | ||
156/155 | 11.133 | (22×3×13)/(5×31) | 2.3.5.13.31 [2 1 -1 1 -1⟩ | ||
187/186 | 9.2828 | (11×17)/(2×3×31) | 2.3.11.17.31 [-1 -1 1 1 -1⟩ | ||
217/216 | 7.9965 | (7×31)/(2×3)3 | 2.3.7.31 [-3 -3 1 1⟩ | ||
248/247 | 6.9949 | (23×31)/(13×19) | 2.13.19.31 [3 -1 -1 1⟩ | ||
280/279 | 6.1940 | (23×5×7)/(32×31) | 2.3.5.7.31 [3 -2 1 1 -1⟩ | ||
341/340 | 5.0844 | (11×31)/(22×5×17) | 2.5.11.17.31 [-2 -1 1 -1 1⟩ | ||
342/341 | 5.0695 | (2×32×19)/(11×31) | 2.3.11.19.31 [1 2 -1 1 -1⟩ | ||
435/434 | 3.9844 | (3×5×29)/(2×7×31) | 2.3.5.7.29.31 [-1 1 1 -1 1 -1⟩ | ||
465/464 | 3.7271 | (3×5×31)/(24×29) | 2.3.5.29.31 [-4 1 1 -1 -1⟩ | ||
496/495 | 3.4939 | (24×31)/(32×5×11) | 2.3.5.11.31 [4 -2 -1 -1 1⟩ | ||
528/527 | 3.2820 | (24×3×11)/(17×31) | 2.3.11.17.31 [4 1 1 -1 -1⟩ | ||
589/588 | 2.9418 | (19×31)/(22×3×72) | 2.3.7.19.31 [-2 -1 -2 1 1⟩ | ||
621/620 | 2.7901 | (33×23)/(22×5×31) | 2.3.5.23.31 [-2 3 -1 1 -1⟩ | Owowhatsthisma | |
900/899 | 1.9247 | (2×3×5)2/(29×31) | 2.3.5.29.31 [2 2 2 -1 -1⟩ | S30 | |
961/960 | 1.8024 | 312/(26×3×5) | 2.3.5.31 [-6 -1 -1 2⟩ | S31 | |
1024/1023 | 1.9247 | 210/(3×11×31) | 2.3.11.31 [10 -1 -1 -1⟩ | S32 | |
3969/3968 | 0.43624 | (32×7)2/(27×31) | 2.3.7.31 [-7 4 2 -1⟩ | Yunzee comma | S63 |
37-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
37/36 | 47.434 | 37/(22×32) | 2.3.37 [-2 -2 1⟩ | Large tricesimoseptimal 1/4-tone, 37th-partial chroma | |
38/37 | 46.169 | (2×19)/37 | 2.19.37 [1 1 -1⟩ | Small tricesimoseptimal 1/4-tone | |
75/74 | 23.238 | (3×52)/(2×37) | 2.3.5.37 [-1 1 2 -1⟩ | ||
1296/1295 | 1.3363 | (2×3)4/(5×7×37) | 2.3.5.7.37 [4 4 -1 -1 -1⟩ | S36 | |
1369/1368 | 1.2651 | 372/(23×32×19) | 2.3.19.37 [-3 -2 -1 2⟩ | S37 | |
1444/1443 | 1.1993 | (2×19)2/(3×13×37) | 2.3.13.19.37 [2 -1 -1 2 -1⟩ | S38 | |
5292/5291 | 0.32717 | (22×33×72)/(11×13×37) | 2.3.7.11.13.37 [2 3 2 -1 -1 -1⟩ | Bullionisma |
41-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
41/40 | 42.749 | 41/(23×5) | 2.5.41 [-3 -1 1⟩ | Large quadracesimoprimal 1/5-tone | |
42/41 | 41.719 | (2×3×7)/41 | 2.3.7.41 [1 1 1 -1⟩ | Small quadracesimoprimal 1/5-tone | |
82/81 | 21.242 | (2×41)/34 | 2.3.41 [1 -4 1⟩ | 41st-partial chroma | |
1600/1599 | 1.0824 | (23×5)2/(3×13×41) | 2.3.5.13.41 [6 -1 2 -1 -1⟩ | S40 | |
1681/1680 | 1.0302 | 412/(24×3×5×7) | 2.3.5.7.41 [-4 -1 -1 -1 2⟩ | S41 | |
1682/1681 | 1.0296 | (2×292)/412 | 2.29.41 [1 2 -2⟩ | Shaftesburisma |
43-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
43/42 | 40.737 | 43/(2×3×7) | 2.3.7.43 [-1 -1 -1 1⟩ | Large quadracesimotertial 1/5-tone | |
44/43 | 39.800 | (22×11)/43 | 2.11.43 [2 1 -1⟩ | Small quadracesimotertial 1/5-tone | |
86/85 | 20.249 | (2×43)/(5×17) | 2.5.17.43 [1 -1 -1 1⟩ | ||
87/86 | 20.014 | (3×29)/(2×43) | 2.3.29.43 [-1 1 1 -1⟩ | ||
129/128 | 13.473 | (3×43)/27 | 2.3.43 [-7 1 1⟩ | 43rd-partial chroma | |
1764/1763 | 0.98170 | (2×3×7)2/(41×43) | 2.3.7.41.43 [2 2 2 -1 -1⟩ | S42 | |
1849/1848 | 0.93656 | 432/(23×3×7×11) | 2.3.7.11.43 [-3 -1 -1 -1 2⟩ | S43 | |
1936/1935 | 0.98170 | (22×11)2/(32×5×43) | 2.3.5.11.43 [4 -2 -1 2 -1⟩ | S44 |
47-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
47/46 | 37.232 | 47/(2×23) | 2.23.47 [-1 -1 1⟩ | ||
48/47 | 36.448 | (24×3)/47 | 2.3.47 [4 1 -1⟩ | ||
94/93 | 18.516 | (2×47)/(3×31) | 2.3.31.47 [1 -1 -1 1⟩ | ||
