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{{Infobox ET}}
{{Infobox ET}}
'''[[Edt|Division of the third harmonic]] into 30 equal parts''' (30edt) is related to [[19edo|19 edo]], but with the [[3/1]] rather than the [[2/1]] being [[just]]. The octave is [[octave stretch|stretched]] by about 4.5715 [[cents]] and the step size is about 63.3985 cents. It is [[consistent]] to the 10-[[integer-limit]].
{{ED intro}}
 
30edt is related to [[19edo]], but with the [[3/1]] rather than the [[2/1]] being [[just]], which results in octaves being is [[stretched and compressed tuning|stretched]] by about 4.5715{{cent}} and the step size is about. It is [[consistent]] to the 10-[[integer-limit]].


Because [[19edo]] has the 3rd, 5th, 7th, and 13th [[harmonic]]s all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 (tritave) is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.
Because [[19edo]] has the 3rd, 5th, 7th, and 13th [[harmonic]]s all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 (tritave) is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.
Line 6: Line 8:
While the fifth is just, the fourth is noticeably sharper and less accurate than in 19edo, being close to that of [[26edo]].
While the fifth is just, the fourth is noticeably sharper and less accurate than in 19edo, being close to that of [[26edo]].


30edt is a [[phoenix]] tuning and exhibits all the benefits of such tunings.
30edt is a [[Phoenix]] tuning and exhibits all the benefits of such tunings.


==Harmonics==
== Harmonics ==
{{Harmonics in equal
{{Harmonics in equal
| steps = 30
| steps = 30
Line 24: Line 26:
}}
}}


==Intervals of 30edt==
== Intervals of 30edt ==
{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
! Degrees
! Degrees
! Cents
! Cents
!Hekts
! Hekts
! Approximate Ratios
! Approximate Ratios
! Lambda scale name
! Lambda scale name
Line 37: Line 39:
| 0
| 0
| 0
| 0
| <span style="color: #660000;">[[1/1|1/1]]</span>
| <span style="color: #660000;">[[1/1]]</span>
| colspan="2" | C
| colspan="2" | C
|-
|-
| | 1
| 1
| | 63.3985
| 63.3985
| 43.333
| 43.333
| | 28/27, 27/26
| 28/27, 27/26
| C^/Dbv
| C^/Dbv
| | C#/Dbb
| C#/Dbb
|-
|-
| | 2
| 2
| | 126.797
| 126.797
| 86.667
| 86.667
| | [[14/13|14/13]], [[15/14|15/14]], [[16/15|16/15]], 29/27
| [[14/13]], [[15/14]], [[16/15]], 29/27
| Db
| Db
| | Cx/Db
| Cx/Db
|-
|-
| | 3
| 3
| | 190.1955
| 190.1955
| 130
| 130
| | 10/9~9/8
| 10/9~9/8
| C#
| C#
| | D
| D
|-
|-
| | 4
| 4
| | 253.594
| 253.594
| 173.333
| 173.333
| | [[15/13|15/13]]
| [[15/13]]
| C#^/Dv
| C#^/Dv
| | D#/Ebb
| D#/Ebb
|-
|-
| | 5
| 5
| | 316.9925
| 316.9925
| 216.667
| 216.667
| | 6/5
| 6/5
| D
| D
| | Dx/Eb
| Dx/Eb
|-
|-
| | 6
| 6
| | 380.391
| 380.391
| 260
| 260
| | <span style="color: #660000;">[[5/4|5/4]]</span>
| <span style="color: #660000;">[[5/4]]</span>
| D^/Ev
| D^/Ev
| | E
| E
|-
|-
| | 7
| 7
| | 443.7895
| 443.7895
| 303.333
| 303.333
| | 9/7
| 9/7
| E
| E
| | E#/Fbb
| E#/Fbb
|-
|-
| | 8
| 8
| | 507.188
| 507.188
| 346.667
| 346.667
| | [[4/3|4/3]]
| [[4/3]]
| E^/Fbv
| E^/Fbv
| | Ex/Fb
| Ex/Fb
|-
|-
| | 9
| 9
| | 570.5865
| 570.5865
| 390
| 390
| | 7/5
| 7/5
| Fb
| Fb
| | F
| F
|-
|-
| | 10
| 10
| | 633.985
| 633.985
| 433.333
| 433.333
| | [[13/9|13/9]]
| [[13/9]]
| E#
| E#
| | F#/Gb
| F#/Gb
|-
|-
| | 11
| 11
| | 697.3835
| 697.3835
| 476.667
| 476.667
| | 3/2
| 3/2
| E#^/Fv
| E#^/Fv
| | G
| G
|-
|-
| | 12
| 12
| | 760.782
| 760.782
| 520
| 520
| | <span style="color: #660000;">[[14/9|14/9]]</span>
| <span style="color: #660000;">[[14/9]]</span>
| F
| F
| | G#/Hbb
| G#/Hbb
|-
|-
| | 13
| 13
| | 824.1805
| 824.1805
| 563.333
| 563.333
| | 8/5
| 8/5
| F^/Gv
| F^/Gv
| | Gx/Hb
| Gx/Hb
|-
|-
| | 14
| 14
| | 887.579
| 887.579
| 606.667
| 606.667
| | [[5/3|5/3]]
| [[5/3]]
| G
| G
| | H
| H
|-
|-
| | 15
| 15
| | 950.9775
| 950.9775
| 650
| 650
| | 19/11
| 19/11
| G^/Hbv
| G^/Hbv
| | H#/Jbb
| H#/Jbb
|-
|-
| | 16
| 16
| | 1014.376
| 1014.376
| 693.333
| 693.333
| | [[9/5|9/5]]
| [[9/5]]
| Hb
| Hb
| | Hx/Jb
| Hx/Jb
|-
|-
| | 17
| 17
| | 1077.7745
| 1077.7745
| 736.667
| 736.667
| | 13/7
| 13/7
| G#
| G#
| | J
| J
|-
|-
| | 18
| 18
| | 1141.173
| 1141.173
| 780
| 780
| | <span style="color: #660000;">[[27/14|27/14]]</span>
| <span style="color: #660000;">[[27/14]]</span>
| G#^/Hv
| G#^/Hv
| | J#/Kbb
| J#/Kbb
|-
|-
| | 19
| 19
| | 1204.5715
| 1204.5715
| 823.333
| 823.333
| | 2/1
| 2/1
|H
| H
| | Jx/Kb
| Jx/Kb
|-
|-
| | 20
| 20
| | 1267.97
| 1267.97
| 866.667
| 866.667
| | [[27/13|27/13]]
| [[27/13]]
| H^/Jv
| H^/Jv
| | K
| K
|-
|-
| | 21
| 21
| | 1331.3685
| 1331.3685
| 910
| 910
| | 28/13
| 28/13
| J
| J
| | K#/Lb
| K#/Lb
|-
|-
| | 22
| 22
| | 1394.767
| 1394.767
| 953.333
| 953.333
| | [[9/4|9/4]] ([[9/8|9/8]] plus an octave)
| [[9/4]] ([[9/8]] plus an octave)
| J^/Av
| J^/Av
| | L
| L
|-
|-
| | 23
| 23
| | 1458.1655
| 1458.1655
| 996.667
| 996.667
| | 7/3
| 7/3
| A
| A
| | L#/Abb
| L#/Abb
|-
|-
| | 24
| 24
| | 1521.564
| 1521.564
| 1040
| 1040
| | [[12/5|12/5]] (<span style="color: #660000;">[[6/5|6/5]]</span> plus an octave)
| [[12/5]] (<span style="color: #660000;">[[6/5]]</span> plus an octave)
| A^/Bbv
| A^/Bbv
| | Lx/Ab
| Lx/Ab
|-
|-
| | 25
| 25
| | 1584.9625
| 1584.9625
| 1083.333
| 1083.333
| | 5/2
| 5/2
| Bb
| Bb
| | A
| A
|-
|-
| | 26
| 26
| | 1648.361
| 1648.361
| 1126.667
| 1126.667
| | [[13/5|13/5]] ([[13/10|13/10]] plus an octave)
| [[13/5]] ([[13/10]] plus an octave)
| A#
| A#
| | A#/Bbb
| A#/Bbb
|-
|-
| | 27
| 27
| | 1711.7595
| 1711.7595
| 1170
| 1170
| | 8/3
| 8/3
| A#^/Bv
| A#^/Bv
| | Ax/Bb
| Ax/Bb
|-
|-
| | 28
| 28
| | 1775.158
| 1775.158
| 1213.333
| 1213.333
| | [[14/5|14/5]] ([[7/5|7/5]] plus an octave)
| [[14/5]] ([[7/5]] plus an octave)
| | B
| B
|-
|-
| | 29
| 29
| | 1838.5565
| 1838.5565
| 1256.667
| 1256.667
| | 26/9
| 26/9
| B^/Cv
| B^/Cv
| | B#/Cb
| B#/Cb
|-
|-
| | 30
| 30
| | 1901.955
| 1901.955
| 1300
| 1300
| | [[3/1|3/1]]
| [[3/1]]
| colspan="2" | C
| colspan="2" | C
|}
|}


