Würschmidt diesis spiral progression: Difference between revisions

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===~~Magic~~ spiral for three voices ~~(basic)~~===

The '''Wurschmidt diesis spiral progression''' is a type of chord progression that hinges on the [[Wurschmidt comma]] being tempered out, enabling three instances of [[128/125]] to add up to [[16/15]]. As such, this progression is available in [[EDO]]s that support Wurschmidt temperament, such as [[31edo]] and [[34edo]].

[[File:Meantone diesis spiral.png|thumb|Descending diesis spiral progression in meantone temperament notation.]]

Arguably the best known form of this type of spiral progression is found in 31edo, though there are other, non-meantone interpretations. Regardless, Each chord change effectively moves upward or downward by a Ptolemaic major third, that is, [[5/4]], thus creating a sort of [[Wikipedia: Chromatic mediant|chromatic-mediant]]-type motion.

=== Wurschmidt diesis spiral for three voices ===

{| class="wikitable"

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<ol><li>Decide on downward (C-E-G#-B#) or upward (C-Ab-Fb-Dbb) root movement. We found downward easier almost every time.</li><li>Sing a just major triad (4:5:6), any inversion, open or closed spacing. Tune and match vowel to lowest voice.</li><li>Move in accordance with the chart. Since two people are moving each time, make eye contact to synchronize the change.</li></ol>

After three moves, you will have the same triad one diesis up or down. ~~Keep going if you can!~~

After three moves, you will have the same triad one diesis up or down, and indeed one can keep going.

recording on [u]: [[:File:magic_spiral_basic_(andrew_jacob_ryan)_5_11_07.mp3|magic spiral basic (andrew jacob ryan) 5_11_07.mp3]]

~~=== Explanation ===~~

~~[[File:Meantone diesis spiral.png|thumb|Descending diesis spiral progression in meantone temperament notation.]]~~

~~This progression plays with the 5-limit diesis [[128/125]]. Each chord change effectively modulates upward or downward by a major third (5/4).~~

When played in a meantone temperament that does not temper out 128/125 such as 31edo, stacking three major thirds does not make it close up into an octave, but instead falls short from the octave by one step/diesis. In 12edo, however, three major thirds close up into an octave, and so every third chord in the progression is the same.

[[Category:Method]]

[[Category:Listen]]

[[Category:Augmented]]

@@ Line 1: / Line 1: @@
-===Magic spiral for three voices (basic)===
+The '''Wurschmidt diesis spiral progression''' is a type of chord progression that hinges on the [[Wurschmidt comma]] being tempered out, enabling three instances of [[128/125]] to add up to [[16/15]].  As such, this progression is available in [[EDO]]s that support Wurschmidt temperament, such as [[31edo]] and [[34edo]].
+[[File:Meantone diesis spiral.png|thumb|Descending diesis spiral progression in meantone temperament notation.]]
+Arguably the best known form of this type of spiral progression is found in 31edo, though there are other, non-meantone interpretations.  Regardless, Each chord change effectively moves upward or downward by a Ptolemaic major third, that is, [[5/4]], thus creating a sort of [[Wikipedia: Chromatic mediant|chromatic-mediant]]-type motion.
+=== Wurschmidt diesis spiral for three voices ===
 {| class="wikitable"
@@ Line 22: / Line 28: @@
 <ol><li>Decide on downward (C-E-G#-B#) or upward (C-Ab-Fb-Dbb) root movement. We found downward easier almost every time.</li><li>Sing a just major triad (4:5:6), any inversion, open or closed spacing. Tune and match vowel to lowest voice.</li><li>Move in accordance with the chart. Since two people are moving each time, make eye contact to synchronize the change.</li></ol>
-After three moves, you will have the same triad one diesis up or down. Keep going if you can!
+After three moves, you will have the same triad one diesis up or down, and indeed one can keep going.
 recording on [u]: [[:File:magic_spiral_basic_(andrew_jacob_ryan)_5_11_07.mp3|magic spiral basic (andrew jacob ryan) 5_11_07.mp3]]
-=== Explanation ===
-[[File:Meantone diesis spiral.png|thumb|Descending diesis spiral progression in meantone temperament notation.]]
-This progression plays with the 5-limit diesis [[128/125]]. Each chord change effectively modulates upward or downward by a major third (5/4).
-When played in a meantone temperament that does not temper out 128/125 such as 31edo, stacking three major thirds does not make it close up into an octave, but instead falls short from the octave by one step/diesis. In 12edo, however, three major thirds close up into an octave, and so every third chord in the progression is the same.
 [[Category:Method]]
 [[Category:Listen]]
 [[Category:Augmented]]