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{{interwiki
{{Interwiki
| en = 26edo
| de = 26-EDO
| de = 26-EDO
| en = 26edo
| es =  
| es =  
| ja =
| ja =
}}
}}
{{Infobox ET}}
{{Infobox ET}}
{{ED intro}}


{{EDO intro|26}}
== Theory ==
== Theory ==
26edo tempers out [[81/80]] in the [[5-limit]], making it a [[meantone]] tuning with a very flat fifth.  
26edo has a [[3/2|perfect fifth]] of about 692 cents and [[tempering out|tempers out]] [[81/80]] in the [[5-limit]], making it a very flat [[meantone]] tuning (0.088957{{c}} flat of the [[4/9-comma meantone]] fifth) with a very soft [[5L 2s|diatonic scale]].  


In the [[7-limit]], it tempers out 50/49, 525/512 and 875/864, and [[support]]s temperaments like [[injera]], [[flattone]], [[lemba]] and [[doublewide]]. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13-odd-limit]] [[consistent]]ly. 26edo has a very good approximation of the harmonic seventh ([[7/4]]), as it is the denominator of a convergent to log<sub>2</sub>7.
In the [[7-limit]], it tempers out [[50/49]], [[525/512]], and [[875/864]], and [[support]]s temperaments like [[injera]], [[flattone]], [[lemba]], and [[doublewide]]. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13-odd-limit]] [[consistent]]ly. 26edo has a very good approximation of the harmonic seventh ([[7/4]]), as it is the denominator of a convergent to log<sub>2</sub>7.


26edo's minor sixth (1.6158) is very close to ''φ'' ≈ 1.6180 (i.e. the golden ratio).
26edo's minor sixth (1.6158) is very close to {{nowrap|''φ'' ≈ 1.6180}} (i.e. the golden ratio).


With a fifth of 15 steps, it can be equally divided into 3 or 5, supporting [[slendric]] temperament and [[bleu]] temperament respectively.
With a fifth of 15 steps, it can be equally divided into 3 or 5, supporting [[slendric]] temperament and [[bleu]] temperament respectively.
Line 19: Line 19:
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 provides an interesting structure but unsatisfying intonation due mainly to the poorly tuned thirds. Extending meantone harmony to the 7-limit is quite intuitive; for example, augmented becomes supermajor, and diminished becomes subminor. Simple mappings for harmonics up to 13 are also achieved.
# 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&amp;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 [[117649/117128]]. 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 117649/117128 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).
# It also has a pretty good 17th harmonic and tempers out the comma 459:448, thus three fourths give a 17:14 and four fifths give 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.


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&amp;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]].
Its step of 46.2{{c}}, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having around the highest [[harmonic entropy]] possible. In other words, there is a common perception of quartertones as being the most dissonant intervals. 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.


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.
Thanks to its sevenths, 26edo is an ideal tuning for its size for [[metallic harmony]].


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).
=== Odd harmonics ===
 
{{Harmonics in equal|26}}
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.
=== Subsets and supersets ===
26edo has [[2edo]] and [[13edo]] as subsets, of which 13edo is non-trivial, sharing the 2.9.5.21.11.13.17.19-subgroup with 26edo.  


=== Odd harmonics ===
26edo tempers out [[Fynn's comma]], which sets ~7/4 to 21\26. This is shared by several notable superset edos. Multiplying 26edo by 3 yields [[78edo]], which corrects several harmonics. [[104edo]] is a notable dual-5's system. [[130edo]], [[364edo]], [[494edo]], and [[624edo]] do well in approximating JI, though they are more complex.
{{Harmonics in equal|26}}


