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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|30}}
{{ED intro}}
 
== Theory ==
== Theory ==
{{Harmonics in equal|30}}
30edo's [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[quindecic]] temperament. If 15edo's mappings are still considered acceptable despite their low relative accuracy in this tuning, it can be seen as supplying an improved mapping of the 13th harmonic to 15edo, much like how 24edo supplies an improved 11 and 13 to 12edo.
[[File:Plot30.png|alt=plot30.png|thumb|A plot of the Z function around 30.]]
However, 5\30 is 200[[{{c}}]], which is a good (and familiar) approximation for 9/8, and hence 30edo can be viewed inconsistently, as having a 9/1 at 95\30 as well as 96\30.


Its [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[quindecic]] temperament.
Instead of the 18\30 fifth of 720 cents, 30edo also makes available a 17\30 fifth of 680 cents. It is possible to interpret this fifth as [[mavila]] temperament using the 30bc [[val]], but the 360-cent [[5/4]] may be undesirable for some. When 30edo is used for pelogic, 5\30 can again be used inconsistently as a 9/8. An alternative option which uses the somewhat more accurate 400-cent [[5/4]] is [[shallowtone]] temperament using the 30b [[val]], although it is of very high [[badness]], being both high-[[error]] and high-[[complexity]].  [[Undecimation]] is also an option.
[[File:Plot30.png|alt=plot30.png|thumb|A plot of the Z function around 30.]]
However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30edo can be viewed inconsistently, as having a 9/1 at 95\30 as well as 96\30.  


Instead of the 18\30 fifth of 720 cents, 30edo also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30edo is used for pelogic, 5\30 can again be used inconsistently as a 9/8.
=== Odd harmonics ===
{{Harmonics in equal|30}}


=== Subsets and supersets ===
=== Subsets and supersets ===
30edo has subset edos {{EDOs|1, 2, 3, 5, 6, 10, 15}} and it is a [[largely composite]] edo.
30edo has subset edos {{EDOs| 1, 2, 3, 5, 6, 10, 15 }} and it is a [[largely composite]] edo.


30edo is the 3rd [[wikipedia:primorial|primorial]] edo, being the product of first three primes and thus the smallest number with three distinct prime factors. As a corollary, 30edo is the smallest EDO that supports [[perfectly balanced]] scales that are minimal and not equally spaced. See the article on perfect balance.
30edo is the 3rd {{w|primorial}} edo, being the product of first three primes and thus the smallest number with three distinct prime factors. As a corollary, 30edo is the smallest EDO that supports [[perfectly balanced]] scales that are minimal and not equally spaced. See the article on perfect balance.


== Intervals ==
== Intervals ==
Inconsistent intervals are in ''italics''.
{| class="wikitable right-1 right-2"
|-
! rowspan="2" | Step
! rowspan="2" | Cents
! colspan="3" | Approximate ratios
|-
! 2.9.15.7.11.13 subgroup
! Ratios of 3 and 5<br>tending sharp
! Ratios of 3 and 5<br>tending flat
|-
| 0
| 0
| colspan="3" | [[1/1]]
|-
| 1
| 40
| [[40/39]]
|
| ''[[25/24]]'', [[36/35]], [[49/48]]
|-
| 2
| 80
| [[21/20]]
| ''[[16/15]]'', [[25/24]], ''[[36/35]]''
| ''[[15/14]]''
|-
| 3
| 120
| [[14/13]], [[15/14]], [[16/15]]
| [[13/12]]
| ''[[12/11]]''
|-
| 4
| 160
|
| ''[[10/9]]'', [[11/10]], [[12/11]], ''[[15/14]]''
| ''[[9/8]]'', ''[[13/12]]'', ''[[16/15]]''
|-
| 5
| 200
| [[9/8]]
|
| [[10/9]], ''[[11/10]]'', ''[[15/13]]''
|-
| 6
| 240
| [[8/7]], [[15/13]]
| ''[[7/6]]'', ''[[9/8]]''
|
|-
| 7
| 280
| [[13/11]]
| ''[[15/13]]''
| [[7/6]]
|-
| 8
| 320
| [[6/5]]
| [[6/5]], ''[[11/9]]''
| [[6/5]]
|-
| 9
| 360
| [[16/13]], [[11/9]]
|
| ''[[5/4]]''
|-
| 10
| 400
| [[14/11]]
| [[5/4]]
| ''[[11/9]]'', ''[[9/7]]''
|-
| 11
| 440
| [[9/7]], [[32/25]]
| [[13/10]]
|
|-
| 12
| 480
|
| ''[[9/7]]'', [[4/3]]
| ''[[13/10]]'', ''[[15/11]]''
|-
| 13
| 520
| [[27/20]], [[15/11]]
|
| ''[[4/3]]'', ''[[18/13]]''
|-
| 14
| 560
| [[11/8]], [[18/13]], [[25/18]]
| ''[[7/5]]'', ''[[15/11]]''
|
|-
| 15
| 600
|
| ''[[13/9]]'', ''[[18/13]]''
| [[7/5]], [[10/7]]
|-
| 16
| 640
| [[16/11]], [[13/9]], [[36/25]]
| ''[[10/7]]'', ''[[22/15]]''
|
|-
| 17
| 680
| [[40/27]], [[22/15]]
|
| ''[[3/2]]'', ''[[13/9]]''
|-
| 18
| 720
|
| ''[[14/9]]'', [[3/2]]
| ''[[20/13]]'', ''[[22/15]]''
|-
| 19
| 760
| [[14/9]], [[25/16]]
| [[20/13]]
|
|-
| 20
| 800
| [[11/7]]
| [[8/5]]
| ''[[14/9]]'', ''[[18/11]]''
|-
| 21
| 840
| [[13/8]], [[18/11]]
|
| ''[[8/5]]''
|-
| 22
| 880
| [[5/3]]
| [[5/3]], ''[[18/11]]''
| [[5/3]]
|-
| 23
| 920
| [[22/13]]
| ''[[26/15]]''
| [[12/7]]
|-
| 24
| 960
| [[7/4]], [[26/15]]
| ''[[12/7]]'', ''[[16/9]]''
|
|-
| 25
| 1000
| [[16/9]]
|
| [[9/5]], ''[[20/11]]'', ''[[26/15]]''
|-
| 26
| 1040
|
| ''[[9/5]]'', [[20/11]], [[11/6]], ''[[28/15]]''
| ''[[16/9]]'', ''[[24/13]]'', ''[[15/8]]''
|-
| 27
| 1080
| [[13/7]], [[28/15]], [[15/8]]
| [[24/13]]
| ''[[11/6]]''
|-
| 28
| 1120
| [[40/21]]
| ''[[15/8]]'', [[48/25]], ''[[35/18]]''
| ''[[28/15]]''
|-
| 29
| 1160
| [[39/20]]
|
| ''[[48/25]]'', [[35/18]], [[96/49]]
|-
| 30
| 1200
| colspan="3" | [[2/1]]
|}
== Notation ==
{| class="wikitable center-all"
{| class="wikitable center-all"
|+ style="font-size: 105%" | Notation systems for 30edo
|-
|-
! Step
! Step
! [[Cent]]s
! Cents
! colspan="3" | [[Ups and downs notation]]
! colspan="3" | [[Ups and downs notation]]
! [[Armodue_theory|Armodue Notation]]
! [[Armodue theory|Armodue notation]]
|-
|-
| 0
| 0
Line 241: Line 439:
|}
|}


