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→Theory: A = 2 and s = 1.01 give a peak of around 46.4 cents, which 26edo is closest
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The structure of 26edo is an interesting beast, with various approaches relating it to various rank-2 temperaments.
The structure of 26edo is an interesting beast, with various approaches relating it to various rank-2 temperaments.


1. In terms of more traditional chord types we have flattone, a variant of meantone with flat fifths, which yields interesting but to some unsatisfying results (due mainly to the dissonance of its thirds, and its major second of approximately [[10/9]] instead of [[9/8]]).
# In terms of more traditional chord types we have flattone, a variant of meantone with flat fifths, which yields interesting but to some unsatisfying results (due mainly to the dissonance of its thirds, and its major second of approximately [[10/9]] instead of [[9/8]]).
 
# As two chains of meantone fifths half an octave apart, it supports injera temperament. The generator for this is an interval which can be called either 21/20 or 15/14, and which represents two steps of 26, and hence one step of 13. Hence in 26edo (as opposed to, for instance, [[38edo]]) it can be viewed as two parallel 13edo scales, and from that point of view we can consider it as supporting the 13b&26 temperament, allowing the two chains be shifted slightly and which can be used for more atonal melodies. In this way its internal dynamics resemble those of [[14edo]].
2. As two chains of meantone fifths half an octave apart, it supports injera temperament. The generator for this is an interval which can be called either 21/20 or 15/14, and which represents two steps of 26, and hence one step of 13. Hence in 26edo (as opposed to, for instance, [[38edo]]) it can be viewed as two parallel 13edo scales, and from that point of view we can consider it as supporting the 13b&26 temperament, allowing the two chains be shifted slightly and which can be used for more atonal melodies. In this way its internal dynamics resemble those of [[14edo]].
# 26edo nearly perfectly approximates the 7th and 11th harmonics, and an entire system may be constructed analogous to that based on the 3rd and 5th harmonics. In terms of subgroups, this is the 2.7.11 subgroup, and on this 26 tempers out the pair of commas [[65536/65219]] and {{monzo| -3 0 0 6 -4 }}. The 65536/65219 comma, the orgonisma, leads to the [[Orgonia|orgone temperament]] with an approximate 77/64 generator of 7\26, with mos scales of size 7, 11 and 15. The {{monzo| -3 0 0 6 -4 }} comma leads to a half-octave period and an approximate [[49/44]] generator of 4\26, leading to mos of size 8 and 14.
 
# We can also treat 26edo as a full 13-limit temperament, since it is consistent on the 13-odd-limit (unlike all lower edos).
3. 26edo nearly perfectly approximates the 7th and 11th harmonics, and an entire system may be constructed analogous to that based on the 3rd and 5th harmonics. In terms of subgroups, this is the 2.7.11 subgroup, and on this 26 tempers out the pair of commas [[65536/65219]] and {{monzo| -3 0 0 6 -4 }}. The 65536/65219 comma, the orgonisma, leads to the [[Orgonia|orgone temperament]] with an approximate 77/64 generator of 7\26, with mos scales of size 7, 11 and 15. The {{monzo| -3 0 0 6 -4 }} comma leads to a half-octave period and an approximate [[49/44]] generator of 4\26, leading to mos of size 8 and 14.
# It also has a pretty good 17th harmonic and tempers out the comma 459:448, thus three fifths gives a 17:14 and four gives a 21:17; "mushtone". Mushtone is high in badness, but 26edo does it pretty well (and [[33edo]] even better). Because 26edo also tempers out 85:84, the septendecimal major and minor thirds are equivalent to their pental counterparts, making mushtone the same as flattone.
 
4. We can also treat 26edo as a full 13-limit temperament, since it is consistent on the 13-odd-limit (unlike all lower edos).
 
5. It also has a pretty good 17th harmonic and tempers out the comma 459:448, thus three fifths gives a 17:14 and four gives a 21:17; "mushtone". Mushtone is high in badness, but 26edo does it pretty well (and [[33edo]] even better). Because 26edo also tempers out 85:84, the septendecimal major and minor thirds are equivalent to their pental counterparts, making mushtone the same as flattone.