== Intervals ==
== Intervals ==
Line 38: Line 41:
|-
|-
! Degrees
! Degrees
! [[Cents|cents]]
! [[Cent]]s
! Approximate Ratios*
! Approximate ratios<ref group="note">{{sg|limit=13-limit}}</ref>
! Interval<br>Name
! Interval<br>name
! Example<br>in D
! [[SKULO interval names|SKULO]]<br>[[SKULO interval names|Interval name]]
! Example<br>in D
! Example<br>in D
! colspan="2" |[[Solfege|Solfeges]]
! colspan="2" | [[Solfege|Solfeges]]
|-
|-
| 0
| 0
Line 49: Line 54:
| P1
| P1
| D
| D
|da
| P1
| D
| da
| do
| do
|-
|-
Line 57: Line 64:
| A1
| A1
| D#
| D#
|du
| A1, S1
| D#, SD
| du
| di
| di
|-
|-
Line 65: Line 74:
| d2
| d2
| Ebb
| Ebb
|fro
| sm2
| sEb
| fro
| rih
| rih
|-
|-
Line 73: Line 84:
| m2
| m2
| Eb
| Eb
|fra
| m2
| Eb
| fra
| ru
| ru
|-
|-
Line 81: Line 94:
| M2
| M2
| E
| E
|ra
| M2
| E
| ra
| re
| re
|-
|-
Line 89: Line 104:
| A2
| A2
| E#
| E#
|ru
| SM2
| SE
| ru
| ri
| ri
|-
|-
Line 97: Line 114:
| d3
| d3
| Fb
| Fb
|no
| sm3
| sF
| no
| ma
| ma
|-
|-
Line 105: Line 124:
| m3
| m3
| F
| F
|na
| m3
| F
| na
| me
| me
|-
|-
| 8
| 8
| 369.23
| 369.23
| [[5/4]], [[11/9]], [[16/13]]
| [[5/4]], [[11/9]], [[16/13]], [[26/21]]
| M3
| F#
| M3
| M3
| F#
| F#
|ma
| ma
| muh/mi
| muh/mi
|-
|-
Line 121: Line 144:
| A3
| A3
| Fx
| Fx
|mu
| SM3
| SF#
| mu
| maa
| maa
|-
|-
| 10
| 10
| 461.54
| 461.54
| [[21/16]], [[13/10]]
| [[21/16]], [[13/10]], [[64/49]]
| d4
| d4
| Gb
| Gb
|fo
| s4
| sG
| fo
| fe
| fe
|-
|-
Line 137: Line 164:
| P4
| P4
| G
| G
|fa
| P4
| G
| fa
| fa
| fa
|-
|-
Line 145: Line 174:
| A4
| A4
| G#
| G#
|fu/pa
| A4
| G#
| 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
| SA4, sd5
| SG#, sAb
| pu/sho
| fi/se
| fi/se
|-
|-
Line 161: Line 194:
| d5
| d5
| Ab
| Ab
|sha/so
| d5
| Ab
| sha/so
| su
| su
|-
|-
Line 169: Line 204:
| P5
| P5
| A
| A
|sa
| P5
| A
| sa
| sol
| sol
|-
|-
| 16
| 16
| 738.46
| 738.46
| [[32/21]], [[20/13]]
| [[32/21]], [[20/13]], [[49/32]]
| A5
| A5
| A#
| A#
|su
| S5
| SA
| su
| si
| si
|-
|-
Line 185: Line 224:
| d6
| d6
| Bbb
| Bbb
|flo
| sm6
| sBb
| flo
| leh
| leh
|-
|-
| 18
| 18
| 830.77
| 830.77
| [[13/8]], [[8/5]]
| [[8/5]], [[13/8]], [[21/13]]
| m6
| Bb
| m6
| m6
| Bb
| Bb
|fla
| fla
| le/lu
| le/lu
|-
|-
Line 201: Line 244:
| M6
| M6
| B
| B
|la
| M6
| B
| la
| la
| la
|-
|-
Line 209: Line 254:
| A6
| A6
| B#
| B#
|lu
| SM6
| SB
| lu
| li
| li
|-
|-
Line 217: Line 264:
| d7
| d7
| Cb
| Cb
|tho
| sm7
| sC
| tho
| ta
| ta
|-
|-
Line 225: Line 274:
| m7
| m7
| C
| C
|tha
| m7
| C
| tha
| te
| te
|-
|-
Line 233: Line 284:
| M7
| M7
| C#
| C#
|ta
| M7
| C#
| ta
| tu/ti
| tu/ti
|-
|-
Line 241: Line 294:
| A7
| A7
| Cx
| Cx
|tu
| SM7
| SC#
| tu
| to
| to
|-
|-
Line 249: Line 304:
| d8
| d8
| Db
| Db
|do
| d8, s8
| Db, sD
| do
| da
| da
|-
|-
Line 257: Line 314:
| P8
| P8
| D
| D
|da
| P8
| D
| da
| do
| do
|}
|}
<references group="note" />


*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:


Line 269: Line 328:
! Quality
! Quality
! Color
! Color
! Monzo format
! Monzo Format
! Examples
! Examples
|-
|-
Line 305: Line 364:
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 Edosteps
! Notes of C chord
! Notes of C Chord
! Written name
! Written Name
! Spoken name
! Spoken Name
|-
|-
| zo
| zo
Line 343: Line 402:
|}
|}


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]].
 
== Notation ==
 
=== Standard notation ===
Because the chromatic semitone is 1 step, only sharps and flats are needed to notate 26edo.
 
{{sharpness-sharp1}}


== Selected just intervals approximated ==
=== Sagittal notation ===
=== 15-odd-limit interval mappings ===
This notation uses the same sagittal sequence as EDOs [[5edo#Sagittal notation|5]], [[12edo#Sagittal notation|12]], and [[19edo#Sagittal notation|19]], is a subset of the notation for [[52edo#Sagittal notation|52-EDO]], and is a superset of the notation for [[13edo#Sagittal notation|13-EDO]].
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;"
==== Evo flavor ====
|+Direct mapping (even if inconsistent)
<imagemap>
|-
File:26-EDO_Evo_Sagittal.svg
! Interval, complement
desc none
! Error (abs, [[Cent|¢]])
rect 80 0 300 50 [[Sagittal_notation]]
|-
rect 463 0 623 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
| [[13/12]], [[24/13]]
default [[File:26-EDO_Evo_Sagittal.svg]]
| 0.111
</imagemap>
|-
| '''[[8/7]], [[7/4]]'''
| '''0.405'''
|-
| [[14/11]], [[11/7]]
| 2.123
|-
| [[10/9]], [[9/5]]
| 2.212
|-
| '''[[11/8]], [[16/11]]'''
| '''2.528'''
|-
| [[13/10]], [[20/13]]
| 7.325
|-
| [[6/5]], [[5/3]]
| 7.436
|-
| [[18/13]], [[13/9]]
| 9.536
|-
| '''[[4/3]], [[3/2]]'''
| '''9.647'''
|-
| '''[[16/13]], [[13/8]]'''
| '''9.758'''
|-
| [[7/6]], [[12/7]]
| 10.052
|-
| [[14/13]], [[13/7]]
| 10.163
|-
| [[12/11]], [[11/6]]
| 12.176
|-
| [[13/11]], [[22/13]]
| 12.287
|-
| ''[[15/11]], [[22/15]]''
| ''16.895''
|-
| [[15/13]], [[26/15]]
| 16.972
|-
| '''[[5/4]], [[8/5]]'''
| '''17.083'''
|-
| [[7/5]], [[10/7]]
| 17.488
|-
| ''[[15/14]], [[28/15]]''
| ''19.019''
|-
| [[9/8]], [[16/9]]
| 19.295
|-
| ''[[16/15]], [[15/8]]''
| ''19.424''
|-
| [[11/10]], [[20/11]]
| 19.611
|-
| [[9/7]], [[14/9]]
| 19.699
|-
| [[11/9]], [[18/11]]
| 21.823
|}


