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{| class="wikitable"
{| class="wikitable"
|+
|-
!Tuning
! Tuning
! [[42ed257/128]]
! [[42ed257/128]]
! [[1ed28.7c|APS720jot]]
! [[1ed28.7c|APS720jot]]
Line 32: Line 32:
| 42.00
| 42.00
|-
|-
! Approximation <br>of harmonics
! Approximation<br>of harmonics
| great: 5 <br>good: 2, 3, 7 <br>okay: <br>bad: 11, 13
| great: 5<br>good: 2, 3, 7 <br>okay: <br>bad: 11, 13
| great: 5 <br>good: 2, 3 <br>okay: 7, 11, 13 <br>bad:  
| great: 5<br>good: 2, 3 <br>okay: 7, 11, 13 <br>bad:  
| great: 5 <br>good: 2, 13 <br>okay: 3, 11 <br>bad: 7
| great: 5<br>good: 2, 13 <br>okay: 3, 11 <br>bad: 7
| great: 2, 7 <br>good: <br>okay: 11 <br>bad: 3, 5, 13
| great: 2, 7<br>good: <br>okay: 11 <br>bad: 3, 5, 13
|-
|-
| colspan="5" | <small><div style="text-align: center;">''“great” = 0-13% relative error • “good” = 13-27% • “okay” = 27-40% • “bad” = 40-50%''</div></small>
| 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>
|}
|}


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{| class="wikitable"
{| class="wikitable"
|+
|-
!Tuning
! Tuning
! [[42edo]]
! [[42edo]]
! [[1ed28.5c|APS715jot]]
! [[1ed28.5c|APS715jot]]
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| great: 3, 5, 11 <br>good: 2 <br>okay: 13 <br>bad: 7
| great: 3, 5, 11 <br>good: 2 <br>okay: 13 <br>bad: 7
|-
|-
| colspan="5" | <small><div style="text-align: center;">''“great” = 0-13% relative error • “good” = 13-27% • “okay” = 27-40% • “bad” = 40-50%''</div></small>
| 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>
|}
|}


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Since 42 factors into {{factorization|42}}, 42edo contains subset edos {{EDOs| 2, 3, 6, 7, 14, and 21 }}.
Since 42 factors into {{factorization|42}}, 42edo contains subset edos {{EDOs| 2, 3, 6, 7, 14, and 21 }}.


