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=62 tone equal temperament=
{{Infobox ET}}
{{ED intro}}


<b>62edo</b> divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for [[31_comma_temperaments#Gallium|gallium]], [[Starling_temperaments#Valentine temperament-Semivalentine|semivalentine]] and [[Meantone_family#Septimal meantone-Unidecimal meantone aka Huygens-Hemimeantone|hemimeantone]] temperaments.
== Theory ==
{{Nowrap| 62 {{=}} 2 × 31 }} and the [[patent val]] of 62edo is a [[contorsion|contorted]] [[31edo]] through the [[11-limit]], but it makes for a good tuning in the higher limits. In the 13-limit it [[tempering out|tempers out]] [[169/168]], [[1188/1183]], [[847/845]] and [[676/675]]; in the [[17-limit]] [[221/220]], [[273/272]], and [[289/288]]; in the [[19-limit]] [[153/152]], [[171/170]], [[209/208]], [[286/285]], and [[361/360]]. Unlike 31edo, which has a sharp profile for primes [[13/1|13]], [[17/1|17]], [[19/1|19]] and [[23/1|23]], 62edo has a flat profile for these, as it removes the distinction of otonal and utonal [[superparticular]] pairs of the primes (e.g. 13/12 vs 14/13 for prime 13) by tempering out the corresponding [[square-particular]]s. This flat tendency extends to higher primes too, as the first prime harmonic that is tuned sharper than its [[5/4]] is its [[59/32]]. Interestingly, the size differences between consecutive harmonics are monotonically decreasing for all first 24 harmonics, and 62edo is one of the few [[meantone]] edos that achieve this, great for those who seek higher-limit meantone harmony.  


Using the 35\62 generator, which leads to the &lt;62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively &lt;62 97 143 172| supports hornbostel.
It provides the [[optimal patent val]] for [[gallium]], [[semivalentine]] and [[hemimeantone]] temperaments.  


==='''62-EDO Intervals'''===
Using the 35\62 generator, which leads to the {{val| 62 97 143 173 }} val, 62edo is also an excellent tuning for septimal [[mavila]] temperament; alternatively {{val| 62 97 143 172 }} [[support]]s [[hornbostel]].


{| class="wikitable"
=== Odd harmonics ===
{{Harmonics in equal|62}}
 
=== Subsets and supersets ===
Since 62 factors into 2 × 31, 62edo does not contain nontrivial subset edos other than [[2edo]] and 31edo. [[186edo]] and [[248edo]] are notable supersets.
 
=== Miscellany ===
62 years is the amount of years in a leap week calendar cycle which corresponds to a year of 365 days 5 hours 48 minutes 23 seconds, meaning it is both a simple cycle for a calendar, and 62 being a multiple of 31 makes it a harmonically useful and playable cycle. The corresponding maximal evenness scales are 15 & 62 and 11 & 62.
 
The 11 & 62 temperament is called mabon, named so because its associated year length corresponds to an autumnal equinoctial year. In the 2.9.7 subgroup tempers out 44957696/43046721, and the three generators of 17\62 correspond to [[16/9]]. It is possible to extend this to the 11-limit with comma basis {896/891, 1331/1296}, where 17\62 is mapped to [[11/9]] and two of them make [[16/11]]. In addition, three generators make the patent val 9/8, which is also created by combining the flat patent val fifth from 31edo with the sharp 37\62 fifth.
 
The 15 & 62 temperament, corresponding to the leap day cycle, is [[demivalentine]] in the 13-limit.
