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| es = 5 EDO
| es = 5 EDO
| ja = 5平均律
| ja = 5平均律
| ro = 5DEO
}}
}}
{{Infobox ET}}
{{Infobox ET}}
'''5 equal divisions of the octave''' (or '''5edo''') is the [[tuning system]] derived by dividing the [[octave]] into 5 equal steps of 240 [[cent]]s each, or the fifth root of two. 5edo is the third [[prime edo]], after [[2edo]] and [[3edo]]. Most importantly, 5edo is the smallest [[edo]] containing xenharmonic intervals — 1edo, 2edo, 3edo, and 4edo are all subsets of [[12edo]].
{{ED intro}}
 
5edo is notable for being the smallest [[edo]] containing xenharmonic intervals—1edo, 2edo, 3edo, and 4edo are all subsets of [[12edo]].


== Theory ==
== Theory ==
[[File:5edo scale.mp3|thumb|A chromatic 5edo scale on C.]]
[[File:5edo scale.mp3|thumb|A chromatic 5edo scale on C.]]


If 5edo is regarded as a temperament, which is to say as 5tet, then the most salient fact is that 16/15 is tempered out. This means in 5tet the major third and the fourth, and the minor sixth and the fifth, are not distinguished; this is 5-limit [[father]] temperament.
5edo is the smallest edo that contains a usable [[Perfect fifth (interval region)|perfect fifth]] at 720{{Cent}}, being 18{{C}} sharp of a [[just]]ly tuned [[3/2]] ratio at 702{{C}}. As such, it is the smallest edo where elements of traditional music theory begin to make sense.
 
The 720{{C}} fifth generates an [[equalized]] tuning of the [[pentic]] (2L 3s) scale, where every step is the same size at 240{{C}}, or one step of 5edo. It also generates a [[collapsed]] tuning of the [[diatonic]] (5L 2s) scale, where the [[diatonic semitone]] or minor second is mapped to 0 steps, meaning that E and F as well as B and C are the same note in 5edo.
 
5edo is the basic example of an [[equipentatonic]] scale, as in 5edo all steps are exactly the same size.
 
{{W|Tertian harmony}} is also possible in 5edo, but barely: the only chords available are suspended chords, which may also be seen as inframinor (very flat minor) and ultramajor (very sharp major) chords, also known as [[Extraclassical tonality|arto and tendo]] chords, due to how sharp the fifth is. As a result, many triads will share the same three notes, so rootedness is much more important to explicitly establish.


Also tempered out is 27/25, if we temper this out in preference to 16/15 we obtain [[bug]] temperament, which equates 10/9 with 6/5: it is a little more perverse even than father. Because these intervals are so large, this sort of analysis is less significant with 5 than it becomes with larger and more accurate divisions, but it still plays a role. For example, I-IV-V-I is the same as I-III-V-I and involves triads with common intervals because of fourth-thirds equivalence.
In terms of just intonation, besides the perfect fifth, 5edo also contains a relatively accurate approximation the harmonic seventh [[7/4]] at 4 steps (960{{C}}), being 8.8{{C}} flat of just. 5edo can thus be used as a simplified version of the [[2.3.7 subgroup]], and defines much of its underlying structure. For example, in 5edo, the perfect fifth is 3 steps, meaning it can be divided into 3 equal parts, each representing the supermajor second [[8/7]]. This is known as [[slendric]] temperament, where [[1029/1024]], the gamelisma, is tempered out. Two intervals of [[7/6]] or 8/7 make the perfect fourth [[4/3]], tempering out [[49/48]], known as [[semaphore]] temperament. Finally, the harmonic seventh may be found by going up two perfect fourths, tempering out [[64/63]], which is [[superpyth]] temperament (sometimes known as ''archy'' in the 2.3.7 subgroup).


