62edo: Difference between revisions

Instruments: Insert music section after this, starting with Bryan Deister's ''microtonal improvisation in 62edo'' (2025)
Notation: SZG notation
 
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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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| 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 [[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.
[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
{{Sharpness-sharp4-szg}}
 
=== 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}}
{{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 ===
=== 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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|  
|  
|}
|}
== 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 ==
== Regular temperament properties ==
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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 ==
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; [[Bryan Deister]]
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/UerD0NqBbng ''microtonal improvisation in 62edo''] (2025)
* [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)