== Notation ==
=== Stein–Zimmermann–Gould notation ===
===Sagittal notation===
[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
====Best fifth notation====
{{Sharpness-sharp6-szg}}
This notation uses the same sagittal sequence as EDOs [[23edo#Sagittal notation|23b]], [[37edo#Sagittal notation|37]], and [[44edo#Sagittal notation|44]], and is a superset of the notations for EDOs [[15edo#Sagittal notation|15]], [[10edo#Sagittal notation|10]], and [[5edo#Sagittal notation|5]].
 
If double arrows are not desirable, arrows can be attached to quarter-tone accidentals:
{{Sharpness-sharp6-qt-szg}}
 
=== Kite's ups and downs notation ===
30edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc.
{{Sharpness-sharp6a}}
 
Half-sharps and half-flats can be used to avoid triple arrows:
{{Sharpness-sharp6b}}
 
=== Sagittal notation ===
==== Best fifth notation ====
This notation uses the same sagittal sequence as edos [[23edo #Second-best fifth notation|23b]], [[37edo #Sagittal notation|37]], and [[44edo #Sagittal notation|44]], and is a superset of the notations for edos [[15edo #Sagittal notation|15]], [[10edo #Sagittal notation|10]], and [[5edo #Sagittal notation|5]].


=====Evo and Revo flavors=====
===== Evo and Revo flavors =====


<imagemap>
<imagemap>
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</imagemap>
</imagemap>


=====Evo-SZ flavor=====
===== Evo-SZ flavor =====


<imagemap>
<imagemap>
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</imagemap>
</imagemap>


====Second-best fifth notation====
==== Second-best fifth notation ====
This notation uses the same sagittal sequence as EDOs [[35edo#Sagittal notation|35]] and [[40edo#Sagittal notation|40]].
This notation uses the same sagittal sequence as edos [[35edo #Sagittal notation|35]] and [[40edo #Sagittal notation|40]].


<imagemap>
<imagemap>
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</imagemap>
</imagemap>


== Commas ==
== Regular temperament properties ==
30 EDO [[tempers out]] the following [[commas]]. (Note: This assumes the [[val]] {{val| 30 48 70 84 104 111 }}.)
=== Rank-2 temperaments ===
As 30edo is largely composite, only 7, 11 and 13 steps create [[MOS scale]]s that cover every interval using one period per octave. 
 
7/30 produces [[No-threes subgroup temperaments#Lovecraft|Lovecraft]], in which 2 generators is a moderately sharp [[11/8]], 3 a near perfect [[13/8]] and 5 the familiar mildly flat [[9/8]] from [[12edo]], creating the possibility of ignoring the 3rd & 5th entirely to use those harmonics as the primary building blocks of harmony in a similar way to [[orgone]]. 
 
11 produces a flat [[sensi]] scale. 13 is an excellent higher order [[Pelogic_family#Mavila|Mavila]] tuning that functions the closest to the familiar diatonic scale you can get in this edo.
 
=== Commas ===
30et [[tempering out|tempers out]] the following [[comma]]s. This assumes the [[val]] {{val| 30 48 70 84 104 111 }}.


