62edo: Difference between revisions
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→Instruments: Insert music section after this, starting with Bryan Deister's ''microtonal improvisation in 62edo'' (2025) |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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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. | ||
=== | === 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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== Notation == | == Notation == | ||
=== Ups and downs notation === | === Ups and downs notation === | ||
62edo can be notated with | 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}} | {{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|31-EDO]]. | ||
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== Approximation to JI == | == Approximation to JI == | ||
=== Zeta peak index === | === 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 | |||
}} | |||
| 19.3741981471691 | |||
| 6.262952 | |||
| 0.952068 | |||
| 15.026453 | |||
| | |||
| 8 | |||
| 8 | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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|} | |} | ||
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | <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) | |||