342edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
ArrowHead294 (talk | contribs)
15,213 edits
mNo edit summary
Contribution (talk | contribs)
3,302 edits
No edit summary
Tag: Reverted
Line 144: Line 144:


* [[11-odd-limit|Diamond11]]: 43 4 5 6 8 10 14 9 11 9 5 18 15 9 10 9 15 18 5 9 11 9 14 10 8 6 5 4 43
* [[11-odd-limit|Diamond11]]: 43 4 5 6 8 10 14 9 11 9 5 18 15 9 10 9 15 18 5 9 11 9 14 10 8 6 5 4 43
== Commas of the 2.3.5.7.11 subgroup tempered out in 342edo patent val ==
Commas with numerator <= 2^32:
{| class="wikitable mw-collapsible mw-collapsed"
! [[Ratio]]
! [[Monzo]]
! [[Cent]]s
|-
| [[781258401/781250000]]
| [-4 2 -11 2 6⟩
| 0.019
|-
| [[3294225/3294172]]
| [-2 2 2 -7 4⟩
| 0.028
|-
| [[199297406/199290375]]
| [1 -13 -3 7 2⟩
| 0.061
|-
| [[78125000/78121827]]
| [3 -13 10 -2⟩
| 0.070
|-
| [[14348907/14348180]]
| [-2 15 -1 -2 -4⟩
| 0.088
|-
| [[1771561/1771470]]
| [-1 -11 -1 0 6⟩
| 0.089
|-
| [[645700815/645657712]]
| [-4 17 1 -9⟩
| 0.116
|-
| [[214375000/214358881]]
| [3 0 7 3 -8⟩
| 0.130
|-
| [[151263/151250]]
| [-1 2 -4 5 -2⟩
| 0.149
|-
| [[35156250/35153041]]
| [1 2 9 -4 -4⟩
| 0.158
|-
| [[9801/9800]]
| [-3 4 -2 -2 2⟩
| 0.177
|-
| [[3955078125/3954653486]]
| [-1 4 11 -11⟩
| 0.186
|-
| [[1291467969/1291315424]]
| [-5 6 0 -9 6⟩
| 0.205
|-
| [[21437500/21434787]]
| [2 -11 6 3 -2⟩
| 0.219
|-
| [[246071287/246037500]]
| [-2 -9 -5 5 4⟩
| 0.238
|-
| [[47265625/47258883]]
| [0 -9 8 -4 2⟩
| 0.247
|-
| [[1162261467/1162084000]]
| [-5 19 -3 -4 -2⟩
| 0.264
|-
| [[214358881/214326000]]
| [-4 -7 -3 -2 8⟩
| 0.266
|-
| [[1771875/1771561]]
| [0 4 5 1 -6⟩
| 0.307
|-
| [[250047/250000]]
| [-4 6 -6 3⟩
| 0.325
|-
| [[56953125/56942116]]
| [-2 6 7 -6 -2⟩
| 0.335
|-
| [[96059601/96040000]]
| [-6 8 -4 -4 4⟩
| 0.353
|-
| [[288240050/288178803]]
| [1 -9 2 8 -4⟩
| 0.368
|-
| [[4375/4374]]
| [-1 -7 4 1⟩
| 0.396
|-
| [[607645423/607500000]]
| [-5 -5 -7 3 6⟩
| 0.414
|-
| [[228765625/228709656]]
| [-3 -5 6 -6 4⟩
| 0.424
|-
| [[428830605/428717762]]
| [-1 6 1 6 -8⟩
| 0.456
|-
| [[3487704605/3486784401]]
| [0 -20 1 8 2⟩
| 0.457
|-
| [[820125/819896]]
| [-3 8 3 -1 -4⟩
| 0.483
|-
| [[1550115875/1549681956]]
| [-2 -18 3 1 6⟩
| 0.485
|-
| [[50014503/50000000]]
| [-7 10 -8 1 2⟩
| 0.502
|-
| [[184528125/184473632]]
| [-5 10 5 -8⟩
| 0.511
|-
| [[117649/117612]]
| [-2 -5 0 6 -2⟩
| 0.545
|-
| [[1220703125/1220312709]]
| [0 -5 13 -3 -4⟩
| 0.554
|-
| [[3025/3024]]
| [-4 -3 2 -1 2⟩
| 0.572
|-
| [[1500512167/1500000000]]