 
== Intervals ==
{| class="wikitable center-all right-2 left-3"
|-
! Steps
! Cents
! Approximate ratios*
! [[Ups and downs notation]]
|-
| 0
| 0.00
| 1/1
| {{UDnote|step=0}}
|-
| 1
| 19.35
| 65/64, 66/65, 78/77, 91/90, 105/104
| {{UDnote|step=1}}
|-
| 2
| 38.71
| ''33/32'', 36/35, 45/44, 49/48, 50/49, 55/54, 56/55, ''64/63''
| {{UDnote|step=2}}
|-
| 3
| 58.06
| ''26/25'', 27/26
| {{UDnote|step=3}}
|-
| 4
| 77.42
| 21/20, 22/21, 23/22, 24/23, 25/24, ''28/27''
| {{UDnote|step=4}}
|-
| 5
| 96.77
| 17/16, 18/17, 19/18, 20/19
| {{UDnote|step=5}}
|-
| 6
| 116.13
| 15/14, 16/15
| {{UDnote|step=6}}
|-
| 7
| 135.48
| 13/12, 14/13
| {{UDnote|step=7}}
|-
| 8
| 154.84
| ''11/10'', 12/11, 23/21
| {{UDnote|step=8}}
|-
| 9
| 174.19
| 21/19
| {{UDnote|step=9}}
|-
| 10
| 193.55
| ''9/8'', ''10/9'', 19/17, 28/25
| {{UDnote|step=10}}
|-
| 11
| 212.90
| 17/15
| {{UDnote|step=11}}
|-
| 12
| 232.26
| 8/7
| {{UDnote|step=12}}
|-
| 13
| 251.61
| 15/13, 22/19
| {{UDnote|step=13}}
|-
| 14
| 270.97
| 7/6
| {{UDnote|step=14}}
|-
| 15
| 290.32
| 13/11, 19/16, 20/17
| {{UDnote|step=15}}
|-
| 16
| 309.68
| 6/5
| {{UDnote|step=16}}
|-
| 17
| 329.03
| 17/14, 23/19
| {{UDnote|step=18}}
|-
| 18
| 348.39
| 11/9, 27/22, 28/23
| {{UDnote|step=18}}
|-
| 19
| 367.74
| 16/13, 21/17, 26/21
| {{UDnote|step=19}}
|-
| 20
| 387.10
| 5/4
| {{UDnote|step=20}}
|-
| 21
| 406.45
| 19/15, 24/19
| {{UDnote|step=21}}
|-
| 22
| 425.81
| 9/7, 14/11, 23/18, 32/25
| {{UDnote|step=22}}
|-
| 23
| 445.16
| 13/10, 22/17
| {{UDnote|step=23}}
|-
| 24
| 464.52
| 17/13, 21/16, 30/23
| {{UDnote|step=24}}
|-
| 25
| 483.87
| 25/19
| {{UDnote|step=25}}
|-
| 26
| 503.23
| 4/3
| {{UDnote|step=26}}
|-
| 27
| 522.58
| 19/14, 23/17
| {{UDnote|step=27}}
|-
| 28
| 541.94
| 11/8, 15/11, 26/19
| {{UDnote|step=28}}
|-
| 29
| 561.29
| 18/13
| {{UDnote|step=29}}
|-
| 30
| 580.65
| 7/5, ''25/18'', 32/23
| {{UDnote|step=30}}
|-
| 31
| 600.00
| 17/12, 24/17
| {{UDnote|step=10}}
|-
| 32
| 619.35
| 10/7, 23/16, ''36/25''
| {{UDnote|step=32}}
|-
| 33
| 638.71
| 13/9
| {{UDnote|step=33}}
|-
| 34
| 658.06
| 16/11, 19/13, 22/15
| {{UDnote|step=34}}
|-
| 35
| 677.42
| 28/19, 34/23
| {{UDnote|step=35}}
|-
| 36
| 696.77
| 3/2
| {{UDnote|step=36}}
|-
| 37
| 716.13
| 38/25
| {{UDnote|step=37}}
|-
| 38
| 735.48
| 23/15, 26/17, 32/21
| {{UDnote|step=38}}
|-
| 39
| 754.84
| 17/11, 20/13
| {{UDnote|step=39}}
|-
| 40
| 774.19
| 11/7, 14/9, 25/16, 36/23
| {{UDnote|step=40}}
|-
| 41
| 793.55
| 19/12, 30/19
| {{UDnote|step=41}}
|-
| 42
| 812.90
| 8/5
| {{UDnote|step=42}}
|-
| 43
| 832.26
| 13/8, 21/13, 34/21
| {{UDnote|step=43}}
|-
| 44
| 851.61
| 18/11, 23/14, 44/27
| {{UDnote|step=44}}
|-
| 45
| 870.97
| 28/17, 38/23
| {{UDnote|step=45}}
|-
| 46
| 890.32
| 5/3
| {{UDnote|step=46}}
|-
| 47
| 909.68
| 17/10, 22/13, 32/19
