Xenoindex: rephrasing

2021-06-01T18:40:01Z

rephrasing

← Older revision		Revision as of 18:40, 1 June 2021
Line 8:		Line 8:
	We begin by chunking also known as dividing the scale into segments called chunks that each contain exactly one s on the right-most end.		We begin by chunking also known as dividing the scale into segments called chunks that each contain exactly one s on the right-most end.

	~~Always start~~ chunking from the '''brightest mode''' to avoid ~~extra steps (that I refuse~~ to ~~explain)~~.		Start chunking from the '''brightest mode''' to avoid having to wrap around.

Xenoindex: typo

2021-06-01T16:40:10Z

typo

← Older revision		Revision as of 16:40, 1 June 2021
Line 107:		Line 107:

	{\| class="wikitable"		{\| class="wikitable"
	!MOS!!len!!MOS Production ~~Rule~~		!MOS!!len!!MOS Production Rules
	\|-		\|-
	!2 Notes!! !!		!2 Notes!! !!

Xenoindex: Created page

2021-06-01T16:35:33Z

Created page

New page

[[MOS scale|MOSes]] have a [[Recursive structure of MOS scales|recursive structure]] so they have [https://en.wikipedia.org/wiki/Production_(computer_science) rules to produce] them.

I'm not really sure how to explain what I've done here with words so I'll just show an example worked out by hand.

'''Lets figure out the MOS Production Rules for the 4L3s MOS scale LLsLsLs'''.

We begin by chunking also known as dividing the scale into segments called chunks that each contain exactly one s on the right-most end.

Always start chunking from the '''brightest mode''' to avoid extra steps (that I refuse to explain).

LLsLsLs chunks into the three chunks LLs, Ls, and Ls.

The largest chunk LLs will be replaced with L and the smallest chunk Ls will be replaced with s.

Note the length of the largest chunk LLs is 3, add it to the beginning of a list: '''[3]'''

LLs -> L

Ls -> s

LLsLsLs becomes Lss

Lss chunks into two chunks Ls and s.

The largest chunk Ls will be replaced with L and the smallest chunk s will be replaced with s.

Note the length of the largest chunk is 2, add it to the beginning of the list. '''[2, 3]'''

Ls -> L

s -> s

Lss becomes Ls

Ls chunks into only one chunk so the process is complete.

Note the length of the final chunk is 2, add it to the beginning of the list. '''[2, 2, 3]'''

'''[2, 2, 3] are the production rules for this MOS (LLsLsLs).'''

In a less compact form the production rules [2, 2, 3] would be something like:

axiom: Ls

iteration 1 rules: (L -> Ls), (s -> s)

iteration 2 rules: (L -> LLs), (s -> Ls)

But that isn't as nice and compact as a simple list of numbers.

'''Now to use the production rules [2, 2, 3] to generate the MOS.'''

The first element from the rules ['''2''', 2, 3] is '''2''' which is the axiom.

Start with a chunk size of 2: '''Ls'''

The next element from the rules [2, '''2''', 3] is '''2''' which is the size of chunk to replace each L by.

2 means each L is to be replaced with a chunk of size 2 or the replacement rule: L -> Ls

'''The replacement rule for s is always one smaller than the one for L. (This feels like a discovery)'''

2-1 is 1 so that means each s is to be replaced with a chunk of size 1 or the replacement rule: s -> s

L -> Ls

s -> s

Ls becomes '''Lss'''

The next and final element from the rules [2, 2, '''3'''] is '''3''' which is the size of chunk to replace each L by.

3 means each L is to be replaced with a chunk of size 3 or the replacement rule: L -> LLs

3-1 is 2 so that means each s is to be replaced with a chunk of size 2 or the replacement rule: s -> Ls

L -> LLs

s -> Ls

Lss becomes '''LLsLsLs'''

The end of the production rules has been reached so the process is complete.

The MOS scale of the MOS production rules [2, 2, 3] is: '''LLsLsLs'''

Below is a table of the production rules of all MOSes up to 19 notes.

Red rows are Multi-MOSes.