{| class="wikitable" style="text-align:center;"
Because it includes no Sagittal symbols, this Evo Sagittal notation is also a conventional notation.
|+Patent val mapping
|-
! Interval, complement
! Error (abs, [[Cent|¢]])
|-
| [[13/12]], [[24/13]]
| 0.111
|-
| '''[[8/7]], [[7/4]]'''
| '''0.405'''
|-
| [[14/11]], [[11/7]]
| 2.123
|-
| [[10/9]], [[9/5]]
| 2.212
|-
| '''[[11/8]], [[16/11]]'''
| '''2.528'''
|-
| [[13/10]], [[20/13]]
| 7.325
|-
| [[6/5]], [[5/3]]
| 7.436
|-
| [[18/13]], [[13/9]]
| 9.536
|-
| '''[[4/3]], [[3/2]]'''
| '''9.647'''
|-
| '''[[16/13]], [[13/8]]'''
| '''9.758'''
|-
| [[7/6]], [[12/7]]
| 10.052
|-
| [[14/13]], [[13/7]]
| 10.163
|-
| [[12/11]], [[11/6]]
| 12.176
|-
| [[13/11]], [[22/13]]
| 12.287
|-
| [[15/13]], [[26/15]]
| 16.972
|-
| '''[[5/4]], [[8/5]]'''
| '''17.083'''
|-
| [[7/5]], [[10/7]]
| 17.488
|-
| [[9/8]], [[16/9]]
| 19.295
|-
| [[11/10]], [[20/11]]
| 19.611
|-
| [[9/7]], [[14/9]]
| 19.699
|-
| [[11/9]], [[18/11]]
| 21.823
|-
| ''[[16/15]], [[15/8]]''
| ''26.730''
|-
| ''[[15/14]], [[28/15]]''
| ''27.135''
|-
| ''[[15/11]], [[22/15]]''
| ''29.258''
|}


== Acoustic π just in between the ϕ intervals ==
==== Revo flavor ====
After [[13edo#Phi vibes|13edo]], the weird coïncidences continue: [[11/7#Proximity with π/2|acoustic π/2]] (17\26) is just in between [[13edo#Phi vibes|the ϕ intervals provided by 13edo]] (16\26 for [[Logarithmic phi|logarithmic ϕ]]/2, and 18\26 for [[Acoustic phi|acoustic ϕ]]).
<imagemap>
File:26-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 511 0 671 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
default [[File:26-EDO_Revo_Sagittal.svg]]
</imagemap>


Not until 1076edo do we find a better EDO in terms of relative error on these intervals (which is not a very relevant EDO for logarithmic ϕ, since 1076 does not belong to the Fibonacci sequence).
== Approximation to JI ==
=== 15-odd-limit interval mappings ===
{{Q-odd-limit intervals|26}}


However, it should be noted that [[Logarithmic constants VS acoustic constants|from an acoustic perspective]], acoustic π and acoustic ϕ are both better represented on [[23edo]].
== Approximation to irrational intervals ==
26edo approximates both [[acoustic phi]] (the [[golden ratio]]) and [[pi]] quite accurately. Not until 1076edo do we find a better edo in terms of relative error on these intervals{{Clarify}}.


{| class="wikitable center-all"
{| class="wikitable center-all"
|+Direct mapping
|+ style="font-size: 105%;" | Direct approximation
|-
|-
! Interval
! Interval
Line 540: Line 467:


