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It provides the [[optimal patent val]] for [[gallium]], [[semivalentine]] and [[hemimeantone]] temperaments.  
It provides the [[optimal patent val]] for [[gallium]], [[semivalentine]] and [[hemimeantone]] temperaments.  


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


=== Odd harmonics ===
=== Odd harmonics ===
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Since 62 factors into 2 × 31, 62edo does not contain nontrivial subset edos other than [[2edo]] and 31edo. [[186edo]] and [[248edo]] are notable 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.  


=== Miscellaneous properties ===
=== 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.  
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.  


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| 600.00
| 600.00
| 17/12, 24/17
| 17/12, 24/17
| {{UDnote|step=10}}
| {{UDnote|step=31}}
|-
|-
| 32
| 32
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== Notation ==
== Notation ==
=== Ups and downs notation ===
=== Stein–Zimmermann–Gould notation ===
62edo can be notated with quarter-tone accidentals and [[Alternative symbols for ups and downs notation #Sharp-4|ups and downs]]. This can be done by combining sharps and flats with arrows borrowed from extended [[Helmholtz–Ellis notation]]:
[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
{{Sharpness-sharp4-szg}}


{{Sharpness-sharp4}}
=== Kite's ups and downs notation ===
62edo can also be notated with [[Kite's ups and downs notation|Kite's 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}}


=== Sagittal notation ===
=== 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]].
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|31edo]].


==== Evo flavor ====
==== Evo flavor ====
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</imagemap>
</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.
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 notation ===
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{| class="wikitable center-all right-3 left-5 mw-collapsible mw-collapsed"
{| class="wikitable center-all right-3 left-5 mw-collapsible mw-collapsed"
|-
|-
! colspan="2" | &#35;
! colspan="2" | #
! Cents
! Cents
! Armodue notation
! Armodue notation
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| 1
| 1
|  
|  
|}
== Approximation to JI ==
=== Zeta peak index ===
{| class="wikitable center-all"
|-
! colspan="3" | Tuning
! colspan="3" | Strength
! colspan="2" | Closest edo
! colspan="2" | Integer limit
|-
! ZPI
! Steps per octave
! Step size (cents)
! Height
! Integral
! Gap
! Edo
! Octave (cents)
! Consistent
! Distinct
|-
| [[314zpi]]
| 61.9380472360525
| 19.3741981471691
| 6.262952
| 0.952068
| 15.026453
| 62edo
| 1201.20028512448
| 8
| 8
|}
|}


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| [[Gallium]]
| [[Gallium]]
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
 
== Octave stretch or compression ==
62edo tunes most simple [[prime]]s flat. [[Octave stretching|Stretching the octave]] of 62edo by the right amount improves its approximations of [[JI]].
 
Some tunings of 62edo which do this include [[ed7|174ed7]] and [[zpi|314zpi]].


== Instruments ==
== Instruments ==
; Fretted instruments
 
* [[Skip fretting system 62 6 11]]
=== Lumatone ===
* [[Skip fretting system 62 9 11]]
* [[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)
* [https://www.youtube.com/watch?v=ujaUA-uwDvE ''62edo improv''] (2025)
* [https://www.youtube.com/watch?v=3_mwEylLEwU&list=WL&index=338 ''62edo prelude''] (2026)
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