# 159edo

(Redirected from Table of 159edo Intervals)
 ← 158edo 159edo 160edo →
Prime factorization 3 × 53
Step size 7.54717¢
Fifth 93\159 (701.887¢) (→31\53)
Semitones (A1:m2) 15:12 (113.2¢ : 90.57¢)
Consistency limit 17
Distinct consistency limit 17

The 159 equal divisions of the octave (159edo), or the 159(-tone) equal temperament (159tet, 159et) when viewed from a regular temperament perspective, divides the octave into 159 equal parts of about 7.55 cents each, a size close to both 243/242, the rastma, and 225/224, the marvel comma.

## Theory

A salient fact about 159edo is that 159 = 3 × 53, and thus, this system has both 3edo and 53edo as subsets- the former subset being shared with 12edo.

### History

Despite being none other than the tripled superset of the famous 53edo, and hence, one would think, fairly easy to find, it is a wonder that the first person to show theoretical interest in it was Ozan Yarman- specifically in terms of extracting a voluminous subset for representing maqams- in late 2005 to early 2006.

Yarman started by dividing the 4/3 perfect fourth into 33 equal parts and continued the resultant 15.1 cent comma until just below the octave, only to then reinstate the final 79th degree with the octave so as to arrive at the "yegah-neva" partition. He then rotated the scale to begin on the Turkish "rast" note which he notated as C according to Sipürde Ahenk (C Ney), and thus the 22.8 cent larger singular comma previously on top now appears just below the Turkish neva note in the midst of his tuning scheme. Not long after proposing said 79-tone system, Yarman visited the now-deceased Ejder Güleç in İzmir who affixed mandals on Yarman's Qanun according to Yarman's instructions.

Gene Ward Smith was the first to point out that Yarman's scheme was a MOS of 159tet and had an 80-pitch twin. Yarman adopted this argument, because his approach and the related MOS subset out of 159tet was, for all intents and purposes, synonymous. Yarman has stated that he thinks he introduced his Qanun to his now-deceased supervisor in Istanbul Technical University Turkish Music State Conservatory sometime during late 2006, and she suggested that Yarman include the double-sharp mandals. At the time this information was added to this article, Yarman remembered that the Qanun in his doctorate defense of 2008 included the double-sharp mandals. The acceptance of his thesis was in June 2008.

Accordingly, it is no coincidence that the first records of 159edo on this Wiki from the days of Wikispaces concern said 79-tone subset related to the yarman temperament which had been proposed by Yarman as a tuning standard for Arabic, Turkish and Persian music. Based on the information given by Ozan Yarman himself, his elder colleague M. Ugur Kececioglu first utilized 159edo in his revamped 2011 release of the Notist score editor and therein allowed the Arel-Ezgi-Uzdilek accidentals to be bent by as little a detail as 1/3rd of a single step of 53edo, while also mapping AEU altogether to a suitable subset of 53edo to allow transpositions throughout.

### Mappings and JI approximation quality

This system inherits its approximations of the 3rd, 5th and 13th harmonics from 53edo, however, the patent vals differ on the mappings for 7, 11 and 17 – in fact, this EDO has a very accurate 11 and an only slightly less accurate 17. Furthermore, 159edo demonstrates 3-to-2 telicity, as despite being contorted in the 5-limit, it is the largest EDO to temper out Mercator's comma in which said comma is less than half the size of a single EDO step. This means, among other things, that there is a perfect match between the direct mapping and the more complicated traditional mapping for an octave-reduced stack of fifty-three tempered 3/2 perfect fifths – a complete circle of fifths for this EDO.

However, while 159edo is consistent up to the 17-odd-limit, it proves to be inconsistent in the 19-odd-limit, with the ~19/17 mapped to the second closest step, and this despite 53edo's approximation of 19/16 being inherited from 53edo. In addition, the direct mapping and the more complicated traditional mapping for intervals such as 49/32, 35/32, and 169/128 do not match, and as a result, 159edo can be thought of as having a perfunctory 7-limit that mainly serves to bridge to the 11-limit and divide the nearly just 3/2 into three, as well as a similarly perfunctory 13-limit that mainly serves to bridge to the 17-limit and to absorb complex combinations of 3 and 5.