{| 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>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
! [[Monzo]]
Line 297: Line 516:
| 90.22
| 90.22
| Sawa
| Sawa
| Limma, Pythagorean minor second
| Blackwood comma, Pythagorean limma
|-
|-
| 5
| 5
Line 304: Line 523:
| 49.17
| 49.17
| Triyo
| Triyo
| Maximal diesis, Porcupine comma
| Porcupine comma, maximal diesis
|-
|-
| 5
| 5
Line 311: Line 530:
| 41.06
| 41.06
| Trigu
| Trigu
| Diesis, augmented comma
| Augmented comma, diesis
|-
|-
| 5
| 5
Line 332: Line 551:
| 35.70
| 35.70
| Zozo
| Zozo
| Slendro diesis
| Semaphoresma, slendro diesis
|-
|-
| 7
| 7
Line 346: Line 565:
| 22.23
| 22.23
| Laquadzo-atrigu
| Laquadzo-atrigu
| Squalentine
| Squalentine comma
|-
|-
| 7
| 7
Line 360: Line 579:
| 13.79
| 13.79
| Zotrigu
| Zotrigu
| Septimal semicomma, Starling comma
| Starling comma, septimal semicomma
|-
|-
| 7
| 7
Line 367: Line 586:
| 13.47
| 13.47
| Rurutriyo
| Rurutriyo
| Octagar
| Octagar comma
|-
|-
| 7
| 7
Line 381: Line 600:
| 5.36
| 5.36
| Saruru-atrigu
| Saruru-atrigu
| Porwell
| Porwell comma
|-
|-
| 7
| 7
Line 437: Line 656:
| 3.03
| 3.03
| Triluyo
| Triluyo
| Wizardharry
| Wizardharry comma
|-
|-
| 11
| 11
Line 448: Line 667:
<references/>
<references/>


== Rank-2 temperaments ==
== Octave stretch or compression ==
As 30edo is largely composite, only 7, 11 and 13 steps create [[MOS scale]]s that cover every interval using one period per octave. 
30edo's simple [[prime]]s with the most error - 3, 5 and 11 - are all tuned sharp, so it can benefit from [[octave shrinking]]. Some compressed-octave 30edo tunings (least to most compressed) include [[zpi|122zpi]], [[equal tuning|100ed10]], [[ed12|108ed12]] or [[ed6|78ed6]].
 
7/30 produces [[No-threes subgroup temperaments#Lovecraft|Lovecraft]], in which 2 generators is a moderately sharp [[11/8]], 3 a near perfect [[13/8]] and 5 the familiar mildly flat [[9/8]] from [[12edo]], creating the possibility of ignoring the 3rd & 5th entirely to use those harmonics as the primary building blocks of harmony in a similar way to [[orgone]].


11 produces a flat [[sensi]] scale. 13 is an excellent higher order [[Pelogic_family#Mavila|Mavila]] tuning that functions the closest to the familiar diatonic scale you can get in this edo.  
Alternatively, if one wishes to use 30edo as a [[dual-fifth]] tuning, [[equal tuning|95ed9]] is a good option, sharing the error equally between both fifths (20{{c}} error each). This does come at the cost of making most of 30edo's worst primes slightly worse, though not enough to affect their usability.


== Scales ==
== Scales ==
=== MOS scales ===
=== MOS scales ===
* [[Lovecraft5|Lovecraft[5]]] - 77772
* [[Lovecraft5|Lovecraft[5]]] - 77772
* [[Lovecraft9|Lovecraft[9]]] - 525252522
* [[Lovecraft9|Lovecraft[9]]] - 525252522
Line 473: Line 688:
* Mavila[23] - 21121121121112112112111
* Mavila[23] - 21121121121112112112111


=== Subsets of [[Mavila]][16] ===
=== Subsets of [[mavila]][16] ===
 
{{Idiosyncratic terms|Most of these names were coined, and have so far been soley used by, [[Budjarn Lambeth]].}}
* Arcade (approximated from [[32afdo]]): 9 3 5 8 5
* Arcade (approximated from [[32afdo]]): 9 3 5 8 5
* [[Blackened skies]] (approximated from [[Compton]] in [[72edo]]): 8 5 2 3 2 8 2
* [[Blackened Skies]] (approximated from [[Compton]] in [[72edo]]): 8 5 2 3 2 8 2
* Carousel (this is the original/default tuning): 9 4 4 9 4
* Carousel (original/default tuning): 9 4 4 9 4
* Dewdrops (this is the original/default tuning): 4 4 4 5 4 4 5
* Dewdrops (original/default tuning): 4 4 4 5 4 4 5
* Geode (approximated from [[6afdo]]): 7 6 4 9 4
* Geode (approximated from [[6afdo]]): 7 6 4 9 4
* [[Lost spirit]] (approximated from [[Meantone]] in [[31edo]]): 7 5 2 3 5 3 5
* [[Lost Spirit]] (approximated from [[Meantone]] in [[31edo]]): 7 5 2 3 5 3 5
* Lost phantom (this is the original/default tuning): 8 5 2 2 6 2 5
* Lost phantom (original/default tuning): 8 5 2 2 6 2 5
* Mechanical (approximated from [[16afdo]]): 7 2 8 8 5
* Mechanical (approximated from [[16afdo]]): 7 2 8 8 5
* Mushroom (approximated from [[30afdo]]): 7 5 5 3 10
* Mushroom (approximated from [[30afdo]]): 7 5 5 3 10
* Nightdrive (this is the original/default tuning): 8 5 4 9 4
* Nightdrive (original/default tuning): 8 5 4 9 4
* Pelagic (this is the original/default tuning): 8 4 2 4 7 5
* Pelagic (original/default tuning): 8 4 2 4 7 5
* Bathypelagic (this is the original/default tuning): 8 4 2 3 8 5
* Bathypelagic (original/default tuning): 8 4 2 3 8 5
* Underpass (approximated from [[10afdo]]): 8 9 5 3 5
* Underpass (approximated from [[10afdo]]): 8 9 5 3 5
* Volcanic (approximated from [[16afdo]]): 3 6 8 8 5
* Volcanic (approximated from [[16afdo]]): 3 6 8 8 5


