Theory of palindromic MOS scales or rhythms: Difference between revisions

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While working on a project to make a MOS rhythm generator audio plugin (to be released in 2019), I found out that I liked the sound of mirror symmetrical or palindromic rhythms, rhythms that are the same pattern both forwards and backwards and so I wanted to find a method to wrestle out ALL the palindromic patterns of a single MOS rhythm.

While working on a project to make a [[MOS rhythm]] generator audio plugin (to be released in 2019), I found out that I liked the sound of mirror symmetrical or palindromic rhythms, rhythms that are the same pattern both forwards and backwards and so I wanted to find a method to wrestle out ALL the palindromic patterns of a single MOS rhythm.

I knew how to make the whole MOS scale palindromic, by using the same amount of positive and negative ~~generators~~. And that only all the palindromic subsets of MOS scales of ODD cardinality could be found in this way. So for MOS scales of even cardinality, the process described here won't work because there is no palindromic mode for the whole scale.

I knew how to make the whole [[MOS scale]] palindromic, by using the same amount of positive and negative [[generator]]s. And that only all the palindromic subsets of MOS scales of ODD cardinality could be found in this way. So for MOS scales of even cardinality, the process described here won't work because there is no palindromic mode for the whole scale.

Since this primary palindromic mode is of course mirror symmetric through and through, all you need to do to find smaller palindromic subsets was to delete two notes from it at a time, one from either end.

A trivial example of this would be the diatonic scale. By using the same amount of positive and negative generators, we end up with the following pattern, which we call the dorian mode:

A trivial example of this would be the [[diatonic scale]]. By using the same amount of positive and negative generators, we end up with the following pattern, which we call the dorian mode:

7 notes: DEFGABC, 7 steps: 2122212

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Paul Erlich then showed me that by removing the middle step of the primary palindromic mode while leaving the notes untouched, would give you another secondary scale which was also palindromic:

[[Paul Erlich]] then showed me that by removing the middle step of the primary palindromic mode while leaving the notes untouched, would give you another secondary scale which was also palindromic:

7 notes: ABCDEFG, 6 steps 212212

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I know of no present mathematical way of verifying if these are indeed ALL the palindromic subsets of these MOS scales, but I think that's all of them and can verify that the method has worked for all the other MOS scales I have tried it on.

-Joakim Bang Larsen (February 2019)

-[[Joakim Bang Larsen]] (February 2019)

[[Category:MOS ~~scales~~]]

[[Category:MOS scale]]

[[Category:Non-scale applications of MOS]]

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-  While working on a project to make a MOS rhythm generator audio plugin (to be released in 2019), I found out that I liked the sound of mirror symmetrical or palindromic rhythms, rhythms that are the same pattern both forwards and backwards and so I wanted to find a method to wrestle out ALL the palindromic patterns of a single MOS rhythm.
+{{archive}}
+  While working on a project to make a [[MOS rhythm]] generator audio plugin (to be released in 2019), I found out that I liked the sound of mirror symmetrical or palindromic rhythms, rhythms that are the same pattern both forwards and backwards and so I wanted to find a method to wrestle out ALL the palindromic patterns of a single MOS rhythm.
-  I knew how to make the whole MOS scale palindromic, by using the same amount of positive and negative generators.  And that only all the palindromic subsets of MOS scales of ODD cardinality could be found in this way. So for MOS scales of even cardinality, the process described here won't work because there is no palindromic mode for the whole scale.
+  I knew how to make the whole [[MOS scale]] palindromic, by using the same amount of positive and negative [[generator]]s.  And that only all the palindromic subsets of MOS scales of ODD cardinality could be found in this way. So for MOS scales of even cardinality, the process described here won't work because there is no palindromic mode for the whole scale.
   Since this primary palindromic mode is of course mirror symmetric through and through, all you need to do to find smaller palindromic subsets was to delete two notes from it at a time, one from either end.
-  A trivial example of this would be the diatonic scale. By using the same amount of positive and negative generators, we end up with the following pattern, which we call the dorian mode:
+  A trivial example of this would be the [[diatonic scale]]. By using the same amount of positive and negative generators, we end up with the following pattern, which we call the dorian mode:
 notes: DEFGABC, 7 steps: 2122212
@@ Line 21: / Line 23: @@
-  Paul Erlich then showed me that by removing the middle step of the primary palindromic mode while leaving the notes untouched, would give you another secondary scale which was also palindromic:
+  [[Paul Erlich]] then showed me that by removing the middle step of the primary palindromic mode while leaving the notes untouched, would give you another secondary scale which was also palindromic:
 notes: ABCDEFG, 6 steps 212212
@@ Line 109: / Line 111: @@
   I know of no present mathematical way of verifying if these are indeed ALL the palindromic subsets of these MOS scales, but I think that's all of them and can verify that the method has worked for all the other MOS scales I have tried it on.
-  -Joakim Bang Larsen (February 2019)
+  -[[Joakim Bang Larsen]] (February 2019)
-[[Category:MOS scales]]
+[[Category:MOS scale]]
+[[Category:Non-scale applications of MOS]]