| [-8 -1 -9 1 8⟩
| 0.591
|-
| [[1107225625/1106841792]]
| [-6 -1 4 -8 6⟩
| 0.600
|-
| [[141776649/141724880]]
| [-4 10 -1 4 -6⟩
| 0.632
|-
| [[1722499009/1721868840]]
| [-3 -16 -1 6 4⟩
| 0.633
|-
| [[2657205/2656192]]
| [-6 12 1 -3 -2⟩
| 0.660
|-
| [[1071794405/1071385056]]
| [-5 -14 1 -1 8⟩
| 0.661
|-
| [[1977326743/1976535000]]
| [-3 -3 -4 11 -4⟩
| 0.693
|-
| [[95703125/95664294]]
| [-1 -3 9 2 -6⟩
| 0.703
|-
| [[2401/2400]]
| [-5 -1 -2 4⟩
| 0.721
|-
| [[48828125/48807528]]
| [-3 -1 11 -5 -2⟩
| 0.730
|-
| [[43923/43904]]
| [-7 1 0 -3 4⟩
| 0.749
|-
| [[19140625/19131876]]
| [-2 -14 8 2⟩
| 0.792
|-
| [[234365481/234256000]]
| [-7 14 -3 2 -4⟩
| 0.809
|-
| [[4253517961/4251528000]]
| [-6 -12 -3 4 6⟩
| 0.810
|-
| [[43046721/43025920]]
| [-9 16 -1 -5⟩
| 0.837
|-
| [[2573571875/2572306572]]
| [-2 -1 5 7 -8⟩
| 0.851
|-
| [[121060821/121000000]]
| [-6 1 -6 9 -2⟩
| 0.870
|-
| [[234375/234256]]
| [-4 1 7 0 -4⟩
| 0.879
|-
| [[160083/160000]]
| [-8 3 -4 2 2⟩
| 0.898
|-
| [[52734375/52706752]]
| [-6 3 9 -7⟩
| 0.907
|-
| [[430489323/430259200]]
| [-10 5 -2 -5 6⟩
| 0.926
|-
| [[514714375/514434888]]
| [-3 -12 4 7 -2⟩
| 0.940
|-
| [[1890625/1889568]]
| [-5 -10 6 0 2⟩
| 0.968
|-
| [[387420489/387200000]]
| [-10 18 -5 0 -2⟩
| 0.986
|-
| [[56723625/56689952]]
| [-5 3 3 5 -6⟩
| 1.028
|-
| [[200120949/200000000]]
| [-9 5 -8 7⟩
| 1.047
|-
| [[759375/758912]]
| [-7 5 5 -2 -2⟩
| 1.056
|-
| [[32019867/32000000]]
| [-11 7 -6 0 4⟩
| 1.074
|-
| [[420175/419904]]
| [-6 -8 2 5⟩
| 1.117
|-
| [[9150625/9144576]]
| [-8 -6 4 -2 4⟩
| 1.145
|-
| [[3750705/3748096]]
| [-8 7 1 3 -4⟩
| 1.205
|-
| [[2460375/2458624]]
| [-10 9 3 -4⟩
| 1.233
|-
| [[282475249/282268800]]
| [-7 -6 -2 10 -2⟩
| 1.266
|-
| [[341796875/341545248]]
| [-5 -6 11 1 -4⟩
| 1.275
|-
| [[41503/41472]]
| [-9 -4 0 3 2⟩
| 1.294
|-
| [[1220703125/1219784832]]
| [-7 -4 13 -6⟩
| 1.303
|-
| [[44289025/44255232]]
| [-11 -2 2 -4 6⟩
| 1.321
|-
| [[1240029/1239040]]
| [-11 11 -1 1 -2⟩
| 1.381
|-
| [[964565415/963780608]]
| [-13 13 1 -6 2⟩
| 1.409
|-
| [[5764801/5760000]]
| [-10 -2 -4 8⟩
| 1.442
|-
| [[1953125/1951488]]
| [-8 -2 9 -1 -2⟩
| 1.452
|-
| [[102487/102400]]
| [-12 0 -2 1 4⟩
| 1.470
|-
| [[1929229929/1927561216]]
| [-14 2 0 -6 8⟩
| 1.498
|-
| [[1838265625/1836660096]]
| [-7 -15 6 6⟩
| 1.513
|-
| [[14348907/14336000]]
| [-14 15 -3 -1⟩
| 1.558
|-
| [[7503125/7496192]]
| [-9 0 5 4 -4⟩
| 1.600
|-
| [[128119761/128000000]]
| [-13 2 -6 6 2⟩
| 1.619
|-
