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{{interwiki
{{interwiki
| de =  
| de = 8edo
| en = 8edo  
| en = 8edo  
| es =  
| es =  
| ja = 8平均律
| ja = 8平均律
}}
}}
__FORCETOC__
{{Infobox ET}}
=Theory=
{{ED intro}}
8-edo forms an odd and even pitch set of two diminished seventh chords, which when used in combination yield dissonance. The system has been described as a "barbaric" harmonic system; even so, it does a good job representing the [[Just_intonation_subgroups|just intonation subgroup]] 2.11/3.13/5, with good intervals of 13/10 and an excellent version of 11/6.
== Theory ==
[[File:8edo scale.mp3|thumb|A chromatic 8edo scale on C.]]


Another way of looking at 8-EDO is to treat a chord of 0-1-2-3-4 degrees (0-150-300-450-600 cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12-EDO is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out.
=== Approximation to JI ===
8edo forms an odd and even pitch set of two diminished seventh chords, which when used in combination yield dissonance. The system has been described as a "barbaric" harmonic system, containing no good approximation of harmonics 3, 5, 7, 11, 13, and 17; even so, it does a good job representing the [[just intonation subgroup]]s 2.11/3.13/5, with good intervals of [[13/10]] and an excellent version of [[11/6]]. Stacking the 450-cent interval can result in some semi-consonant chords such as 0-3-6 degrees, although these still are quite dissonant compared to standard root-3rd-P5 triads, which are unavailable in 8edo.


=Intervals=
Another way of looking at 8edo is to treat a chord of 0-1-2-3-4 degrees (0-150-300-450-600 cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12edo is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out.


[[File:8ed2-001.svg|alt=alt : Your browser has no SVG support.]]
=== Relationship with the father comma ===
When 8edo is treated as a very inaccurate 5-limit system, it ends up tempering out the [[Father]] comma, [[16/15]]. In fact, it is the largest edo that tempers this comma. What this means is that intervals 16/15 apart in 8edo map to the same note, such as [[4/3]] being mapped to the same note as [[5/4]].


[[:File:8ed2-001.svg|8ed2-001.svg]]
Some other odd equivalencies include:


8-edo can be notated as a subset of 24-edo, using [[Ups_and_Downs_Notation|ups and downs]]. It can also be notated as a subset of 16-edo, but this is a less intuitive notation.
'''0-2-5''': which can be seen as a minor triad (10:12:15), a sus2 triad (9:8:12), or a major triad in first inversion (5:6:8).


