Xenharmonic Wiki

30edo: Difference between revisions

← Older edit
VisualWikitext
Francium (talk | contribs)
4,859 edits
→Music: Sorted list
Eliora (talk | contribs)
autopatrolled, emailconfirmed
3,499 edits
 
(102 intermediate revisions by 15 users not shown)
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
'''30 equal divisions of the octave''' ('''30edo''') is the [[tuning system]] derived by dividing the [[octave]] into 30 equal steps of 40{{cent}} each.
{{ED intro}}


== Theory ==
== Theory ==
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.
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.
=== Odd harmonics ===
{{Harmonics in equal|30}}
{{Harmonics in equal|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 [[Trienstonic_clan#Quindecic|quindecic temperament]].
=== Subsets and supersets ===
30edo has subset edos {{EDOs| 1, 2, 3, 5, 6, 10, 15 }} and it is a [[largely composite]] edo.


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.
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.


Being the smallest positive integer with three distinct prime factors, 30edo is the smallest EDO that supports [[perfectly balanced]] scales that are minimal and not equally spaced. See the article on perfect balance.  
Some multiples of 30edo have high consistency limits - [[270edo]], [[1920edo]], and others are simply useful like [[60edo]]. [[Zinc]] temperament is a rich augmentation of 30edo.


== 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]]
|-
|-
| 0
| 0
Line 23: Line 228:
| unison, minor 2nd
| unison, minor 2nd
| D, Eb
| D, Eb
| 1
|-
|-
| 1
| 1
Line 29: Line 235:
| up unison, upminor 2nd
| up unison, upminor 2nd
| ^D, ^Eb
| ^D, ^Eb
| 2b
|-
|-
| 2
| 2
Line 35: Line 242:
| dup unison, downmid 2nd
| dup unison, downmid 2nd
| ^^D, ^^Eb
| ^^D, ^^Eb
| 9#
|-
|-
| 3
| 3
Line 41: Line 249:
| mid 2nd
| mid 2nd
| v<span style="font-size: 90%; vertical-align: super;">3</span>E
| v<span style="font-size: 90%; vertical-align: super;">3</span>E
| 1#
|-
|-
| 4
| 4
Line 47: Line 256:
| upmid 2nd
| upmid 2nd
| vvE
| vvE
| 2
|-
|-
| 5
| 5
Line 53: Line 263:
| downmajor 2nd
| downmajor 2nd
| vE
| vE
| 3b
|-
|-
| 6
| 6
Line 59: Line 270:
| major 2nd, minor 3rd
| major 2nd, minor 3rd
| E, F
| E, F
| 1x, 4bb
|-
|-
| 7
| 7
Line 65: Line 277:
| upminor 3rd
| upminor 3rd
| ^F
| ^F
| 2#
|-
|-
| 8
| 8
Line 71: Line 284:
| downmid 3rd
| downmid 3rd
| ^^F
| ^^F
| 3
|-
|-
| 9
| 9
Line 77: Line 291:
| mid 3rd
| mid 3rd
| ^<span style="font-size: 90%; vertical-align: super;">3</span>F, v<span style="font-size: 90%; vertical-align: super;">3</span>F#
| ^<span style="font-size: 90%; vertical-align: super;">3</span>F, v<span style="font-size: 90%; vertical-align: super;">3</span>F#
| 4b
|-
|-
| 10
| 10
Line 83: Line 298:
| upmid 3rd
| upmid 3rd
| vvF#
| vvF#
| 5b
|-
|-
| 11
| 11
Line 89: Line 305:
| downmajor 3rd, down 4th
| downmajor 3rd, down 4th
| vF#, vG
| vF#, vG
| 3#
|-
|-
| 12
| 12
| 480
| 480
| P4
| M3, P4
| major 3rd, perfect 4th
| major 3rd, perfect 4th
| F#, G
| F#, G
| 4
|-
|-
| 13
| 13
| 520
| 520
| ^4, ^d5
| ^4
| up 4th, updim 5th
| up 4th
| ^G, ^Ab
| ^G
| 5
|-
|-
| 14
| 14
Line 107: Line 326:
| downmid 4th, downmid 5th
| downmid 4th, downmid 5th
| ^^G, ^^Ab
| ^^G, ^^Ab
| 6b
|-
|-
| 15
| 15
Line 113: Line 333:
| mid 4th, mid 5th
| mid 4th, mid 5th
| ^<span style="font-size: 90%; vertical-align: super;">3</span>G, v<span style="font-size: 90%; vertical-align: super;">3</span>A
| ^<span style="font-size: 90%; vertical-align: super;">3</span>G, v<span style="font-size: 90%; vertical-align: super;">3</span>A
| 4#
|-
|-
| 16
| 16
| 640
| 640
| ^~A4, ^~5
| ^~4, ^~5
| upmid 4th, upmid 5th
| upmid 4th, upmid 5th
| vvG#, vvA
| vvG#, vvA
| 5#
|-
|-
| 17
| 17
| 680
| 680
| vA4, v5
| v5
| downaug 4th, down 5th
| down 5th
| vG#, vA
| vA
| 6
|-
|-
| 18
| 18
| 720
| 720
| P5
| P5, m6
| perfect 5th, minor 6th
| perfect 5th, minor 6th
| A, Bb
| A, Bb
| 7b
|-
|-
| 19
| 19
Line 137: Line 361:
| up 5th, upminor 6th
| up 5th, upminor 6th
| ^A, ^Bb
| ^A, ^Bb
| 5x, 8bb
|-
|-
| 20
| 20
Line 143: Line 368:
| downmid 6th
| downmid 6th
| ^^Bb
| ^^Bb
| 6#
|-
|-
| 21
| 21
Line 149: Line 375:
| mid 6th
| mid 6th
| v<span style="font-size: 90%; vertical-align: super;">3</span>B
| v<span style="font-size: 90%; vertical-align: super;">3</span>B
| 7
|-
|-
| 22
| 22
Line 155: Line 382:
| upmid 6th
| upmid 6th
| vvB
| vvB
| 8b
|-
|-
| 23
| 23
Line 161: Line 389:
| downmajor 6th
| downmajor 6th
| vB
| vB
| 6x, 9bb
|-
|-
| 24
| 24
Line 167: Line 396:
| major 6th, minor 7th
| major 6th, minor 7th
| B, C
| B, C
| 7#
|-
|-
| 25
| 25
Line 173: Line 403:
| upminor 7th
| upminor 7th
| ^C
| ^C
| 8
|-
|-
| 26
| 26
Line 179: Line 410:
| downmid 7th
| downmid 7th
| ^^C
| ^^C
| 9b
|-
|-
| 27
| 27
Line 185: Line 417:
| mid 7th
| mid 7th
| ^<span style="font-size: 90%; vertical-align: super;">3</span>C
| ^<span style="font-size: 90%; vertical-align: super;">3</span>C
| 1b
|-
|-
| 28
| 28
Line 191: Line 424:
| upmid 7th, dud 8ve
| upmid 7th, dud 8ve
| vvC#, vvD
| vvC#, vvD
| 8#
|-
|-
| 29
| 29
Line 197: Line 431:
| downmajor 7th, down 8ve
| downmajor 7th, down 8ve
| vC#, vD
| vC#, vD
| 9
|-
|-
| 30
| 30
Line 203: Line 438:
| major 7th, 8ve
| major 7th, 8ve
| C#, D
| C#, D
| 1
|}
|}