95/94 | 18.320 | (5×19)/(2×47) | 2.5.19.47 [-1 1 1 -1⟩ | ||
2116/2115 | 0.81836 | (2×23)2/(32×5×47) | 2.3.5.23.47 [2 -2 -1 2 -1⟩ | S46 | |
2209/2208 | 0.78390 | 472/(25×3×5) | 2.3.23.47 [-5 -1 -1 2⟩ | S47 | |
2304/2303 | 0.75157 | (24×3)2/(72×47) | 2.3.7.47 [8 2 -2 -1⟩ | S48 |
53-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
53/52 | 32.977 | 53/(22×13) | 2.13.53 [-2 -1 1⟩ | ||
54/53 | 32.360 | (2×33)/53 | 2.3.53 [1 3 -1⟩ | ||
106/105 | 16.410 | (2×53)/(3×5×7) | 2.3.5.7.53 [1 -1 -1 -1 1⟩ | ||
2809/2808 | 0.61643 | 532/(23×33×13) | 2.3.13.53 [-3 -3 -1 2⟩ | S53 | |
4081/4080 | 0.42427 | (7×11×53)/(24×3×5×17) | 2.3.5.7.11.17.53 [-4 -1 -1 1 1 -1 1⟩ |
59-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
59/58 | 29.594 | 59/(2×29) | 2.29.59 [-1 -1 1⟩ | ||
60/59 | 29.097 | (22×3×5)/59 | 2.3.5.59 [2 1 1 -1⟩ | ||
3481/3480 | 0.49741 | 592/(23×3×5×29) | 2.3.5.29.59 [-3 -1 -1 -1 2⟩ | S59 |
61-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
61/60 | 28.616 | 61/(22×3×5) | 2.3.5.61 [-2 -1 -1 1⟩ | ||
62/61 | 28.151 | (2×31)/61 | 2.31.61 [1 1 -1⟩ | ||
672/671 | 2.5782 | (25×3×7)/(11×61) | 2.3.7.11.61 [5 1 1 -1 -1⟩ | ||
1404/1403 | 1.2335 | (22×33×13)/(23×61) | 2.3.13.23.61 [2 3 1 -1 -1⟩ | ||
3721/3720 | 0.46532 | 612/(23×3×5×31) | 2.3.5.31.61 [-3 -1 -1 -1 2⟩ | S61 |
67-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
67/66 | 26.034 | 67/(2×3×11) | 2.3.11.67 [-1 -1 -1 1⟩ | ||
68/67 | 25.648 | (22×17)/67 | 2.17.67 [2 1 -1⟩ |
71-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
71/70 | 24.557 | 71/(2×5×7) | 2.5.7.71 [-1 -1 -1 1⟩ | ||
72/71 | 24.213 | (23×32)/71 | 2.3.71 [3 2 -1⟩ |
73-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
73/72 | 23.879 | 73/(23×32) | 2.3.73 [-3 -2 1⟩ | ||
74/73 | 23.555 | (2×37)/73 | 2.37.73 [1 1 -1⟩ |
79-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
79/78 | 22.054 | 79/(2×3×13) | 2.3.13.79 [-1 -1 -1 1⟩ | ||
80/79 | 21.777 | (24×5)/79 | 2.5.79 [4 1 -1⟩ |
83-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
83/82 | 20.985 | 83/(2×41) | 2.41.83 [-1 -1 1⟩ | ||
84/83 | 20.734 | (22×3×7)/83 | 2.3.7.83 [2 1 1 -1⟩ |
89-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
89/88 | 19.562 | 89/(23×11) | 2.11.89 [-3 -1 1⟩ | Sky comma | |
90/89 | 19.344 | (2×32×5)/89 | 2.3.5.89 [1 2 1 -1⟩ |
97-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
97/96 | 17.940 | 97/(25×3) | 2.3.97 [-5 -1 1⟩ | ||
98/97 | 17.756 | (2×72)/97 | 2.7.97 [1 2 -1⟩ |
101-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
101/100 | 17.226 | 101/(2×5)2 | 2.5.101 [-2 -2 1⟩ | ||
102/101 | 17.057 | (2×3×17)/101 | 2.3.17.101 [1 1 1 -1⟩ | ||
7777/7776 | 0.223 | 7×11×101/(2×3)5 | 2.3.7.11.101 [-5 -5 1 1 1⟩ | Pulsar comma |
103-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
103/102 | 16.890 | 103/(2×3×17) | 2.3.17.103 [-1 -1 -1 1⟩ | ||
104/103 | 16.727 | (23×13)/103 | 2.13.103 [3 1 -1⟩ |
107-limit (incomplete)
Ratio | Cents | Factorization | Monzo | Name(s) | Meta[1] |
---|---|---|---|---|---|
107/106 | 16.256 | 107/(2×53) | 2.53.107 [-1 -1 1⟩ | ||
108/107 | 16.105 | (22×33)/107 | 2.3.107 [2 3 -1⟩ | ||
750/749 | 2.3099 | (2×3×53)/(7×107) | 2.3.5.7.107 [1 1 3 -1 -1⟩ | Ancient Chinese tempering comma |
See also
Notes
External links
- List of intervals on the Huygens-Fokker Foundation website