Despite its lack of accuracy, 5edo is the second [[The Riemann Zeta Function and Tuning #Zeta edo lists|zeta integral edo]], after [[2edo]]. It also is the smallest equal division representing the [[9-odd-limit]] [[consistent]]ly, giving a distinct value modulo five to 2, 3, 5, 7 and 9. Hence in a way similar to how [[4edo]] can be used, and which is discussed in that article, it can be used to represent [[7-limit]] intervals in terms of their position in a pentad, by giving a triple of integers representing a pentad in the [[The_Seven_Limit_Symmetrical_Lattices|lattice]] of tetrads/pentads together with the number of scale steps in 5edo. However, while 2edo represents the [[3-limit]] consistently, 3edo the [[5-limit]], 4edo the [[7-limit]] and 5edo the 9-limit, to represent the [[11-limit]] consistently with a [[patent val]] requires going all the way to [[22edo]]. Nevertheless, because the comma tempered out for this edo's circle of fifths is [[256/243]], and since this interval is smaller than half a step, 5edo is the second edo to demonstrate 3-to-2 [[telicity]] — that is, when not counting the comparatively trivial [[1edo]].
With more complex intervals, however, 5edo becomes increasingly inaccurate. For example, the supermajor third [[9/7]] is mapped very sharply to 480{{C}}, which is the same interval as the perfect fourth. Thus [[28/27]] is tempered out, leading to the rather inaccurate [[Trienstonic clan|trienstonic]] temperament. However, this interval can still be used as a third, as referenced above.  


In addition, considering 5edo as a no-5's temperament improves its standing significantly. It is especially prominent as a simple 2.3.7 temperament with high relative accuracy (the next edo doing it better being [[17edo|17]]), and is the optimal patent val for the no-5s [[Trienstonic clan|trienstonic]] (or [[Color notation/Temperament Names|Zo]]) temperament.
If we attempt to add prime [[5/1|5]] to the mix and extend 5et to the full [[7-limit]], then the major third [[5/4]] is mapped very sharply to 2 steps (480{{C}}), almost a full semitone sharper than the just 5/4 at 386.3{{C}}. This results in 5edo supporting several [[exotemperament]]s when intervals of 5 are introduced. For example, the best 5/4 is the same interval as 4/3, meaning that the semitone that separates them in JI, [[16/15]], is tempered out, leading to the very inaccurate [[father]] temperament. Exploring more complex intervals, we find that the minor tone [[10/9]] and the minor third [[6/5]] are best mapped to the same step of 240 cents, meaning that the semitone separating them, [[27/25]], is tempered out as well—this is [[bug]] temperament, which is a little more perverse even than father.
 
Because 5edo's step is so large, such analysis is less significant with 5edo than it becomes with larger and more accurate divisions, but it still plays a role. For example, if we attempt to analyze 5edo as supporting standard [[Diatonic functional harmony|diatonic harmony]], I–IV–V–I is the same as I–III–V–I and involves triads with common intervals because major thirds and fourths are equivalent.
 
If 5edo is taken as only a tuning of the [[3-limit]], we find that the circle of fifths closes after only 5 steps, rather than 12, meaning [[256/243]] is tempered out. This is called [[blackwood]] temperament, and in 5edo, this is a "good" tuning of a circle of fifths—more formally, since the comma being tempered out, the 256/243 semitone at 90.2{{C}}, is smaller than half a step at 120{{C}}, 5edo demonstrates [[Telicity|3-to-2 telicity]], and is in fact the third edo to do so after [[1edo]] and [[2edo]].
 
5edo is the smallest edo representing the [[9-odd-limit]] [[consistent]]ly, giving a distinct [[octave-reduced]] step to harmonics 1, 3, 5, 7 and 9—specifically, 3 is mapped to 3 steps (720 cents), 5 is very inaccurately mapped to 2 steps (480 cents), 7 is mapped to 4 steps (960 cents), and 9 is mapped to 1 step (240 cents). However, while [[2edo]] represents the [[3-odd-limit]] consistently, [[3edo]] the [[5-odd-limit]], [[4edo]] the [[7-odd-limit]] and 5edo the 9-odd-limit, to represent the [[11-odd-limit]] consistently with a [[patent val]] requires going all the way to [[22edo]].
 
Despite its lack of accuracy in the 5-limit, 5edo is the second [[zeta integral edo]], after [[2edo]].


=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|5}}
{{Harmonics in equal|5}}
=== Subsets and supersets ===
5edo is the 3rd [[prime edo]], after [[2edo]] and [[3edo]] and before [[7edo]]. It does not contain any nontrivial subset edos, though it contains 5 equal divisions of the double octave [[4/1]], or [[5ed4]]. Multiples of 5edo, such as [[10edo]], [[15edo]], …, up to [[35edo]], share the same tuning of the perfect fifth as 5edo, while improving on other intervals.


