Theory of palindromic MOS scales or rhythms - Revision history

BudjarnLambeth: Added links (did not edit the text at all, only added links), and also added archive notice

2024-01-09T07:08:44Z

Added links (did not edit the text at all, only added links), and also added archive notice

← Older revision		Revision as of 07:08, 9 January 2024
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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.		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		7 notes: DEFGABC, 7 steps: 2122212
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	2		2

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

BudjarnLambeth: Added to non-scale applications of MOS

2023-04-29T05:17:08Z

Added to non-scale applications of MOS

← Older revision		Revision as of 05:17, 29 April 2023
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	-Joakim Bang Larsen (February 2019)		-Joakim Bang Larsen (February 2019)
	[[Category:MOS scale]]		[[Category:MOS scale]]
			[[Category:Non-scale applications of MOS]]

BudjarnLambeth: “

2023-04-28T22:32:18Z

“

← Older revision		Revision as of 22:32, 28 April 2023
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	-Joakim Bang Larsen (February 2019)		-Joakim Bang Larsen (February 2019)
	[[Category:MOS ~~scales~~]]		[[Category:MOS scale]]

Fredg999 category edits: Removing from Category:Theory using Cat-a-lot

2023-04-23T21:45:45Z

Removing from Category:Theory using Cat-a-lot

← Older revision		Revision as of 21:45, 23 April 2023
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	-Joakim Bang Larsen (February 2019)		-Joakim Bang Larsen (February 2019)
	[[Category:MOS scales]]		[[Category:MOS scales]]
	~~[[Category:Theory]]~~

BudjarnLambeth: Categorised this uncategorised page

2023-04-23T20:14:57Z

Categorised this uncategorised page

← Older revision		Revision as of 20:14, 23 April 2023
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	-Joakim Bang Larsen (February 2019)		-Joakim Bang Larsen (February 2019)
			[[Category:MOS scales]]
			[[Category:Theory]]

Jimble: Changed the text into a fixed width font by applying the "PREFORMATTED" level to the whole text in the visual editor.

2019-02-19T16:13:03Z

Changed the text into a fixed width font by applying the "PREFORMATTED" level to the whole text in the visual editor.

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Jimble: Created page with "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 rhythm..."

2019-02-18T17:34:19Z

Created page with "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 rhythm..."

New page

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 sequences 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. Added together along with the starting note, it turned out that I all of them odd.

And since this palindromic mode is mirror symmetric through and through, all you need to do to find the smaller palindromic sequences was to delete two notes from it, 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:

7 notes: DEFGABC, 7 steps: 2122212

And by chopping of both the end notes repeatedly, we end up with the following patterns that are also palindromic:

DEFGABCD
EFGABC
FGAB
GA

2122212
12221
222
2

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

7 notes: ABCDEFG, 6 steps 212212

And by chopping of both the end notes repeatedly, we end up with the additional patterns that are also palindromic:

ABCDEFG
BCDEF
CDE

212212
1221
22

So now we had a neat way of finding the palindromic mode of a scale and it's counterpart on the other end of the scale (when the scale is viewed as a complete circle anyway), that would let us repeatedly chop of both ends to locate ALL the palindromic patterns.

Still, I could find palindromic patterns that were not part of any of these "parent palindrome" rhythms, like 212 and so the quest was on to find the missing parent that contained the rest of them.

I can't remember how I discovered it, but I know that the rhythm I was working on was 34.21.13, where the palindromic mode is:

13 notes and 13 steps: 3232332332323

By chopping of both the end notes repeatedly, we end up with the additional patterns that are also palindromic:

3232332332323
23233233232
323323323
2332332
33233
323
2

By removing the middle step of it we get the other parent palindromic scale:
13 notes and 12 steps: 332323323233

By chopping of both the end notes repeatedly, we end up with the additional patterns that are also palindromic:

332323323233
3232332323
23233232
323323
2332
33

It was while I was working with this scale I discovered that if you delete either the first or the last note of the symmetrical chain of generators that was used to make the first or primary palindromic mode, that you hit upon a new palindromic parent scale that contained the remaining palindromic patterns.

32332323323
233232332
3323233
32323
232
3

It may be a bit hard to picture this with such an unfamiliar scale, but if we go back to our first example with the diatonic scale, we see that while we already have DEFGABCD and ABCDEFG, we can chop of either F or B from the chain FCGDAEB that was used to generate them both, we end up with either FCGDAE or CGDAEB as the generator chain for our new parent palindromic scale:

CDEFGA
DEFG
EF

22122
212
1

or...

GABCDE
ABCD
BC

22122
212
1

So, depending on your definition of palindromic scale (is a scale consisting of two notes with one step between them a "scale"?), the diatonic scale has the following palindromic step sequences:

2122212, 212212, 12221, 22122, 1221, 222, 212, 22, 2, 1

10 or 8 if you discount the one step patterns.

And for the 34.21.13 scale:

3232332332323, 332323323233, 23233233232, 32332323323, 3232332323, 323323323, 233232332, 23233232, 3323233, 2332332, 323323, 33233, 32323, 2332, 323, 232, 33, 3, 2

A total of 19 or 17 if you discount the one step patterns.

I have no way of verifying if these indeed are all the palindromic step sequences of these MOS scales, but I think that's all of them and I have verified that the method finds them all in two more MOS scales.

It would be fun if someone good with maths could verify if my theory of the three parent palindromic patterns is true.

You might think, what is the point of all of this? But when it comes to rhythm it can now be proven that these three parent palindromic rhythms contain all of the smaller palindromic rhythms and it makes a cool feature of the rhythm generator to be able to rotate the rhythm to the three modes that together contain all of them.

-Joakim Bang Larsen (February 2019)