=== Subsets of [[15edo]] ===
=== Polymicrotonal scales ===
 
* 10-tone 5&6edo scale: 5 1 4 2 3 3 2 4 1 5
* Augmented[6] MOS: 8 2 8 2 8 2
* 12-tone 6&10edo scale{{idio}}: 3 2 1 3 3 3 3 2 1 3 3 3
* Equipentatonic (exact from [[5edo]]): 6 6 6 6 6
* 12-tone 6&15edo scale{{idio}}: 2 3 3 2 2 3 3 2 2 3 3 2
* Rockpool (approximated from [[47zpi]]): 2 8 2 6 6 6
* 12-tone 10&15edo scale{{idio}}: 3 1 2 3 3 3 3 3 1 2 3 3
* 14-tone 6&10edo scale: 3 2 1 3 1 2 3 3 2 1 3 1 2 3
* 18-tone 6&15edo scale: 2 2 1 1 2 2 2 2 1 1 2 2 2 2 1 1 2 2
* 20-tone 10&15edo scale: 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2


=== Other notable scales ===
=== Other notable scales ===
* Approximation of [[Pelog]] lima: 3 4 10 3 10
* Approximation of [[Pelog]] lima: 3 4 10 3 10
* [[Amiot]] scale
* Approximation of Hirajoshi for metallic/percussive timbres: 5 3 9 3 10
* [[Amiot]] scale: 6 1 6 1 6 1 6
* Augmented[6] (exact from [[15edo]]): 8 2 8 2 8 2
* Dusty{{idio}} (original tuning): 8 5 5 3 7 2
* [[Equipentatonic]] (exact from [[5edo]]): 6 6 6 6 6
* Iron filing{{idio}} (original tuning): 3 2 2 2 1 2 2 3 1 3 1 2 2 1 3
* [[Moon dust]] (approximated from [[JI]]): ''nonoctave''
* Rockpool{{idio}} (approximated from [[47zpi]]): 2 8 2 6 6 6
* ''More listed in: [[User:BudjarnLambeth/Quasipelog theory#Scales]]''


== Delta-rational harmony ==
== Delta-rational harmony ==
The tables below show chords that approximate 3-integer-limit [[delta-rational]] chords with least-squares error less than 0.001.  
The tables below show chords that approximate 3-integer-limit [[delta-rational]] chords with least-squares error less than 0.001.
 
=== Fully delta-rational triads ===
=== Fully delta-rational triads ===
{| class="mw-collapsible mw-collapsed class="wikitable sortable"
{| class="mw-collapsible mw-collapsed class="wikitable sortable"
!|chord
!|delta signature
!|error
|-
|-
|0,1,2
! Chord
! Delta signature
! Error
|-
| 0,1,2
| +1+1
| +1+1
|0.00026
| 0.00026
|-
|-
|0,1,3
| 0,1,3
| +1+2
| +1+2
|0.00058
| 0.00058
|-
|-
|0,1,4
| 0,1,4
| +1+3
| +1+3
|0.00094
| 0.00094
|-
|-
|0,2,3
| 0,2,3
| +2+1
| +2+1
|0.00047
| 0.00047
|-
|-
|0,3,4
| 0,3,4
| +3+1
| +3+1
|0.00068
| 0.00068
|-
|-
|0,3,11
| 0,3,11
| +1+3
| +1+3
|0.00064
| 0.00064
|-
|-
|0,4,11
| 0,4,11
| +1+2
| +1+2
|0.00039
| 0.00039
|-
|-
|0,5,8
| 0,5,8
| +3+2
| +3+2
|0.00057
| 0.00057
|-
|-
|0,6,16
| 0,6,16
| +1+2
| +1+2
|0.00042
| 0.00042
|-
|-
|0,7,13
| 0,7,13
| +1+1
| +1+1
|0.00035
| 0.00035
|-
|-
|0,7,23
| 0,7,23
| +1+3
| +1+3
|0.00024
| 0.00024
|-
|-
|0,10,25
| 0,10,25
| +1+2
| +1+2
|0.00072
| 0.00072
|-
|-
|0,11,17
| 0,11,17
| +3+2
| +3+2
|0.00063
| 0.00063
|-
|-
|0,11,27
| 0,11,27
| +1+2
| +1+2
|0.00072
| 0.00072
|-
|-
|0,13,23
| 0,13,23
| +1+1
| +1+1
|0.00030
| 0.00030
|-
|-
|0,14,29
| 0,14,29
| +2+3
| +2+3
|0.00019
| 0.00019
|-
|-
|0,15,19
| 0,15,19
| +3+1
| +3+1
|0.00069
| 0.00069
|-
|-
|0,20,25
| 0,20,25
| +3+1
| +3+1
|0.00085
| 0.00085
|}
|}