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Just intonation subgroup|Subgroup]]
! rowspan="2" |[[Comma basis|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal
8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
|-
![[TE error|Absolute]] (¢)
! rowspan="2" | [[Subgroup]]
![[TE simple badness|Relative]] (%)
! rowspan="2" | [[Comma basis]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
|-
|2.3
! [[TE error|Absolute]] (¢)
|[-41 26⟩
! [[TE simple badness|Relative]] (%)
|[⟨26 41]]
|-
| 2.3
| {{monzo| -41 26 }}
| {{mapping| 26 41 }}
| +3.043
| +3.043
|3.05
| 3.05
|6.61
| 6.61
|-
|-
|2.3.5
| 2.3.5
|81/80, 78125/73728
| 81/80, 78125/73728
|[⟨26 41 60]]
| {{mapping| 26 41 60 }}
| +4.489
| +4.489
|3.22
| 3.22
|6.98
| 6.98
|-
|-
|2.3.5.7
| 2.3.5.7
|50/49, 81/80, 405/392
| 50/49, 81/80, 405/392
|[⟨26 41 60 73]]
| {{mapping| 26 41 60 73 }}
| +3.324
| +3.324
|3.44
| 3.44
|7.45
| 7.45
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|45/44, 50/49, 81/80, 99/98
| 45/44, 50/49, 81/80, 99/98
|[⟨26 41 60 73 90]]
| {{mapping| 26 41 60 73 90 }}
| +2.509
| +2.509
|3.48
| 3.48
|7.53
| 7.53
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|45/44, 50/49, 65/64, 78/77, 81/80
| 45/44, 50/49, 65/64, 78/77, 81/80
|[⟨26 41 60 73 90 96]]
| {{mapping| 26 41 60 73 90 96 }}
| +2.531
| +2.531
|3.17
| 3.17
|6.87
| 6.87
|-
|-
|2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
|45/44, 50/49, 65/64 78/77, 81/80, 85/84
| 45/44, 50/49, 65/64, 78/77, 81/80, 85/84
|[⟨26 41 60 73 90 96 106]]
| {{mapping| 26 41 60 73 90 96 106 }}
| +2.613
| +2.613
|2.94
| 2.94
|6.38
| 6.38
|-
|-
|2.3.5.7.11.13.17.19
| 2.3.5.7.11.13.17.19
|45/44, 50/49, 57/56, 65/64, 78/77, 81/80, 85/84
| 45/44, 50/49, 57/56, 65/64, 78/77, 81/80, 85/84
|[⟨26 41 60 73 90 96 106 110]]
| {{mapping| 26 41 60 73 90 96 106 110 }}
| +2.894
| +2.894
|2.85
| 2.85
|6.18
| 6.18
|}
|}
26et is lower in relative error than any previous equal temperaments in the [[17-limit|17-]], [[19-limit|19-]], [[23-limit|23-]], and [[29-limit]] (using the 26i val for the 23- and 29-limit). The next equal temperaments performing better in those subgroups are [[27edo|27eg]], 27eg, [[29edo|29g]], and [[46edo|46]], respectively.  
* 26et is lower in relative error than any previous equal temperaments in the [[17-limit|17-]], [[19-limit|19-]], [[23-limit|23-]], and [[29-limit]] (using the 26i val for the 23- and 29-limit). The next equal temperaments performing better in those subgroups are [[27edo|27eg]], 27eg, [[29edo|29g]], and [[46edo|46]], respectively.  


=== Rank-2 Temperaments ===
=== Rank-2 Temperaments ===
* [[List of 26et rank two temperaments by badness]]
* [[List of 26et rank two temperaments by badness]]
* [[List of edo-distinct 26et rank two temperaments]]
* [[List of edo-distinct 26et rank two temperaments]]
Important MOSes include (in addition to ones found in [[13edo]]):
* diatonic ([[flattone]]) 4443443 (15\26, 1\1)
* chromatic ([[flattone]]) 313131331313 (15\26, 1\1)
* enharmonic ([[flattone]]) 2112112112121121121 (15\26, 1\1)
* [[orgone]] 5525252 (7\26, 1\1)
* [[orgone]] 32322322322 (7\26, 1\1)
* [[orgone]] 212212221222122 (7\26, 1\1)
* [[lemba]] 553553 (5\26, 1\2)
* [[lemba]] 3232332323 (5\26, 1\2)
* [[lemba]] 2122122121221221 (5\26, 1\2)


{| class="wikitable center-all left-3"
{| class="wikitable center-all left-3"
|-
|-
! Periods<br>per octave
! Periods<br>per 8ve
! Generator
! Generator
! Temperaments
! Temperaments
Line 625: Line 541:
| 1
| 1
| 1\26
| 1\26
| [[Quartonic]]/[[Quarto]]
| [[Quartonic]] / [[quarto]]
|-
|-
| 1
| 1
| 3\26
| 3\26
| [[Jerome]]/[[Chromatic_pairs|Bleu]]/[[Secund]]/[[Glacier]]
| [[Glacier]] / [[bleu]] / [[jerome]] / [[secund]]
|-
|-
| 1
| 1
| 5\26
| 5\26
| [[Cynder]]/[[Mothra]]
| [[Cynder]] / [[mothra]]
|-
|-
| 1
| 1
| 7\26
| 7\26
| [[Superkleismic]]/[[Orgone]]/[[Shibboleth]]
| [[Orgone]] / [[superkleismic]]
|-
|-
| 1
| 1
| 9\26
| 9\26
| [[Roman]]/[[Wesley]]
| [[Wesley]] / [[roman]]
|-
|-
| 1
| 1
| 11\26
| 11\26
| [[Meantone]]/[[Flattone]]
| [[Flattone]] / [[flattertone]]
|-
|-
| 2
| 2
Line 657: Line 573:
| 2
| 2
| 3\26
| 3\26
| [[Fifive]]/[[Crepuscular]]
| [[Fifive]] / [[crepuscular]]
|-
|-
| 2
| 2
| 4\26
| 4\26
| [[Unidec]]/[[Gamelismic_clan#Unidec-Hendec|Hendec]]/[[Dubbla]]
| [[Dubbla]]<br>[[Unidec]] / [[hendec]]
|-
|-
| 2
| 2
| 5\26
| 5\26
| | [[Lemba]]
| [[Lemba]]
|-
|-
| 2
| 2
| 6\26
| 6\26
| [[Doublewide]]/[[Cavalier]]
| [[Doublewide]] / [[Jubilismic_clan#Cavalier|cavalier]]
|-
|-
| 13
| 13
| 1\26
| 1\26
| [[Triskaidekic]]
| [[Orwellismic_temperaments#Triskaidekic|Triskaidekic]]
|}
|}


=== Hendec in 26et ===
=== Hendec in 26et ===
[[Gamelismic_clan#Unidec-Hendec|Hendec]], the 13-limit 26&amp;46 temperament with generator ~10/9, concentrates the intervals of greatest accuracy in 26et into the lower ranges of complexity. It has a period of half an octave, with 13/12 reachable by four generators, 8/7 by two, 14/11 by one, 10/9 by one, and 11/8 by three. All of these are tuned to within 2.5 cents of accuracy.
[[Hendec]], the 13-limit {{nowrap|26 & 46}} temperament with generator ~10/9, concentrates the intervals of greatest accuracy in 26et into the lower ranges of complexity. It has a period of half an octave, with 13/12 reachable by four generators, 8/7 by two, 14/11 by one, 10/9 by one, and 11/8 by three. All of these are tuned to within 2.5 cents of accuracy.