{| class="wikitable"
!MOS!!len!!MOS Production Rule
|-
!2 Notes!! !!
|-
|1L 1s||1||[ 2 ]
|-
!3 Notes!! !!
|-
|1L 2s||2||[ 2, 2 ]
|-
|2L 1s||1||[ 3 ]
|-
!4 Notes!! !!
|-
|1L 3s||3||[ 2, 2, 2 ]
|-
|2L 2s ||1 ||[ 2 ]
|-
|3L 1s||1||[ 4 ]
|-
!5 Notes!! !!
|-
|1L 4s||4||[ 2, 2, 2, 2 ]
|-
|2L 3s||2||[ 3, 2 ]
|-
|3L 2s||2||[ 2, 3 ]
|-
|4L 1s||1||[ 5 ]
|-
!6 Notes!! !!
|-
|1L 5s||5||[ 2, 2, 2, 2, 2 ]
|-
|2L 4s ||2 ||[ 2, 2 ]
|-
|3L 3s ||1 ||[ 2 ]
|-
|4L 2s ||1 ||[ 3 ]
|-
|5L 1s||1||[ 6 ]
|-
!7 Notes!! !!
|-
|1L 6s||6||[ 2, 2, 2, 2, 2, 2 ]
|-
|2L 5s||3||[ 3, 2, 2 ]
|-
|3L 4s||2||[ 4, 2 ]
|-
|4L 3s||3||[ 2, 2, 3 ]
|-
|5L 2s||2||[ 2, 4 ]
|-
|6L 1s||1||[ 7 ]
|-
!8 Notes!! !!
|-
|1L 7s||7||[ 2, 2, 2, 2, 2, 2, 2 ]
|-
|2L 6s ||3 ||[ 2, 2, 2 ]
|-
|3L 5s||3||[ 2, 3, 2 ]
|-
|4L 4s ||1 ||[ 2 ]
|-
|5L 3s||2||[ 3, 3 ]
|-
|6L 2s ||1 ||[ 4 ]
|-
|7L 1s||1||[ 8 ]
|-
!9 Notes!! !!
|-
|1L 8s||8||[ 2, 2, 2, 2, 2, 2, 2, 2 ]
|-
|2L 7s||4||[ 3, 2, 2, 2 ]
|-
|3L 6s ||2 ||[ 2, 2 ]
|-
|4L 5s||2||[ 5, 2 ]
|-
|5L 4s||4||[ 2, 2, 2, 3 ]
|-
|6L 3s ||1 ||[ 3 ]
|-
|7L 2s||2||[ 2, 5 ]
|-
|8L 1s||1||[ 9 ]
|-
!10 Notes!! !!
|-
|1L 9s||9||[ 2, 2, 2, 2, 2, 2, 2, 2, 2 ]
|-
|2L 8s ||4 ||[ 2, 2, 2, 2 ]
|-
|3L 7s||3||[ 4, 2, 2 ]
|-
|4L 6s ||2 ||[ 3, 2 ]
|-
|5L 5s ||1 ||[ 2 ]
|-
|6L 4s ||2 ||[ 2, 3 ]
|-
|7L 3s||3||[ 2, 2, 4 ]
|-
|8L 2s ||1 ||[ 5 ]
|-
|9L 1s||1||[ 10 ]
|-
!11 Notes!! !!
|-
|1L 10s||10||[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]
|-
|2L 9s||5||[ 3, 2, 2, 2, 2 ]
|-
|3L 8s||4||[ 2, 3, 2, 2 ]
|-
|4L 7s||4||[ 2, 2, 3, 2 ]
|-
|5L 6s||2||[ 6, 2 ]
|-
|6L 5s||5||[ 2, 2, 2, 2, 3 ]
|-
|7L 4s||2||[ 4, 3 ]
|-
|8L 3s||2||[ 3, 4 ]
|-
|9L 2s||2||[ 2, 6 ]
|-
|10L 1s||1||[ 11 ]
|-
!12 Notes!! !!
|-
|1L 11s||11||[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]
|-
|2L 10s ||5 ||[ 2, 2, 2, 2, 2 ]
|-
|3L 9s ||3 ||[ 2, 2, 2 ]
|-