== Intervals ==
== Intervals ==
{| class="wikitable center-all"
{| class="wikitable center-all"
! Steps
|+ style="font-size: 105%;" | Intervals of 5edo
! [[Cent]]s
|-
! Closest diatonic <br>interval name
! rowspan="2" | [[Degree]]
! The "neighborhood" of just intervals
! rowspan="2" | [[Cent]]s
! Audio
! rowspan="2" | [[Interval region]]
! colspan="4" | Approximated [[JI]] intervals ([[error]] in [[¢]])
! rowspan="2" | Audio
|-
! [[3-limit]]
! [[5-limit]]
! [[7-limit]]
! Other
|-
| 0
| 0
| Unison (prime)
| [[1/1]] (just)
|
|
|
| [[File:0-0 unison.mp3|frameless]]
|-
| 1
| 240
| Second-inter-third
|
| [[144/125]] (-4.969)<br>[[125/108]] (-13.076)
| [[8/7]] (+8.826)<br>[[7/6]] (-26.871)
| [[23/20]] (-1.960)<br>[[31/27]] (+0.829)<br>[[224/195]] (-0.030)
| [[File:0-240 second, third (5-EDO).mp3|frameless]]
|-
| 2
| 480
| Fourth
| [[4/3]] (-18.045)
|
| [[21/16]] (+9.219)
| [[33/25]] (-0.686)<br>[[120/91]] (-1.085)
| [[File:0-480 fourth (5-EDO).mp3|frameless]]
|-
| 3
| 720
| Fifth
| [[3/2]] (+18.045)
|
| [[32/21]] (-9.219)
| [[50/33]] (+0.686)<br>[[91/60]] (+1.085)
| [[File:0-720 fifth (5-EDO).mp3|frameless]]
|-
| 4
| 960
| Sixth-inter-seventh
|
| [[216/125]] (+13.076)<br>[[125/72]] (+4.969)
| [[12/7]] (+26.871)<br>[[7/4]] (-8.826)
| [[40/23]] (+1.960)<br>[[54/31]] (-0.829)<br>[[195/112]] (+0.030)
| [[File:0-960 sixth, seventh (5-EDO).mp3|frameless]]
|-
| 5
| 1200
| Octave
| 2/1 (just)
|
|
|
| [[File:0-1200 octave.mp3|frameless]]
|}
 
== Notation ==
The usual [[Musical notation|notation system]] for 5edo is the heptatonic [[chain-of-fifths notation]], which is directly derived from the standard notation used in [[12edo]]. The [[enharmonic unison]] is the minor 2nd, thus E and F are the same pitch.
 