== Commas ==
=== Commas ===
26et [[tempers out]] the following [[commas]]. (Note: This assumes the [[val]] {{val| 26 41 60 73 90 96 }}.)
26et [[tempering out|tempers out]] the following [[commas]]. This assumes the [[val]] {{val| 26 41 60 73 90 96 }}.


{| class="commatable wikitable center-all left-3 right-4 left-6"
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
|-
! [[Harmonic limit|Prime<br>Limit]]
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Monzo]]
! [[Monzo]]
! [[Cents]]
! [[Cents]]
Line 703: Line 619:
| 0.23
| 0.23
| Quadla-sepquingu
| Quadla-sepquingu
| [[Senior]]
| [[Senior comma]]
|-
|-
| 7
| 7
Line 717: Line 633:
| 34.98
| 34.98
| Biruyo
| Biruyo
| Tritonic diesis, Jubilisma
| Jubilisma, tritonic diesis
|-
|-
| 7
| 7
Line 731: Line 647:
| 13.47
| 13.47
| Sarurutriyo
| Sarurutriyo
| Octagar
| Octagar comma
|-
|-
| 7
| 7
Line 738: Line 654:
| 13.07
| 13.07
| Triru-agu
| Triru-agu
| Orwellisma, Orwell comma
| Orwellisma
|-
|-
| 7
| 7
Line 822: Line 738:
| 16.57
| 16.57
| Thuzoyo
| Thuzoyo
| Animist
| Animist comma
|}
|}
<references/>
<references group="note" />


== Orgone Temperament ==
== Octave stretch or compression ==
[[Andrew_Heathwaite|Andrew Heathwaite]] first proposed [[Orgonia|orgone]] temperament to take advantage of 26edo's excellent 11 and 7 approximations. 7 degrees of 26edo is a wide minor third of approximately 323.077 cents, and that interval taken as a generator produces 7-tone and 11-tone MOS scales:
26edo's simple [[prime]]s with the most error - 3, 5 and 13 - are all tuned flat, so it can benefit from [[octave stretching]]. Some suitable stretched-octave 26edo tunings include [[ed12|93ed12]] or [[zpi|100zpi]].


The 7-tone scale in degrees-in-between: 5 2 5 2 5 2 5. [[MOSScales|MOS]] of type [[4L_3s|4L 3s (mish)]].
== Scales ==
=== MOS scales ===
{{main|List of MOS scales in 26edo}}


The 7-tone scale in cents: 0 231 323 554 646 877 969 1200.
; Most important [[mos scale]]s
* [[Flattone]][7] (diatonic) 4 4 4 3 4 4 3 (15\26, 1\1) (quasi-[[equiheptatonic]])
* [[Flattone]][12] (chromatic) 3 1 3 1 3 1 3 3 1 3 1 3 (15\26, 1\1)
* [[Flattone]][19] (enharmonic) 2 1 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 (15\26, 1\1)
* [[Orgone]][7] 5 5 2 5 2 5 2 (7\26, 1\1)
* [[Orgone]][11] 3 2 3 2 2 3 2 2 3 2 2 (7\26, 1\1)
* [[Orgone]][15] 2 1 2 2 1 2 2 2 1 2 2 2 1 2 2 (7\26, 1\1)
* [[Lemba]][6] 5 5 3 5 5 3 (5\26, 1\2)
* [[Lemba]][10] 3 2 3 2 3 3 2 3 2 3 (5\26, 1\2)
* [[Lemba]][16] 2 1 2 2 1 2 2 1 2 1 2 2 1 2 2 1 (5\26, 1\2)


The 11-tone scale in degrees-in-between: 2 3 2 2 3 2 3 2 2 3 2. [[MOSScales|MOS]] of type [[4L_7s|4L 7s]].
; Additional mos scales
Since the perfect 5th in 26edo spans 15 degrees, it can be divided into three equal parts (each approximately an 8/7) as well as five equal parts (each approximately a 13/12).  


The 11-tone scale in cents: 0 92 231 323 415 554 646 785 877 969 1108 1200.
The former approach produces MOS at:
* 1L+4s (5 5 5 5 6) ([[mothra]][5])
* 5L+1s (5 5 5 5 5 1) ([[mothra]][6])
* 5L+6s (4 1 4 1 4 1 4 1 4 1 1) ([[mothra]][11])
* 5L+11s (1 3 1 1 3 1 1 1 3 1 1 3 1 1 3 1) ([[mothra]][16])
and is excellent for 4:6:7 triads.  


The primary triad for orgone temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. 2g approximates [[16/11|16:11]] and 3g approximates [[7/4|7:4]] (and I would call that the definition of Orgone Temperament). That also implies that g approximates the difference between 7:4 and 16:11, which is 77:64, about 320.1 cents.
The latter produces MOS at:
* 1L+7s (3 3 3 3 3 3 3 5) ([[secund]][8])
* 8L+1s (3 3 3 3 3 3 3 3 2) ([[secund]][9])
and is fairly well-supplied with 4:6:7:11:13 pentads. It also works well for more conventional (though further from Just) 6:7:9 triads, as well as 4:5:6 triads that use the worse mapping for 5 (making 5/4 the 415.38-cent interval).