| [[703125/702464]]
| [-11 2 7 -3⟩
| 1.628
|-
| [[143496441/143360000]]
| [-15 4 -4 -1 6⟩
| 1.647
|-
| [[181575625/181398528]]
| [-10 -11 4 4 2⟩
| 1.689
|-
| [[1815912315/1814078464]]
| [-10 2 1 9 -6⟩
| 1.749
|-
| [[496125/495616]]
| [-12 4 3 2 -2⟩
| 1.777
|-
| [[275653125/275365888]]
| [-14 6 5 -5 2⟩
| 1.805
|-
| [[40353607/40310784]]
| [-11 -9 0 9⟩
| 1.838
|-
| [[1220703125/1219401216]]
| [-9 -9 13 0 -2⟩
| 1.847
|-
| [[17935225/17915904]]
| [-13 -7 2 2 4⟩
| 1.866
|-
| [[600362847/599695360]]
| [-13 6 -1 7 -4⟩
| 1.926
|-
| [[32805/32768]]
| [-15 8 1⟩
| 1.954
|-
| [[99648703/99532800]]
| [-14 -5 -2 7 2⟩
| 2.015
|-
| [[48828125/48771072]]
| [-12 -5 11 -2⟩
| 2.024
|-
| [[1771561/1769472]]
| [-16 -3 0 0 6⟩
| 2.043
|-
| [[992436543/991232000]]
| [-16 10 -3 5 -2⟩
| 2.103
|-
| [[64304361/64225280]]
| [-18 12 -1 -2 2⟩
| 2.130
|-
| [[26796875/26763264]]
| [-13 -3 7 3 -2⟩
| 2.173
|-
| [[246071287/245760000]]
| [-17 -1 -4 5 4⟩
| 2.191
|-
| [[236328125/236027904]]
| [-15 -1 9 -4 2⟩
| 2.201
|-
| [[643076643/642252800]]
| [-19 1 -2 -2 8⟩
| 2.219
|-
| [[1640558367/1638400000]]
| [-19 14 -5 3⟩
| 2.279
|-
| [[720600125/719634432]]
| [-14 -1 3 8 -4⟩
| 2.322
|-
| [[65625/65536]]
| [-16 1 5 1⟩
| 2.349
|-
| [[15882615/15859712]]
| [-17 3 1 6 -2⟩
| 2.498
|-
| [[3675375/3670016]]
| [-19 5 3 -1 2⟩
| 2.526
|-
| [[1722499009/1719926784]]
| [-18 -8 0 6 4⟩
| 2.587
|-
| [[5250987/5242880]]
| [-20 7 -1 4⟩
| 2.675
|-
| [[1440894015/1438646272]]
| [-22 9 1 -3 4⟩
| 2.703
|-
| [[95703125/95551488]]
| [-17 -6 9 2⟩
| 2.745
|-
| [[4253517961/4246732800]]
| [-21 -4 -2 4 6⟩
| 2.764
|-
| [[1050304563/1048576000]]
| [-23 11 -3 2 2⟩
| 2.852
|-
| [[2573571875/2569273344]]
| [-18 -4 5 7 -2⟩
| 2.894
|-
| [[9453125/9437184]]
| [-20 -2 7 0 2⟩
| 2.922
|-
| [[2100875/2097152]]
| [-21 0 3 5⟩
| 3.071
|-
| [[411778125/411041792]]
| [-23 2 5 -2 4⟩
| 3.099
|-
| [[2542277241/2537553920]]
| [-22 2 -1 10 -2⟩
| 3.219
|-
| [[16808715/16777216]]
| [-24 4 1 3 2⟩
| 3.247
|-
| [[4202539929/4194304000]]
| [-25 6 -3 8⟩
| 3.396
|-
| [[672417207/671088640]]
| [-27 8 -1 1 4⟩
| 3.424
|-
| [[907878125/905969664]]
| [-25 -3 5 4 2⟩
| 3.643
|-
| [[201768035/201326592]]
| [-26 -1 1 9⟩
| 3.792
|-
| [[269028375/268435456]]
| [-28 1 3 2 4⟩
| 3.820
|-
| [[1076168025/1073741824]]
| [-30 16 2⟩
| 3.907
|-
| [[2690514981/2684354560]]
| [-29 3 -1 7 2⟩
| 3.969
|-
| [[2152446615/2147483648]]
| [-31 5 1 0 6⟩
| 3.996
|-
| [[2152828125/2147483648]]
| [-31 9 6 1⟩
| 4.303
|}