=== Partially delta-rational tetrads ===
=== Partially delta-rational tetrads ===
{| class="mw-collapsible mw-collapsed class="wikitable sortable"
{| class="mw-collapsible mw-collapsed class="wikitable sortable"
!|chord
!|delta signature
!|error
|-
|-
|0,1,2,3
! Chord
! Delta signature
! Error
|-
| 0,1,2,3
| +1+?+1
| +1+?+1
|0.00064
| 0.00064
|-
|-
|0,1,3,4
| 0,1,3,4
| +1+?+1
| +1+?+1
|0.00097
| 0.00097
|-
|-
|0,1,15,16
| 0,1,15,16
| +2+?+3
| +2+?+3
|0.00097
| 0.00097
|-
|-
|0,1,15,17
| 0,1,15,17
| +1+?+3
| +1+?+3
|0.00098
| 0.00098
|-
|-
|0,1,16,17
| 0,1,16,17
| +2+?+3
| +2+?+3
|0.00060
| 0.00060
|-
|-
|0,1,16,18
| 0,1,16,18
| +1+?+3
| +1+?+3
|0.00050
| 0.00050
|-
|-
|0,1,17,18
| 0,1,17,18
| +2+?+3
| +2+?+3
|0.00021
| 0.00021
|-
|-
|0,1,17,19
| 0,1,17,19
| +1+?+3
| +1+?+3
|0.00002
| 0.00002
|-
|-
|0,1,18,19
| 0,1,18,19
| +2+?+3
| +2+?+3
|0.00018
| 0.00018
|-
|-
|0,1,18,20
| 0,1,18,20
| +1+?+3
| +1+?+3
|0.00047
| 0.00047
|-
|-
|0,1,19,20
| 0,1,19,20
| +2+?+3
| +2+?+3
|0.00058
| 0.00058
|-
|-
|0,1,19,21
| 0,1,19,21
| +1+?+3
| +1+?+3
|0.00098
| 0.00098
|-
|-
|0,1,20,21
| 0,1,20,21
| +2+?+3
| +2+?+3
|0.00099
| 0.00099
|-
|-
|0,1,28,29
| 0,1,28,29
| +1+?+2
| +1+?+2
|0.00086
| 0.00086
|-
|-
|0,2,3,4
| 0,2,3,4
| +2+?+1
| +2+?+1
|0.00094
| 0.00094
|-
|-
|0,2,6,11
| 0,2,6,11
| +1+?+3
| +1+?+3
|0.00036
| 0.00036
|-
|-
|0,2,7,12
| 0,2,7,12
| +1+?+3
| +1+?+3
|0.00063
| 0.00063
|-
|-
|0,2,11,12
| 0,2,11,12
| +3+?+2
| +3+?+2
|0.00089
| 0.00089
|-
|-
|0,2,11,14
| 0,2,11,14
| +1+?+2
| +1+?+2
|0.00084
| 0.00084
|-
|-
|0,2,12,13
| 0,2,12,13
| +3+?+2
| +3+?+2
|0.00044
| 0.00044
|-
|-
|0,2,12,15
| 0,2,12,15
| +1+?+2
| +1+?+2
|0.00005
| 0.00005
|-
|-
|0,2,13,14
| 0,2,13,14
| +3+?+2
| +3+?+2
|0.00002
| 0.00002
|-
|-
|0,2,13,16
| 0,2,13,16
| +1+?+2
| +1+?+2
|0.00095
| 0.00095
|-
|-
|0,2,14,15
| 0,2,14,15
| +3+?+2
| +3+?+2
|0.00049
| 0.00049
|-
|-
|0,2,15,16
| 0,2,15,16
| +3+?+2
| +3+?+2
|0.00098
| 0.00098
|-
|-
|0,2,16,20
| 0,2,16,20
| +1+?+3
| +1+?+3
|0.00053
| 0.00053
|-
|-
|0,2,17,19
| 0,2,17,19
| +2+?+3
| +2+?+3
|0.00043
| 0.00043
|-
|-
|0,2,17,21
| 0,2,17,21
| +1+?+3
| +1+?+3
|0.00046
| 0.00046
|-
|-
|0,2,18,20
| 0,2,18,20
| +2+?+3
| +2+?+3
|0.00036
| 0.00036
|-
|-
|0,3,4,8
| 0,3,4,8
| +2+?+3
| +2+?+3
|0.00071
| 0.00071
|-
|-
|0,3,5,9
| 0,3,5,9
| +2+?+3
| +2+?+3
|0.00050
| 0.00050
|-
|-
|0,3,7,12
| 0,3,7,12
| +1+?+2
| +1+?+2
|0.00017
| 0.00017
|-
|-
|0,3,9,16
| 0,3,9,16
| +1+?+3
| +1+?+3
|0.00024
| 0.00024
|-
|-
|0,3,16,22
| 0,3,16,22
| +1+?+3
| +1+?+3
|0.00003
| 0.00003
|-
|-
|0,3,17,18
| 0,3,17,18
| +2+?+1
| +2+?+1
|0.00085
| 0.00085
|-
|-
|0,3,17,19
| 0,3,17,19
| +1+?+1
| +1+?+1
|0.00100
| 0.00100
|-
|-
|0,3,17,20
| 0,3,17,20
| +2+?+3
| +2+?+3
|0.00066
| 0.00066
|-
|-
|0,3,17,21
| 0,3,17,21
| +1+?+2
| +1+?+2
|0.00006
| 0.00006
|-
|-
|0,3,18,19
| 0,3,18,19
| +2+?+1
| +2+?+1
|0.00031
| 0.00031
|-
|-
|0,3,18,20
| 0,3,18,20
| +1+?+1
| +1+?+1
|0.00005
| 0.00005
|-
|-
|0,3,18,21
| 0,3,18,21
| +2+?+3
| +2+?+3
|0.00055
| 0.00055
|-
|-
|0,3,19,20
| 0,3,19,20
| +2+?+1
| +2+?+1
|0.00025
| 0.00025
|-
|-
|0,3,19,21
| 0,3,19,21
| +1+?+1
| +1+?+1
|0.00092
| 0.00092
|-
|-
|0,3,20,21
| 0,3,20,21
| +2+?+1
| +2+?+1
|0.00081
| 0.00081
|-
|-
|0,3,24,29
| 0,3,24,29
| +1+?+3
| +1+?+3
|0.00063
| 0.00063
|-
|-
|0,4,5,15
| 0,4,5,15