== JI approximation ==
=== Stein–Zimmermann–Gould notation ===
=== Zeta function ===
[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
Below is a plot of the Z function around 30:
{{Sharpness-sharp6-szg}}
 
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 =====
 
<imagemap>
File:30-EDO_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 519 0 679 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 519 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
default [[File:30-EDO_Sagittal.svg]]
</imagemap>
 
===== Evo-SZ flavor =====
 
<imagemap>
File:30-EDO_Evo-SZ_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 495 0 655 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 495 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
default [[File:30-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>
 
==== Second-best fifth notation ====
This notation uses the same sagittal sequence as edos [[35edo #Sagittal notation|35]] and [[40edo #Sagittal notation|40]].


[[File:plot30.png|alt=plot30.png|plot30.png]]
<imagemap>
File:30b_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 479 0 639 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 479 106 [[Fractional_3-limit_notation#Bad-fifths_limma-fraction_notation | limma-fraction notation]]
default [[File:30b_Sagittal.svg]]
</imagemap>


== Rank-2 temperaments ==
== Regular temperament properties ==
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 [[Chromatic_pairs#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.
=== 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.


; MOS scales:
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]]. 


* [[Lovecraft5|Lovecraft[5]]] - 77772
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.
* [[Lovecraft9|Lovecraft[9]]] - 525252522
* [[Lovecraft13|Lovecraft[13]]] - 3223223223222
* Lovecraft[17] - 22221222122212221
* [[Sensi5|Sensi[5]]] - 83838
* [[Sensi8|Sensi[8]]] - 53353353
* [[Sensi11|Sensi[11]]] - 33323332332
* [[Sensi19|Sensi[19]]] - 2121212212121221212
* Mavila[5] - 94944
* Mavila[7] - 5445444
* Mavila[9] - 444414441
* Mavila[16] - 3131313113131311
* Mavila[23] - 21121121121112112112111


