42edo: Difference between revisions
m →Theory: + ''See regular temperament for more about what all this means and how to use it.'' Tag: Reverted |
|||
| (7 intermediate revisions by 4 users not shown) | |||
| Line 5: | Line 5: | ||
42edo has a [[patent val]] [[3/2|fifth]] (the step of which is not from [[7edo]], this being a first for edos of the form 7''n'') and a third both over 12 cents sharp, using the same 400-cent interval to represent [[5/4]] as does [[12edo]], which means it [[tempering out|tempers out]] [[128/125]]. In the [[7-limit]], it tempers out [[64/63]] and [[126/125]], making it a tuning [[support]]ing the [[augene]] temperament. | 42edo has a [[patent val]] [[3/2|fifth]] (the step of which is not from [[7edo]], this being a first for edos of the form 7''n'') and a third both over 12 cents sharp, using the same 400-cent interval to represent [[5/4]] as does [[12edo]], which means it [[tempering out|tempers out]] [[128/125]]. In the [[7-limit]], it tempers out [[64/63]] and [[126/125]], making it a tuning [[support]]ing the [[augene]] temperament. | ||
42edo is on the [[optimal ET sequence]] of the [[Augmented family#eugene|eugene]], [[joan]], [[lemba]], [[neutron]], [[qeema]], [[seville]], [[sevond]], [[skateboard]], [[tritikleismic]] and [[vines]] temperaments. | 42edo is on the [[optimal ET sequence]] of the [[Augmented family#eugene|eugene]], [[joan]], [[lemba]], [[neutron]], [[qeema]], [[seville]], [[sevond]], [[skateboard]], [[tritikleismic]] and [[vines]] temperaments. | ||
42edo is a diatonic edo because its 5th falls between {{nowrap|4\7 {{=}} 686{{c}}}} and {{nowrap|3\5 {{=}} 720{{c}}}}. 42edo is one of the most difficult diatonic edos to notate, because no other diatonic edo's fifth is as sharp (see [[47edo]] for the opposite extreme). | 42edo is a diatonic edo because its 5th falls between {{nowrap|4\7 {{=}} 686{{c}}}} and {{nowrap|3\5 {{=}} 720{{c}}}}. 42edo is one of the most difficult diatonic edos to notate, because no other diatonic edo's fifth is as sharp (see [[47edo]] for the opposite extreme). | ||
| Line 23: | Line 23: | ||
! Tuning | ! Tuning | ||
! [[42ed257/128]] | ! [[42ed257/128]] | ||
! [[ | ! [[11ed6/5]] | ||
! [[zpi|189zpi]] | ! [[zpi|189zpi]] | ||
! [[42edo]] | ! [[42edo]] | ||
| Line 48: | Line 48: | ||
! Tuning | ! Tuning | ||
! [[42edo]] | ! [[42edo]] | ||
! [[ | ! [[Equal-step tuning|34ed7/4]] | ||
! [[191zpi]] | ! [[191zpi]] | ||
! [[ | ! [[AS|AS123/121]] | ||
|- | |- | ||
! Steps / octave | ! Steps / octave | ||
| Line 66: | Line 66: | ||
| 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 === | ||
| Line 391: | Line 389: | ||
</imagemap> | </imagemap> | ||
== JI | == Approximation to JI == | ||
{{Q-odd-limit intervals}} | {{Q-odd-limit intervals}} | ||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 473: | Line 457: | ||
== 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 == | ||
| Line 488: | Line 501: | ||
=== 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) | ||