| +1+?+3
| +1+?+3
|0.00038
| 0.00038
|-
|-
|0,4,7,12
| 0,4,7,12
| +2+?+3
| +2+?+3
|0.00062
| 0.00062
|-
|-
|0,4,10,19
| 0,4,10,19
| +1+?+3
| +1+?+3
|0.00023
| 0.00023
|-
|-
|0,4,11,17
| 0,4,11,17
| +1+?+2
| +1+?+2
|0.00078
| 0.00078
|-
|-
|0,4,12,13
| 0,4,12,13
| +3+?+1
| +3+?+1
|0.00099
| 0.00099
|-
|-
|0,4,13,14
| 0,4,13,14
| +3+?+1
| +3+?+1
|0.00049
| 0.00049
|-
|-
|0,4,13,15
| 0,4,13,15
| +3+?+2
| +3+?+2
|0.00044
| 0.00044
|-
|-
|0,4,13,16
| 0,4,13,16
| +1+?+1
| +1+?+1
|0.00005
| 0.00005
|-
|-
|0,4,14,15
| 0,4,14,15
| +3+?+1
| +3+?+1
|0.00002
| 0.00002
|-
|-
|0,4,14,16
| 0,4,14,16
| +3+?+2
| +3+?+2
|0.00052
| 0.00052
|-
|-
|0,4,15,16
| 0,4,15,16
| +3+?+1
| +3+?+1
|0.00054
| 0.00054
|-
|-
|0,4,17,21
| 0,4,17,21
| +2+?+3
| +2+?+3
|0.00089
| 0.00089
|-
|-
|0,4,18,22
| 0,4,18,22
| +2+?+3
| +2+?+3
|0.00074
| 0.00074
|-
|-
|0,4,20,25
| 0,4,20,25
| +1+?+2
| +1+?+2
|0.00030
| 0.00030
|-
|-
|0,4,22,29
| 0,4,22,29
| +1+?+3
| +1+?+3
|0.00041
| 0.00041
|-
|-
|0,5,6,9
| 0,5,6,9
| +3+?+2
| +3+?+2
|0.00051
| 0.00051
|-
|-
|0,5,6,18
| 0,5,6,18
| +1+?+3
| +1+?+3
|0.00011
| 0.00011
|-
|-
|0,5,8,16
| 0,5,8,16
| +1+?+2
| +1+?+2
|0.00028
| 0.00028
|-
|-
|0,5,9,15
| 0,5,9,15
| +2+?+3
| +2+?+3
|0.00030
| 0.00030
|-
|-
|0,5,10,14
| 0,5,10,14
| +1+?+1
| +1+?+1
|0.00027
| 0.00027
|-
|-
|0,5,10,21
| 0,5,10,21
| +1+?+3
| +1+?+3
|0.00084
| 0.00084
|-
|-
|0,5,11,13
| 0,5,11,13
| +2+?+1
| +2+?+1
|0.00017
| 0.00017
|-
|-
|0,5,12,14
| 0,5,12,14
| +2+?+1
| +2+?+1
|0.00078
| 0.00078
|-
|-
|0,5,14,21
| 0,5,14,21
| +1+?+2
| +1+?+2
|0.00095
| 0.00095
|-
|-
|0,5,15,25
| 0,5,15,25
| +1+?+3
| +1+?+3
|0.00006
| 0.00006
|-
|-
|0,5,18,23
| 0,5,18,23
| +2+?+3
| +2+?+3
|0.00093
| 0.00093
|-
|-
|0,5,20,29
| 0,5,20,29
| +1+?+3
| +1+?+3
|0.00014
| 0.00014
|-
|-
|0,5,22,28
| 0,5,22,28
| +1+?+2
| +1+?+2
|0.00093
| 0.00093
|-
|-
|0,5,23,24
| 0,5,23,24
| +3+?+1
| +3+?+1
|0.00073
| 0.00073
|-
|-
|0,5,23,25
| 0,5,23,25
| +3+?+2
| +3+?+2
|0.00075
| 0.00075
|-
|-
|0,5,23,26
| 0,5,23,26
| +1+?+1
| +1+?+1
|0.00020
| 0.00020
|-
|-
|0,5,24,25
| 0,5,24,25
| +3+?+1
| +3+?+1
|0.00009
| 0.00009
|-
|-
|0,5,24,26
| 0,5,24,26
| +3+?+2
| +3+?+2
|0.00045
| 0.00045
|-
|-
|0,5,25,26
| 0,5,25,26
| +3+?+1
| +3+?+1
|0.00057
| 0.00057
|-
|-
|0,6,7,21
| 0,6,7,21
| +1+?+3
| +1+?+3
|0.00086
| 0.00086
|-
|-
|0,6,8,13
| 0,6,8,13
| +1+?+1
| +1+?+1
|0.00079
| 0.00079
|-
|-
|0,6,10,17
| 0,6,10,17
| +2+?+3
| +2+?+3
|0.00091
| 0.00091
|-
|-
|0,6,11,20
| 0,6,11,20
| +1+?+2
| +1+?+2
|0.00026
| 0.00026
|-
|-
|0,6,14,17
| 0,6,14,17
| +3+?+2
| +3+?+2
|0.00003
| 0.00003
|-
|-
|0,6,19,21
| 0,6,19,21
| +2+?+1
| +2+?+1
|0.00066
| 0.00066
|-
|-
|0,6,19,23
| 0,6,19,23
| +1+?+1
| +1+?+1
|0.00086
| 0.00086
|-
|-
|0,6,20,22
| 0,6,20,22
| +2+?+1
| +2+?+1
|0.00048
| 0.00048
|-
|-
|0,7,8,11
| 0,7,8,11
| +2+?+1
| +2+?+1
|0.00095
| 0.00095
|-
|-
|0,7,8,12
| 0,7,8,12
| +3+?+2
| +3+?+2
|0.00035
| 0.00035
|-
|-
|0,7,9,11
| 0,7,9,11
| +3+?+1
| +3+?+1
|0.00020
| 0.00020
|-
|-
|0,7,9,12
| 0,7,9,12
| +2+?+1
| +2+?+1
|0.00039
| 0.00039
|-
|-
|0,7,10,12
| 0,7,10,12
| +3+?+1
| +3+?+1
|0.00074
| 0.00074
|-
|-
|0,7,11,19
| 0,7,11,19
| +2+?+3
| +2+?+3
|0.00075
| 0.00075
|-
|-
|0,7,13,23
| 0,7,13,23
| +1+?+2
| +1+?+2
|0.00005
| 0.00005
|-
|-
|0,7,14,28
| 0,7,14,28
| +1+?+3
| +1+?+3
|0.00034
| 0.00034
|-