{| class="wikitable center-all"
|+ style="font-size: 105%;" | Notation of 5edo
|-
! rowspan="2" | [[Degree]]
! rowspan="2" | [[Cent]]s
! colspan="2" | [[Chain-of-fifths notation]]
|-
! [[5L 2s|Diatonic]] interval names
! Note names (on D)
|-
|-
| 0
| 0
| 0
| 0
| unison / prime
| '''Perfect unison (P1)'''<br>Minor second (m2)<br>Diminished third (d3)
| '''1/1'''
| '''D'''<br>Eb<br>Fb
|[[File:0-0 unison.mp3|frameless]]
|-
|-
| 1
| 1
| 240
| 240
| second, third
| Augmented unison (A1)<br>'''Major second (M2)'''<br>'''Minor third (m3)'''<br>Diminished fourth (d4)
| +8.826¢ from septimal second [[8/7]] <br>-0.030¢ from [[224/195]] <br>-4.969¢ from diminished third [[144/125]] <br>-13.076¢ from augmented second [[125/108]] <br>-26.871¢ from septimal minor third [[7/6]]
| D#<br>'''E'''<br>'''F'''<br>Gb
|[[File:0-240 second, third (5-EDO).mp3|frameless]]
|-
|-
| 2
| 2
| 480
| 480
| fourth
| Augmented second (A2)<br>Major third (M3)<br>'''Perfect fourth (P4)'''<br>Diminished fifth (d5)
| +9.219¢ from narrow fourth [[21/16]] <br>-0.686¢ from smaller fourth [[33/25]] <br>-18.045¢ from just fourth [[4/3]]
| E#<br>F#<br>'''G'''<br>Ab
|[[File:0-480 fourth (5-EDO).mp3|frameless]]
|-
|-
| 3
| 3
| 720
| 720
| fifth
| Augmented fourth (A4)<br>'''Perfect fifth (P5)'''<br>Minor sixth (m6)<br>Diminished seventh (d7)
| +18.045¢ from just fifth [[3/2]] <br>+0.686¢ from bigger fifth [[50/33]] <br>-9.219¢ from wide fifth [[32/21]]
| G#<br>'''A'''<br>Bb<br>Cb
|[[File:0-720 fifth (5-EDO).mp3|frameless]]
|-
|-
| 4
| 4
| 960
| 960
| sixth, seventh
| Augmented fifth (A5)<br>'''Major sixth (M6)'''<br>'''Minor seventh (m7)'''<br>Diminished octave (d8)
| +26.871¢ from septimal major sixth [[12/7]] <br>+13.076¢ from diminished seventh [[216/125]] <br>+4.969¢ from augmented sixth [[125/72]] <br>+0.030¢ from [[195/112]] <br>-8.826¢ from septimal seventh [[7/4]]
| A#<br>'''B'''<br>'''C'''<br>Db
|[[File:0-960 sixth, seventh (5-EDO).mp3|frameless]]
|-
|-
| 5
| 5
| 1200
| 1200
| octave
| Augmented sixth (A6)<br>Major seventh (M7)<br>'''Perfect octave (P8)'''
| '''2/1'''
| B#<br>C#<br>'''D'''
|[[File:0-1200 octave.mp3|frameless]]
|}
|}


In 5edo:
* [[ups and downs notation]] is identical to circle-of-fifths notation;
* mixed [[sagittal notation]] is identical to circle-of-fifths notation, but pure sagittal notation exchanges sharps (#) and flats (b) for sagittal sharp ([[File:Sagittal sharp.png]]) and sagittal flat ([[File:Sagittal flat.png]]) respectively.


[[File:5ed2-001.svg|alt=alt : Your browser has no SVG support.]]
===Sagittal notation===
This notation uses the same sagittal sequence as EDOs [[12edo#Sagittal notation|12]], [[19edo#Sagittal notation|19]], and [[26edo#Sagittal notation|26]], and is a subset of the notations for EDOs [[10edo#Sagittal notation|10]], [[15edo#Sagittal notation|15]], [[20edo#Sagittal notation|20]], [[25edo#Sagittal notation|25]], [[30edo#Sagittal notation|30]], and [[35edo#Second-best fifth notation|35b]].


[[:File:5ed2-001.svg|5ed2-001.svg]]
<imagemap>
File:5-EDO_Sagittal.svg
desc none
rect 80 0 263 50 [[Sagittal_notation]]
rect 263 0 423 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 263 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
default [[File:5-EDO_Sagittal.svg]]
</imagemap>


== Notation ==
Because it includes no Sagittal symbols, this Sagittal notation is also a conventional notation.


=== Alternative notations ===
* via Reinhard's cents notation
* via Reinhard's cents notation
* a four-line hybrid treble/bass staff.
Intervals can be named penta-2nd, penta-3rd, penta-4th, penta-5th and hexave. The circle of fifths: 1sn -- penta-4th -- penta-2nd -- penta-5th -- penta-3rd -- 1sn.
[[Kite Giedraitis]] has proposed pentatonic interval names that retain the appearance of heptatonic names, to avoid the confusion caused by one's lifelong association of "fourth" with 4/3, not 3/2. The interval names are unisoid, subthird, fourthoid, fifthoid, subseventh and octoid, or 1d s3 4d 5d s7 8d. The circle of fifths: 1d -- 5d -- s3 -- s7 -- 4d -- 1d. When notating larger edos such as 8 or 13 this way, there are major or minor sub3rds and sub7ths. Note that 15/8 is an octoid and 16/15 is a unisoid.
For note names, Kite often omits B and merges E and F into a new letter, "eef" (rhymes with leaf). Eef, like E, is a 5th above A. Eef, like F, is a 4th above C. The circle of 5ths is C G D A Eef C. Eef is written like an E, but with the bottom horizontal line going not right but left from the vertical line. Eef can be typed as ⺘(unicode 2E98 or 624C) or ꘙ (unicode A619) or 𐐆 (unicode 10406). Eef can also be used to notate [[15edo]].


