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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|26}}
{{ED intro}}


== 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.


# 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]].
# 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 {{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.
# 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).
# 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 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.
# 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.


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


=== Odd harmonics ===
=== Odd harmonics ===
{{Harmonics in equal|26}}
{{Harmonics in equal|26}}
=== Subsets and supersets ===
26edo has [[2edo]] and [[13edo]] as subsets, of which 13edo is non-trivial, sharing harmonics 5 and 9 through 23 (including direct approximations) with 26edo. Multiplying 26edo by 3 yields [[78edo]], which corrects several harmonics.


== Intervals ==
== Intervals ==
Line 35: Line 40:
! Degrees
! Degrees
! [[Cent]]s
! [[Cent]]s
! Approximate Ratios*
! Approximate ratios<ref group="note">{{sg|limit=13-limit}}</ref>
! Interval<br>Name
! Interval<br>name
! Example<br>in D
! Example<br>in D
! colspan="2" |[[Solfege|Solfeges]]
! [[SKULO interval names|SKULO]]<br>[[SKULO interval names|Interval name]]
! Example<br>in D
! colspan="2" | [[Solfege|Solfeges]]
|-
|-
| 0
| 0
| 0.00
| 0.00
| 1/1
| 1/1
| P1
| D
| P1
| P1
| D
| D
Line 53: Line 62:
| A1
| A1
| D#
| D#
| A1, S1
| D#, SD
| du
| du
| di
| di
Line 61: Line 72:
| d2
| d2
| Ebb
| Ebb
| sm2
| sEb
| fro
| fro
| rih
| rih
Line 67: Line 80:
| 138.46
| 138.46
| [[12/11]], [[13/12]], [[14/13]], [[16/15]]
| [[12/11]], [[13/12]], [[14/13]], [[16/15]]
| m2
| Eb
| m2
| m2
| Eb
| Eb
Line 75: Line 90:
| 184.62
| 184.62
| [[9/8]], [[10/9]], [[11/10]]
| [[9/8]], [[10/9]], [[11/10]]
| M2
| E
| M2
| M2
| E
| E
Line 85: Line 102:
| A2
| A2
| E#
| E#
| SM2
| SE
| ru
| ru
| ri
| ri
Line 93: Line 112:
| d3
| d3
| Fb
| Fb
| sm3
| sF
| no
| no
| ma
| ma
Line 99: Line 120:
| 323.08
| 323.08
| [[135/112]], [[6/5]]
| [[135/112]], [[6/5]]
| m3
| F
| m3
| m3
| F
| F
Line 107: Line 130:
| 369.23
| 369.23
| [[5/4]], [[11/9]], [[16/13]]
| [[5/4]], [[11/9]], [[16/13]]
| M3
| F#
| M3
| M3
| F#
| F#
Line 117: Line 142:
| A3
| A3
| Fx
| Fx
| SM3
| SF#
| mu
| mu
| maa
| maa
Line 125: Line 152:
| d4
| d4
| Gb
| Gb
| s4
| sG
| fo
| fo
| fe
| fe
Line 131: Line 160:
| 507.69
| 507.69
| [[75/56]], [[4/3]]
| [[75/56]], [[4/3]]
| P4
| G
| P4
| P4
| G
| G
Line 139: Line 170:
| 553.85
| 553.85
| [[11/8]], [[18/13]]
| [[11/8]], [[18/13]]
| A4
| G#
| A4
| A4
| G#
| G#
Line 149: Line 182:
| AA4, dd5
| AA4, dd5
| Gx, Abb
| Gx, Abb
| SA4, sd5
| SG#, sAb
| pu/sho
| pu/sho
| fi/se
| fi/se
Line 155: Line 190:
| 646.15
| 646.15
| [[16/11]], [[13/9]]
| [[16/11]], [[13/9]]
| d5
| Ab
| d5
| d5
| Ab
| Ab
Line 163: Line 200:
| 692.31
| 692.31
| [[112/75]], [[3/2]]
| [[112/75]], [[3/2]]
| P5
| A
| P5
| P5
| A
| A
Line 173: Line 212:
| A5
| A5
| A#
| A#
| S5
| SA
| su
| su
| si
| si
Line 181: Line 222:
| d6
| d6
| Bbb
| Bbb
| sm6
| sBb
| flo
| flo
| leh
| leh
Line 187: Line 230:
| 830.77
| 830.77
| [[13/8]], [[8/5]]
| [[13/8]], [[8/5]]
| m6
| Bb
| m6
| m6
| Bb
| Bb
Line 195: Line 240:
| 876.92
| 876.92
| [[5/3]], [[224/135]]
| [[5/3]], [[224/135]]
| M6
| B
| M6
| M6
| B
| B
Line 205: Line 252:
| A6
| A6
| B#
| B#
| SM6
| SB
| lu
| lu
| li
| li
Line 213: Line 262:
| d7
| d7
| Cb
| Cb
| sm7
| sC
| tho
| tho
| ta
| ta
Line 219: Line 270:
| 1015.38
| 1015.38
| [[9/5]], [[16/9]], [[20/11]]
| [[9/5]], [[16/9]], [[20/11]]
| m7
| C
| m7
| m7
| C
| C
Line 227: Line 280:
| 1061.54
| 1061.54
| [[11/6]], [[13/7]], [[15/8]], [[24/13]]
| [[11/6]], [[13/7]], [[15/8]], [[24/13]]
| M7
| C#
| M7
| M7
| C#
| C#
Line 237: Line 292:
| A7
| A7
| Cx
| Cx
| SM7
| SC#
| tu
| tu
| to
| to
Line 245: Line 302:
| d8
| d8
| Db
| Db
| d8, s8
| Db, sD
| do
| do
| da
| da
Line 251: Line 310:
| 1200.00
| 1200.00
| 2/1
| 2/1
| P8
| D
| P8
| P8
| D
| D
Line 256: Line 317:
| do
| do
|}
|}
* based on treating 26edo as a [[13-limit]] temperament; other approaches are possible.