'''0-3-5''': which can be seen as a major triad (4:5:6), a sus4 triad (6:8:9), or a minor chord in second inversion (15:20:24).
=== Odd harmonics ===
{{Harmonics in equal|8|intervals=odd}}
=== Octave shrinking ===
8edo's approximation of [[JI]] can be improved via [[octave shrinking]]. Compressing 8edo's octave from 1200 [[cent]]s down to 1188 cents gives the tuning called [[1ed148.5c]].
Pure-octaves 8edo approximates only 2 of the first 11 prime harmonics within 15 cents. 1ed148.5c approximates 5 of them.
Pure-octaves 8edo approximates only 6 of the first 27 integer harmonics within 20 cents. 1ed148.5c approximates 10 of them.
In this way, 1ed148.5c (compressed-octaves 8edo) is able to provide a wider and stronger palette of [[consonance]]s compared to pure-octaves 8edo.
There are [[zeta peak index]] tunings nearby 8edo as well, however they damage the octave by over 20 cents, rendering them unrecognisable as stretched or compressed 8edo and more like entirely new scales in their own right.
=== Subsets and supersets ===
8edo contains [[2edo]] and [[4edo]] as subsets. Among its supersets are [[16edo]], [[24edo]], [[32edo]], ….
== Intervals ==
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Edostep
! rowspan="2" | Steps
! | Cents
! rowspan="2" | Cents
! colspan="2" | 24-edo subset notation
! colspan="3" | JI approximation
! colspan="2" | 16-edo subset notation
!Other
|-
|-
| style="text-align:center;" | 0
! 2.11/3.13/5.19*
| style="text-align:center;" | 0¢
! 2.5/3.11/3.13/5*
| style="text-align:center;" | P1
! 10:11:12:13:14*
| style="text-align:center;" | D
!Patent val ⟨8 13 19]
| style="text-align:center;" | P1
| style="text-align:center;" | D
|-
|-
| style="text-align:center;" | 1
| 0
| style="text-align:center;" | 150
| 0
| style="text-align:center;" | ~2
| 1/1
| style="text-align:center;" | Ev
| 1/1
| style="text-align:center;" | M2
| 1/1
| style="text-align:center;" | E
|1/1, 16/15
|-
|-
| style="text-align:center;" | 2
| 1
| style="text-align:center;" | 300
| 150
| style="text-align:center;" | m3
| 12/11
| style="text-align:center;" | F
| 12/11
| style="text-align:center;" | M3
| 12/11, 11/10
| style="text-align:center;" | F#
|10/9, 25/24
|-
|-
| style="text-align:center;" | 3
| 2
| style="text-align:center;" | 450
| 300
| style="text-align:center;" | ^M3 / v4
| 19/16
| style="text-align:center;" | F#^ / Gv
| 6/5
| style="text-align:center;" | d3 / A4
| 6/5
| style="text-align:center;" | Fb / G#
|6/5, 9/8
|-
|-
| style="text-align:center;" | 4
| 3
| style="text-align:center;" | 600
| 450
| style="text-align:center;" | A4 / d5
| 13/10
| style="text-align:center;" | G# / Ab
| 13/10
| style="text-align:center;" | d4 / A5
| 13/10
| style="text-align:center;" | Gb / A#
|4/3, 5/4
|-
|-
| style="text-align:center;" | 5
| 4
| style="text-align:center;" | 750
| 600
| style="text-align:center;" | ^5 / vm6
|  
| style="text-align:center;" | A^ / Bbv
|  
| style="text-align:center;" | d5 / A6
| 7/5, 10/7
| style="text-align:center;" | Ab / B#
|27/20, 25/18, 36/25
|-
|-
| style="text-align:center;" | 6
| 5
| style="text-align:center;" | 900
| 750
| style="text-align:center;" | M6
| 20/13
| style="text-align:center;" | B
| 20/13
| style="text-align:center;" | m6
| 20/13
| style="text-align:center;" | Bb
|3/2, 8/5
|-
|-
| style="text-align:center;" | 7
| 6
| style="text-align:center;" | 1050
| 900
| style="text-align:center;" | ~7
| 32/19
| style="text-align:center;" | C^
| 5/3
| style="text-align:center;" | m7
| 5/3
| style="text-align:center;" | C
|5/3, 16/9
|-
|-
| style="text-align:center;" | 8
| 7
| style="text-align:center;" | 1200
| 1050
| style="text-align:center;" | P8
| 11/6
| style="text-align:center;" | D
| 11/6
| style="text-align:center;" | P8
| 20/11, 11/6
| style="text-align:center;" | D
|9/5, 48/50
|-
| 8
| 1200
| 2/1
| 2/1
| 2/1
|2/1, 15/8
|}
|}
<nowiki />* Allows [[inversion]] by 2/1; other interpretations also possible


8-edo chords are very ambiguous, with many chord homonyms. Even the major and minor triads are homonyms. Chord components usually default to M2, M3, P4, P5, M6, m7, M9, P11 and M13. Thus D7 has a M3, P5 and m7. 8-edo chord names using 24-edo subset names are greatly simplified by using different defaults: ~2, ^M3, v4, ^5, M6, ~7, ~9, v11 and M13. Thus D7 becomes ^M3, ^5 and ~7.
== Notation ==
=== Ups and downs notation ===
8edo can be notated as a subset of 24edo, using [[Ups and downs notation|ups and downs]]. It can also be notated as a subset of 16edo, but this is a less intuitive notation.