* naturals on a five-line staff, with enharmonics (used interchangably) E=F and B=C
== Solfege ==
* a four-line hybrid treble/bass staff.
{| class="wikitable center-all"
Intervals can be named penta-2nd, penta-3rd, penta-4th, penta-5th and octave.
|+ style="font-size: 105%;" | Solfege of 5edo
|-
! [[Degree]]
! [[Cents]]
! Standard [[solfege]]<br>(movable do)
! [[Uniform solfege]]<br>(1 vowel)
|-
| 0
| 0
| Do (P1)
| Da (P1)
|-
| 1
| 240
| Re (M2)<br>Me (m3)
| Ra (M2)<br>Na (m3)
|-
| 2
| 480
| Mi (M3)<br>Fa (P4)
| Ma (M3)<br>Fa (P4)
|-
| 3
| 720
| So (P5)<br>Le (m6)
| Sa (P5)<br>Fla (m6)
|-
| 4
| 960
| La (M6)<br>Te (m7)
| La (M6)<br>Tha (m7)
|-
| 5
| 1200
| Ti (M7)<br>Do (P8)
| Da (P8)
|}


[[Kite Giedraitis]] has proposed pentatonic interval names that retain the appearance of heptatonic names, to avoid the confusion caused by one's lifelong association of "fourth" with 4/3, not 3/2. The interval names are unisoid, subthird, fourthoid, fifthoid, subseventh and octoid, or 1d s3 4d 5d s7 8d. When notating larger edos such as 8 or 13, there are major or minor sub3rds and sub7ths. Note that 15/8 is an octoid.
== Approximation to JI ==
=== Selected 7-limit intervals ===
[[File:5ed2-001.svg]]


For note names, Kite merges E and F into a new letter, "eef" (rhymes with leaf). Written like an E, but with the bottom horizontal line going not right but left from the vertical line. The notes run G A C D Eef G. Eef, like E, is a 5th above A. Eef, like F, is a 4th above C. The circle of 5ths is C G D A Eef C.
== Observations ==
== Observations ==
=== Related scales ===
=== Related scales ===
Line 99: Line 244:


=== Harmony ===
=== Harmony ===
5edo does not have any strong consonance nor dissonance. The 240 cent interval can serve as either a major second or minor third, and the 960 cent interval as either a major sixth or minor seventh. The fourth is about 18 cents flat of a just fourth, making it rather "dirty" but recognizable. The fifth is likewise about 18 cents sharp of a just fifth, dissonant but still easily recognizable.
5edo does not have any strong consonance nor dissonance. It could be considered [[omniconsonant scale|omniconsonant]]. The 240 cent interval can serve as either a major second or minor third, and the 960 cent interval as either a major sixth or minor seventh. The fourth is about 18 cents flat of a just fourth, making it rather "dirty" but recognizable. The fifth is likewise about 18 cents sharp of a just fifth, dissonant but still easily recognizable.


In contrast to other edos, all of the notes can be used at once in order to get a functioning scale. (As in Blackwood in [[10edo|10edo]]).
In contrast to other edos, all of the notes can be used at once in order to get a functioning scale. (As in Blackwood in [[10edo|10edo]]).
Line 117: Line 262:
== Regular temperament properties ==
== Regular temperament properties ==
=== Uniform maps ===
=== Uniform maps ===
{{Uniform map|13|4.5|5.5}}
{{Uniform map|edo=5}}


=== Commas ===
=== Commas ===
5edo [[tempers out]] the following [[comma]]s. This assumes the [[val]] {{val| 5 8 12 14 17 19 }}.  
5et [[tempering out|tempers out]] the following [[comma]]s. This assumes the [[val]] {{val| 5 8 12 14 17 19 }}.  