=== Interval quality and chord names in color notation ===
=== Interval quality and chord names in color notation ===
Line 305: Line 365:
! [[Kite's color notation|Color of the 3rd]]
! [[Kite's color notation|Color of the 3rd]]
! JI chord
! JI chord
! Notes as Edoteps
! Notes as Edosteps
! Notes of C Chord
! Notes of C Chord
! Written Name
! Written Name
Line 340: Line 400:


For a more complete list, see [[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 ==
=== Sagittal notation ===
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]].
==== Evo flavor ====
<imagemap>
File:26-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 463 0 623 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
default [[File:26-EDO_Evo_Sagittal.svg]]
</imagemap>
Because it includes no Sagittal symbols, this Evo Sagittal notation is also a conventional notation.
==== Revo flavor ====
<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>


== Approximation to JI ==
== Approximation to JI ==
=== 15-odd-limit interval mappings ===
=== 15-odd-limit interval mappings ===
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''.
{{Q-odd-limit intervals|26}}
 
{| class="wikitable mw-collapsible mw-collapsed center-all"
|+style=white-space:nowrap| 15-odd-limit intervals by direct approximation (even if inconsistent)
|-
! 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
|-
| ''[[15/11]], [[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
|}
{{15-odd-limit|26}}


== Approximation to irrational intervals ==
== Approximation to irrational intervals ==
After [[13edo #Approximation to irrational intervals|13edo]], the weird coïncidences continue: [[11/7 #Proximity with π/2|acoustic π/2]] (17\26) is just in between the ϕ intervals provided by 13edo (16\26 for [[Logarithmic phi|logarithmic ϕ]]/2, and 18\26 for [[Acoustic phi|acoustic ϕ]]).
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.
 
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).
 
However, it should be noted that [[User:Contribution/Logarithmic constants VS acoustic constants (opinion piece article)|from an acoustic perspective]], acoustic π and acoustic ϕ are both better represented on [[23edo]].