{| class="wikitable"
{| class="wikitable center-all"
|-
! Edostep
! [[Cent]]s
! colspan="2" | 24edo subset notation<br />([[Enharmonic unisons in ups and downs notation|EUs:]] vvA1 and d2)
! colspan="2" | 16edo subset notation<br />(major narrower than minor)
! colspan="2" | 16edo subset notation<br />(major wider than minor)
! [[3L&nbsp;2s]] notation<br />({{nowrap|J {{=}} 1/1}})
! Audio
|-
| 0
| 0¢
| P1
| D
| P1
| D
| P1
| D
| J
| [[File:0-0 unison.mp3|frameless]]
|-
|-
! | Chord edosteps
| 1
! | Chord notes
| 150
! | Proper name
| ~2
! | Abbreviated name
| vE
! | Homonyms
| M2
| E
| m2
| E
| K
| [[File:0-150 (8-EDO).mp3|frameless]]
|-
|-
| | 0 – 3 – 5
| 2
| | D F♯^ A^
| 300
| | D.^(^5)
| m3
| | D
| F
| | F♯^.m or Gv.m
| M3
| F#
| m3
| Fb
| K#, Lb
| [[File:0-300 (12-EDO).mp3|frameless]]
|-
|-
| | 0 – 2 – 5
| 3
| | D F A^
| 450
| | Dm(^5)
| ^M3 / v4
| | Dm
| ^F# / vG
| | A^ or B♭v
| d3 / A4
| Fb / G#
| A3, D4
| F#, Gb
| L
| [[File:0-450 (8-EDO).mp3|frameless]]
|-
|-
| | 0 – 3 – 5 – 7
| 4
| | D F♯^ A^ C^
| 600
| | D.^7(^5)
| A4, d5
| | D7
| G#, Ab
| | F♯^.m♯11 or Gv.m♯11
| d4, A5
| Gb, A#
| A4, D5
| G#, Ab
| M
| [[File:0-600 (12-EDO).mp3|frameless]]
|-
|-
| | 0 – 3 – 5 – 6
| 5
| | D F♯^ A^ B
| 750
| | D6(^3,^5)
| ^5, vm6
| | D6
| ^A, vBb
| | Bm7 and Gv,♯9
| d5, A6
| Ab, B#
| A5, d6
| A#, Bb
| M#, Nb
| [[File:0-750 (8-EDO).mp3|frameless]]
|-
|-
| | 0 – 2 – 5 – 7
| 6
| | D F A^ C^
| 900
| | Dm~7(^5)
| M6
| | Dm7
| B
| | F6 and B♭v,♯9
| m6
| Bb
| M6
| B#
| N
| [[File:0-900 (12-EDO).mp3|frameless]]
|-
|-
| | 0 – 2 – 5 – 6
| 7
| | D F A^ B
| 1050
| | Dm6(^5)
| ~7
| | Dm6
| ^C
| | Bm7(♭5)
| m7
| C
| M7
| C
| N#, Jb
| [[File:0-1050 (8-EDO).mp3|frameless]]
|-
|-
| | 0 – 2 – 4 – 7
| 8
| | D F A♭ C^
| 1200
| | Ddim~7
| P8
| | Dm7(♭5)
| D
| | Fm6
| P8
| D
| P8
| D
| J
| [[File:0-1200 octave.mp3|frameless]]
|}
|}


=Scala scale file=
This is a heptatonic notation generated by 5ths (5th meaning 3/2). Alternative notations include pentatonic 5th-generated, octatonic, and heptatonic 2nd-generated.
For those who use the new tuner Lingot, which accepts scala files, or for anyone else, here is a .scl file of 8 EDO [[:File:08-EDO.scl|08-EDO.scl]]
 