=== Orgone temperament ===
[[Andrew Heathwaite]] first proposed [[Orgonia|orgone]] temperament to take advantage of 26edo's excellent 11 and 7 approximations. 7 degrees of 26edo is a wide minor third of approximately 323.077 cents, and that interval taken as a generator produces 7-tone and 11-tone MOS scales:
* The 7-tone scale in degrees-in-between: 5 2 5 2 5 2 5. [[MOSScales|MOS]] of type [[4L_3s|4L 3s (mish)]].
* The 7-tone scale in cents: 0 231 323 554 646 877 969 1200.
* The 11-tone scale in degrees-in-between: 2 3 2 2 3 2 3 2 2 3 2. [[MOSScales|MOS]] of type [[4L_7s|4L 7s]].
* The 11-tone scale in cents: 0 92 231 323 415 554 646 785 877 969 1108 1200.


The primary triad for orgone temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. 2g approximates [[16/11|16:11]] and 3g approximates [[7/4|7:4]] (and I would call that the definition of Orgone Temperament). That also implies that g approximates the difference between 7:4 and 16:11, which is 77:64, about 320.1 cents.


[[File:orgone_heptatonic.jpg|alt=orgone_heptatonic.jpg|orgone_heptatonic.jpg]]
[[File:orgone_heptatonic.jpg|alt=orgone_heptatonic.jpg|orgone_heptatonic.jpg]]


== Additional Scalar Bases Available in 26-EDO ==
=== Other scales ===
Since the perfect 5th in 26-EDO spans 15 degrees, it can be divided into three equal parts (each approximately an 8/7) as well as five equal parts (each approximately a 13/12). The former approach produces MOS at 1L+4s, 5L+1s, and 5L+6s (5 5 5 5 6, 5 5 5 5 5 1, and 4 1 4 1 4 1 4 1 4 1 1 respectively), and is excellent for 4:6:7 triads. The latter produces MOS at 1L+7s and 8L+1s (3 3 3 3 3 3 3 5 and 3 3 3 3 3 3 3 3 2 respectively), and is fairly well-supplied with 4:6:7:11:13 pentads. It also works well for more conventional (though further from Just) 6:7:9 triads, as well as 4:5:6 triads that use the worse mapping for 5 (making 5/4 the 415.38-cent interval).
* Approximate [[5afdo]]: 4 4 7 6 5
 
* Approximate [[6afdo]]: 6 5 4 4 4 3
-Igs
* Free range octatonic{{idio}} ([[modmos]] of [[hendec]][8]): 2 7 2 2 2 7 2 2
* Free range 14-tonic{{idio}} ([[modmos]] of [[hendec]][14]): 1 1 1 7 1 1 1 1 1 1 7 1 1 1
* Pseudo-[[equipentatonic]]: 5 6 4 6 5 or 6 5 4 5 6


== Instruments ==
== Instruments ==
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[[File:12072608 10207851395433055 404343132969239728 n.jpg|none|thumb|960x960px]]
[[File:12072608 10207851395433055 404343132969239728 n.jpg|none|thumb|960x960px]]


* [[Lumatone mapping for 26edo]]
== Literature ==
== Literature ==
[http://www.ronsword.com Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.]
[http://www.ronsword.com Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.]
Line 858: Line 804:
{{Catrel|26edo tracks}}
{{Catrel|26edo tracks}}


=== Modern renderings ===
=== 26 equal divisions of the octave (26edo proper) ===
==== Modern renderings ====
; {{W|Johann Sebastian Bach}}
; {{W|Johann Sebastian Bach}}
* [https://www.youtube.com/watch?v=LUNOFjiyZ0Y "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
* [https://www.youtube.com/watch?v=LUNOFjiyZ0Y ''Contrapunctus 4'' from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
* ''Contrapunctus 11'' from ''The Art of Fugue'', BWV 1080 (1742–1749) – rendered by Claudi Meneghin
** [https://www.youtube.com/watch?v=dlXFoIoc_uk organ rendition] (2024)
** [https://www.youtube.com/watch?v=NUo1uvUuOlo harpsichord rendition] (2025)
* [https://www.youtube.com/watch?v=PcQIojtN-lk ''"Ricercar a 3" from ''The Musical Offering'', BWV 1079] (1747) – rendered by Claudi Meneghin (2025)


; {{W|Nicolaus Bruhns}}
; {{W|Nicolaus Bruhns}}
* [https://www.youtube.com/watch?v=K7oTEXgmdKY ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)
* [https://www.youtube.com/watch?v=K7oTEXgmdKY ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)
* [https://www.youtube.com/watch?v=-EVO5ntuoSM ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)


=== 21st century ===
==== 21st century ====
; [[Abnormality]]
* [https://www.youtube.com/watch?v=Tl-AN2zQeAI ''Break''] (2024)
* [https://www.youtube.com/watch?v=f5eYIH3TO4o ''Moondust''] (2024)


; [[Jim Aikin]]
; [[Jim Aikin]]
Line 872: Line 827:
; [[Beheld]]
; [[Beheld]]
* [https://www.youtube.com/watch?v=0WbLTtDZUms ''Damp vibe''] (2022)
* [https://www.youtube.com/watch?v=0WbLTtDZUms ''Damp vibe''] (2022)
; [[benyamind]]
* [https://www.youtube.com/watch?v=H1hYI2hBcEU ''Cinematic music in 26-tone equal temperament''] (2024)


; [[Cameron Bobro]]
; [[Cameron Bobro]]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/LittleFugueIn26_CBobro.mp3 Little Fugue in 26]{{dead link}}
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/LittleFugueIn26_CBobro.mp3 ''Little Fugue in 26'']{{dead link}}
 