Notably, 159edo provides the optimal patent val for 11-limit guiron, 13-limit tritikleismic, the 13-limit rank-3 temperament portending, as well as the 17-limit rank-6 temperament tempering out 273/272. In addition to this, it also supports both forms of the yarman temperament, with a generator of 2\159 which can be taken as an approximate 105/104. Both have a MOS of 79 or 80 notes to the octave, and have their optimal patent vals supplied by 159edo in 7-limit, 11-limit, 13-limit, 17-limit and even 19-limit forms. While the patent val supports both cartography and iodine temperaments, which are among the best 13-limit temperaments in the Mercator family, the 159d and 159f mappings support other members of this temperament family.

### Prime harmonics

Approximation of prime harmonics in 159edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37
Error absolute (¢) +0.00 -0.07 -1.41 -2.79 -0.37 -2.79 +0.70 -3.17 -1.86 -3.16 +2.13 -2.29
relative (%) +0 -1 -19 -37 -5 -37 +9 -42 -25 -42 +28 -30
Steps
(reduced)
159
(0)
252
(93)
369
(51)
446
(128)
550
(73)
588
(111)
650
(14)
675
(39)
719
(83)
772
(136)
788
(152)
828
(33)

### Additional Properties of 159-tone equal temperament

The approximations of everything in the 17-odd-limit and even the approximations of 19/16, 29/16 and 31/16 all fall within the boundaries of the harmonic JND, and similarly this system can approximate the sounds of other systems such as 10edo, 13edo, 22edo and 31edo. Furthermore, the step size of 159edo is simultaneously above the average peak melodic JND and small enough to be well within the margin of error between Just 5-limit intervals and their 12edo counterparts, 159edo offers a decent balance between allowing the possibility of seamless modulation to keys that are not in the same series of fifths, and not having a step-size so small as to have individual steps blend completely into one another, even as it also allows one to also control the bandwidth of certain sounds. As a result of tempering out some of the commas, it allows essentially tempered chords including marveltwin chords, gentle chords, keenanismic chords, werckismic chords, and sinbadmic chords in the 13-odd-limit, in addition to island chords and nicolic chords in the 15-odd-limit.

### MOSes and other scales

No less than five possible generators for the diatonic MOS Scale are supported by 159edo, though these different diatonic scales have different descendants. The 91\159 generator results in large and small scale steps at 23\159 and 22\159 respectively, making for a quasi-equalized diatonic scale, which can be extended to a siskontyttonic MOS, while the 95\159 results in large and small scale steps at 31\159 and 2\159 respectively, making for a version approaching paucitonic, which can be extended to a reinatonic MOS. The 92\159 generator results in large and small scale steps at 25\159 and 17\159 respectively, and this makes for a very meantone-like diatonic scale perfect for xenharmonic pieces that follow in the classical tradition, though this can be extended to a veljentyttonic MOS. Conversely, the 94\159 generator results in results in large and small scale steps at 29\159 and 7\159 respectively, and this makes for a superpyth diatonic scale that is slightly harder and better than that of 22edo, which can be extended to an antireinatonic MOS. Finally, the patent 93\159 generator results in the same diatonic MOS scale found in 53edo, which, despite now having competition from other possible generators, is still the go-to for those looking for something more akin to the classic Pythagorean tuning, as well as for those looking to deal with good approximations of related 5-limit scales, or even just the basic form of the pythamystonic MOS.

In addition, 159edo has no less than four possible generators for the oneirotonic MOS scale, and of these, two of them are also supported by 53edo. The 60\159 generator results in large and small scale steps at 21\159 and 18\159 respectively, making for a distinctly ultra-soft scale, while the 63\159 generator results in large and small scale steps at 30\159 and 3\159 respectively, making for a distinctly ultra-hard scale. As for the remaining two generators, the 61\159 generator results in large and small scale steps at 24\159 and 13\159 respectively and comes the closest to any sort of basic form of this scale, however, the 62\159 generator is also a solid choice, and is also useful for at least one related non-MOS scale due to 62\159 approximating 21/16.

Furthermore, this EDO supports Wyschnegradsky's "Diatonicized Chromatic Scale" with large and small scale steps at 13\159 and 8\159 respectively.

## Intervals

The following table assumes 17-limit patent val 159 252 369 446 550 588 650].

Intervals highlighted in bold are prime harmonics or subharmonics. In addition, intervals that differ from assigned steps by more than 50%, multiples of such intervals, and intervals of odd limit higher than 1024, are not shown. Furthermore, when multiple well-known intervals for a given prime-limit share a step size, they may share a cell in the chart; conversely, a "?" in the chart means that no known interval meets the criteria for inclusion. Note that no 5-limit intervals can be represented by degrees other than multiples of 3, so those entries are left blank.