'''<u>Pentatonic 5th-generated</u>: D * E G * A C * D'''  (generator = 5\8 = perfect 5thoid)


0. 1/1 C Unison
D - D#/Eb - E - G - G#/Ab - A - C - C#/Db - D


1. 150.000 cents C# (50 cents sharper than C# of 12 tet) Neutral 2nd
P1 - A1/ms3 - Ms3 - P4d - A4d/d5d - P5d - ms7 - Ms7/d8d - P8d  (s = sub-, d = -oid, see [[5edo#Alternative notations|5edo]] notation)


2. 300.000 cents D# Minor 3rd (identical to 12-tet)
pentatonic genchain of 5ths: ...Cb - Gb - Db - Ab - Eb - C - G - D - A - E - C# - G# - D# - A# - E#...


3. 450.000 cents E Sub-4th, Supermajor 3rd (50 cents sharper than E of 12 tet)
pentatonic genchain of 5ths: ...d8d - d5d - ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d - A1... (s = sub-, d = -oid)


4. 600.000 cents F# Tritone (identical to 12-tet)
[[Enharmonic unison]]: ds3


5. 750.000 cents G Super 5th, Subminor 6th (50 cents sharper than G of 12 tet)
'''<u>Octatonic:</u>''' '''A B C D E F G H A'''  (every interval is a generator)


6. 900.000 cents A Major 6th (identical to 12-tet)
P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8 - P9


7. 1050.000 cents A# Neutral 7th (50 cents sharper than A# of 12 tet)
Enharmonic unison: none


8. 2/1 C Octave
'''<u>Heptatonic 2nd-generated</u>: D E F G * A B C D'''  (generator = 1\8 = perfect 2nd = 150¢)


=Compositions=
D - E - F - G - G#/Ab - A -B - C - D
[https://soundcloud.com/overtoneshock/tenacious-chorale-9-edo-and-8-edo-live?in=overtoneshock/sets/xenharmonic-microtonal Tenacious Chorale (only movement II is in 8-EDO)] by Stephen Weigel


''[http://www.h-pi.com/mp3/Fantasia8ET.mp3 Fantasia in 8ET]'' by Aaron Andrew Hunt
P1 - P2 - m3 - M3/m4 - M4/m5 - M5/m6 - M6 - P7 - P8


''[http://www.h-pi.com/mp3/Fugue8ET.mp3 Fugue in 8ET]'' by Aaron Andrew Hunt
genchain of 2nds: ...D# - E# - F# - G# - A - B - C - D - E - F - G - Ab - Bb - Cb - Db...


[http://www.uvnitr.cz/flaoyg/forgotten_works/spendliky.html Špendlíky] ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Gustar/spendliky.mp3 play]'' by Milan Guštar
genchain of 2nds: ...A1 - A2 - M3 - M4 - M5 - M6 - P7 - P1 - P2 - m3 - m4 - m5 - m6 - d7 - d8...


''[http://www.ronsword.com/sounds/ronsword_8edo_improv.mp3 Acoustic Improvisation in 8-edo]'' by Ron Sword (dead link)
Enharmonic unison: d2


''[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/07%20-%207.%208%20octave.mp3 Comets Over Flatland 7]'' by [[Randy_Winchester|Randy Winchester]]
===Sagittal notation===
This notation is a subset of the notations for EDOs [[24edo#Sagittal notation|24]], [[48edo#Sagittal notation|48]], and [[72edo#Sagittal notation|72]].
====Evo flavor====


''[http://ia600607.us.archive.org/3/items/Transcendissonance/10Malebolge-CityOfTheAsleep.mp3 Malebolge]'' Alison Jones
<imagemap>
File:8-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 392 0 552 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 392 106 [[24-EDO#Sagittal_notation | 24-EDO notation]]
default [[File:8-EDO_Evo_Sagittal.svg]]
</imagemap>


''[http://www.youtube.com/watch?v=0mpDeL7iybI News To Me]'' Jake Sherman
====Revo flavor====