Revision as of 21:22, 8 November 2025

← 341edo 342edo 343edo →
Prime factorization 2 × 32 × 19
Step size 3.50877 ¢ 
Fifth 200\342 (701.754 ¢) (→ 100\171)
Semitones (A1:m2) 32:26 (112.3 ¢ : 91.23 ¢)
Consistency limit 11
Distinct consistency limit 11

342 equal divisions of the octave (abbreviated 342edo or 342ed2), also called 342-tone equal temperament (342tet) or 342 equal temperament (342et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 342 equal parts of about 3.51 ¢ each. Each step represents a frequency ratio of 21/342, or the 342nd root of 2.

Theory

342edo is a very strong 11-limit system. It is, as one would expect, distinctly consistent through the 11-odd-limit, but goes no higher; nonetheless, it is a zeta peak edo. A basis for the 11-limit commas consists of 2401/2400, 3025/3024, 4375/4374 and 32805/32768. It is the optimal patent val for 11-limit hemitert temperament, and supports hemiennealimmal.

Prime harmonics

Approximation of prime harmonics in 342edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.20 -0.35 -0.40 -0.44 +1.58 +0.31 +0.73 -0.20 -1.51 -1.18
Relative (%) +0.0 -5.7 -9.9 -11.5 -12.6 +45.0 +8.8 +20.9 -5.8 -43.0 -33.5
Steps
(reduced) 		342
(0) 		542
(200) 		794
(110) 		960
(276) 		1183
(157) 		1266
(240) 		1398
(30) 		1453
(85) 		1547
(179) 		1661
(293) 		1694
(326)

Subset and supersets

342 factors as 2 × 32 × 19, with subset edos 2, 3, 6, 9, 18, 19, 38, 57, 114, and 171.

684edo, which doubles 342edo, provides an approximation of harmonic 13 that works well with the flat tendency of its 11-limit mapping.