== Commas ==
=== Commas ===
30 EDO [[tempers out]] the following [[commas]]. (Note: This assumes the [[val]] {{val| 30 48 70 84 104 111 }}.)
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 247: Line 518:
| 90.22
| 90.22
| Sawa
| Sawa
| Limma, Pythagorean minor sedond
| Blackwood comma, Pythagorean limma
|-
|-
| 5
| 5
Line 254: Line 525:
| 49.17
| 49.17
| Triyo
| Triyo
| Maximal diesis, Porcupine comma
| Porcupine comma, maximal diesis
|-
|-
| 5
| 5
Line 261: Line 532:
| 41.06
| 41.06
| Trigu
| Trigu
| Diesis, augmented comma
| Augmented comma, diesis
|-
|-
| 5
| 5
Line 282: Line 553:
| 35.70
| 35.70
| Zozo
| Zozo
| Slendro diesis
| Semaphoresma, slendro diesis
|-
|-
| 7
| 7
Line 296: Line 567:
| 22.23
| 22.23
| Laquadzo-atrigu
| Laquadzo-atrigu
| Squalentine
| Squalentine comma
|-
|-
| 7
| 7
Line 310: Line 581:
| 13.79
| 13.79
| Zotrigu
| Zotrigu
| Septimal semicomma, Starling comma
| Starling comma, septimal semicomma
|-
|-
| 7
| 7
Line 317: Line 588:
| 13.47
| 13.47
| Rurutriyo
| Rurutriyo
| Octagar
| Octagar comma
|-
|-
| 7
| 7
Line 331: Line 602:
| 5.36
| 5.36
| Saruru-atrigu
| Saruru-atrigu
| Porwell
| Porwell comma
|-
|-
| 7
| 7
Line 387: Line 658:
| 3.03
| 3.03
| Triluyo
| Triluyo
| Wizardharry
| Wizardharry comma
|-
|-
| 11
| 11
Line 397: Line 668:
|}
|}
<references/>
<references/>
== Octave stretch or compression ==
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]].
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 ==
=== MOS scales ===
{{Main|List of MOS scales in 30edo}}
* [[Lovecraft5|Lovecraft[5]]] - 77772
* [[Lovecraft9|Lovecraft[9]]] - 525252522
* [[Lovecraft13|Lovecraft[13]]] - 3223223223222
* Lovecraft[17] - 22221222122212221
* [[Sensi5|Sensi[5]]] - 83838
* [[Sensi8|Sensi[8]]] - 53353353
* [[Sensi11|Sensi[11]]] - 33323332332
* [[Sensi19|Sensi[19]]] - 2121212212121221212
* Mavila[5] - 94944
* Mavila[7] - 5445444
* Mavila[9] - 444414441
* Mavila[16] - 3131313113131311
* Mavila[23] - 21121121121112112112111
=== 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
* [[Blackened Skies]] (approximated from [[Compton]] in [[72edo]]): 8 5 2 3 2 8 2
* Carousel (original/default tuning): 9 4 4 9 4
* Dewdrops (original/default tuning): 4 4 4 5 4 4 5
* Geode (approximated from [[6afdo]]): 7 6 4 9 4
* [[Lost Spirit]] (approximated from [[Meantone]] in [[31edo]]): 7 5 2 3 5 3 5
* Lost phantom (original/default tuning): 8 5 2 2 6 2 5
* Mechanical (approximated from [[16afdo]]): 7 2 8 8 5
* Mushroom (approximated from [[30afdo]]): 7 5 5 3 10
* Nightdrive (original/default tuning): 8 5 4 9 4
* Pelagic (original/default tuning): 8 4 2 4 7 5
* Bathypelagic (original/default tuning): 8 4 2 3 8 5
* Underpass (approximated from [[10afdo]]): 8 9 5 3 5
* Volcanic (approximated from [[16afdo]]): 3 6 8 8 5
=== Polymicrotonal scales ===
* 10-tone 5&6edo scale: 5 1 4 2 3 3 2 4 1 5
* 12-tone 6&10edo scale{{idio}}: 3 2 1 3 3 3 3 2 1 3 3 3
* 12-tone 6&15edo scale{{idio}}: 2 3 3 2 2 3 3 2 2 3 3 2