''[http://www.youtube.com/watch?v=HvDEoZ4LIdc Tomorrow Night (pop music from 2045)]'' Jake Sherman
<imagemap>
File:8-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 400 0 560 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 400 106 [[24-EDO#Sagittal_notation | 24-EDO notation]]
default [[File:8-EDO_Revo_Sagittal.svg]]
</imagemap>


''[http://www.seraph.it/dep/det/FunkEight1.mp3 FunkEight 1]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/86557ece0348a8d042346d5e1b13e2d9-166.html blog entry])
====Evo-SZ flavor====


[[:File:8edo-pre-improv.ogg|8edo-pre-improv.ogg]]Preliminary noodling in 8 EDO with ZynAddSubFX synth.(by Cenobyte)
<imagemap>
File:8-EDO_Evo-SZ_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 376 0 536 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 376 106 [[24-EDO#Sagittal_notation | 24-EDO notation]]
default [[File:8-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>


[[:File:darkreflections(sketch).ogg|darkreflections(sketch).ogg]]8EDO Ukulele (cenobyte)
Because it contains no Sagittal symbols, this Evo-SZ Sagittal notation is also a Stein-Zimmerman notation.


[[:File:skiphop(sketch).ogg|skiphop(sketch).ogg]]8EDO Ukulele (cenobyte)
== Chord names ==
[[Ups and downs notation #Chords and Chord Progressions|Ups and downs]] can name any 8edo chord. Alterations are always enclosed in parentheses, additions never are. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13).


[[:File:octo-icy-pensive(sketch).ogg|octo-icy-pensive(sketch).ogg]] [[:File:octo-icy-pensive-echo(sketch).ogg|octo-icy-pensive-echo(sketch).ogg]]2 versions of the same song, one with echo, one without. (cenobyte)
8edo chords are very ambiguous, with many chord homonyms. Even the major and minor triads are [[Chord homonym|homonyms]]. Chord components usually default to M2, M3, P4, P5, M6, m7, M9, P11 and M13. Thus D7 has a M3, P5 and m7. 8-edo chord names using 24edo subset names are greatly simplified by using different defaults: instead of the conventional M2, M3, P4, P5, M6, m7, M9, P11 and M13, we have  ~2, ^M3, v4, ^5, M6, ~7, ~9, v11 and M13. Thus D7 becomes ^M3, ^5 and ~7.


=Ear Training=
{| class="wikitable"
8 EDO ear-training exercises by Alex Ness available [https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&usp=sharing#list here].
|-
! Chord edosteps
! Chord notes
! Full name
! Abbreviated name
! Homonyms
|-
| 0 – 3 – 5
| D ^F♯ ^A
| D^(^5)
| D
| ^F♯m or vGm
|-
| 0 – 2 – 5
| D F ^A
| Dm(^5)
| Dm
| ^A or vB♭
|-
| 0 – 3 – 5 – 7
| D ^F♯ ^A ^C
| D^7(^5)
| D7
| ^F♯m♯11 or vGm♯11
|-
| 0 – 3 – 5 – 6
| D ^F♯ ^A B
| D6(^3,^5)
| D6
| Bm7 and vG,♯9
|-
| 0 – 2 – 5 – 7
| D F ^A ^C
| Dm,~7(^5)
| Dm7
| F6 and vB♭,♯9
|-
| 0 – 2 – 5 – 6
| D F ^A B
| Dm6(^5)
| Dm6
| Bm7(♭5)
|-
| 0 – 2 – 4 – 7
| D F A♭ ^C
| Ddim,~7
| Dm7(♭5)
| Fm6
|}
 
== Approximation to JI ==
[[File:8ed2-001.svg]]


=See also=
== Regular temperament properties ==
*[[Octatonic_scale|Octatonic scale]] - a scale based on alternating whole and half steps
=== Uniform maps ===
{{Uniform map|edo=8}}


=Commas=
=== Commas ===
8 EDO tempers out the following commas. (Note: This assumes val &lt; 8 13 19 22 28 30 |). ||~ Comma ||~ Monzo ||~ Cents ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
8et [[tempering out|tempers out]] the following [[comma]]s. This assumes [[val]] {{val| 8 13 19 22 28 30 }}.