|4L 8s ||2 ||[ 2, 2 ]
|-
|5L 7s||3||[ 2, 4, 2 ]
|-
|6L 6s ||1 ||[ 2 ]
|-
|7L 5s||3||[ 3, 2, 3 ]
|-
|8L 4s ||1 ||[ 3 ]
|-
|9L 3s ||1 ||[ 4 ]
|-
|10L 2s ||1 ||[ 6 ]
|-
|11L 1s||1||[ 12 ]
|-
!13 Notes!! !!
|-
|1L 12s||12||[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]
|-
|2L 11s||6||[ 3, 2, 2, 2, 2, 2 ]
|-
|3L 10s||4||[ 4, 2, 2, 2 ]
|-
|4L 9s||3||[ 5, 2, 2 ]
|-
|5L 8s||3||[ 3, 3, 2 ]
|-
|6L 7s||2||[ 7, 2 ]
|-
|7L 6s||6||[ 2, 2, 2, 2, 2, 3 ]
|-
|8L 5s||3||[ 2, 3, 3 ]
|-
|9L 4s||4||[ 2, 2, 2, 4 ]
|-
|10L 3s||3||[ 2, 2, 5 ]
|-
|11L 2s||2||[ 2, 7 ]
|-
|12L 1s||1||[ 13 ]
|-
!14 Notes!! !!
|-
|1L 13s||13||[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]
|-
|2L 12s ||6 ||[ 2, 2, 2, 2, 2, 2 ]
|-
|3L 11s||5||[ 2, 3, 2, 2, 2 ]
|-
|4L 10s ||3 ||[ 3, 2, 2 ]
|-
|5L 9s||5||[ 2, 2, 2, 3, 2 ]
|-
|6L 8s ||2 ||[ 4, 2 ]
|-
|7L 7s ||1 ||[ 2 ]
|-
|8L 6s ||3 ||[ 2, 2, 3 ]
|-
|9L 5s||2||[ 5, 3 ]
|-
|10L 4s ||2 ||[ 2, 4 ]
|-
|11L 3s||2||[ 3, 5 ]
|-
|12L 2s ||1 ||[ 7 ]
|-
|13L 1s||1||[ 14 ]
|-
!15 Notes!! !!
|-
|1L 14s||14||[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]
|-
|2L 13s||7||[ 3, 2, 2, 2, 2, 2, 2 ]
|-
|3L 12s ||4 ||[ 2, 2, 2, 2 ]
|-
|4L 11s||5||[ 2, 2, 3, 2, 2 ]
|-
|5L 10s ||2 ||[ 2, 2 ]
|-
|6L 9s ||2 ||[ 3, 2 ]
|-
|7L 8s||2||[ 8, 2 ]
|-
|8L 7s||7||[ 2, 2, 2, 2, 2, 2, 3 ]
|-
|9L 6s ||2 ||[ 2, 3 ]
|-
|10L 5s ||1 ||[ 3 ]
|-
|11L 4s||2||[ 4, 4 ]
|-
|12L 3s ||1 ||[ 5 ]
|-
|13L 2s||2||[ 2, 8 ]
|-
|14L 1s||1||[ 15 ]
|-
!16 Notes!! !!
|-
|1L 15s||15||[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]
|-
|2L 14s ||7 ||[ 2, 2, 2, 2, 2, 2, 2 ]
|-
|3L 13s||5||[ 4, 2, 2, 2, 2 ]
|-
|4L 12s ||3 ||[ 2, 2, 2 ]
|-
|5L 11s||3||[ 6, 2, 2 ]
|-
|6L 10s ||3 ||[ 2, 3, 2 ]
|-
|7L 9s||3||[ 2, 5, 2 ]
|-
|8L 8s ||1 ||[ 2 ]
|-
|9L 7s||4||[ 3, 2, 2, 3 ]
|-
|10L 6s ||2 ||[ 3, 3 ]
|-
|11L 5s||5||[ 2, 2, 2, 2, 4 ]
|-