Table of 159edo intervals
Step Cents 5 limit 7 limit 11 limit 13 limit 17 limit
0 0 1/1
1 7.5471698 225/224 243/242 196/195, 351/350 256/255
2 15.0943396 ? 121/120, 100/99 144/143 120/119
3 22.6415094 81/80 ? ? 78/77 85/84
4 30.1886792 64/63 56/55, 55/54 ? 52/51
5 37.7358491 ? 45/44 ? 51/50
6 45.2830189 ? ? ? 40/39 192/187
7 52.8301887 ? 33/32 ? 34/33
8 60.3773585 28/27 ? ? 88/85
9 67.9245283 25/24 ? ? 26/25, 27/26 ?
10 75.4716981 ? ? ? 160/153
11 83.0188679 21/20 22/21 ? ?
12 90.5660377 256/243, 135/128 ? ? ? ?
13 98.1132075 ? 128/121 55/52 18/17
14 105.6603774 ? ? ? 17/16
15 113.2075472 16/15 ? ? ? ?
16 120.7547170 15/14 275/256 ? ?
17 128.3018868 ? ? 14/13 128/119
18 135.8490566 27/25 ? ? 13/12 ?
19 143.3962264 ? 88/81 ? ?
20 150.9433962 ? 12/11 ? ?
21 158.4905660 ? ? ? 128/117 561/512, 1024/935
22 166.0377358 ? 11/10 ? ?
23 173.5849057 567/512 243/220 ? 425/384
24 181.1320755 10/9 ? 256/231 ? ?
25 188.6792458 ? ? 143/128 512/459
26 196.2264151 28/25 121/108 ? ?
27 203.7735849 9/8 ? ? ? ?
28 211.3207547 ? ? 44/39 289/256
29 218.8679245 ? 25/22 ? 17/15
30 226.4150943 256/225 ? 154/135 ? ?
31 233.9622642 8/7 55/48 ? ?
32 241.5094340 ? 1024/891 ? ?
33 249.0566038 ? ? ? 15/13 ?
34 256.6037736 ? 297/256 ? ?
35 264.1509434 7/6 64/55 ? ?
36 271.6981132 75/64 ? ? 117/100 ?
37 279.2452830 ? ? ? 20/17
38 286.7924528 ? 33/28 13/11 85/72
39 294.3396226 32/27 ? ? ? ?
40 301.8867925 25/21 144/121 ? ?
41 309.4339622 ? ? 512/429 153/128
42 316.9811321 6/5 ? 77/64 ? ?
43 324.5283019 135/112 ? ? 512/425
44 332.0754717 ? 40/33, 121/100 ? 144/119, 165/136
45 339.6226415 ? ? ? 39/32 17/14
46 347.1698113 ? 11/9 ? ?
47 354.7169811 ? 27/22 ? ?
48 362.2641509 ? ? ? 16/13 21/17
49 369.8113208 ? ? 26/21 68/55
50 377.3584906 56/45 1024/825 ? ?
51 384.9056604 5/4 ? 96/77 ? ?
52 392.4528302 ? ? ? 64/51
53 400 63/50 121/96 ? 34/27
54 407.5471698 81/64 ? ? ? ?
55 415.0943396 ? 14/11 33/26 108/85
56 422.6415094 ? ? 143/112 51/40
57 430.1886792 32/25 ? ? 50/39 ?
58 437.7358491 9/7 165/128 ? ?
59 445.2830189 ? 128/99 ? 22/17
60 452.8301887 ? ? ? 13/10 ?
61 460.3773585 ? 176/135 ? ?
62 467.9245283 21/16 55/42, 72/55 ? 17/13
63 475.4716981 320/243, 675/512 ? ? ? ?
64 483.0188679 ? 33/25 ? 45/34
65 490.5660377 ? ? ? 85/64
66 498.1132075 4/3 ? ? ? ?
67 505.6603774 75/56 162/121 ? ?
68 513.2075472 ? 121/90 ? ?
69 520.7547170 27/20 ? ? 104/77 ?
70 528.3018868 256/189 110/81 ? ?
71 535.8490566 ? 15/11 ? ?
72 543.3962264 ? ? ? 160/117 256/187
73 550.9433962 ? 11/8 ? ?
74 558.4905660 112/81 ? ? ?
75 566.0377358 25/18 ? ? 18/13 ?
76 573.5849057 ? ? ? 357/256
77 581.1320755 7/5 ? ? ?
78 588.6792458 1024/729, 45/32 ? ? ? ?
79 596.2264151 ? ? ? 24/17