; [[User:CellularAutomaton|CellularAutomaton]]
* [https://cellularautomaton.bandcamp.com/track/innerstate ''Innerstate''] (2024)


; [[City of the Asleep]]
; [[City of the Asleep]]
* [https://cityoftheasleep.bandcamp.com/track/two-pairs-of-socks-26edo Two Pairs of Socks (26edo)]{{dead link}}
* [https://cityoftheasleep.bandcamp.com/track/two-pairs-of-socks-26edo ''Two Pairs of Socks (26edo)'']{{dead link}}
* [https://cityoftheasleep.bandcamp.com/track/between-the-branes-26edo Between the Branes (26edo)]{{dead link}}
* [https://cityoftheasleep.bandcamp.com/track/between-the-branes-26edo ''Between the Branes (26edo)'']{{dead link}}


; [[Zach Curley]]
; [[Zach Curley]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Guitar%20Serenade%20in%20Q%20Major.mp3 Guitar Serenade in Q Major]{{dead link}}
* [http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Guitar%20Serenade%20in%20Q%20Major.mp3 ''Guitar Serenade in Q Major'']{{dead link}}


; [[User:Francium|Francium]]
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/FxTxQ0ayDpg ''Microtonal Improvisation in 26edo''] (2023)
* [https://www.youtube.com/shorts/Gw9Fu5MAozs ''Waltz in 26edo''] (2025)
* [https://www.youtube.com/shorts/OFSK_9QjebE ''Change of Generation - Unlucky Morpheus (microtonal cover in 26edo)''] (2025)
* [https://www.youtube.com/watch?v=cXdhuyibzQs ''What Is This Diddy Blud Doing On The Calculator (26edo microtonal Lumatone cover)''] (2025)
* [https://www.youtube.com/watch?v=n6v7xxM9mmc ''Harpy Hare - Yaelokre (microtonal cover in 26edo)''] (2025)
* [https://www.youtube.com/shorts/yr35O0hnedM ''26edo lullaby''] (2025)
* [https://www.youtube.com/shorts/1aCl6tuVS0c ''Happy Together - The Turtles (microtonal cover in 26edo)''] (2026)
* ''My Violet - 26edo'' (2026)
** [https://www.youtube.com/shorts/m76bQWxg_CA <nowiki>[short 1]</nowiki>] (Lumatone view)
** [https://www.youtube.com/shorts/L2JzCNj6jak <nowiki>[short 2]</nowiki>] (Lumatone view)
** [https://www.youtube.com/watch?v=XplpKE_Tc38 <nowiki>[full version[</nowiki>] (with animation by WIRED0006)
* [https://www.youtube.com/shorts/wHGLOaeAkt8 ''26edo groove''] (2026)
 
; [[User:Eboone|Ebooone]]
* [https://www.youtube.com/watch?v=KvaEyzCuBwA ''26-EDO Nocturne No. 1 in F♯ Minor''] (2024)
 
; [[Francium]]
* [https://www.youtube.com/watch?v=4i6no5-zwKQ ''Eskalation''] (2022)
* [https://www.youtube.com/watch?v=4i6no5-zwKQ ''Eskalation''] (2022)
* [https://www.youtube.com/watch?v=tIZjchfF2Iw ''Dark Forest''] (2023)
* [https://www.youtube.com/watch?v=tIZjchfF2Iw ''Dark Forest''] (2023)
* [https://www.youtube.com/watch?v=FRd_sLuTpQQ ''Lembone''] (2024)
* [https://www.youtube.com/watch?v=XzQ09i6RBsg ''Happy Birthday in 26edo''] (2024)


; [[IgliashonJones|Igliashon Jones]]
; [[IgliashonJones|Igliashon Jones]]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20A%20Time-Yellowed%20Photograph%20of%20Cliffs%20Hangs%20in%20the%20Hall.mp3 A Time-Yellowed Photo of the Cliffs Hangs on the Wall]{{dead link}}
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20A%20Time-Yellowed%20Photograph%20of%20Cliffs%20Hangs%20in%20the%20Hall.mp3 ''A Time-Yellowed Photo of the Cliffs Hangs on the Wall'']{{dead link}}
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Two%20Pairs%20of%20Socks.mp3 Two Pairs of Socks]{{dead link}}
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Two%20Pairs%20of%20Socks.mp3 ''Two Pairs of Socks'']{{dead link}}
 
; [[Budjarn Lambeth]]
* [https://youtu.be/U_1cxfS5pfE ''26 edo piece for solo harp, loosely inspired by Javanese gamelan''] (2023)


; [[Melopœia]]
; [[Melopœia]]
* [https://melopoeia.bandcamp.com/album/ainulindal Ainulindalë] (2016) – A text to music translation of Tolkien's Silmarillion using 26edo.
* [https://melopoeia.bandcamp.com/album/ainulindal ''Ainulindalë''] (2016) – A text to music translation of Tolkien's ''Silmarillion'' using 26edo.
* [https://melopoeia.bandcamp.com/album/valaquenta Valaquenta] (2023)
* [https://melopoeia.bandcamp.com/album/valaquenta ''Valaquenta''] (2023)