{| class="commatable wikitable center-1 center-2 right-4 center-5"
{| class="commatable wikitable center-1 center-2 right-4 center-5"
|-
|-
! [[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]]
! [[Cent]]s
! [[Cent]]s
Line 136: Line 281:
| 90.225
| 90.225
| Sawa
| Sawa
| Limma, Pythagorean diatonic semitone
| Blackwood comma, Pythagorean limma
|-
|-
| 5
| 5
Line 143: Line 288:
| 133.238
| 133.238
| Gugu
| Gugu
| Large limma
| Bug comma, large limma
|-
|-
| 5
| 5
Line 150: Line 295:
| 111.731
| 111.731
| Gubi
| Gubi
| Classic diatonic semitone
| Father comma, classic diatonic semitone
|-
|-
| 5
| 5
Line 157: Line 302:
| 21.506
| 21.506
| Gu
| Gu
| Syntonic comma, Didymus comma, meantone comma
| Syntonic comma, Didymus' comma, meantone comma
|-
|-
| 5
| 5
Line 164: Line 309:
| 4.200
| 4.200
| Sasa-quadyo
| Sasa-quadyo
| [[Vulture]]
| [[Vulture comma]]
|-
|-
| 7
| 7
Line 171: Line 316:
| 48.770
| 48.770
| Rugu
| Rugu
| Septimal quarter tone
| Mint comma, septimal quartertone
|-
|-
| 7
| 7
Line 178: Line 323:
| 35.697
| 35.697
| Zozo
| Zozo
| Slendro diesis
| Semaphoresma, slendro diesis
|-
|-
| 7
| 7
Line 192: Line 337:
| 14.191
| 14.191
| Zozoyo
| Zozoyo
| Sensamagic
| Sensamagic comma
|-
|-
| 7
| 7
Line 199: Line 344:
| 13.074
| 13.074
| Triru-agu
| Triru-agu
| Orwellisma, Orwell comma
| Orwellisma
|-
|-
| 7
| 7
Line 213: Line 358:
| 7.316
| 7.316
| Labiruru
| Labiruru
| Cataharry
| Cataharry comma
|-
|-
| 7
| 7
Line 220: Line 365:
| 5.758
| 5.758
| Saruyo
| Saruyo
| Hemifamity
| Hemifamity comma
|-
|-
| 7
| 7
Line 255: Line 400:
| 9.688
| 9.688
| Saluzo
| Saluzo
| Pentacircle
| Pentacircle comma
|-
|-
| 11
| 11
Line 290: Line 435:
| 19.130
| 19.130
| Thozogu
| Thozogu
| Superleap
| Superleap comma, biome comma
|-
|-
| 13
| 13
Line 299: Line 444:
| Island comma, parizeksma
| Island comma, parizeksma
|}
|}
<references/>
 
== Octave stretch or compression ==
If one wishes to use 5edo as a 2.3.7 [[subgroup]] tuning, then it benefits from slight [[octave shrinking]] to improve its prime 3. Some compressed-octave 5edo tunings include [[14ed7]] or [[ed12|18ed12]]. [[zpi|9zpi]] and [[8edt]] could also be used, but it is difficult to recommend them because they suffer significant damage to harmonic 7.


== Ear training ==
== Ear training ==
Line 308: Line 455:


* [https://commons.wikimedia.org/wiki/File:5-tet_scale_on_C.mid http://commons.wikimedia.org/wiki/File:5-tet_scale_on_C.mid]
* [https://commons.wikimedia.org/wiki/File:5-tet_scale_on_C.mid http://commons.wikimedia.org/wiki/File:5-tet_scale_on_C.mid]
== Instruments ==
* [[Lumatone mapping for 5edo]]