80 603.7735849 ? ? ? 17/12
81 611.3207547 729/512, 64/45 ? ? ? ?
82 618.8679245 10/7 ? ? ?
83 626.4150943 ? ? ? 512/357
84 633.9622642 36/25 ? ? 13/9 ?
85 641.5094340 81/56 ? ? ?
86 649.0566038 ? 16/11 ? ?
87 656.6037736 ? ? ? 117/80 187/128
88 664.1509434 ? 22/15 ? ?
89 671.6981132 189/128 81/55 ? ?
90 679.2452830 40/27 ? ? 77/52 ?
91 686.7924528 ? 180/121 ? ?
92 694.3396226 112/75 121/81 ? ?
93 701.8867925 3/2 ? ? ? ?
94 709.4339622 ? ? ? 128/85
95 716.9811321 ? 50/33 ? 68/45
96 724.5283019 243/160, 1024/675 ? ? ? ?
97 732.0754717 32/21 84/55, 55/36 ? 26/17
98 739.6226415 ? 135/88 ? ?
99 747.1698113 ? ? ? 20/13 ?
100 754.7169811 ? 99/64 ? 17/11
101 762.2641509 14/9 256/165 ? ?
102 769.8113208 25/16 ? ? 39/25 ?
103 777.3584906 ? ? 224/143 80/51
104 784.9056604 ? 11/7 52/33 85/54
105 792.4528302 128/81 ? ? ? ?
106 800 100/63 192/121 ? 27/17
107 807.5471698 ? ? ? 51/32
108 815.0943396 8/5 ? 77/48 ? ?
109 822.6415094 45/28 825/512 ? ?
110 830.1886792 ? ? 21/13 55/34
111 837.7358491 ? ? ? 13/8 34/21
112 845.2830189 ? 44/27 ? ?
113 852.8301887 ? 18/11 ? ?
114 860.3773585 ? ? ? 64/39 28/17
115 867.9245283 ? 33/20, 200/121 ? 119/72, 272/165
116 875.4716981 224/135 ? ? 425/256
117 883.0188679 5/3 ? 128/77 ? ?
118 890.5660377 ? ? 429/256 256/153
119 898.1132075 42/25 121/72 ? ?
120 905.6603774 27/16 ? ? ? ?
121 913.2075472 ? 56/33 22/13 144/85
122 920.7547170 ? ? ? 17/10
123 928.3018868 128/75 ? ? 200/117 ?
124 935.8490566 12/7 55/32 ? ?
125 943.3962264 ? 512/297 ? ?
126 950.9433962 ? ? ? 26/15 ?
127 958.4905660 ? 891/512 ? ?
128 966.0377358 7/4 96/55 ? ?
129 973.5849057 225/128 ? 135/77 ? ?
130 981.1320755 ? 44/25 ? 30/17
131 988.6792458 ? ? 39/22 512/289
132 996.2264151 16/9 ? ? ? ?
133 1003.7735849 25/14 216/121 ? ?
134 1011.3207547 ? ? 256/143 459/256
135 1018.8679245 9/5 ? 231/128 ? ?
136 1026.4150943 1024/567 440/243 ? 768/425
137 1033.9622642 ? 20/11 ? ?
138 1041.5094340 ? ? ? 117/64 1024/561, 935/512
139 1049.0566038 ? 11/6 ? ?
140 1056.6037736 ? 81/44 ? ?
141 1064.1509434 50/27 ? ? 24/13 ?
142 1071.6981132 ? ? 13/7 119/64
143 1079.2452830 28/15 512/275 ? ?
144 1086.7924528 15/8 ? ? ? ?
145 1094.3396226 ? ? ? 32/17
146 1101.8867925 ? 121/64 104/55 17/9
147 1109.4339622 243/128, 256/135 ? ? ? ?
148 1116.9811321 40/21 21/11 ? ?
149 1124.5283019 ? ? ? 153/80
150 1132.0754717 48/25 ? ? 25/13, 52/27 ?
151 1139.6226415 27/14 ? ? 85/44
152 1147.1698113 ? 64/33 ? 33/17
153 1154.7169811 ? ? ? 39/20 187/96
154 1162.2641509 ? 88/45 ? 100/51
155 1169.8113208 63/32 55/28, 108/55 ? 51/26
156 1177.3584906 160/81 ? ? 77/39 168/85
157 1184.9056604 ? 240/121, 99/50 143/72 119/60
158 1192.4528302 448/225 484/243 195/98, 700/351 255/128
159 1200 2/1