| {{UDnote|step=47}}
|-
| 48
| 929.03
| 12/7
| {{UDnote|step=48}}
|-
| 49
| 948.39
| 19/11, 26/15
| {{UDnote|step=49}}
|-
| 50
| 967.74
| 7/4
| {{UDnote|step=50}}
|-
| 51
| 987.10
| 30/17
| {{UDnote|step=51}}
|-
| 52
| 1006.45
| ''9/5'', ''16/9'', 25/14, 34/19
| {{UDnote|step=52}}
|-
| 53
| 1025.81
| 38/21
| {{UDnote|step=53}}
|-
| 54
| 1045.16
| 11/6, ''20/11'', 42/23
| {{UDnote|step=54}}
|-
| 55
| 1064.52
| 13/7, 24/13
| {{UDnote|step=55}}
|-
| 56
| 1083.87
| 15/8, 28/15
| {{UDnote|step=56}}
|-
| 57
| 1103.23
| 17/9, 19/10, 32/17, 36/19
| {{UDnote|step=57}}
|-
| 58
| 1122.58
| 21/11, 23/12, ''27/14'', 40/21, 44/23, 48/25
| {{UDnote|step=58}}
|-
| 59
| 1141.94
| ''25/13'', 52/27
| {{UDnote|step=59}}
|-
|-
| | '''ARMODUE NOMENCLATURE 8;3 RELATION'''
| 60
| 1161.29
| 35/18, 49/25, 55/28, ''63/32'', ''64/33'', 88/45, 96/49, 108/55
| {{UDnote|step=60}}
|-
|-
| | <ul><li>'''Ɨ''' = Thick (1/8-tone up)</li><li>'''‡''' = Semisharp (1/4-tone up)</li><li>'''b''' = Flat (5/8-tone down)</li><li>'''◊''' = Node (sharp/flat blindspot 1/2-tone)</li><li>'''#''' = Sharp (5/8-tone up)</li><li>'''v''' = Semiflat (1/4-tone down)</li><li>'''⌐''' = Thin (1/8-tone down)</li></ul>
| 61
| 1180.65
| 65/33, 77/39, 128/65, 180/91, 208/105
| {{UDnote|step=61}}
|-
| 62
| 1200.00
| 2/1
| {{UDnote|step=62}}
|}
|}
<nowiki />* 23-limit patent val, inconsistent intervals in ''italic''
== Notation ==
=== Ups and downs notation ===
62edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
{{Sharpness-sharp4a}}
[[Alternative symbols for ups and downs notation]] uses sharps and flats and quarter-tone accidentals combined with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp4}}
=== Sagittal notation ===
This notation uses the same sagittal sequence as EDOs [[69edo#Sagittal notation|69]] and [[76edo#Sagittal notation|76]], and is a superset of the notation for [[31edo#Sagittal notation|31-EDO]].
==== Evo flavor ====
<imagemap>
File:62-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 703 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 170 106 [[1053/1024]]
rect 170 80 290 106 [[33/32]]
default [[File:62-EDO_Evo_Sagittal.svg]]
</imagemap>
==== Revo flavor ====
<imagemap>
File:62-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 687 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 170 106 [[1053/1024]]
rect 170 80 290 106 [[33/32]]
default [[File:62-EDO_Revo_Sagittal.svg]]
</imagemap>
==== Evo-SZ flavor ====
<imagemap>
File:62-EDO_Evo-SZ_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 679 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 170 106 [[1053/1024]]
rect 170 80 290 106 [[33/32]]
default [[File:62-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>
In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.