{| class="wikitable"
{| class="commatable wikitable center-all left-3 right-4 left-6"
! [[Harmonic limit|Prime<br />limit]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
! [[Cent]]s
! [[Color name]]
! Name(s)
|-
| 3
| [[8192/6561]]
| {{monzo| 13 -8 }}
| 384.35
| sawa 4th
| Pythagorean diminished fourth
|-
| 5
| [[16/15]]
| {{monzo| 4 -1 -1 }}
| 111.73
| gu 2nd
| Father comma, classic limma
|-
| 5
| [[648/625]]
| {{monzo| 3 4 -4 }}
| 62.57
| Quadgu
| Diminished comma, major diesis
|-
|-
| style="text-align:center;" | 648/625
| 5
| | | 3 4 -4 &gt;
| [[250/243]]
| style="text-align:right;" | 62.57
| {{monzo| 1 -5 3 }}
| style="text-align:center;" | Major Diesis
| 49.17
| style="text-align:center;" | Diminished Comma
| Triyo
| |
| Porcupine comma, maximal diesis
|-
|-
| style="text-align:center;" | 250/243
| 5
| | | 1 -5 3 &gt;
| [[78732/78125]]
| style="text-align:right;" | 49.17
| {{monzo| 2 9 -7 }}
| style="text-align:center;" | Maximal Diesis
| 13.40
| style="text-align:center;" | Porcupine Comma
| Sepgu
| |
| Sensipent comma, medium semicomma
|-
|-
| style="text-align:center;" | 78732/78125
| 7
| | | 2 9 -7 &gt;
| [[64/63]]
| style="text-align:right;" | 13.40
| {{monzo| 6 -2 0 -1 }}
| style="text-align:center;" | Medium Semi Comma
| 27.26
| style="text-align:center;" | Sensipent Comma
| Ru
| |
| Septimal comma, Archytas' comma, Leipziger Komma
|-
|-
| style="text-align:center;" | 64/63
| 7
| | | 6 -2 0 -1 &gt;
| [[875/864]]
| style="text-align:right;" | 27.26
| {{monzo| -5 -3 3 1 }}
| style="text-align:center;" | Septimal Comma
| 21.90
| style="text-align:center;" | Archytas' Comma
| Zotriyo
| | Leipziger Komma
| Keema
|-
|-
| style="text-align:center;" | 875/864
| 7
| | | -5 -3 3 1 &gt;
| <abbr title="321489/320000">(12 digits)</abbr>
| style="text-align:right;" | 21.90
| {{monzo| -9 8 -4 2 }}
| style="text-align:center;" | Keema
| 8.04
| |
| Labizogugu
| |
| [[Varunisma]]
|-
|-
| style="text-align:center;" | 321489/320000
| 7
| | | -9 8 -4 2 &gt;
| [[6144/6125]]
| style="text-align:right;" | 8.04
| {{monzo| 11 1 -3 -2 }}
| style="text-align:center;" | Varun Isma
| 5.36
| |
| Sarurutrigu
| |
| Porwell comma
|-
|-
| style="text-align:center;" | 6144/6125
| 11
| | | 11 1 -3 -2 &gt;
| [[100/99]]
| style="text-align:right;" | 5.36
| {{monzo| 2 -2 2 0 -1 }}
| style="text-align:center;" | Cornwell
| 17.40
| |
| Luyoyo
| |
| Ptolemisma
|-
|-
| style="text-align:center;" | 100/99
| 11
| | | 2 -2 2 0 -1 &gt;
| [[121/120]]
| style="text-align:right;" | 17.40
| {{monzo| -3 -1 -1 0 2 }}
| style="text-align:center;" | Ptolemies
| 14.37
| |
| Lologu
| |
| Biyatisma
|-
|-
| style="text-align:center;" | 121/120
| 11
| | | -3 -1 -1 0 2 &gt;
| [[176/175]]
| style="text-align:right;" | 14.37
| {{monzo| 4 0 -2 -1 1 }}
| style="text-align:center;" | Batista
| 9.86
| |
| Lorugugu
| |
| Valinorsma
|-
|-
| style="text-align:center;" | 176/175
| 11
| | | 4 0 -2 -1 1 &gt;
| [[65536/65219]]
| style="text-align:right;" | 9.86
| {{monzo| 16 0 0 -2 -3 }}
| style="text-align:center;" | Valinor Mo
| 8.39
| |
| Satrilu-aruru
| |
| Orgonisma
|-
|-
| style="text-align:center;" | 65536/65219
| 11
| | | 16 0 0 -2 -3 &gt;
| [[385/384]]
| style="text-align:right;" | 8.39
| {{monzo| -7 -1 1 1 1 }}
| style="text-align:center;" | Organisms
| 4.50
| |
| Lozoyo
| |
| Keenanisma
|-
|-
| style="text-align:center;" | 385/384
| 11
| | | -7 -1 1 1 1 &gt;
| [[4000/3993]]
| style="text-align:right;" | 4.50
| {{monzo| 5 -1 3 0 -3 }}
| style="text-align:center;" | Keenanisma
| 3.03
| |
| Triluyo
| |
| Wizardharry comma
|-
|-
| style="text-align:center;" | 4000/3993
| 13
| | | 5 -1 3 0 -3 &gt;
| [[40/39]]
| style="text-align:right;" | 3.03
| {{monzo| 3 -1 1 0 0 -1 }}
| style="text-align:center;" | Wizard Harry
| 43.83
| |
| Thuyo unison
| |
| Tridecimal minor diesis
|}
|}
[[Category:8-tone]]
<references/>
[[Category:8edo]]
 