Approximation to JI

Zeta peak index

Tuning Strength Octave (cents) Integer limit
ZPI Steps
per 8ve 		Step size
(cents) 		Height Integral Gap Size Stretch Consistent Distinct
Tempered Pure
2568zpi 341.974851 3.50903 13.478611 12.437722 1.890555 20.767404 1200.088249 0.088249 12 12

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3.5.7.11 2401/2400, 3025/3024, 4375/4374, 32805/32768 [⟨342 542 794 960 1183]] +0.110 0.0556 1.59
2.3.5.7.11.13 676/675, 1001/1000, 1716/1715, 3025/3024, 19773/19712 [⟨342 542 794 960 1183 1265]] (342f) +0.178 0.1618 4.61
2.3.5.7.11.13 625/624, 729/728, 847/845, 1575/1573, 4096/4095 [⟨342 542 794 960 1183 1266]] (342) +0.020 0.2061 5.87
  • 342et is lower in relative error than any previous equal temperaments in the 11-limit, being the first to beat 270. Not until 612 do we find a better equal temperament in terms of absolute error, and not until 1848 do we find one in terms of relative error.

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperaments
1 11\342 38.60 45/44 Hemitert
2 5\342 17.54 99/98 Poseidon
2 50\342 175.44 448/405 Bisesqui
2 124\342
(47\342) 		435.09
(164.91) 		9/7
(11/10) 		Semisupermajor
2 142\342
(29\342) 		498.25
(101.75) 		4/3
(35/33) 		Bipont
3 71\342
(43\342) 		249.12
(150.88) 		15/13
(12/11) 		Hemiterm
6 97\342
(17\342) 		340.35
(59.65) 		162/133
(88/85) 		Semiseptichrome
6 142\342
(28\342) 		498.25
(98.25) 		4/3
(18/17) 		Semiterm
9 63\342
(13\342) 		221.05
(45.61) 		25/22
(77/75) 		Quadraennealimmal
18 71\342
(5\342) 		249.12
(17.54) 		15/13
(99/98) 		Hemiennealimmal
38 142\342
(2\342) 		498.25
(7.02) 		4/3
(225/224) 		Hemienneadecal

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct

Scales

  • Diamond11: 43 4 5 6 8 10 14 9 11 9 5 18 15 9 10 9 15 18 5 9 11 9 14 10 8 6 5 4 43

Commas of the 2.3.5.7.11 subgroup tempered out in 342edo patent val

Commas with numerator <= 2^32:

Ratio Monzo Cents
781258401/781250000 [-4 2 -11 2 6⟩ 0.019
3294225/3294172 [-2 2 2 -7 4⟩ 0.028
199297406/199290375 [1 -13 -3 7 2⟩ 0.061
78125000/78121827 [3 -13 10 -2⟩ 0.070
14348907/14348180 [-2 15 -1 -2 -4⟩ 0.088
1771561/1771470 [-1 -11 -1 0 6⟩ 0.089
645700815/645657712 [-4 17 1 -9⟩ 0.116
214375000/214358881 [3 0 7 3 -8⟩ 0.130
151263/151250 [-1 2 -4 5 -2⟩ 0.149
35156250/35153041 [1 2 9 -4 -4⟩ 0.158
9801/9800 [-3 4 -2 -2 2⟩ 0.177
3955078125/3954653486 [-1 4 11 -11⟩ 0.186
1291467969/1291315424 [-5 6 0 -9 6⟩ 0.205
21437500/21434787 [2 -11 6 3 -2⟩ 0.219
246071287/246037500 [-2 -9 -5 5 4⟩ 0.238
47265625/47258883 [0 -9 8 -4 2⟩ 0.247
1162261467/1162084000 [-5 19 -3 -4 -2⟩ 0.264
214358881/214326000 [-4 -7 -3 -2 8⟩ 0.266
1771875/1771561 [0 4 5 1 -6⟩ 0.307
250047/250000 [-4 6 -6 3⟩ 0.325
56953125/56942116 [-2 6 7 -6 -2⟩ 0.335
96059601/96040000 [-6 8 -4 -4 4⟩ 0.353
288240050/288178803 [1 -9 2 8 -4⟩ 0.368
4375/4374 [-1 -7 4 1⟩ 0.396
607645423/607500000 [-5 -5 -7 3 6⟩ 0.414
228765625/228709656 [-3 -5 6 -6 4⟩ 0.424
428830605/428717762 [-1 6 1 6 -8⟩ 0.456
3487704605/3486784401 [0 -20 1 8 2⟩ 0.457
820125/819896 [-3 8 3 -1 -4⟩ 0.483
1550115875/1549681956 [-2 -18 3 1 6⟩ 0.485
50014503/50000000 [-7 10 -8 1 2⟩ 0.502
184528125/184473632 [-5 10 5 -8⟩ 0.511
117649/117612 [-2 -5 0 6 -2⟩ 0.545
1220703125/1220312709 [0 -5 13 -3 -4⟩ 0.554
3025/3024 [-4 -3 2 -1 2⟩ 0.572
1500512167/1500000000 [-8 -1 -9 1 8⟩ 0.591
1107225625/1106841792 [-6 -1 4 -8 6⟩ 0.600
141776649/141724880 [-4 10 -1 4 -6⟩ 0.632
1722499009/1721868840 [-3 -16 -1 6 4⟩ 0.633
2657205/2656192 [-6 12 1 -3 -2⟩ 0.660
1071794405/1071385056 [-5 -14 1 -1 8⟩ 0.661
1977326743/1976535000 [-3 -3 -4 11 -4⟩ 0.693
95703125/95664294 [-1 -3 9 2 -6⟩ 0.703
2401/2400 [-5 -1 -2 4⟩ 0.721
48828125/48807528 [-3 -1 11 -5 -2⟩ 0.730
43923/43904 [-7 1 0 -3 4⟩ 0.749
19140625/19131876 [-2 -14 8 2⟩ 0.792
234365481/234256000 [-7 14 -3 2 -4⟩ 0.809
4253517961/4251528000 [-6 -12 -3 4 6⟩ 0.810
43046721/43025920 [-9 16 -1 -5⟩ 0.837
2573571875/2572306572 [-2 -1 5 7 -8⟩ 0.851
121060821/121000000 [-6 1 -6 9 -2⟩ 0.870
234375/234256 [-4 1 7 0 -4⟩ 0.879
160083/160000 [-8 3 -4 2 2⟩ 0.898
52734375/52706752 [-6 3 9 -7⟩ 0.907
430489323/430259200 [-10 5 -2 -5 6⟩ 0.926
514714375/514434888 [-3 -12 4 7 -2⟩ 0.940
1890625/1889568 [-5 -10 6 0 2⟩ 0.968
387420489/387200000 [-10 18 -5 0 -2⟩ 0.986
56723625/56689952 [-5 3 3 5 -6⟩ 1.028
200120949/200000000 [-9 5 -8 7⟩ 1.047
759375/758912 [-7 5 5 -2 -2⟩ 1.056
32019867/32000000 [-11 7 -6 0 4⟩ 1.074
420175/419904 [-6 -8 2 5⟩ 1.117
9150625/9144576 [-8 -6 4 -2 4⟩ 1.145