=== Armodue notation ===
; Armodue nomenclature 8;3 relation
* '''Ɨ''' = Thick (1/8-tone up)
* '''‡''' = Semisharp (1/4-tone up)
* '''b''' = Flat (5/8-tone down)
* '''◊''' = Node (sharp/flat blindspot 1/2-tone)
* '''#''' = Sharp (5/8-tone up)
* '''v''' = Semiflat (1/4-tone down)
* '''⌐''' = Thin (1/8-tone down)


{| class="wikitable"
{| class="wikitable center-all right-3 left-5 mw-collapsible mw-collapsed"
|-
! colspan="2" | &#35;
! Cents
! Armodue notation
! Associated ratio
|-
| 0
|
| 0.0
| 1
|
|-
| 1
|
| 19.4
| 1Ɨ
|
|-
| 2
|
| 38.7
| 1‡ (9#)
|
|-
| 3
|
| 58.1
| 2b
|
|-
| 4
|
| 77.4
| 1◊2
|
|-
| 5
|
| 96.8
| 1#
|
|-
| 6
|
| 116.1
| 2v
|
|-
| 7
|
| 135.5
| 2⌐
|
|-
| 8
|
| 154.8
| 2
| 11/10~12/11
|-
| 9
|
| 174.2
| 2Ɨ
|
|-
| 10
|
| 193.5
| 2‡
|
|-
| 11
|
| 212.9
| 3b
| 8/7
|-
| 12
|
| 232.3
| 2◊3
|
|-
|-
!  rowspan="2"| [[Degree|Degree]]
| 13
!  colspan="3"| Size
|  
!  rowspan="2"| Armodue notation
| 251.6
!  rowspan="2"| Approximate intervals
| 2#
|  
|-
|-
![[cent|Cents]]
| 14
!pions
|
!7mus
| 271.0
| 3v
|
|-
|-
| style="text-align:center;" | 0
| 15
| colspan="3" style="text-align:right;" | 0
|  
| style="text-align:center;" | 1
| 290.3
| |  
| 3⌐
|  
|-
|-
| style="text-align:center;" | 1
| 16
| style="text-align:right;" | 19.3548
|  
|20.5161
| 309.7
|24.7742 (18.C632<sub>16</sub>)
| 3
| style="text-align:center;" | 1Ɨ
| 6/5~7/6
| |
|-
|-
| style="text-align:center;" | 2
| 17
| style="text-align:right;" | 38.7097
|  
|41.0323
| 329.0
|49.5484 (31.8C63<sub>16</sub>)
| 3Ɨ
| style="text-align:center;" | 1‡ (9#)
|  
| |  
|-
|-
| style="text-align:center;" | 3
| 18
| style="text-align:right;" | 58.0645
|  
|61.5484
| 348.4
|74.3226 (4A.5295<sub>16</sub>)
| 3‡
| style="text-align:center;" | 2b
|  
| |  
|-
|-
| style="text-align:center;" | 4
| 19
| style="text-align:right;" | 77.41935
| ·
|82.0645
| 367.7
|99.0968 (63.18C6<sub>16</sub>)
| 4b
| style="text-align:center;" | 1◊2
| 5/4
| |
|-
|-
| style="text-align:center;" | 5
| 20
| style="text-align:right;" | 96.7742
|  
|102.58065
| 387.1
|123.871 (7B.DEF8<sub>16</sub>)
| 3◊4
| style="text-align:center;" | 1#
|  
| |  
|-
|-
| style="text-align:center;" | 6
| 21
| style="text-align:right;" | 116.129
|  
|123.0968
| 406.5
|148.6452 (94.A529<sub>16</sub>)
| 3#
| style="text-align:center;" | 2v
|  
| |  
|-
|-
| style="text-align:center;" | 7
| 22
| style="text-align:right;" | 135.4839
|  
|143.6129
| 425.8
|173.41935 (AD.7B5B<sub>16</sub>)
| 4v (5b)
| style="text-align:center;" | 2⌐
|  
| |  
|-
|-
| style="text-align:center;" | 8
| 23
| style="text-align:right;" | 154.8387
|  
|164.129
| 445.2
|198.19355 (C6.318C<sub>16</sub>)
| 4⌐
| style="text-align:center;" | 2
|  
| |  
|-
|-
| style="text-align:center;" | 9
| 24
| style="text-align:right;" | 174.19355
|  
|184.6452
| 464.5
|222.9677 (DE.F7BE<sub>16</sub>)
| 4
| style="text-align:center;" | 2Ɨ
|  
| |  
|-
|-
| style="text-align:center;" | 10
| 25
| style="text-align:right;" | 193.5484
|  
|205.1613
| 483.9
|247.7419 (F7.BDEF8<sub>16</sub>)
| 4Ɨ (5v)
| style="text-align:center;" | 2‡
|  
| |  
|-
|-
| style="text-align:center;" | 11
| 26
| style="text-align:right;" | 212.9032
|  
|225.6774
| 503.2
|272.5161 (110.8421<sub>16</sub>)
| 5⌐ (4‡)
| style="text-align:center;" | 3b
|  
| | ·
|-
|-
| style="text-align:center;" | 12
| 27
| style="text-align:right;" | 232.2581