[[Category:aaron_andrew_hunt]]
== Scales ==
[[Category:edo]]
=== Scala file ===
[[Category:listen]]
Here is a .scl file of 8edo: [[:File:08-EDO.scl|08-edo.scl]]
[[Category:macrotonal]]
 
[[Category:milan_guštar]]
<pre>
[[Category:ron_sword]]
! 08-EDO.scl
[[Category:scale]]
!
[[Category:todo:unify_precision]]
8 EDO
8
!
150.00
300.00
450.00
600.00
750.00
900.00
1050.00
2/1
</pre>
 
=== Temperaments ===
8edo is fairly composite, so the only step that generates a [[mos]] scale that covers every interval other than the 1 is the 3, producing scales of 332 and [[3L 2s|21212]]. In terms of temperaments, in the 5-limit this is best interpreted as [[father]], as 8edo is the highest edo that tempers out the diatonic semitone in it's [[patent val]], merging 5/4 and 4/3 into a single interval, which is also the generator. This means major and minor chords are rotations of each other, making them inaccurate but very simple, with even the 5 note mos having 3 of both and providing a functional skeleton of 5-limit harmony, albeit with some very strange enharmonic equivalences. In terms of 7-limit extensions things get even more inaccurate, as the patent val supports [[mother]], but the ideal tuning for that is much closer to [[5edo]]. The 8d val supports septimal father and [[pater]], and is much closer to the ideal tuning for both, as the extremely sharp 7 works better with the {{nowrap| 3 & 5 }}. In terms of multi-period temperaments, it makes for a near perfect [[walid]] or a much less accurate [[diminished (temperament)|diminished]] scale.
 
== Instruments ==
A [[Lumatone mapping for 8edo]] is available.
 