|12L 4s ||1 ||[ 4 ]
|-
|13L 3s||3||[ 2, 2, 6 ]
|-
|14L 2s ||1 ||[ 8 ]
|-
|15L 1s||1||[ 16 ]
|-
!17 Notes!! !!
|-
|1L 16s||16||[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]
|-
|2L 15s||8||[ 3, 2, 2, 2, 2, 2, 2, 2 ]
|-
|3L 14s||6||[ 2, 3, 2, 2, 2, 2 ]
|-
|4L 13s||4||[ 5, 2, 2, 2 ]
|-
|5L 12s||4||[ 2, 4, 2, 2 ]
|-
|6L 11s||6||[ 2, 2, 2, 2, 3, 2 ]
|-
|7L 10s||4||[ 2, 2, 4, 2 ]
|-
|8L 9s||2||[ 9, 2 ]
|-
|9L 8s||8||[ 2, 2, 2, 2, 2, 2, 2, 3 ]
|-
|10L 7s||3||[ 4, 2, 3 ]
|-
|11L 6s||2||[ 6, 3 ]
|-
|12L 5s||3||[ 3, 2, 4 ]
|-
|13L 4s||4||[ 2, 2, 2, 5 ]
|-
|14L 3s||2||[ 3, 6 ]
|-
|15L 2s||2||[ 2, 9 ]
|-
|16L 1s||1||[ 17 ]
|-
!18 Notes!! !!
|-
|1L 17s||17||[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]
|-
|2L 16s ||8 ||[ 2, 2, 2, 2, 2, 2, 2, 2 ]
|-
|3L 15s ||5 ||[ 2, 2, 2, 2, 2 ]
|-
|4L 14s ||4 ||[ 3, 2, 2, 2 ]
|-
|5L 13s||4||[ 3, 3, 2, 2 ]
|-
|6L 12s ||2 ||[ 2, 2 ]
|-
|7L 11s||3||[ 4, 3, 2 ]
|-
|8L 10s ||2 ||[ 5, 2 ]
|-
|9L 9s ||1 ||[ 2 ]
|-
|10L 8s ||4 ||[ 2, 2, 2, 3 ]
|-
|11L 7s||4||[ 2, 2, 3, 3 ]
|-
|12L 6s ||1 ||[ 3 ]
|-
|13L 5s||3||[ 2, 3, 4 ]
|-
|14L 4s ||2 ||[ 2, 5 ]
|-
|15L 3s ||1 ||[ 6 ]
|-
|16L 2s ||1 ||[ 9 ]
|-
|17L 1s||1||[ 18 ]
|-
!19 Notes!! !!
|-
|1L 18s||18||[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]
|-
|2L 17s||9||[ 3, 2, 2, 2, 2, 2, 2, 2, 2 ]
|-
|3L 16s||6||[ 4, 2, 2, 2, 2, 2 ]
|-
|4L 15s||6||[ 2, 2, 3, 2, 2, 2 ]
|-
|5L 14s||6||[ 2, 2, 2, 3, 2, 2 ]
|-
|6L 13s||3||[ 7, 2, 2 ]
|-
|7L 12s||4||[ 3, 2, 3, 2 ]
|-
|8L 11s||3||[ 3, 4, 2 ]
|-
|9L 10s||2||[ 10, 2 ]
|-
|10L 9s||9||[ 2, 2, 2, 2, 2, 2, 2, 2, 3 ]
|-
|11L 8s||4||[ 2, 3, 2, 3 ]
|-
|12L 7s||3||[ 2, 4, 3 ]
|-
|13L 6s||6||[ 2, 2, 2, 2, 2, 4 ]
|-
|14L 5s||2||[ 5, 4 ]
|-
|15L 4s||2||[ 4, 5 ]
|-
|16L 3s||3||[ 2, 2, 7 ]
|-
|17L 2s||2||[ 2, 10 ]
|-
|18L 1s||1||[ 19 ]
|}

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