36edo: Difference between revisions

Line 15:

As a 5-limit temperament, the patent val for 36edo is [[Wedgies and Multivals|contorted]], meaning there are notes of it which cannot be reached from the unison using only 5-limit intervals. A curious alternative val for the 5-limit is <36 65 116| which is not contorted. It is also a meantone val, in the sense that 81/80 is tempered out. However, the "comma" {{monzo|29 0 -9}} is also tempered out, and the "fifth", 29\36, is actually approximately 7/4, whereas the "major third", 44\36, is actually approximately 7/3. Any 5-limit musical piece or scale which is a [[transversal]] for a meantone piece or scale will be converted to a no-fives piece tempering out 1029/1024 in place of 81/80 by applying this val.

Another 5-limit alternative val {{monzo|36 57 83}} (36c-edo), which maps 5/4 to the 367-cent submajor third rather than the major third, supports very sharp [[porcupine]] temperament using 5\36 as a generator. Heinz Bohlen proposed it as a suitable temperament for approximating his 833-cents scale. The 13th harmonic (octave reduced) is so closely mapped on [[acoustic phi]] that 36edo could be treated as a 2.3.7.ϕ.17

Another 5-limit alternative val {{monzo|36 57 83}} (36c-edo), which maps 5/4 to the 367-cent submajor third rather than the major third, supports very sharp [[porcupine]] temperament using 5\36 as a generator.

Heinz Bohlen proposed 36edo as a suitable temperament for approximating his 833-cents scale. The 13th harmonic (octave reduced) is so closely mapped on [[acoustic phi]] that 36edo could be treated as a 2.3.7.ϕ.17

=== Prime harmonics ===

@@ Line 15: / Line 15: @@
 As a 5-limit temperament, the patent val for 36edo is [[Wedgies and Multivals|contorted]], meaning there are notes of it which cannot be reached from the unison using only 5-limit intervals. A curious alternative val for the 5-limit is &lt;36 65 116| which is not contorted. It is also a meantone val, in the sense that 81/80 is tempered out. However, the "comma" {{monzo|29 0 -9}} is also tempered out, and the "fifth", 29\36, is actually approximately 7/4, whereas the "major third", 44\36, is actually approximately 7/3. Any 5-limit musical piece or scale which is a [[transversal]] for a meantone piece or scale will be converted to a no-fives piece tempering out 1029/1024 in place of 81/80 by applying this val.
-Another 5-limit alternative val {{monzo|36 57 83}} (36c-edo), which maps 5/4 to the 367-cent submajor third rather than the major third, supports very sharp [[porcupine]] temperament using 5\36 as a generator. Heinz Bohlen proposed it as a suitable temperament for approximating his 833-cents scale. The 13th harmonic (octave reduced) is so closely mapped on [[acoustic phi]] that 36edo could be treated as a 2.3.7.ϕ.17
+Another 5-limit alternative val {{monzo|36 57 83}} (36c-edo), which maps 5/4 to the 367-cent submajor third rather than the major third, supports very sharp [[porcupine]] temperament using 5\36 as a generator.
+Heinz Bohlen proposed 36edo as a suitable temperament for approximating his 833-cents scale. The 13th harmonic (octave reduced) is so closely mapped on [[acoustic phi]] that 36edo could be treated as a 2.3.7.ϕ.17
 === Prime harmonics ===
 {{harmonics in equal|36}}