## Notation

Main article: 159edo notation

Because of the complexity of 159edo, notation requires systems that make use of multiple extra pairs of accidentals. This is because at high EDOs, systems with only a single extra accidental pair become unwieldy due to the sheer number of such accidentals required for notating some pitches, which in turn results in high amounts of clutter on scores. So far, several notation systems addressing this problem have been proposed.

## Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢)
Tuning error
Absolute (¢) Relative (%)
2.3.5.7 1029/1024, 10976/10935, 15625/15552 [159 252 369 446]] +0.411 0.413 5.47
2.3.5.7.11 385/384, 441/440, 4000/3993, 10976/10935 [159 252 369 446 550]] +0.350 0.389 5.15
2.3.5.7.11.13 325/324, 364/363, 385/384, 625/624, 10976/10935 [159 252 369 446 550 588]] +0.418 0.385 5.11
2.3.5.7.11.13.17 273/272, 325/324, 364/363, 375/374, 385/384, 3773/3757 [159 252 369 446 550 588 650]] +0.333 0.412 5.46

Notably, while 159edo plays host to a number of fun temperaments like gamelan and gentle, a number of microtemperaments have also been found hiding within its structure. This means that 159edo is well-balanced in terms of the possibilities for interesting temperament usage.

### Commas

Assuming the val 159 252 369 446 550 588 650], 159tet tempers out the following commas in the 17-limit.

Prime
limit
Ratio[1] Monzo Cents Color name Name
3 (52 digits) [-84 53 3.6150 Wa-53 Mercator's comma
5 (14 digits) [-21 3 7 10.0610 Lasepyo Semicomma
5 15625/15552 [-6 -5 6 8.1073 Tribiyo Kleisma
5 (14 digits) [9 -13 5 6.1536 Saquinyo Amity comma
5 (22 digits) [24 -21 4 4.1998 Sasaquadyo Vulture comma
5 (28 digits) [39 -29 3 2.2461 Tricot comma
5 32805/32768 [-15 8 1 1.9537 Layo Schisma
5 (44 digits) [-69 45 -1 1.6613 Counterschisma
5 (36 digits) [54 -37 2 0.2924 Monzisma
7 1029/1024 [-10 1 0 3 8.4327 Latrizo Gamelisma
7 (12 digits) [1 -1 -7 6 6.8044
7 10976/10935 [5 -7 -1 3 6.4790 Satrizo-agu Hemimage comma
7 (20 digits) [16 -9 -8 6 4.8507
7 (20 digits) [-19 14 -5 3 2.2792 Forge comma
7 (12 digits) [-11 2 7 -3 1.6283 Meter
7 (12 digits) [-4 6 -6 3 0.3254 Landscape comma
7 (58 digits) [9 -28 37 -18 0.0011 Satritribiru-athiseyo Termite comma
11 4375/4356 [-2 -2 4 1 -2 7.5349
11 385/384 [-7 -1 1 1 1 4.5026 Lozoyo Keenanisma
11 441/440 [-3 2 -1 2 -1 3.9302 Luzozogu Werckisma
11 6250/6237 [1 -4 5 -1 -1 3.6047 Liganellus comma
11 (36 digits) [-51 12 3 -1 11 3.4902 Tritonoquartisma
11 4000/3993 [5 -1 3 0 -3 3.0323 Triluyo Wizardharry comma
11 19712/19683 [8 -9 0 1 1 2.5488 Salozo Symbiotic comma
11 (14 digits) [16 -3 0 0 6 2.0427 Tribilo Nexus comma
11 (28 digits) [-34 28 0 0 -3 0.7862 Quadla-trilu Frameshift comma
11 3025/3024 [-4 -3 2 -1 2 0.5724 Loloruyoyo Lehmerisma
11 (18 digits) [24 -6 0 1 -5 0.5062 Saquinlu-azo Quartisma
11 (14 digits) [-1 -11 -1 0 6 0.0889 Satribilo-agu Parimo
13 2197/2187 [0 -7 0 0 0 3 7.8980 Satritho Threedie
13 325/324 [-2 -4 2 0 0 1 5.3351 Thoyoyo Marveltwin comma
13 364/363 [2 -1 0 1 -2 1 4.7627 Tholuluzo Gentle comma
13 13720/13689 [3 -4 1 3 0 -2 3.9161
13 625/624 [-4 -1 4 0 0 -1 2.7722 Thuquadyo Tunbarsma
13 676/675 [2 -3 -2 0 0 2 2.5629 Bithogu Island comma
13 1575/1573 [0 2 2 1 -2 -1 2.1998 Nicola
13 1001/1000 [-3 0 -3 1 1 1 1.7304 Fairytale comma
13 10985/10976 [-5 0 1 -3 0 3 1.4190 Cantonisma
13 43904/43875 [7 -3 -3 3 0 1 1.1439
13 2080/2079 [5 -3 1 -1 -1 1 0.8325 Tholuruyo Ibnsinma
13 (12 digits) [11 -9 3 0 0 -1 0.8185 Sathutriyo Phaotic comma
13 6656/6655 [9 0 -1 0 -3 1 0.2601 Thotrilu-agu Jacobin comma
13 (12 digits) [-6 2 6 0 0 -3 0.2093
13 (12 digits) [-6 6 -2 -1 -1 2 0.0141 Lathotholurugugu Chalmersia
17 15379/15300 [-2 -2 -2 1 0 3 -1 8.9161
17 273/272 [-4 1 0 1 0 1 -1 6.3532 Suthozo Tannisma
17 375/374 [-1 1 3 0 -1 0 -1 4.6228 Ursulisma
17 595/594 [-1 -3 1 1 -1 0 1 2.9121 Dakotisma
17 715/714 [-1 -1 1 -1 1 1 -1 2.4230 September comma
17 833/832 [-6 0 0 2 0 -1 1 2.0796 Sothuzozo Horizon comma
17 936/935 [3 2 -1 0 -1 1 -1 1.8506 Ainos comma
17 2025/2023 [0 4 2 -1 0 0 -2 1.7107 Fidesma
17 1089/1088 [-6 2 0 0 2 0 -1 1.5905 Twosquare comma
17 1701/1700 [-2 5 -2 1 0 0 -1 1.0181 Palingenetic comma
17 24576/24565 [13 1 -1 0 0 0 -3 0.7751 Archagallisma
17 2431/2430 [-1 -5 -1 0 1 1 1 0.7123
17 (12 digits) [-10 -5 0 0 4 0 1 0.44522
17 12376/12375 [3 -2 -3 1 -1 1 1 0.1399 Flashma
17 14400/14399 [6 2 2 -1 -2 0 -1 0.1202 Sululuruyoyo Sparkisma