| ·
|246.19355
| 522.6
|297.2903 (129.4A53<sub>16</sub>)
| 5
| style="text-align:center;" | 2◊3
| 4/3~11/8
| |
|-
|-
| style="text-align:center;" | 13
| 28
| style="text-align:right;" | 251.6129
|  
|266.7097
| 541.9
|322.0645 (142.1084<sub>16</sub>)
| 5Ɨ
| style="text-align:center;" | 2#
|  
| |  
|-
|-
| style="text-align:center;" | 14
| 29
| style="text-align:right;" | 270.9677
|  
|287.2258
| 561.3
|346.8387 (15A.D6B6<sub>16</sub>)
| 5‡ (4#)
| style="text-align:center;" | 3v
|  
| |  
|-
|-
| style="text-align:center;" | 15
| 30
| style="text-align:right;" | 290.3226
|  
|307.7419
| 580.6
|371.6129 (173.9CE7<sub>16</sub>)
| 6b
| style="text-align:center;" | 3⌐
| 10/7
| |
|-
|-
| style="text-align:center;" | 16
| 31
| style="text-align:right;" | 309.6774
|  
|328.2581
| 600.0
|396.3871 (18C.6319<sub>16</sub>)
| 5◊6
| style="text-align:center;" | 3
|  
| |  
|-
|-
| style="text-align:center;" | 17
| 32
| style="text-align:right;" | 329.0323
|  
|348.7742
| 619.4
|421.1613 (1A5.294A<sub>16</sub>)
| 5#
| style="text-align:center;" | 3Ɨ
| 7/5
| |
|-
|-
| style="text-align:center;" | 18
| 33
| style="text-align:right;" | 348.3871
|  
|369.2903
| 638.7
|445.9355 (1BD.EF7C<sub>16</sub>)
| 6v
| style="text-align:center;" | 3‡
|  
| |  
|-
|-
| style="text-align:center;" | 19
| 34
| style="text-align:right;" | 367.7419
|  
|389.80645
| 658.1
|470.7097 (1D6.B5AD<sub>16</sub>)
| 6⌐
| style="text-align:center;" | 4b
|  
| | ·
|-
|-
| style="text-align:center;" | 20
| 35
| style="text-align:right;" | 387.0968
| ·
|410.3225
| 677.4
|495.4838 (1EF.7BDF<sub>16</sub>)
| 6
| style="text-align:center;" | 3◊4
| 3/2~16/11
| |
|-
|-
| style="text-align:center;" | 21
| 36
| style="text-align:right;" | 406.4516
|  
|430.8387
| 696.8
|520.2581 (208.42108<sub>16</sub>)
| 6Ɨ
| style="text-align:center;" | 3#
|  
| |  
|-
|-
| style="text-align:center;" | 22
| 37
| style="text-align:right;" | 425.80645
|  
|451.3548
| 716.1
|545.0323 (221.0842<sub>16</sub>)
| 6‡
| style="text-align:center;" | 4v (5b)
|  
| |  
|-
|-
| style="text-align:center;" | 23
| 38
| style="text-align:right;" | 445.1613
|  
|471.871
| 735.5
|569.80645 (239.CE74<sub>16</sub>)
| 7b
| style="text-align:center;" | 4⌐
|  
| |  
|-
|-
| style="text-align:center;" | 24
| 39
| style="text-align:right;" | 464.5161
|  
|492.3871
| 754.8
|594.58065 (252.94A5<sub>16</sub>)
| 6◊7
| style="text-align:center;" | 4
|  
| |  
|-
|-
| style="text-align:center;" | 25
| 40
| style="text-align:right;" | 483.871
|  
|512.9032
| 774.2
|619.3548 (26B.5AD7<sub>16</sub>)
| 6#
| style="text-align:center;" | 4Ɨ (5v)
|  
| |  
|-
|-
| style="text-align:center;" | 26
| 41
| style="text-align:right;" | 503.2258
|  
|533.41935
| 793.5
|644.129 (284.2108<sub>16</sub>)
| 7v
| style="text-align:center;" | 5⌐ (4‡)
|  
| |  
|-
|-
| style="text-align:center;" | 27
| 42
| style="text-align:right;" | 522.58065
|  
|553.9355
| 812.9
|668.9032 (29C.E73A<sub>16</sub>)
| 7⌐
| style="text-align:center;" | 5
|  
| | ·
|-
|-
| style="text-align:center;" | 28
| 43
| style="text-align:right;" | 541.9355
| ·
|574.4516
| 832.3
|693.6774 (2B5.AD6B<sub>16</sub>)
| 7
| style="text-align:center;" | 5Ɨ
| 8/5
| |
|-
|-
| style="text-align:center;" | 29
| 44
| style="text-align:right;" | 561.2903
|  
|594.9677
| 851.6
|718.4516 (2C4.739D<sub>16</sub>)
| 7Ɨ
| style="text-align:center;" | 5‡ (4#)