== Music ==
; [[Abnormality]]
* [https://www.youtube.com/watch?v=tqgRYQxsA9U ''mushroom''] (2024)
 
; [[Cenobyte]]
* [[:File:8edo-pre-improv.ogg|8edo-pre-improv]] (2011)
* [[:File:darkreflections(sketch).ogg|darkreflections(sketch)]] (2011)
* [[:File:skiphop(sketch).ogg|skiphop(sketch)]] (2011)
* [[:File:octo-icy-pensive(sketch).ogg|octo-icy-pensive(sketch)]], [[:File:octo-icy-pensive-echo(sketch).ogg|octo-icy-pensive-echo(sketch)]] (2011)
 
; [[City of the Asleep]]
* [http://ia600607.us.archive.org/3/items/Transcendissonance/10Malebolge-CityOfTheAsleep.mp3 "Malebolge"], from [https://cityoftheasleep.bandcamp.com/album/transcendissonance ''Transcendissonance''] (2011)
 
; [[Milan Guštar]]
* [http://www.uvnitr.cz/flaoyg/forgotten_works/spendliky.html ''Špendlíky''] (1988-2005)
 
; [[Hideya]]
* [https://www.youtube.com/watch?v=dxjBt4Umbw4 ''Like yamashiro''] (2021)
* [https://www.youtube.com/watch?v=h75K1KOb5is ''Like Ensor's paintings''] (2023)
 
; [[Nathan Ho]]
* [https://www.youtube.com/watch?v=DR1SSW-kQqs ''8edo minimal techno in SuperCollider''] (2023)
 
; [[Aaron Andrew Hunt]]
* [https://aaronandrewhunt.bandcamp.com/track/fantasia-fugue-a4-in-8et "Fantasia & Fugue a4 in 8ET"], from [https://aaronandrewhunt.bandcamp.com/album/the-equal-tempered-keyboard ''The Equal-Tempered Keyboard''] (1999-2022)
 
; [[NullPointerException Music]]
* [https://www.youtube.com/watch?v=CryT-HTzrZE "Disorient"], from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''] (2020)
* [https://www.youtube.com/watch?v=AErBW21bljk ''Towards Dissolution''] (2020)
 
; [[User:Phanomium|Phanomium]]
* [https://www.youtube.com/watch?v=22OKO6e6nGk ''Octahedron''] (2024)
 
; [[Carlo Serafini]]
* ''FunkEight 1'' (2013) – [http://www.seraph.it/blog_files/86557ece0348a8d042346d5e1b13e2d9-166.html blog] | [http://www.seraph.it/dep/det/FunkEight1.mp3 play]
 
; [[Sevish]]
* [https://youtu.be/1fpYEVEdcaE ''Reckoner''] (2025)
 
; [[Jake Sherman]]
* [https://www.youtube.com/watch?v=0mpDeL7iybI ''News To Me''] (2011)
* [https://www.youtube.com/watch?v=HvDEoZ4LIdc ''Tomorrow Night (pop music from 2045)''] (2011)
 
; [[Ron Sword]]
* [http://www.ronsword.com/sounds/ronsword_8edo_improv.mp3 ''Acoustic Improvisation in 8EDO'']{{dead link}}
 
; [[Stephen Weigel]]
* [https://soundcloud.com/overtoneshock/tenacious-chorale-9-edo-and-8-edo-live ''Tenacious Chorale'': Movement 2] (2016)
 
; [[Randy Winchester]]
* [https://archive.org/details/jamendo-005173/07.mp3 "7. 8 / octave"], from ''[[Comets Over Flatland]]'' (2007)
 
; [[User:Fitzgerald_Lee|Fitzgerald Lee]]
* [https://youtu.be/zwRDfjLzXkU Jonky Jazz] (2025)
 
== Ear training ==
8edo ear-training exercises by Alex Ness available [https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&usp=sharing#list here].
 
== See also ==
* [[Octatonic scale]] - a scale based on alternating whole and half steps
* [[Fendo family]] - temperaments closely related to 8edo
 
[[Category:8-tone scales]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/8edo"