In the 19-limit, it is known to temper out 343/342 and 361/360, but since it is inconsistent in the 19-limit, there are other potential mappings available that temper out different commas. In the 23-limit, with the 19-limit skipped, this system is known to temper out 392/391, 460/459, 507/506, 529/528, 897/896, 1105/1104, 1288/1287, 2024/2023, 2025/2024, and 2646/2645 among others.

### Rank-2 temperaments

Note: 5-limit temperaments supported by 53et are not included.

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator
(reduced)
Cents
(reduced)
Associated
ratio
Temperament
1 2\159 15.09 121/120 Yarman I / yarman II
1 7\159 52.83 33/32 Quartkeenlig
1 11\159 83.02 21/20 Sextilififths
1 22\159 166.04 11/10 Tertiaschis
1 31\159 233.96 8/7 Slendric / guiron
1 38\159 286.79 13/11 Gamity
1 41\159 309.43 448/375 Triwell
1 64\159 483.02 160/121 Quarterframe
1 67\159 505.66 75/56 Marfifths
1 68\159 513.21 121/90 Trinity
1 74\159 558.49 112/81 Condor
3 8\159 60.38 28/27 Chromat
3 22\159 166.04 11/10 Tritricot
3 33\159
(20\159)
249.06
(150.94)
15/13
(12/11)
Altinex / hemiterm
3 42\159
(11\159)
316.981
(83.02)
6/5
(21/20)
Tritikleismic
3 66\159
(13\159)
498.11
(98.11)
4/3
(35/33)
Term / terminal
53 31\159
(1\159)
233.96
(7.55)
8/7
(225/224)
Schismerc / cartography
53 121\159
(1\159)
913.21
(7.55)
441/260
(196/195)
Iodine

## Music

The songs below are written in 159edo, or, in approximations that differ from the actual 159edo by only fractions of a cent.

## References

1. Ratios longer than 10 digits are presented by placeholders with informative hints