==Intervals==
== Intervals ==
 
{| class="wikitable center-all right-2 left-4"
{| class="wikitable center-all right-2 left-4"
|-
|-
!#
! #
!Cents
! Cents
! colspan="3" |[[Ups and Downs Notation]]
! colspan="3" |[[Ups and Downs Notation]]
|-
|-
|0
| 0
| 0.000
| 0.000
|P1
| P1
|perfect unison
| perfect unison
| D
| D
|-
|-
|1
| 1
|28.571
| 28.571
|^1, m2
| ^1, m2
| up unison, minor 2nd
| up unison, minor 2nd
|^D, Eb
| ^D, Eb
|-
|-
|2
| 2
|57.143
| 57.143
|^^1, ^m2
| ^^1, ^m2
|dup 1sn, upminor 2nd
| dup 1sn, upminor 2nd
| ^^D, ^Eb
| ^^D, ^Eb
|-
|-
|3
| 3
|85.714
| 85.714
|^^m2
| ^^m2
|dupminor 2nd
| dupminor 2nd
|^^Eb
| ^^Eb
|-
|-
| 4
| 4
|114.286
| 114.286
|^<sup>3</sup>m
| ^<sup>3</sup>m
|trupminor 2nd
| trupminor 2nd
|^<sup>3</sup>Eb
| ^<sup>3</sup>Eb
|-
|-
|5
| 5
|143.857
| 143.857
|v<sup>3</sup>M
| v<sup>3</sup>M
|trudmajor 2nd
| trudmajor 2nd
|v<sup>3</sup>E
| v<sup>3</sup>E
|-
|-
|6
| 6
|171.429
| 171.429
|vvM2
| vvM2
| dudmajor 2nd
| dudmajor 2nd
|vvE
| vvE
|-
|-
|7
| 7
|200.000
| 200.000
|vM2
| vM2
|downmajor 2nd
| downmajor 2nd
|vE
| vE
|-
|-
| 8
| 8
|228.571
| 228.571
|M2
| M2
|major 2nd
| major 2nd
| E
| E
|-
|-
|9
| 9
|257.143
| 257.143
|m3
| m3
|minor 3rd
| minor 3rd
|F
| F
|-
|-
|10
| 10
| 285.714
| 285.714
|^m3
| ^m3
| upminor 3rd
| upminor 3rd
|^F
| ^F
|-
|-
|11
| 11
|314.286
| 314.286
|^^m3
| ^^m3
|dupminor 3rd
| dupminor 3rd
|^^F
| ^^F
|-
|-
|12
| 12
|342.857
| 342.857
|^<sup>3</sup>m3
| ^<sup>3</sup>m3
| trupminor 3rd
| trupminor 3rd
|^<sup>3</sup>F
| ^<sup>3</sup>F
|-
|-
|13
| 13
|371.429
| 371.429
|v<sup>3</sup>M3
| v<sup>3</sup>M3
|trudmajor 3rd
| trudmajor 3rd
|v<sup>3</sup>F#
| v<sup>3</sup>F#
|-
|-
|14
| 14
|400.000
| 400.000
|vvM3
| vvM3
|dudmajor 3rd
| dudmajor 3rd
|vvF#
| vvF#
|-
|-
|15
| 15
|428.571
| 428.571
|vM3
| vM3
|downmajor 3rd
| downmajor 3rd
| vF#
| vF#
|-
|-
|16
| 16
| 457.143
| 457.143
|M3, v4
| M3, v4
|major 3rd, down 4th
| major 3rd, down 4th
|F#, vG
| F#, vG
|-
|-
| 17
| 17
|485.714
| 485.714
|P4
| P4
|perfect 4th
| perfect 4th
|G
| G
|-
|-
|18
| 18
| 514.286
| 514.286
|^4
| ^4
|up 4th
| up 4th
|^G
| ^G
|-
|-
|19
| 19
|543.857
| 543.857
| ^^4
| ^^4
|dup 4th
| dup 4th
|^^G
| ^^G
|-
|-
|20
| 20
|571.429
| 571.429
|^<sup>3</sup>4, ^^d5
| ^<sup>3</sup>4, ^^d5
| trup 4th, dupdim 5th
| trup 4th, dupdim 5th
| ^<sup>3</sup>G, ^^Ab
| ^<sup>3</sup>G, ^^Ab
|-
|-
|21
| 21
|600.000
| 600.000
|v<sup>3</sup>A4, ^<sup>3</sup>d5
| v<sup>3</sup>A4, ^<sup>3</sup>d5
|trudaug 4th, trupdim 5th
| trudaug 4th, trupdim 5th
|v<sup>3</sup>G#, ^<sup>3</sup>Ab
| v<sup>3</sup>G#, ^<sup>3</sup>Ab
|-
|-
|22
| 22
|628.571
| 628.571
|vvA4, v<sup>3</sup>5
| vvA4, v<sup>3</sup>5
|dudaug 4th, trud 5th
| dudaug 4th, trud 5th
|vvG#, v<sup>3</sup>A
| vvG#, v<sup>3</sup>A
|-
|-
|23
| 23
|657.143
| 657.143
|vv5
| vv5
|dud 5th
| dud 5th
|vvA
| vvA
|-
|-
|24
| 24
| 685.714
| 685.714
|v5
| v5
|down 5th
| down 5th
| vA
| vA
|-
|-
|25
| 25
|714.286
| 714.286
|P5
| P5
|perfect 5th
| perfect 5th
|A
| A
|-
|-
|26
| 26
|742.857
| 742.857
|^5, m6
| ^5, m6
|up 5th, minor 6th
| up 5th, minor 6th
|^A, Bb
| ^A, Bb
|-
|-
|27
| 27
|771.429
| 771.429
|^m6
| ^m6
|upminor 6th
| upminor 6th
|^Bb
| ^Bb
|-
|-
|28
| 28
|800.000
| 800.000
|^^m6
| ^^m6
|dupminor 6th
| dupminor 6th
|^^Bb
| ^^Bb
|-
|-
|29
| 29
|828.571
| 828.571
|^<sup>3</sup>m6
| ^<sup>3</sup>m6
| trupminor 6th
| trupminor 6th
| ^<sup>3</sup>Bb
| ^<sup>3</sup>Bb
|-
|-
|30
| 30
|857.143
| 857.143
|v<sup>3</sup>M6
| v<sup>3</sup>M6
|trudmajor 6th
| trudmajor 6th
|v<sup>3</sup>B
| v<sup>3</sup>B
|-
|-
| 31
| 31
|885.714
| 885.714
|vvM6
| vvM6
|dudmajor 6th
| dudmajor 6th
|vvB
| vvB
|-
|-
|32
| 32
|914.286
| 914.286
|vM6
| vM6
|downmajor 6th
| downmajor 6th
|vB
| vB
|-
|-
|33
| 33
|942.857
| 942.857
|M6
| M6
|major 6th
| major 6th
|B
| B
|-
|-
| 34
| 34
|971.429
| 971.429
|m7
| m7
|minor 7th
| minor 7th
|C
| C
|-
|-
|35
| 35
|1000.000
| 1000.000
|^m7
| ^m7
|upminor 7th
| upminor 7th
|^C
| ^C
|-
|-
|36
| 36
|1028.571
| 1028.571
|^^m7
| ^^m7
| dupminor 7th
| dupminor 7th
|^^C
| ^^C
|-
|-
|37
| 37
|1057.143
| 1057.143
|^<sup>3</sup>m7
| ^<sup>3</sup>m7
|trupminor 7th
| trupminor 7th
|^<sup>3</sup>C
| ^<sup>3</sup>C
|-
|-
|38
| 38
|1085.714
| 1085.714
|v<sup>3</sup>M7
| v<sup>3</sup>M7
|trudmajor 7th
| trudmajor 7th
| v<sup>3</sup>C#
| v<sup>3</sup>C#
|-
|-
|39
| 39
| 1114.286
| 1114.286
|vvM7
| vvM7
|dudmajor 7th
| dudmajor 7th
| vvC#
| vvC#
|-
|-
|40
| 40
|1142.857
| 1142.857
|vM7
| vM7
|downmajor 7th
| downmajor 7th
|vC#
| vC#
|-
|-
|41
| 41
| 1171.429
| 1171.429
|M7, v8
| M7, v8
|major 7th, down 8ve
| major 7th, down 8ve
|C#, vD
| C#, vD
|-
|-
|42
| 42
| 1200.000
| 1200.000
|P8
| P8
| perfect 8ve
| perfect 8ve
|D
| D
|}
|}


Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and Downs Notation #Chords and Chord Progressions]].
Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and Downs Notation #Chords and Chord Progressions]].


==Notation==
== Notation ==
=== Ups and downs notation ===
=== Ups and downs notation ===
Assuming the natural notes form a [[chain of fifths]], the major 2nd is 8 edosteps and the minor 2nd is only one. The naturals create a [[5edo]]-like scale, with two of the notes inflected by a [[comma]]-sized edostep:
Assuming the natural notes form a [[chain of fifths]], the major 2nd is 8 edosteps and the minor 2nd is only one. The naturals create a [[5edo]]-like scale, with two of the notes inflected by a [[comma]]-sized edostep:
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D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D


D# is next to E. The notation requires triple ups and downs, even more if chords are to be spelled correctly. For example, a 1/1 - 5/4 - 3/2 - 9/5 chord with a root on the key or fret midway between G and A would be written either as v<sup>3</sup>G# - v<sup>5</sup>B# - v<sup>3</sup>D# - vF# or as ^<sup>3</sup>Ab - ^C - ^<sup>3</sup>Eb - ^<sup>5</sup>Gb. This is a dud dup-seven chord, written either as v<sup>3</sup>G#vv,^^7 or as ^<sup>3</sup>Abvv,^^7.
D♯ is next to E. The notation requires triple ups and downs, even more if chords are to be spelled correctly. For example, a {{dash|1/1, 5/4, 3/2, 9/5|med}} chord with a root on the key or fret 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.
 
Alternatively, sharps and flats with arrows borrowed from [[Helmholtz–Ellis notation]] can be used:


===Sagittal notation===
{{sharpness-sharp7}}
====Best fifth notation====
 
=== Sagittal notation ===
==== Best fifth notation ====
This notation uses the same sagittal sequence as [[35edo#Second-best fifth notation|35b]].
This notation uses the same sagittal sequence as [[35edo#Second-best fifth notation|35b]].
=====Evo flavor=====


===== Evo flavor =====
<imagemap>
<imagemap>
File:42-EDO_Evo_Sagittal.svg
File:42-EDO_Evo_Sagittal.svg
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</imagemap>
</imagemap>


=====Revo flavor=====
===== Revo flavor =====
 
<imagemap>
<imagemap>
File:42-EDO_Revo_Sagittal.svg
File:42-EDO_Revo_Sagittal.svg
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</imagemap>
</imagemap>


====Second-best fifth notation====
==== Second-best fifth notation ====
This notation uses the same sagittal sequence as [[47edo#Sagittal notation|47-EDO]], and is a superset of the notations for EDOs [[21edo#Sagittal notation|21]], [[14edo#Sagittal notation|14]], and [[7edo#Sagittal notation|7]].
This notation uses the same sagittal sequence as [[47edo#Sagittal notation|47-EDO]], and is a superset of the notations for EDOs [[21edo#Sagittal notation|21]], [[14edo#Sagittal notation|14]], and [[7edo#Sagittal notation|7]].


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</imagemap>
</imagemap>


==Scales==
== Scales ==
 
{{main|List of MOS scales in 42edo}}
;[[MOS scale]]s
; [[MOS scale]]s
* Eugene/Tritikleismic[9]: '''3 8 3 3 8 3 3 8 3'''
* Eugene/Tritikleismic[9]: '''3 8 3 3 8 3 3 8 3'''
* Eugene/Tritikleismic[15]: '''3 3 2 3 3 3 3 2 3 3 3 3 2 3 3'''
* Eugene/Tritikleismic[15]: '''3 3 2 3 3 3 3 2 3 3 3 3 2 3 3'''
Line 396: Line 398:
* 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  
Line 409: Line 410:
** Yokai pentatonic: '''3 14 8 3 14'''
** Yokai pentatonic: '''3 14 8 3 14'''


==Instruments==
== Instruments ==
;Lumatone
; Lumatone
 
{{main|Lumatone mapping for 42edo}}
See [[Lumatone mapping for 42edo]]


== Music ==
== Music ==
Retrieved from "https://en.xen.wiki/w/42edo"