3750705/3748096 [-8 7 1 3 -4⟩ 1.205
2460375/2458624 [-10 9 3 -4⟩ 1.233
282475249/282268800 [-7 -6 -2 10 -2⟩ 1.266
341796875/341545248 [-5 -6 11 1 -4⟩ 1.275
41503/41472 [-9 -4 0 3 2⟩ 1.294
1220703125/1219784832 [-7 -4 13 -6⟩ 1.303
44289025/44255232 [-11 -2 2 -4 6⟩ 1.321
1240029/1239040 [-11 11 -1 1 -2⟩ 1.381
964565415/963780608 [-13 13 1 -6 2⟩ 1.409
5764801/5760000 [-10 -2 -4 8⟩ 1.442
1953125/1951488 [-8 -2 9 -1 -2⟩ 1.452
102487/102400 [-12 0 -2 1 4⟩ 1.470
1929229929/1927561216 [-14 2 0 -6 8⟩ 1.498
1838265625/1836660096 [-7 -15 6 6⟩ 1.513
14348907/14336000 [-14 15 -3 -1⟩ 1.558
7503125/7496192 [-9 0 5 4 -4⟩ 1.600
128119761/128000000 [-13 2 -6 6 2⟩ 1.619
703125/702464 [-11 2 7 -3⟩ 1.628
143496441/143360000 [-15 4 -4 -1 6⟩ 1.647
181575625/181398528 [-10 -11 4 4 2⟩ 1.689
1815912315/1814078464 [-10 2 1 9 -6⟩ 1.749
496125/495616 [-12 4 3 2 -2⟩ 1.777
275653125/275365888 [-14 6 5 -5 2⟩ 1.805
40353607/40310784 [-11 -9 0 9⟩ 1.838
1220703125/1219401216 [-9 -9 13 0 -2⟩ 1.847
17935225/17915904 [-13 -7 2 2 4⟩ 1.866
600362847/599695360 [-13 6 -1 7 -4⟩ 1.926
32805/32768 [-15 8 1⟩ 1.954
99648703/99532800 [-14 -5 -2 7 2⟩ 2.015
48828125/48771072 [-12 -5 11 -2⟩ 2.024
1771561/1769472 [-16 -3 0 0 6⟩ 2.043
992436543/991232000 [-16 10 -3 5 -2⟩ 2.103
64304361/64225280 [-18 12 -1 -2 2⟩ 2.130
26796875/26763264 [-13 -3 7 3 -2⟩ 2.173
246071287/245760000 [-17 -1 -4 5 4⟩ 2.191
236328125/236027904 [-15 -1 9 -4 2⟩ 2.201
643076643/642252800 [-19 1 -2 -2 8⟩ 2.219
1640558367/1638400000 [-19 14 -5 3⟩ 2.279
720600125/719634432 [-14 -1 3 8 -4⟩ 2.322
65625/65536 [-16 1 5 1⟩ 2.349
15882615/15859712 [-17 3 1 6 -2⟩ 2.498
3675375/3670016 [-19 5 3 -1 2⟩ 2.526
1722499009/1719926784 [-18 -8 0 6 4⟩ 2.587
5250987/5242880 [-20 7 -1 4⟩ 2.675
1440894015/1438646272 [-22 9 1 -3 4⟩ 2.703
95703125/95551488 [-17 -6 9 2⟩ 2.745
4253517961/4246732800 [-21 -4 -2 4 6⟩ 2.764
1050304563/1048576000 [-23 11 -3 2 2⟩ 2.852
2573571875/2569273344 [-18 -4 5 7 -2⟩ 2.894
9453125/9437184 [-20 -2 7 0 2⟩ 2.922
2100875/2097152 [-21 0 3 5⟩ 3.071
411778125/411041792 [-23 2 5 -2 4⟩ 3.099
2542277241/2537553920 [-22 2 -1 10 -2⟩ 3.219
16808715/16777216 [-24 4 1 3 2⟩ 3.247
4202539929/4194304000 [-25 6 -3 8⟩ 3.396
672417207/671088640 [-27 8 -1 1 4⟩ 3.424
907878125/905969664 [-25 -3 5 4 2⟩ 3.643
201768035/201326592 [-26 -1 1 9⟩ 3.792
269028375/268435456 [-28 1 3 2 4⟩ 3.820
1076168025/1073741824 [-30 16 2⟩ 3.907
2690514981/2684354560 [-29 3 -1 7 2⟩ 3.969
2152446615/2147483648 [-31 5 1 0 6⟩ 3.996
2152828125/2147483648 [-31 9 6 1⟩ 4.303
Retrieved from "https://en.xen.wiki/index.php?title=342edo&oldid=216543"