|  
| |  
|-
|-
| style="text-align:center;" | 30
| 45
| style="text-align:right;" | 580.6452
|  
|615.4839
| 871.0
|743.2258 (2E7.39CD<sub>16</sub>)
| 7‡
| style="text-align:center;" | 6b
|  
| |  
|-
|-
| style="text-align:center;" | 31
| 46
| style="text-align:right;" | 600
|  
|636
| 890.3
|768 (300<sub>16</sub>)
| 8b
| style="text-align:center;" | 5◊6
| 5/3~12/7
| |
|-
|-
| style="text-align:center;" | 32
| 47
| style="text-align:right;" | 619.3548
|  
|656.5161
| 909.7
|792.7742 (318.C632<sub>16</sub>)
| 7◊8
| style="text-align:center;" | 5#
|  
| |  
|-
|-
| style="text-align:center;" | 33
| 48
| style="text-align:right;" | 638.7097
|  
|677.0323
| 929.0
|813.5484 (331.8C63<sub>16</sub>)
| 7#
| style="text-align:center;" | 6v
|  
| |  
|-
|-
| style="text-align:center;" | 34
| 49
| style="text-align:right;" | 658.0645
|  
|697.5484
| 948.4
|842.3226 (34A.5295<sub>16</sub>)
| 8v
| style="text-align:center;" | 6⌐
|  
| |  
|-
|-
| style="text-align:center;" | 35
| 50
| style="text-align:right;" | 677.41935
|  
|718.0645
| 967.7
|867.0968 (363.18C6<sub>16</sub>)
| 8⌐
| style="text-align:center;" | 6
|  
| | ·
|-
|-
| style="text-align:center;" | 36
| 51
| style="text-align:right;" | 696.7742
|  
|738.58065
| 987.1
|891.871 (37B.DEF8<sub>16</sub>)
| 8
| style="text-align:center;" | 6Ɨ
| 7/4
| |
|-
|-
| style="text-align:center;" | 37
| 52
| style="text-align:right;" | 716.129
|  
|759.0968
| 1006.5
|916.6452 (394.A529<sub>16</sub>)
| 8Ɨ
| style="text-align:center;" | 6‡
|  
| |  
|-
|-
| style="text-align:center;" | 38
| 53
| style="text-align:right;" | 735.4839
|  
|779.6129
| 1025.8
|941.41935 (3AD.7B5B<sub>16</sub>)
| 8‡
| style="text-align:center;" | 7b
|  
| |  
|-
|-
| style="text-align:center;" | 39
| 54
| style="text-align:right;" | 754.8387
|  
|800.129
| 1045.2
|966.19355 (3C6.318C<sub>16</sub>)
| 9b
| style="text-align:center;" | 6◊7
| 11/6~20/11
| |
|-
|-
| style="text-align:center;" | 40
| 55
| style="text-align:right;" | 774.19355
|  
|820.6452
| 1064.5
|990.9677 (3DE.F7BE<sub>16</sub>)
| 8◊9
| style="text-align:center;" | 6#
|  
| |  
|-
|-
| style="text-align:center;" | 41
| 56
| style="text-align:right;" | 793.5484
|  
|841.1613
| 1083.9
|1015.7419 (3F7.BDEF8<sub>16</sub>)
| 8#
| style="text-align:center;" | 7v
|  
| |  
|-
|-
| style="text-align:center;" | 42
| 57
| style="text-align:right;" | 812.9032
|  
|861.6774
| 1103.2
|1040.5161 (410.8421<sub>16</sub>)
| 9v (1b)
| style="text-align:center;" | 7⌐
|  
| |  
|-
|-
| style="text-align:center;" | 43
| 58
| style="text-align:right;" | 832.2581
|  
|882.19355
| 1122.6
|1065.2903 (429.4A53<sub>16</sub>)
| 9⌐
| style="text-align:center;" | 7
|  
| | ·
|-
|-
| style="text-align:center;" | 44
| 59
| style="text-align:right;" | 851.6129
|
|902.7097
| 1141.9
|1090.0645 (442.1084<sub>16</sub>)
| 9
| style="text-align:center;" | 7Ɨ
|
| |
|-
| 60
|
| 1161.3
| 9Ɨ (1v)
|
|-
| 61
|
| 1180.6
| 1⌐ (9‡)
|
|-
| 62
|
| 1200.0
| 1
|
|}
 
== Approximation to JI ==
=== Zeta peak index ===
{{ZPI
| zpi = 314
| steps = 61.9380472360525
| step size = 19.3741981471691
| tempered height = 6.262952
| pure height = 4.11259
| integral = 0.952068
| gap = 15.026453
| octave = 1201.20028512448
| consistent = 8
| distinct = 8
}}
 
== Regular temperament properties ==
62edo is contorted 31edo through the 11-limit.