{| class="wikitable center-all"
{| class="wikitable center-all"
|+Direct mapping
|+ style="font-size: 105%;" | Direct approximation
|-
|-
! Interval
! Interval
Line 458: Line 458:


== 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" | [[Subgroup]]
! rowspan="2" | [[Comma basis]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning Error
! colspan="2" | Tuning error
|-
|-
! [[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
Line 469: Line 470:
|-
|-
| 2.3
| 2.3
| [-41 26⟩
| {{monzo| -41 26 }}
| [⟨26 41]]
| {{mapping| 26 41 }}
| +3.043
| +3.043
| 3.05
| 3.05
Line 477: Line 478:
| 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
Line 484: Line 485:
| 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
Line 491: Line 492:
| 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
Line 498: Line 499:
| 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
Line 505: Line 506:
| 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
Line 512: Line 513:
| 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)
Important mos scales include (in addition to ones found in [[13edo]]):
* chromatic ([[flattone]]) 313131331313 (15\26, 1\1)
* [[Flattone]][7] (diatonic) 4443443 (15\26, 1\1)
* enharmonic ([[flattone]]) 2112112112121121121 (15\26, 1\1)
* [[Flattone]][12] (chromatic) 313131331313 (15\26, 1\1)
* [[orgone]] 5525252 (7\26, 1\1)
* [[Flattone]][19] (enharmonic) 2112112112121121121 (15\26, 1\1)
* [[orgone]] 32322322322 (7\26, 1\1)
* [[Orgone]][7] 5525252 (7\26, 1\1)
* [[orgone]] 212212221222122 (7\26, 1\1)
* [[Orgone]][11] 32322322322 (7\26, 1\1)
* [[lemba]] 553553 (5\26, 1\2)
* [[Orgone]][15] 212212221222122 (7\26, 1\1)
* [[lemba]] 3232332323 (5\26, 1\2)
* [[Lemba]][6] 553553 (5\26, 1\2)
* [[lemba]] 2122122121221221 (5\26, 1\2)
* [[Lemba]][10] 3232332323 (5\26, 1\2)
* [[Lemba]][16] 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 542: Line 543:
| 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 574: Line 575:
| 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]] / [[cavalier]]
|-
|-
| 13
| 13
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=== 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]]
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| 0.23
| 0.23
| Quadla-sepquingu
| Quadla-sepquingu
| [[Senior]]
| [[Senior comma]]
|-
|-
| 7
| 7
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| 34.98
| 34.98
| Biruyo
| Biruyo
| Tritonic diesis, Jubilisma
| Jubilisma, tritonic diesis
|-
|-
| 7
| 7
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| 13.47
| 13.47
| Sarurutriyo
| Sarurutriyo
| Octagar
| Octagar comma
|-
|-
| 7
| 7
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| 13.07
| 13.07
| Triru-agu
| Triru-agu
| Orwellisma, Orwell comma
| Orwellisma
|-
|-
| 7
| 7
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| 16.57
| 16.57
| Thuzoyo
| Thuzoyo
| Animist
| Animist comma
|}
|}
<references/>


== Scales ==
== Scales ==
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-Igs
-Igs
=== MOS scales ===
''See [[List of MOS scales in 26edo]]''


== 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.]
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; {{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)
* [https://www.youtube.com/watch?v=dlXFoIoc_uk "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)


; {{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 788: Line 797:
; [[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]]
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* [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)
 
; [[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]]
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* [https://www.youtube.com/watch?v=r0jCdHEZpzM Claudi Meneghin - Suite (Prelude, Variations, Fugue) in 26edo, for Synth & Baroque Bassoon] (2023)
* [https://www.youtube.com/watch?v=r0jCdHEZpzM Claudi Meneghin - 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/watch?v=rjo3X1-D57Y Canon 3-in-1 on a Ground for Baroque Ensemble] (2023)
; [[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]]
Line 845: Line 872:
; [[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 ==
== Notes ==
* [[Lumatone mapping for 26edo]]
<references group="note" />


[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/26edo"