Diaphonic cycle: Difference between revisions

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A diaphonic cycle is a type of scale described by [[Erv Wilson]] which joins two ~~overtone (~~harmonic) or ~~undertone (~~subharmonic) series segments together at a junction or disjunction, and then repeats.

A diaphonic cycle is a type of scale described by [[Erv Wilson]] which joins two harmonic or subharmonic series segments together at a junction or disjunction, and then repeats.

For example, one of the subharmonic genus, using a junction:

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! scale step !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 (Junction) !! 8 !! 9 !! 10 !! 11 !! 12 !! (1)

|-

| upper section || || || || || || || 21/21 || 21/20 || 21/19 || 21/18 || 21/17 || 21/16 || (21/15)

| '''upper section''' <br> (subharmonics 21 - 15, rebased onto 20/14 = 10/7) || || || || || || || 21/21 || 21/20 || 21/19 || 21/18 || 21/17 || 21/16 || (21/15)

|-

| lower section || 20/20 || 20/19 || 20/18 || 20/17 || 20/16 || 20/15 || 20/14 || || || || || ||

| '''lower section''' <br> (subharmonics 20 - 14) || 20/20 || 20/19 || 20/18 || 20/17 || 20/16 || 20/15 || 20/14 || || || || || ||

|-

| combined scale || 60/60 || 60/57 || 60/54 || 60/51 || 60/48 || 60/45 || 60/42 || 60/40 || 60/38 || 60/36 || 60/34 || 60/32 || (60/30)

| '''combined scale''' <br> (using LCM) || 60/60 || 60/57 || 60/54 || 60/51 || 60/48 || 60/45 || 60/42 || 60/40 || 60/38 || 60/36 || 60/34 || 60/32 || (60/30)

|-

| reduced || 1/1 || 20/19 || 10/9 || 20/17 || 5/4 || 4/3 || 10/7 || 3/2 || 30/19 || 5/3 || 30/17 || 15/8 || (2/1)

| '''combined scale''' <br> (reduced to lowest terms) || 1/1 || 20/19 || 10/9 || 20/17 || 5/4 || 4/3 || 10/7 || 3/2 || 30/19 || 5/3 || 30/17 || 15/8 || (2/1)

|}

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* http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/chapter8.pdf

* http://anaphoria.com/helixintro.html

[[Category:Erv Wilson]]

[[Category:Harmonic series]]

[[Category:Subharmonic series]]

[[Category:Terms]]

[[Category:Scale]]

@@ Line 1: / Line 1: @@
-A diaphonic cycle is a type of scale described by [[Erv Wilson]] which joins two overtone (harmonic) or undertone (subharmonic) series segments together at a junction or disjunction, and then repeats.
+A diaphonic cycle is a type of scale described by [[Erv Wilson]] which joins two harmonic or subharmonic series segments together at a junction or disjunction, and then repeats.
 For example, one of the subharmonic genus, using a junction:
@@ Line 7: / Line 7: @@
 ! scale step !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 (Junction) !! 8 !! 9 !! 10 !! 11 !! 12 !! (1)
 |-
-| upper section || || || || || || || 21/21 || 21/20 || 21/19 || 21/18 || 21/17 || 21/16 || (21/15)
+| '''upper section''' <br> (subharmonics 21 - 15, rebased onto 20/14 = 10/7) || || || || || || || 21/21 || 21/20 || 21/19 || 21/18 || 21/17 || 21/16 || (21/15)
 |-
-| lower section || 20/20 || 20/19 || 20/18 || 20/17 || 20/16 || 20/15 || 20/14 || || || || || ||
+| '''lower section''' <br> (subharmonics 20 - 14) || 20/20 || 20/19 || 20/18 || 20/17 || 20/16 || 20/15 || 20/14 || || || || || ||
 |-
-| combined scale || 60/60 || 60/57 || 60/54 || 60/51 || 60/48 || 60/45 || 60/42 || 60/40 || 60/38 || 60/36 || 60/34 || 60/32 || (60/30)
+| '''combined scale''' <br> (using LCM) || 60/60 || 60/57 || 60/54 || 60/51 || 60/48 || 60/45 || 60/42 || 60/40 || 60/38 || 60/36 || 60/34 || 60/32 || (60/30)
 |-
-| reduced || 1/1 || 20/19 || 10/9 || 20/17 || 5/4 || 4/3 || 10/7 || 3/2 || 30/19 || 5/3 || 30/17 || 15/8 || (2/1)
+| '''combined scale''' <br> (reduced to lowest terms) || 1/1 || 20/19 || 10/9 || 20/17 || 5/4 || 4/3 || 10/7 || 3/2 || 30/19 || 5/3 || 30/17 || 15/8 || (2/1)
 |}
@@ Line 21: / Line 21: @@
 * http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/chapter8.pdf
 * http://anaphoria.com/helixintro.html
+[[Category:Erv Wilson]]
+[[Category:Harmonic series]]
+[[Category:Subharmonic series]]
+[[Category:Terms]]
+[[Category:Scale]]