30edt contains all [[19edo|19edo]] intervals within 3/1, all temepered progressively sharper. The accumulation of the .241 cent sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615 cents flatter than that in 6edo.
30edt contains all [[19edo]] intervals within 3/1, all temepered progressively sharper. The accumulation of the 0.241{{c}} sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615{{c}} flatter than that in 6edo.


30edt also contains all the MOS contained in 15edt, being the double of this equal division. Being even, 30edt introduces MOS with an even number of periods per tritave such as a 6L 6s similar to Hexe Dodecatonic. This MOS has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a "real" 3/2, the interval of 11 degrees generates an unfair Sigma scale of 8L 3s and the major scale is LLLsLLLsLLs. The sharp 9/7 of 7 degrees, in addition to generating a Lambda MOS will generate a 4L 9s unfair Superlambda MOS which does not border on being atonal as the 17edt rendition does.
30edt also contains all the MOS contained in 15edt, being the double of this equal division. Being even, 30edt introduces MOS with an even number of periods per tritave such as a {{sl|6L 6s}} similar to Hexe Dodecatonic. This MOS has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a "real" 3/2, the interval of 11 degrees generates an unfair Sigma scale of {{sl|8L 3s}} and the major scale is LLLsLLLsLLs. The sharp 9/7 of 7 degrees, in addition to generating a Lambda MOS will generate a {{sl|4L 9s}} unfair "Superlambda" MOS which does not border on being atonal as the 17edt rendition does.


== Music ==
== Music ==
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; [[Ray Perlner]]
; [[Ray Perlner]]
* [https://www.youtube.com/watch?v=fEQ13hzs3fY ''Fugue for Piano in 30EDT Bohlen-Pierce-Stearns<nowiki>[</nowiki>9<nowiki>]</nowiki> sLsLssLsL "Dur I"''] (2024)
* [https://www.youtube.com/watch?v=fEQ13hzs3fY ''Fugue for Piano in 30EDT Bohlen-Pierce-Stearns{{lbrack}}9{{rbrack}} sLsLssLsL "Dur I"''] (2024)


[[Category:Edt]]
[[Category:Edt]]
[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/30edt"