{| class="wikitable center-4 center-5 center-6"
|-
|-
| style="text-align:center;" | 45
! rowspan="2" | [[Subgroup]]
| style="text-align:right;" | 870.9677
! rowspan="2" | [[Comma list]]
|923.2268
! rowspan="2" | [[Mapping]]
|1114.8387 (45A.D6B6<sub>16</sub>)
! rowspan="2" | Optimal<br>8ve stretch (¢)
| style="text-align:center;" | 7‡
! colspan="2" | Tuning error
| |
|-
|-
| style="text-align:center;" | 46
! [[TE error|Absolute]] (¢)
| style="text-align:right;" | 890.3226
! [[TE simple badness|Relative]] (%)
|943.7419
|1139.6129 (473.9CE7<sub>16</sub>)
| style="text-align:center;" | 8b
| |
|-
|-
| style="text-align:center;" | 47
| 2.3.5.7.11.13
| style="text-align:right;" | 909.6774
| 81/80, 99/98, 121/120, 126/125, 169/168
|964.2581
| {{mapping| 62 98 144 174 214 229 }}
|1164.3871 (48C.6319<sub>16</sub>)
| +1.38
| style="text-align:center;" | 7◊8
| 1.41
| |
| 7.28
|-
|-
| style="text-align:center;" | 48
| 2.3.5.7.11.13.17
| style="text-align:right;" | 929.0323
| 81/80, 99/98, 121/120, 126/125, 169/168, 221/220
|984.7742
| {{mapping| 62 98 144 174 214 229 253 }}
|1189.1613 (4A5.294A<sub>16</sub>)
| +1.47
| style="text-align:center;" | 7#
| 1.32
| |
| 6.83
|-
|-
| style="text-align:center;" | 49
| 2.3.5.7.11.13.17.19
| style="text-align:right;" | 948.3871
| 81/80, 99/98, 121/120, 126/125, 153/152, 169/168, 209/208
|1005.2903
| {{mapping| 62 98 144 174 214 229 253 263 }}
|1213.9355 (4BD.EF7C<sub>16</sub>)
| +1.50
| style="text-align:center;" | 8v
| 1.24
| |
| 6.40
|-
|-
| style="text-align:center;" | 50
| 2.3.5.7.11.13.17.19.23
| style="text-align:right;" | 967.7419
| 81/80, 99/98, 121/120, 126/125, 153/152, 161/160, 169/168, 209/208
|1025.80645
| {{mapping| 62 98 144 174 214 229 253 263 280 }}
|1238.7097 (4D6.B5AD<sub>16</sub>)
| +1.55
| style="text-align:center;" | 8⌐
| 1.18
| |
| 6.09
|}
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
| style="text-align:center;" | 51
! Periods<br>per 8ve
| style="text-align:right;" | 987.0968
! Generator*
|1046.3225
! Cents*
|1263.4838 (4EF.7BDF<sub>16</sub>)
! Associated<br>ratio*
| style="text-align:center;" | 8
! Temperament
| | ·
|-
|-
| style="text-align:center;" | 52
| 1
| style="text-align:right;" | 1006.4516
| 3\62
|1066.8387
| 58.1
|1288.2581 (508.42108<sub>16</sub>)
| 27/26
| style="text-align:center;" | 8Ɨ
| [[Hemisecordite]]
| |
|-
|-
| style="text-align:center;" | 53
| 1
| style="text-align:right;" | 1025.80645
| 7\62
|1087.3548
| 135.5
|1313.0323 (521.0842<sub>16</sub>)
| 13/12
| style="text-align:center;" | 8‡
| [[Doublethink]]
| |
|-
|-
| style="text-align:center;" | 54
| 1
| style="text-align:right;" | 1045.1613
| 13\62
|1107.871
| 251.6
|1337.80645 (539.CE74<sub>16</sub>)
| 15/13
| style="text-align:center;" | 9b
| [[Hemimeantone]]
| |
|-
|-
| style="text-align:center;" | 55