|-
|0,7,16,21
| 0,7,16,21
| +1+?+1
| +1+?+1
|0.00097
| 0.00097
|-
|-
|0,7,18,27
| 0,7,18,27
| +1+?+2
| +1+?+2
|0.00030
| 0.00030
|-
|-
|0,7,21,24
| 0,7,21,24
| +3+?+2
| +3+?+2
|0.00028
| 0.00028
|-
|-
|0,7,27,29
| 0,7,27,29
| +2+?+1
| +2+?+1
|0.00032
| 0.00032
|-
|-
|0,8,10,27
| 0,8,10,27
| +1+?+3
| +1+?+3
|0.00088
| 0.00088
|-
|-
|0,8,12,21
| 0,8,12,21
| +2+?+3
| +2+?+3
|0.00022
| 0.00022
|-
|-
|0,8,14,18
| 0,8,14,18
| +3+?+2
| +3+?+2
|0.00099
| 0.00099
|-
|-
|0,8,15,17
| 0,8,15,17
| +3+?+1
| +3+?+1
|0.00054
| 0.00054
|-
|-
|0,8,15,18
| 0,8,15,18
| +2+?+1
| +2+?+1
|0.00001
| 0.00001
|-
|-
|0,8,16,18
| 0,8,16,18
| +3+?+1
| +3+?+1
|0.00053
| 0.00053
|-
|-
|0,8,22,27
| 0,8,22,27
| +1+?+1
| +1+?+1
|0.00033
| 0.00033
|-
|-
|0,9,10,15
| 0,9,10,15
| +3+?+2
| +3+?+2
|0.00013
| 0.00013
|-
|-
|0,9,10,29
| 0,9,10,29
| +1+?+3
| +1+?+3
|0.00029
| 0.00029
|-
|-
|0,9,12,19
| 0,9,12,19
| +1+?+1
| +1+?+1
|0.00028
| 0.00028
|-
|-
|0,9,12,25
| 0,9,12,25
| +1+?+2
| +1+?+2
|0.00000
| 0.00000
|-
|-
|0,9,16,28
| 0,9,16,28
| +1+?+2
| +1+?+2
|0.00005
| 0.00005
|-
|-
|0,9,19,25
| 0,9,19,25
| +1+?+1
| +1+?+1
|0.00028
| 0.00028
|-
|-
|0,9,20,24
| 0,9,20,24
| +3+?+2
| +3+?+2
|0.00025
| 0.00025
|-
|-
|0,9,21,23
| 0,9,21,23
| +3+?+1
| +3+?+1
|0.00015
| 0.00015
|-
|-
|0,9,21,24
| 0,9,21,24
| +2+?+1
| +2+?+1
|0.00068
| 0.00068
|-
|-
|0,10,13,17
| 0,10,13,17
| +2+?+1
| +2+?+1
|0.00052
| 0.00052
|-
|-
|0,10,13,24
| 0,10,13,24
| +2+?+3
| +2+?+3
|0.00042
| 0.00042
|-
|-
|0,10,15,20
| 0,10,15,20
| +3+?+2
| +3+?+2
|0.00006
| 0.00006
|-
|-
|0,10,17,24
| 0,10,17,24
| +1+?+1
| +1+?+1
|0.00005
| 0.00005
|-
|-
|0,10,25,29
| 0,10,25,29
| +3+?+2
| +3+?+2
|0.00048
| 0.00048
|-
|-
|0,10,26,28
| 0,10,26,28
| +3+?+1
| +3+?+1
|0.00028
| 0.00028
|-
|-
|0,10,26,29
| 0,10,26,29
| +2+?+1
| +2+?+1
|0.00061
| 0.00061
|-
|-
|0,11,13,16
| 0,11,13,16
| +3+?+1
| +3+?+1
|0.00032
| 0.00032
|-
|-
|0,11,17,21
| 0,11,17,21
| +2+?+1
| +2+?+1
|0.00085
| 0.00085
|-
|-
|0,11,20,25
| 0,11,20,25
| +3+?+2
| +3+?+2
|0.00095
| 0.00095
|-
|-
|0,12,14,23
| 0,12,14,23
| +1+?+1
| +1+?+1
|0.00005
| 0.00005
|-
|-
|0,12,17,20
| 0,12,17,20
| +3+?+1
| +3+?+1
|0.00014
| 0.00014
|-
|-
|0,12,22,26
| 0,12,22,26
| +2+?+1
| +2+?+1
|0.00081
| 0.00081
|-
|-
|0,12,24,29
| 0,12,24,29
| +3+?+2
| +3+?+2
|0.00014
| 0.00014
|-
|-
|0,13,18,27
| 0,13,18,27
| +1+?+1
| +1+?+1
|0.00000
| 0.00000
|-
|-
|0,13,21,24
| 0,13,21,24
| +3+?+1
| +3+?+1
|0.00013
| 0.00013
|-
|-
|0,14,16,23
| 0,14,16,23
| +3+?+2
| +3+?+2
|0.00035
| 0.00035
|-
|-
|0,14,19,24
| 0,14,19,24
| +2+?+1
| +2+?+1
|0.00067
| 0.00067
|-
|-
|0,14,25,28
| 0,14,25,28
| +3+?+1
| +3+?+1
|0.00040
| 0.00040
|-
|-
|0,15,23,28
| 0,15,23,28
| +2+?+1
| +2+?+1
|0.00083
| 0.00083
|-
|-
|0,16,19,23
| 0,16,19,23
| +3+?+1
| +3+?+1
|0.00076
| 0.00076
|-
|-
|0,17,20,28
| 0,17,20,28
| +3+?+2
| +3+?+2
|0.00099
| 0.00099
|-
|-
|0,17,21,27
| 0,17,21,27
| +2+?+1
| +2+?+1
|0.00067
| 0.00067
|-
|-
|0,17,22,26
| 0,17,22,26
| +3+?+1
| +3+?+1
|0.00042
| 0.00042
|-
|-
|0,18,25,29
| 0,18,25,29
| +3+?+1
| +3+?+1
|0.00042
| 0.00042
|-
|-
|0,19,20,29
| 0,19,20,29
| +3+?+2
| +3+?+2
|0.00033
| 0.00033
|-
|-
|0,21,23,28
| 0,21,23,28
| +3+?+1
| +3+?+1
|0.00012
| 0.00012
|}
|}
== Instruments ==
[[Lumatone mapping for 30edo|Lumatone mappings for 30edo]] are available.