* 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 ===
* Approximation of [[Pelog]] lima: 3 4 10 3 10
* 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 ==
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 ===
{| class="mw-collapsible mw-collapsed class="wikitable sortable"
|-
! Chord
! Delta signature
! Error
|-
| 0,1,2
| +1+1
| 0.00026
|-
| 0,1,3
| +1+2
| 0.00058
|-
| 0,1,4
| +1+3
| 0.00094
|-
| 0,2,3
| +2+1
| 0.00047
|-
| 0,3,4
| +3+1
| 0.00068
|-
| 0,3,11
| +1+3
| 0.00064
|-
| 0,4,11
| +1+2
| 0.00039
|-
| 0,5,8
| +3+2
| 0.00057
|-
| 0,6,16
| +1+2
| 0.00042
|-
| 0,7,13
| +1+1
| 0.00035
|-
| 0,7,23
| +1+3
| 0.00024
|-
| 0,10,25
| +1+2
| 0.00072
|-
| 0,11,17
| +3+2
| 0.00063
|-
| 0,11,27
| +1+2
| 0.00072
|-
| 0,13,23
| +1+1
| 0.00030
|-
| 0,14,29
| +2+3
| 0.00019
|-
| 0,15,19
| +3+1
| 0.00069
|-
| 0,20,25
| +3+1
| 0.00085
|}
=== Partially delta-rational tetrads ===
{| class="mw-collapsible mw-collapsed class="wikitable sortable"
|-
! Chord
! Delta signature
! Error
|-
| 0,1,2,3
| +1+?+1
| 0.00064
|-
| 0,1,3,4
| +1+?+1
| 0.00097
|-
| 0,1,15,16
| +2+?+3
| 0.00097
|-
| 0,1,15,17
| +1+?+3
| 0.00098
|-
| 0,1,16,17
| +2+?+3
| 0.00060
|-
| 0,1,16,18
| +1+?+3
| 0.00050
|-
| 0,1,17,18
| +2+?+3
| 0.00021
|-
| 0,1,17,19
| +1+?+3
| 0.00002
|-
| 0,1,18,19
| +2+?+3
| 0.00018
|-
| 0,1,18,20
| +1+?+3
| 0.00047
|-
| 0,1,19,20
| +2+?+3
| 0.00058
|-
| 0,1,19,21
| +1+?+3
| 0.00098
|-
| 0,1,20,21
| +2+?+3
| 0.00099
|-
| 0,1,28,29
| +1+?+2
| 0.00086
|-
| 0,2,3,4
| +2+?+1
| 0.00094
|-
| 0,2,6,11
| +1+?+3
| 0.00036
|-
| 0,2,7,12
| +1+?+3
| 0.00063
|-
| 0,2,11,12
| +3+?+2
| 0.00089
|-
| 0,2,11,14
| +1+?+2
| 0.00084
|-
| 0,2,12,13
| +3+?+2
| 0.00044
|-
| 0,2,12,15
| +1+?+2
| 0.00005
|-
| 0,2,13,14
| +3+?+2
| 0.00002
|-
| 0,2,13,16
| +1+?+2
| 0.00095
|-
| 0,2,14,15
| +3+?+2
| 0.00049
|-
| 0,2,15,16
| +3+?+2
| 0.00098
|-
| 0,2,16,20
| +1+?+3
| 0.00053
|-
| 0,2,17,19
| +2+?+3
| 0.00043
|-
| 0,2,17,21
| +1+?+3
| 0.00046
|-
| 0,2,18,20
| +2+?+3
| 0.00036
|-
| 0,3,4,8
| +2+?+3
| 0.00071
|-
| 0,3,5,9
| +2+?+3
| 0.00050
|-
| 0,3,7,12
| +1+?+2
| 0.00017
|-
| 0,3,9,16
| +1+?+3
| 0.00024
|-
| 0,3,16,22
| +1+?+3
| 0.00003
|-
| 0,3,17,18
| +2+?+1
| 0.00085
|-
| 0,3,17,19
| +1+?+1
| 0.00100
|-
| 0,3,17,20
| +2+?+3
| 0.00066
|-
| 0,3,17,21
| +1+?+2
| 0.00006
|-
| 0,3,18,19
| +2+?+1
| 0.00031
|-
| 0,3,18,20
| +1+?+1
| 0.00005
|-
| 0,3,18,21
| +2+?+3
| 0.00055
|-
| 0,3,19,20
| +2+?+1
| 0.00025
|-
| 0,3,19,21
| +1+?+1
| 0.00092
|-
| 0,3,20,21
| +2+?+1
| 0.00081
|-
| 0,3,24,29
| +1+?+3
| 0.00063
|-
| 0,4,5,15
| +1+?+3
| 0.00038
|-
| 0,4,7,12
| +2+?+3
| 0.00062
|-
| 0,4,10,19
| +1+?+3
| 0.00023
|-
| 0,4,11,17
| +1+?+2
| 0.00078
|-
| 0,4,12,13
| +3+?+1
| 0.00099
|-
| 0,4,13,14
| +3+?+1
| 0.00049
|-
| 0,4,13,15
| +3+?+2
| 0.00044
|-
| 0,4,13,16
| +1+?+1
| 0.00005
|-
| 0,4,14,15
| +3+?+1
| 0.00002
|-
| 0,4,14,16
| +3+?+2
| 0.00052
|-
| 0,4,15,16
| +3+?+1
| 0.00054
|-
| 0,4,17,21
| +2+?+3
| 0.00089
|-
| 0,4,18,22
| +2+?+3
| 0.00074
|-
| 0,4,20,25