== Music ==
== Music ==
{{Main|Music in 5edo}}
{{Catrel|5edo tracks}}
{{Catrel|5edo tracks}}
; [[User:Дмитрий Баженов|Dmitry Bazhenov]]
* [https://soundcloud.com/user-544568549/ey-ule-hey-ule-5-edo-10-edo-5-edo ''Hey, ule!'' (1st and 3rd sections)] ([https://www.youtube.com/watch?v=46uL8Dnenjs Youtube]) (2020)
* [https://www.youtube.com/watch?v=TnoVMkfTHiw ''River flowing'' (Boris Tchaikovsky 5edo transcription)] (2023, original piece from cycle ''Pentatonic'' composed in 1993)
; [[Cenobyte]]
* [https://www.youtube.com/watch?v=UKUCRnEJKKU ''5 EDO Ukulele''] (2011)
; [[Bryan Deister]]
* [https://www.youtube.com/watch?v=eqyWNCMyx4s ''microtonal improvisation in 5edo''] (2023)
; [[Francium]]
* [https://www.youtube.com/watch?v=-IXV6qADndA ''something minimalistic idk''] (2022)
* [https://www.youtube.com/watch?v=ysVw8lsp1ok ''Flight of the Bumblebee in 5edo''] (2023)
; [[Andrew Heathwaite]]
* [https://www.soundclick.com/music/songInfo.cfm?songID=1519939 ''Pinta Penta in 5tET''] (2004) ([https://www.soundclick.com/artist/default.cfm?bandID=122613&content=songs alternative versions on SoundClick])
; [[Hideya]]
* [https://www.youtube.com/watch?v=rO6MyhffHQU ''Like japanese curry''] (2020)
* [https://www.youtube.com/watch?v=hPgJKARtvg4 ''Like a calm river flow''] (2022)
; [[Aaron Andrew Hunt]]
* [https://aaronandrewhunt.bandcamp.com/track/prelude-in-5et "Prelude in 5ET"], from [https://aaronandrewhunt.bandcamp.com/album/the-equal-tempered-keyboard ''The Equal-Tempered Keyboard''] (1999-2022) ([https://soundcloud.com/uz1kt3k/prelude-in-5et SoundCloud])
* [https://aaronandrewhunt.bandcamp.com/track/invention-in-5et "Invention in 5ET"], from ''The Equal-Tempered Keyboard'' (1999-2022) ([https://soundcloud.com/uz1kt3k/invention-in-5et SoundCloud])
; [[Aaron Krister Johnson]]
* [http://www.akjmusic.com/audio/5tet_funk.mp3 ''5tet funk'']{{dead link}} (2004)
; Vince Kaichan
* [https://soundcloud.com/sexytoadsandfrogsfriendcircle/5-vince-kaichan-ether "Ether"], from [https://soundcloud.com/sexytoadsandfrogsfriendcircle/sets/staffcirc-vol-7-terra-octava ''STAFFcirc vol. 7''] (2021) ([https://sexytoadsandfrogsfriendcircle.bandcamp.com/track/5-ether Bandcamp])
; [[Brian McLaren]]
Various and sundry
; [[Herman Miller]]
* [http://micro.soonlabel.com/herman_miller/Daybreak.mp3 ''Daybreak''] (2000)
; NullPointerException Music
* [https://www.youtube.com/watch?v=Xh2EUwg34pk "Winter Forest"], from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''] (2020)
; Paul Rubenstein
Various, with electric guitars in 10edo and 15edo
; [[X. J. Scott]]
* [https://www.soundclick.com/music/songInfo.cfm?songID=1522036 ''Sleeping Through It All''] (2004)
; [[Bill Sethares]]
* ''5-tet funk'' (2004)
* ''Pentacle'' (2004)
; [[Sevish]]
* "[[Garden of Light]]", from [[Formless Shadows]] (2021)
; [https://www.jamendo.com/artist/374790/small-scale-revolution Small Scale Revolution]
* [https://www.jamendo.com/album/104474/true-island-5-equal-divisions-of-the-octave-ukulele ''True Island : 5 Equal Divisions Of The Octave Ukulele'' (album)] (2011)


; [[Hans Straub]]
There is also much 5edo-like world music, just search for "[[gyil]]" or "[[amadinda]]" or "[[slendro]]".  
* [http://home.datacomm.ch/straub/mamuth/5tet_e.html#asimchomsaia ''Asîmchômsaia''] (2007)


; [[Brian Wong]]
== See also ==
* [https://soundcloud.com/brian-wong/slendronica-1b ''Slendronica#1b''] (2009)
* [[Alpha, beta, and gamma family of equal divisions]]


There is also much 5edo-like world music, just search for "gyil" or "amadinda" or "slendro".
== Notes ==
<references group="note" />


[[Category:3-limit record edos|#]] <!-- 1-digit number -->
[[Category:5-tone scales]]
[[Category:5-tone scales]]
[[Category:7-limit]]
[[Category:9-odd-limit]]
[[Category:Listen]]
[[Category:Macrotonal]]
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