; [[Claudi Meneghin]]
; [[Claudi Meneghin]]
* [https://www.youtube.com/watch?v=siNzE3d_WsQ Canon 3-in-1 on a ground "The Tempest", in 26edo] (2023)
* [https://www.youtube.com/watch?v=2ziAZx03KF8 ''Lemba Suite, for two organs''] (2022)
* [https://youtube.com/shorts/uh7auNGakk4 Greensleeves for three soprano saxes and baroque bassoon, in 26edo] (2023)
* [https://www.youtube.com/watch?v=siNzE3d_WsQ ''Canon 3-in-1 on a ground "The Tempest", in 26edo''] (2023)
* [https://www.youtube.com/watch?v=r0jCdHEZpzM Claudi Meneghin - Suite (Prelude, Variations, Fugue) in 26edo, for Synth & Baroque Bassoon] (2023)
* [https://youtube.com/shorts/uh7auNGakk4 ''Greensleeves for three soprano saxes and baroque bassoon, in 26edo''] (2023)
* [https://www.youtube.com/watch?v=rjo3X1-D57Y Canon 3-in-1 on a Ground for Baroque Ensemble] (2023)
* [https://www.youtube.com/watch?v=r0jCdHEZpzM ''Suite (Prelude, Variations, Fugue) in 26edo, for Synth & Baroque Bassoon''] (2023)
* [https://www.youtube.com/watch?v=rjo3X1-D57Y ''Canon 3-in-1 on a Ground for Baroque Ensemble''] (2023)
* [https://www.youtube.com/shorts/hPW4hXlu8cc ''THE TEMPEST - CANON in 26edo, 3-in-1 for 3 Baroque Violins and Continuo''] (2025)
 
; [[Microtonal Maverick]] (formerly The Xen Zone)
* [https://www.youtube.com/watch?v=qm_k9xjXRf0 ''The Microtonal Magic of 26EDO (with 13-limit jam)''] (2024)
* [https://www.youtube.com/watch?v=im2097HVqgA ''The Blues but with 26 Notes per Octave''] (2024) (explanatory video &mdash; contiguous music starts at 08:48)


; [[Herman Miller]]
; [[Herman Miller]]
* [https://sites.google.com/site/teamouse/26-et-Pianoteq-Bechstein.mp3 Etude in 26-tone equal temperament]{{dead link}}
* [https://sites.google.com/site/teamouse/26-et-Pianoteq-Bechstein.mp3 ''Etude in 26-tone equal temperament'']{{dead link}}


; [[Shaahin Mohajeri]]
; [[Shaahin Mohajeri]]
* [http://www.96edo.com/music/micro900607.mp3 Microtonal music in 26-EDO]{{dead link}}
* [http://www.96edo.com/music/micro900607.mp3 ''Microtonal music in 26-EDO'']{{dead link}}


; [[Mundoworld]]
; [[Mundoworld]]
Line 917: Line 906:


; [[Ray Perlner]]
; [[Ray Perlner]]
* [https://youtu.be/rivfU8Rw4IM Scherzo in 26 EDO for Oboe, Horn, and Organ] (2020)
* [https://youtu.be/rivfU8Rw4IM ''Scherzo in 26 EDO for Oboe, Horn, and Organ''] (2020)
* [https://www.youtube.com/watch?v=hsd00wrSJnE Octatonic Groove] (2021)
* [https://www.youtube.com/watch?v=hsd00wrSJnE ''Octatonic Groove''] (2021)
* [https://www.youtube.com/watch?v=xhn5lz2cB-4 A Little Prog Rock in 26EDO] (2023)
* [https://www.youtube.com/watch?v=xhn5lz2cB-4 ''A Little Prog Rock in 26EDO''] (2023)


; [[Sevish]]
; [[Sevish]]
Line 925: Line 914:


; [[Jon Lyle Smith]]
; [[Jon Lyle Smith]]
* [http://archive.org/details/UnderTheHeatdome under the heatDome]{{dead link}} [http://archive.org/download/UnderTheHeatdome/under_the_heatDome.mp3 play]{{dead link}}
* [http://archive.org/details/UnderTheHeatdome ''under the heatDome'']{{dead link}} [http://archive.org/download/UnderTheHeatdome/under_the_heatDome.mp3 play]{{dead link}}


; [[Tapeworm Saga]]
; [[Tapeworm Saga]]
* [https://www.youtube.com/watch?v=pJOlZ9sHCjk ''Languor Study''] (2022)
* [https://www.youtube.com/watch?v=pJOlZ9sHCjk ''Languor Study''] (2022)
; [[Uncreative Name]]
* [https://www.youtube.com/watch?v=OjW8dgooG9Q ''Spring''] (2024)


; [[Chris Vaisvil]]
; [[Chris Vaisvil]]
* [http://micro.soonlabel.com/26edo/20161224_26edo_wing.mp3 ''Morpheous Wing'' in 26 edo] (2016)
* [http://micro.soonlabel.com/26edo/20161224_26edo_wing.mp3 ''Morpheous Wing'' in 26 edo] (2016)


== See also ==
; [[Stephen Weigel]]
* [[Lumatone mapping for 26edo]]
* [https://www.youtube.com/watch?v=rfIbSZh7Iuw ''When She Loved Me (Toy Story 2)'' - microtonal cover] (2023)
 
; [[YoVariable]]
* [https://www.youtube.com/watch?v=01w70PbbT3o ''Jingle Bells (26edo microtonal Lumatone cover + Mystery Song)''] (2025)
 
=== Unequal Derivatives of 26edo ===
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/mzUGcki6H0Y ''<nowiki>Daisy Bell - Harry Dacre (microtonal cover in unequal 26ish tone [displaced from 26edo in dozens])</nowiki>''] (2026) &mdash; from Bryan Deister's video comments, "displacement in cents roughly: 0, -8, -3, -12, 14, 5, 18, 3, -12, 13, -15, 10" (these repeat every 12 notes, NOT every 13 note semi-octave, thus causing each octave to be different)


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