| +1+?+2
| 0.00030
|-
| 0,4,22,29
| +1+?+3
| 0.00041
|-
| 0,5,6,9
| +3+?+2
| 0.00051
|-
| 0,5,6,18
| +1+?+3
| 0.00011
|-
| 0,5,8,16
| +1+?+2
| 0.00028
|-
| 0,5,9,15
| +2+?+3
| 0.00030
|-
| 0,5,10,14
| +1+?+1
| 0.00027
|-
| 0,5,10,21
| +1+?+3
| 0.00084
|-
| 0,5,11,13
| +2+?+1
| 0.00017
|-
| 0,5,12,14
| +2+?+1
| 0.00078
|-
| 0,5,14,21
| +1+?+2
| 0.00095
|-
| 0,5,15,25
| +1+?+3
| 0.00006
|-
| 0,5,18,23
| +2+?+3
| 0.00093
|-
| 0,5,20,29
| +1+?+3
| 0.00014
|-
| 0,5,22,28
| +1+?+2
| 0.00093
|-
| 0,5,23,24
| +3+?+1
| 0.00073
|-
| 0,5,23,25
| +3+?+2
| 0.00075
|-
| 0,5,23,26
| +1+?+1
| 0.00020
|-
| 0,5,24,25
| +3+?+1
| 0.00009
|-
| 0,5,24,26
| +3+?+2
| 0.00045
|-
| 0,5,25,26
| +3+?+1
| 0.00057
|-
| 0,6,7,21
| +1+?+3
| 0.00086
|-
| 0,6,8,13
| +1+?+1
| 0.00079
|-
| 0,6,10,17
| +2+?+3
| 0.00091
|-
| 0,6,11,20
| +1+?+2
| 0.00026
|-
| 0,6,14,17
| +3+?+2
| 0.00003
|-
| 0,6,19,21
| +2+?+1
| 0.00066
|-
| 0,6,19,23
| +1+?+1
| 0.00086
|-
| 0,6,20,22
| +2+?+1
| 0.00048
|-
| 0,7,8,11
| +2+?+1
| 0.00095
|-
| 0,7,8,12
| +3+?+2
| 0.00035
|-
| 0,7,9,11
| +3+?+1
| 0.00020
|-
| 0,7,9,12
| +2+?+1
| 0.00039
|-
| 0,7,10,12
| +3+?+1
| 0.00074
|-
| 0,7,11,19
| +2+?+3
| 0.00075
|-
| 0,7,13,23
| +1+?+2
| 0.00005
|-
| 0,7,14,28
| +1+?+3
| 0.00034
|-
| 0,7,16,21
| +1+?+1
| 0.00097
|-
| 0,7,18,27
| +1+?+2
| 0.00030
|-
| 0,7,21,24
| +3+?+2
| 0.00028
|-
| 0,7,27,29
| +2+?+1
| 0.00032
|-
| 0,8,10,27
| +1+?+3
| 0.00088
|-
| 0,8,12,21
| +2+?+3
| 0.00022
|-
| 0,8,14,18
| +3+?+2
| 0.00099
|-
| 0,8,15,17
| +3+?+1
| 0.00054
|-
| 0,8,15,18
| +2+?+1
| 0.00001
|-
| 0,8,16,18
| +3+?+1
| 0.00053
|-
| 0,8,22,27
| +1+?+1
| 0.00033
|-
| 0,9,10,15
| +3+?+2
| 0.00013
|-
| 0,9,10,29
| +1+?+3
| 0.00029
|-
| 0,9,12,19
| +1+?+1
| 0.00028
|-
| 0,9,12,25
| +1+?+2
| 0.00000
|-
| 0,9,16,28
| +1+?+2
| 0.00005
|-
| 0,9,19,25
| +1+?+1
| 0.00028
|-
| 0,9,20,24
| +3+?+2
| 0.00025
|-
| 0,9,21,23
| +3+?+1
| 0.00015
|-
| 0,9,21,24
| +2+?+1
| 0.00068
|-
| 0,10,13,17
| +2+?+1
| 0.00052
|-
| 0,10,13,24
| +2+?+3
| 0.00042
|-
| 0,10,15,20
| +3+?+2
| 0.00006
|-
| 0,10,17,24
| +1+?+1
| 0.00005
|-
| 0,10,25,29
| +3+?+2
| 0.00048
|-
| 0,10,26,28
| +3+?+1
| 0.00028
|-
| 0,10,26,29
| +2+?+1
| 0.00061
|-
| 0,11,13,16
| +3+?+1
| 0.00032
|-
| 0,11,17,21
| +2+?+1
| 0.00085
|-
| 0,11,20,25
| +3+?+2
| 0.00095
|-
| 0,12,14,23
| +1+?+1
| 0.00005
|-
| 0,12,17,20
| +3+?+1
| 0.00014
|-
| 0,12,22,26
| +2+?+1
| 0.00081
|-
| 0,12,24,29
| +3+?+2
| 0.00014
|-
| 0,13,18,27
| +1+?+1
| 0.00000
|-
| 0,13,21,24
| +3+?+1
| 0.00013
|-
| 0,14,16,23
| +3+?+2
| 0.00035
|-
| 0,14,19,24
| +2+?+1
| 0.00067
|-
| 0,14,25,28
| +3+?+1
| 0.00040
|-
| 0,15,23,28
| +2+?+1
| 0.00083
|-
| 0,16,19,23
| +3+?+1
| 0.00076
|-
| 0,17,20,28
| +3+?+2
| 0.00099
|-
| 0,17,21,27
| +2+?+1
| 0.00067
|-
| 0,17,22,26
| +3+?+1
| 0.00042
|-
| 0,18,25,29
| +3+?+1
| 0.00042
|-
| 0,19,20,29
| +3+?+2
| 0.00033
|-
| 0,21,23,28
| +3+?+1
| 0.00012
|}
== Instruments ==
[[Lumatone mapping for 30edo|Lumatone mappings for 30edo]] are available.