Its step, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having around the highest [[harmonic entropy]] possible and thus is, in theory, most dissonant, assuming the relatively common values of ''a'' = 2 and ''s'' = 1.01. This property is shared with all edos between around 20 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant.
Its step, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having around the highest [[harmonic entropy]] possible and thus is, in theory, most dissonant, assuming the relatively common values of ''a'' = 2 and ''s'' = 1.01. This property is shared with all edos between around 20 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant.
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| P1
| P1
| D
| D
|da
| da
| do
| do
|-
|-
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| A1
| A1
| D#
| D#
|du
| du
| di
| di
|-
|-
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| d2
| d2
| Ebb
| Ebb
|fro
| fro
| rih
| rih
|-
|-
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| m2
| m2
| Eb
| Eb
|fra
| fra
| ru
| ru
|-
|-
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| M2
| M2
| E
| E
|ra
| ra
| re
| re
|-
|-
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| A2
| A2
| E#
| E#
|ru
| ru
| ri
| ri
|-
|-
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| d3
| d3
| Fb
| Fb
|no
| no
| ma
| ma
|-
|-
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| m3
| m3
| F
| F
|na
| na
| me
| me
|-
|-
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| M3
| M3
| F#
| F#
|ma
| ma
| muh/mi
| muh/mi
|-
|-
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| A3
| A3
| Fx
| Fx
|mu
| mu
| maa
| maa
|-
|-
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| d4
| d4
| Gb
| Gb
|fo
| fo
| fe
| fe
|-
|-
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| P4
| P4
| G
| G
|fa
| fa
| fa
| fa
|-
|-
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| A4
| A4
| G#
| G#
|fu/pa
| fu/pa
| fu
| fu
|-
|-
| 13
| 13
|600.00
| 600.00
| [[7/5]], [[10/7]]
| [[7/5]], [[10/7]]
| AA4, dd5
| AA4, dd5
| Gx, Abb
| Gx, Abb
|pu/sho
| pu/sho
| fi/se
| fi/se
|-
|-
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| d5
| d5
| Ab
| Ab
|sha/so
| sha/so
| su
| su
|-
|-
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| P5
| P5
| A
| A
|sa
| sa
| sol
| sol
|-
|-
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| A5
| A5
| A#
| A#
|su
| su
| si
| si
|-
|-
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| d6
| d6
| Bbb
| Bbb
|flo
| flo
| leh
| leh
|-
|-
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| m6
| m6
| Bb
| Bb
|fla
| fla
| le/lu
| le/lu
|-
|-
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| M6
| M6
| B
| B
|la
| la
| la
| la
|-
|-
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| A6
| A6
| B#
| B#
|lu
| lu
| li
| li
|-
|-
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| d7
| d7
| Cb
| Cb
|tho
| tho
| ta
| ta
|-
|-
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| m7
| m7
| C
| C
|tha
| tha
| te
| te
|-
|-
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| M7
| M7
| C#
| C#
|ta
| ta
| tu/ti
| tu/ti
|-
|-
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| A7
| A7
| Cx
| Cx
|tu
| tu
| to
| to
|-
|-
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| d8
| d8
| Db
| Db
|do
| do
| da
| da
|-
|-
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| P8
| P8
| D
| D
|da
| da
| do
| do
|}
|}
* based on treating 26edo as a [[13-limit]] temperament; other approaches are possible.


*based on treating 26-EDO as a [[13-limit]] temperament; other approaches are possible.
=== Interval quality and chord names in color notation ===
 
Using [[color notation]], qualities can be loosely associated with colors:
Using [[color notation]], qualities can be loosely associated with colors:


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! Quality
! Quality
! Color
! Color
! Monzo format
! Monzo Format
! Examples
! Examples
|-
|-
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All 26edo chords can be named using conventional methods, expanded to include augmented and diminished 2nd, 3rds, 6ths and 7ths. Spelling certain chords properly may require triple sharps and flats, especially if the tonic is anything other than the 11 keys in the Eb-C# range. Here are the zo, gu, yo and ru triads:
All 26edo chords can be named using conventional methods, expanded to include augmented and diminished 2nd, 3rds, 6ths and 7ths. Spelling certain chords properly may require triple sharps and flats, especially if the tonic is anything other than the 11 keys in the Eb-C# range. Here are the zo, gu, yo and ru triads:


{| class="wikitable" style="text-align:center;"
{| class="wikitable center-all"
|-
|-
! [[Kite's color notation|color of the 3rd]]
! [[Kite's color notation|Color of the 3rd]]
! JI chord
! JI chord
! Notes as EDO steps
! Notes as Edoteps
! Notes of C chord
! Notes of C Chord
! Written name
! Written Name
! Spoken name
! Spoken Name
|-
|-
| zo
| zo
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|}
|}


For a more complete list, see [[Ups_and_Downs_Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]].
For a more complete list, see [[Ups and downs notation #Chord names in other EDOs]].


== Selected just intervals approximated ==
== Selected just intervals approximated ==
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The following table shows how [[15-odd-limit intervals]] are represented in 26edo. Prime harmonics are in '''bold'''; intervals with a non-[[consistent]] mapping are in ''italic''.  
The following table shows how [[15-odd-limit intervals]] are represented in 26edo. Prime harmonics are in '''bold'''; intervals with a non-[[consistent]] mapping are in ''italic''.  


{| class="wikitable" style="text-align:center;"
{| class="wikitable center-all"
|+Direct mapping (even if inconsistent)
|+Direct mapping (even if inconsistent)
|-
|-
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