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=== Octave stretch ===
=== Octave stretch ===
Since the harmonics whose intervals it approximates well (3, 5, 7, 13, and 19) are all tuned sharp of just, 27edo is a prime candidate for [[stretched and compressed tuning|octave compression]]. The local zeta peak around 27 is at 27.086614, which corresponds to a step size of 44.3023{{c}}. More generally, narrowing the steps to between 44.2 and 44.35{{c}} would be better in theory; [[43edt]], [[70ed6]], [[90ed10]] and [[97ed12]] are good options if octave compression is acceptable, and these narrow the octaves by 5.75, 3.53, 4.11, and 2.55{{c}}, respectively.
Since the harmonics whose intervals it approximates well (3, 5, 7, 13, and 19) are all tuned sharp of just, 27edo is a prime candidate for [[stretched and compressed tuning|octave compression]]. The local zeta peak around 27 is at 27.086614, which corresponds to a step size of 44.3023{{c}}. More generally, narrowing the steps to between 44.2 and 44.35{{c}} would be better in theory; [[43edt]], [[70ed6]], [[90ed10]], and [[97ed12]] are good options if octave compression is acceptable, and these narrow the octaves by 5.75, 3.53, 4.11, and 2.55{{c}}, respectively.


=== Subsets and supersets ===
=== Subsets and supersets ===
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| do
| do
|}
|}
<references group="note" />


=== Interval quality and chord names in color notation ===
=== Interval quality and chord names in color notation ===
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{{Q-odd-limit intervals|27}}
{{Q-odd-limit intervals|27}}
{{Q-odd-limit intervals|27.1|apx=val|header=none|tag=none|title=15-odd-limit intervals by 27e val mapping}}
{{Q-odd-limit intervals|27.1|apx=val|header=none|tag=none|title=15-odd-limit intervals by 27e val mapping}}
=== Zeta peak index ===
{{ZPI
| zpi = 106
| steps = 27.0866140827635
| step size = 44.3023257293579
| tempered height = 6.069233
| pure height = 3.605183
| integral = 1.185939
| gap = 16.215619
| octave = 1196.16279469266
| consistent = 10
| distinct = 8
}}


== Regular temperament properties ==
== Regular temperament properties ==
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| 19th-partial chroma
| 19th-partial chroma
|}
|}
<references group="note" />