== Music ==
== Music ==
'''[[Todd Harrop]]'''
=== Modern renderings ===
* [https://spectropolrecords.bandcamp.com/track/todd-harrop-fifteen-short-pieces Fifteen Short Pieces]
; {{W|Evanescence}}
'''[[Micronaive]]'''
* [https://www.youtube.com/watch?v=ppHcUOpbnbI ''Bring Me To Life''] (2003) – microtonal cover in 30edo by [[Bryan Deister]] (2024)
* [https://youtu.be/tAxEetp1TaE No.27.62]
 
; LouisF (Luis Clemente)
* [https://www.youtube.com/shorts/ujkKJekgDhM ''Balatro Main Theme''] via {{W|Balatro}} (2024) – microtonal cover in 30edo by [[Bryan Deister]] (2026)
 
; {{W|Mitski}}
* [https://www.youtube.com/shorts/4MI2opBMkd4 ''Eric''] (2012) – microtonal cover in 30edo by [[Bryan Deister]] (2025)
 
=== 21st century ===
; [[Bryan Deister]]
* [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]]
* [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]]
* [https://youtu.be/tAxEetp1TaE ''No.27.62'']
 
; [[NullPointerException Music]]
* [https://www.youtube.com/watch?v=6gydbVD7Xdc ''Edolian - Shift''] (2020)
 
== Related pages ==
* [[Mavila]]


[[Category:Pelogic]]
[[Category:Pelogic]]
 
[[Category:Todo:add rank 2 temperaments table]]
{{Todo
[[Category:Listen]]
| unify precision
| cleanup
}}
Retrieved from "https://en.xen.wiki/w/30edo"