== Music ==
== Music ==
=== Modern renderings ===
; {{W|Evanescence}}
* [https://www.youtube.com/watch?v=ppHcUOpbnbI ''Bring Me To Life''] (2003) – microtonal cover in 30edo by [[Bryan Deister]] (2024)
; {{W|Mitski}}
* [https://www.youtube.com/shorts/4MI2opBMkd4 ''Eric''] (2012) – microtonal cover in 30edo by [[Bryan Deister]] (2025)
=== 21st century ===
; [[Bryan Deister]]
; [[Bryan Deister]]
* [https://www.youtube.com/watch?v=uSpDz2Dmksw ''microtonal improvisation in 30edo''] (2023)
* [https://www.youtube.com/watch?v=uSpDz2Dmksw ''microtonal improvisation in 30edo''] (2023)
* [https://www.youtube.com/watch?v=NP3HGr3ZD70&lc=UgxFBmbxZa5dF4ZPj0F4AaABAg.AFzcn1LkVZNAG4JYIvXZvZ ''minuet in 30edo''] (2025)
* [https://www.youtube.com/watch?v=pa4YMCae2tE ''waltz in 30edo''] (2025)
* [https://www.youtube.com/watch?v=2TxCWDYUvYc ''30edo improv''] (2025)
* ''Ferris Wheel - 30edo'' (2026)
** [https://www.youtube.com/shorts/O6nOiLxYPdE <nowiki>[short]</nowiki>] (with Lumatone view)
** [https://www.youtube.com/watch?v=gyrb2-tt_m8 <nowiki>[full version]</nowiki>]
* [https://www.youtube.com/shorts/ZlXSZDSlH2c ''Fantasy in 30edo''] (2026)


; [[Todd Harrop]]
; [[Todd Harrop]]
* [https://spectropolrecords.bandcamp.com/track/todd-harrop-fifteen-short-pieces ''Fifteen Short Pieces'']
* [https://spectropolrecords.bandcamp.com/track/todd-harrop-fifteen-short-pieces ''Fifteen Short Pieces'']
; [[Budjarn Lambeth]]
* [https://www.youtube.com/watch?v=XT2K75X79sE ''Mavila(7) improvisation''] (2026)


; [[Micronaive]]
; [[Micronaive]]
Line 1,171: Line 1,420:


== Related pages ==
== Related pages ==
* [[Lumatone mapping for 30edo]]
* [[Mavila]]
* [[Mavila]]


Retrieved from "https://en.xen.wiki/w/30edo"