30edt: Difference between revisions

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{{Harmonics in equal|30|3|1|intervals=integer|columns=12|start=12|collapsed=1|Approximation of harmonics in 30edt (continued)}}

=== Subsets and supersets ===

Since 30 factors into primes as 2 × 3 × 5, 30edt has subset edts {{EDs|equave=t| 2, 3, 5, 6, 10, and 15 }}.

== Intervals ==

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30edt contains all [[19edo]] intervals within 3/1, all tempered 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 {{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.

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 ==

@@ Line 14: / Line 14: @@
 {{Harmonics in equal|30|3|1|intervals=integer}}
 {{Harmonics in equal|30|3|1|intervals=integer|columns=12|start=12|collapsed=1|Approximation of harmonics in 30edt (continued)}}
+=== Subsets and supersets ===
+Since 30 factors into primes as 2 × 3 × 5, 30edt has subset edts {{EDs|equave=t| 2, 3, 5, 6, 10, and 15 }}.
 == Intervals ==
@@ Line 244: / Line 247: @@
 edt contains all [[19edo]] intervals within 3/1, all tempered 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.
-edt 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.
+edt 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 ==