== Scales ==
== Scales ==
=== MOS scales ===
=== MOS scales ===
{{Main|List of MOS scales in 27edo}}
{{Main|List of MOS scales in 27edo}}
* Superpyth pentatonic – Superpyth[5] [[2L 3s]] (gen = 11\27): 5 5 6 5 6
* Superpyth pentic – Superpyth[5] [[2L 3s]] (gen = 11\27): 5 5 6 5 6
* Superpyth diatonic – Superpyth[7] [[5L 2s]] (gen = 11\27): 5 5 1 5 5 5 1
* Superpyth diatonic – Superpyth[7] [[5L 2s]] (gen = 11\27): 5 5 1 5 5 5 1
* Superpyth chromatic – Superpyth[12] [[5L 7s]] (gen = 11\27): 4 1 1 4 1 4 1 4 1 1 4 1
* Superpyth chromatic – Superpyth[12] [[5L 7s]] (gen = 11\27): 4 1 1 4 1 4 1 4 1 1 4 1
* Superpyth hyperchromatic – Superpyth[17] [[5L 12s]] (gen = 11\27): 1 3 1 1 3 1 1 1 3 1 1 3 1 1 3 1 1
* Superpyth enharmonic – Superpyth[17] [[5L 12s]] (gen = 11\27): 1 3 1 1 3 1 1 1 3 1 1 3 1 1 3 1 1
* Augene[6] [[3L 3s]] (period = 9\27, gen = 2\27): 7 2 7 2 7 2
* Augene[6] [[3L 3s]] (period = 9\27, gen = 2\27): 7 2 7 2 7 2
* Augene[9] [[3L 6s]] (period = 9\27, gen = 2\27): 5 2 2 5 2 2 5 2 2
* Augene[9] [[3L 6s]] (period = 9\27, gen = 2\27): 5 2 2 5 2 2 5 2 2
Line 1,200: Line 1,188:
* [[SNS (2/1, 3/2, 5/4)-7|5-limit / pental double harmonic major]]: 2 7 2 5 2 7 2
* [[SNS (2/1, 3/2, 5/4)-7|5-limit / pental double harmonic major]]: 2 7 2 5 2 7 2
* enharmonic tetrachord octave species: 9 1 1 5 9 1 1, 1 9 1 5 1 9 1 (also Superpyth double harmonic major), 1 1 9 5 1 1 9
* enharmonic tetrachord octave species: 9 1 1 5 9 1 1, 1 9 1 5 1 9 1 (also Superpyth double harmonic major), 1 1 9 5 1 1 9
* [[The Pinetone System#The Pinetone diatonic|Pinetone diatonic]]: 4 3 4 5 4 3 4
* [[The Pinetone System #The Pinetone diatonic|Pinetone diatonic]]: 4 3 4 5 4 3 4
* [[The Pinetone System#Pinetone octatonic scales|Pinetone major-harmonic octatonic]]: 4 3 4 2 3 4 3 4
* [[The Pinetone System #Pinetone octatonic scales|Pinetone major-harmonic octatonic]]: 4 3 4 2 3 4 3 4
* [[The Pinetone System#Pinetone octatonic scales|Pinetone minor-harmonic octatonic]]: 4 3 2 4 3 4 4 3
* [[The Pinetone System #Pinetone octatonic scales|Pinetone minor-harmonic octatonic]]: 4 3 2 4 3 4 4 3
* [[The Pinetone System#Pinetone diminished octatonic|Pinetone diminished octatonic]] / [[Porcusmine]]: 3 4 2 4 3 4 3 4  
* [[The Pinetone System #Pinetone diminished octatonic|Pinetone diminished octatonic]] / [[Porcusmine]]: 3 4 2 4 3 4 3 4  
* [[The Pinetone System#Pinetone harmonic diminished octatonic|Pinetone harmonic diminished]]: 3 4 2 5 2 4 3 4
* [[The Pinetone System #Pinetone harmonic diminished octatonic|Pinetone harmonic diminished]]: 3 4 2 5 2 4 3 4
* [[The Pinetone System#Pinetone chromatic|Pinetone chromatic]] / pinechrome: 1 3 3 1 3 2 3 1 3 3 1 3
* [[The Pinetone System #Pinetone chromatic|Pinetone chromatic]] / pinechrome: 1 3 3 1 3 2 3 1 3 3 1 3
* 5-limit / pental double harmonic nonatonic (subset of Augene[12]): 2 5 2 2 5 2 5 2 2, 2 2 5 2 5 2 2 5 2 (Augene[9] [[4M]])
* 5-limit / pental double harmonic nonatonic (subset of Augene[12]): 2 5 2 2 5 2 5 2 2, 2 2 5 2 5 2 2 5 2 (Augene[9] [[4M]])
* 5-limit / pental double harmonic decatonic (subset of Augene[12]): 2 5 2 2 3 2 2 5 2 2
* 5-limit / pental double harmonic decatonic (subset of Augene[12]): 2 5 2 2 3 2 2 5 2 2
Line 1,211: Line 1,199:
* [[Blackdye]] / [[syntonic dipentatonic]] (superset of [[Zarlino]]): 1 4 2 4 1 4 2 4 1 4
* [[Blackdye]] / [[syntonic dipentatonic]] (superset of [[Zarlino]]): 1 4 2 4 1 4 2 4 1 4
* [[Blackville]] / [[SNS ((2/1, 3/2)-5, 16/15)-10|5-limit dipentatonic]] (superset of [[Zarlino]]): 3 2 4 2 3 2 4 2 3 2
* [[Blackville]] / [[SNS ((2/1, 3/2)-5, 16/15)-10|5-limit dipentatonic]] (superset of [[Zarlino]]): 3 2 4 2 3 2 4 2 3 2
 
* Direct sunlight (original/default tuning; subset of [[Sensi]][19]): 1 2 8 5 1 9 1 ((1, 3, 11, 16, 17, 26, 27)\27)
Direct sunlight (this is its original/default tuning; subset of [[Sensi]][19])
* Hypersakura (original/default tuning; subset of Sensi[19]): 1 10 5 1 10 ((1 11 16 17 27)\27)
* 44.444
* 133.333
* 488.889
* 711.111
* 755.555
* 1155.555
* 1200.000
 
Hypersakura (this is its original/default tuning; subset of Sensi[19])
* 44.444
* 488.889
* 711.111
* 755.555
* 1200.000


== Instruments ==
== Instruments ==
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; [[Xotla]]
; [[Xotla]]
* "Funkrotonal" from ''Microtonal Allsorts'' (2023) – [https://open.spotify.com/track/1zjNkbm8kIkuCxtodyFCL0 Spotify] | [https://xotla.bandcamp.com/track/funkrotonal-27edo Bandcamp] | [https://www.youtube.com/watch?v=7gt1BBJuJsE YouTube]
* "Funkrotonal" from ''Microtonal Allsorts'' (2023) – [https://open.spotify.com/track/1zjNkbm8kIkuCxtodyFCL0 Spotify] | [https://xotla.bandcamp.com/track/funkrotonal-27edo Bandcamp] | [https://www.youtube.com/watch?v=7gt1BBJuJsE YouTube]
== Notes ==
<references group="note" />


[[Category:Augene]]
[[Category:Augene]]
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