| 1
| style="text-align:right;" | 1064.5161
| 17\62
|1128.3871
| 329.0
|1362.58065 (552.94A5<sub>16</sub>)
| 16/11
| style="text-align:center;" | 8◊9
| [[Mabon]]
| |
|-
|-
| style="text-align:center;" | 56
| 1
| style="text-align:right;" | 1083.871
| 29\62
|1148.9032
| 561.3
|1387.3548 (56B.5AD7<sub>16</sub>)
| 18/13
| style="text-align:center;" | 8#
| [[Demivalentine]]
| |
|-
|-
| style="text-align:center;" | 57
| 2
| style="text-align:right;" | 1103.2258
| 3\62
|1169.41935
| 58.1
|1412.129 (584.2108<sub>16</sub>)
| 27/26
| style="text-align:center;" | 9v (1b)
| [[Semihemisecordite]]
| |
|-
|-
| style="text-align:center;" | 58
| 2
| style="text-align:right;" | 1122.58065
| 4\62
|1189.9355
| 77.4
|1436.9032 (59C.E73A<sub>16</sub>)
| 21/20
| style="text-align:center;" | 9⌐
| [[Semivalentine]]
| |
|-
|-
| style="text-align:center;" | 59
| 2
| style="text-align:right;" | 1141.9355
| 6\62
|1210.4516
| 116.1
|1461.6774 (5B5.AD6B<sub>16</sub>)
| 15/14
| style="text-align:center;" | 9
| [[Semimiracle]]
| |
|-
|-
| style="text-align:center;" | 60
| 2
| style="text-align:right;" | 1161.2903
| 26\62
|1230.9677
| 503.2
|1486.4516 (5C4.739D<sub>16</sub>)
| 4/3
| style="text-align:center;" | 9Ɨ (1v)
| [[Semimeantone]]
| |
|-
|-
| style="text-align:center;" | 61
| 31
| style="text-align:right;" | 1180.6452
| 29\62<br>(1\62)
|1251.4839
| 561.3<br>(19.4)
|1411.2258 (5E7.39CD<sub>16</sub>)
| 11/8<br>(196/195)
| style="text-align:center;" | 1⌐ (9‡)
| [[Kumhar]] (62e)
| |
|-
|-
| style="text-align:center;" | 62
| 31
| style="text-align:right;" | 1200
| 19\62<br>(1\62)
|1272
| 367.7<br>(19.4)
|1536 (600<sub>16</sub>)
| 16/13<br>(77/76)
| style="text-align:center;" | 1
| [[Gallium]]
| |
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
== Instruments ==
=== Lumatone ===
* [[Lumatone mapping for 62edo]]
=== Skip fretting ===
'''[[Skip fretting]] system 62 6 11''' has strings tuned 11\62 apart, while frets are 6\62.
On a 4-string bass, here are your open strings:
0 11 22 33
A good supraminor 3rd is found on the 2nd string, 1st fret. A supermajor third is found on the open 3rd string. The major 6th can be found on the 4th string, 2nd fret.
5-string bass
51 0 11 22 33
This adds an interval of a major 7th (minus an 8ve) at the first string, 1st fret.
6-string guitar
0 11 22 33 44 55
”Major” 020131
7-string guitar
0 11 22 33 44 55 4
'''Skip fretting system 62 9 11''' is another 62edo skip fretting system. The 5th is on the 5th string. The major 3rd is on the 2nd string, 1st fret.
{{todo|add illustration|text=Base it off of the diagram from [[User:MisterShafXen/Skip fretting system 62 9 11]]}}
== Music ==
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/UerD0NqBbng ''microtonal improvisation in 62edo''] (2025)
Retrieved from "https://en.xen.wiki/w/62edo"