8edo: Difference between revisions

{{ED intro}}

! rowspan="2" | Steps

! rowspan="2" | Cents

! colspan="3" | JI approximation

!Other

! 2.5/3.11/3.13/5*

| 0

| 1/1

| 1/1

| 1/1

|1/1, 16/15

| 1

| 150

| 12/11

| 12/11

| 12/11, 11/10

| 3

| 450

| 13/10

| 13/10

| 13/10

| 4

| 600

|  

|  

| 7/5, 10/7

| 5

| 750

| 20/13

| 20/13

| 20/13

| 6

| 900

| 32/19

| 5/3

| 5/3

|5/3, 16/9

| 7

| 1050

| 11/6

| 11/6

| 20/11, 11/6

| 8

| 1200

| 2/1

| 2/1

| 2/1

<nowiki />* Allows [[inversion]] by 2/1; other interpretations also possible

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.

! 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

| [[File:0-0 unison.mp3|frameless]]

| [[File:0-150 (8-EDO).mp3|frameless]]

| [[File:0-300 (12-EDO).mp3|frameless]]

| [[File:0-450 (8-EDO).mp3|frameless]]

| [[File:0-600 (12-EDO).mp3|frameless]]

| [[File:0-750 (8-EDO).mp3|frameless]]

| [[File:0-900 (12-EDO).mp3|frameless]]

| [[File:0-1050 (8-EDO).mp3|frameless]]

| [[File:0-1200 octave.mp3|frameless]]

[[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).  

! 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

[[File:8ed2-001.svg]]

{{Uniform map|edo=8}}

8et [[tempering out|tempers out]] the following [[comma]]s. This assumes [[val]] {{val| 8 13 19 22 28 30 }}.

! [[Harmonic limit|Prime<br />limit]]

!  

!  

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.

 

A [[Lumatone mapping for 8edo]] is available.