42edo: Difference between revisions
→Notations: added the modern (as opposed to the classical) version of the ups and downs accidentals |
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! Tuning | ! Tuning | ||
! [[42ed257/128]] | ! [[42ed257/128]] | ||
! [[ | ! [[11ed6/5]] | ||
! [[zpi|189zpi]] | ! [[zpi|189zpi]] | ||
! [[42edo]] | ! [[42edo]] | ||
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! Tuning | ! Tuning | ||
! [[42edo]] | ! [[42edo]] | ||
! [[ | ! [[Equal-step tuning|34ed7/4]] | ||
! [[191zpi]] | ! [[191zpi]] | ||
! [[ | ! [[AS|AS123/121]] | ||
|- | |- | ||
! Steps / octave | ! Steps / octave | ||
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| colspan="5" | <span style="font-size: 0.75em;"><div style="text-align: center;">''“great” = 0-13% relative error • “good” = 13-27% • “okay” = 27-40% • “bad” = 40-50%''</div></span> | | colspan="5" | <span style="font-size: 0.75em;"><div style="text-align: center;">''“great” = 0-13% relative error • “good” = 13-27% • “okay” = 27-40% • “bad” = 40-50%''</div></span> | ||
|} | |} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
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D♯ is next to E. The notation requires ups and downs with three arrows, and if chords are to be spelled correctly four or more arrows may be required in certain cases. For example, a {{dash|1/1, 5/4, 3/2, 9/5|med}} chord with a root on the edostep midway between G and A would be written either as {{dash|v<sup>3</sup>G♯–v<sup>5</sup>B♯, v<sup>3</sup>D♯, vF♯|med}} or as {{dash|^<sup>3</sup>A♭, ^C, ^<sup>3</sup>E♭, ^<sup>5</sup>G♭}}. This is a dud dup-seven chord, written either as v<sup>3</sup>G♯vv,^^7 or as ^<sup>3</sup>A♭vv,^^7. | D♯ is next to E. The notation requires ups and downs with three arrows, and if chords are to be spelled correctly four or more arrows may be required in certain cases. For example, a {{dash|1/1, 5/4, 3/2, 9/5|med}} chord with a root on the edostep midway between G and A would be written either as {{dash|v<sup>3</sup>G♯–v<sup>5</sup>B♯, v<sup>3</sup>D♯, vF♯|med}} or as {{dash|^<sup>3</sup>A♭, ^C, ^<sup>3</sup>E♭, ^<sup>5</sup>G♭}}. This is a dud dup-seven chord, written either as v<sup>3</sup>G♯vv,^^7 or as ^<sup>3</sup>A♭vv,^^7. | ||
In this table, dup is | In this table, dup is equivalent to quidsharp, trup is equivalent to quudsharp, trudsharp is equivalent to quup, dudsharp is equivalent to quip, etc. | ||
{{sharpness-sharp7a}} | {{sharpness-sharp7a}} | ||
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</imagemap> | </imagemap> | ||
== JI | == Approximation to JI == | ||
{{Q-odd-limit intervals}} | {{Q-odd-limit intervals}} | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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* Seville/Sevond[14] 2nd mode: '''5 1 5 1 5 1 5 1 5 1 5 1 5 1''' | * Seville/Sevond[14] 2nd mode: '''5 1 5 1 5 1 5 1 5 1 5 1 5 1''' | ||
* Seville/Sevond[21]: '''1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4''' | * Seville/Sevond[21]: '''1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4''' | ||
; Subsets of MOS scales | ; Subsets of MOS scales | ||
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** Undecimal lydian-aeolian pentatonic: '''8 14 3 11 6''' | ** Undecimal lydian-aeolian pentatonic: '''8 14 3 11 6''' | ||
** Yokai pentatonic: '''3 14 8 3 14''' | ** Yokai pentatonic: '''3 14 8 3 14''' | ||
; Approximations of [[gamelan]] scales: | |||
* 5-tone pelog: 4 5 15 3 15 | |||
* 7-tone pelog: 4 5 9 6 3 10 5 | |||
* 5-tone slendro: 8 9 8 9 8 | |||
== Instruments == | == Instruments == | ||
=== Lumatone === | |||
{{main|Lumatone mapping for 42edo}} | {{main|Lumatone mapping for 42edo}} | ||
=== Skip fretting === | |||
'''[[Skip fretting]] system 42 3 11''': One way to play [[42edo]] on a [[14edo]] guitar is to tune the strings 11\42, or approximately a [[just]] 6/5, apart. All examples on this page are for 7-string guitar. | |||
; Prime intervals | |||
1/1: string 2 open | |||
2/1: string 5 fret 3 | |||
3/2: string 4 fret 1 and string 7 fret 4 | |||
5/4: string 3 fret 1 | |||
7/4: string 1 fret 1 and string 4 fret 4 | |||
11/8: string 7 fret 2 | |||
13/8: string 3 fret 6 | |||
17/16: string 1 fret 5 | |||
19/16: string 1 fret 7 | |||
23/16: string 4 open and string 7 fret 3 | |||
29/16: string 5 fret 1 | |||
31/16: string 1 fret 3 and string 4 fret 6 | |||
; Chords | |||
Minor 7th: 100123X | |||
== Music == | == Music == | ||
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=== 21st century === | === 21st century === | ||
; [[Bryan Deister]] | ; [[Bryan Deister]] | ||
* [https://www.youtube.com/watch?v=PJw8gZyNPjg ''improv 42edo''] (2023) | |||
* [https://www.youtube.com/watch?v=ljaSpsQP2qc ''Improvisation in 42edo''] (2023), transcribed by [[Stephen Weigel]] (2024) | * [https://www.youtube.com/watch?v=ljaSpsQP2qc ''Improvisation in 42edo''] (2023), transcribed by [[Stephen Weigel]] (2024) | ||