User:Ganaram inukshuk/Tables

This page is for xen-related tables that I've made but don't have an exact place elsewhere on the wiki (yet).

Golden ratio tunings of mosses

Parent scale	Child scale	Grandchild scale	Great-grandchild scale	4th-order descendant	5th-order descendant	6-order descendant
xL ys	(x+y)L xs	(2x+y)L (x+y)s	(3x+2y)L (2x+y)s	(5x+3y)L (3x+2y)s	(8x+5y)L (5x+3y)s	(13x+8y)L (8x+5y)s

1L 5s	6L 1s	7L 6s	13L 7s	20L 13s	33L 20s	53L 33s
2L 4s	6L 2s	8L 6s	14L 8s	22L 14s	36L 22s	58L 36s
3L 3s	6L 3s	9L 6s	15L 9s	24L 15s	39L 24s	63L 39s
4L 3s	7L 4s	11L 7s	18L 11s	29L 18s	47L 29s	76L 47s
5L 1s	6L 5s	11L 6s	17L 11s	28L 17s	45L 28s	73L 45s

1L 6s	7L 1s	8L 7s	15L 8s	23L 15s	38L 23s	61L 38s
2L 5s	7L 2s	9L 7s	16L 9s	25L 16s	41L 25s	66L 41s
3L 4s	7L 3s	10L 7s	17L 10s	27L 17s	44L 27s	71L 44s
4L 3s	7L 4s	11L 7s	18L 11s	29L 18s	47L 29s	76L 47s
5L 2s	7L 5s	12L 7s	19L 12s	31L 19s	50L 31s	81L 50s
6L 1s	7L 6s	13L 7s	20L 13s	33L 20s	53L 33s	86L 53s

1L 7s	8L 1s	9L 8s	17L 9s	26L 17s	43L 26s	69L 43s
2L 6s	8L 2s	10L 8s	18L 10s	28L 18s	46L 28s	74L 46s
3L 5s	8L 3s	11L 8s	19L 11s	30L 19s	49L 30s	79L 49s
4L 4s	8L 4s	12L 8s	20L 12s	32L 20s	52L 32s	84L 52s
5L 3s	8L 5s	13L 8s	21L 13s	34L 21s	55L 34s	89L 55s
6L 2s	8L 6s	14L 8s	22L 14s	36L 22s	58L 36s	94L 58s
7L 1s	8L 7s	15L 8s	23L 15s	38L 23s	61L 38s	99L 61s

1L 8s	9L 1s	10L 9s	19L 10s	29L 19s	48L 29s	77L 48s
2L 7s	9L 2s	11L 9s	20L 11s	31L 20s	51L 31s	82L 51s
3L 6s	9L 3s	12L 9s	21L 12s	33L 21s	54L 33s	87L 54s
4L 5s	9L 4s	13L 9s	22L 13s	35L 22s	57L 35s	92L 57s
5L 4s	9L 5s	14L 9s	23L 14s	37L 23s	60L 37s	97L 60s
6L 3s	9L 6s	15L 9s	24L 15s	39L 24s	63L 39s	102L 63s
7L 2s	9L 7s	16L 9s	25L 16s	41L 25s	66L 41s	107L 66s
8L 1s	9L 8s	17L 9s	26L 17s	43L 26s	69L 43s	112L 69s

1L 9s	10L 1s	11L 10s	21L 11s	32L 21s	53L 32s	85L 53s
2L 8s	10L 2s	12L 10s	22L 12s	34L 22s	56L 34s	90L 56s
3L 7s	10L 3s	13L 10s	23L 13s	36L 23s	59L 36s	95L 59s
4L 6s	10L 4s	14L 10s	24L 14s	38L 24s	62L 38s	100L 62s
5L 5s	10L 5s	15L 10s	25L 15s	40L 25s	65L 40s	105L 65s
6L 4s	10L 6s	16L 10s	26L 16s	42L 26s	68L 42s	110L 68s
7L 3s	10L 7s	17L 10s	27L 17s	44L 27s	71L 44s	115L 71s
8L 2s	10L 8s	18L 10s	28L 18s	46L 28s	74L 46s	120L 74s
9L 1s	10L 9s	19L 10s	29L 19s	48L 29s	77L 48s	125L 77s

Scale Table

I've had the idea of using a rectangular horogram to represent how mosses of a specific generator pair are related to one another, only to learn that I can copy-paste the entire tables from Excel into the wiki editor. I doubt I'd be the first person to do this, but this would be a nice way to list the mosses of an edo. The idea to include scale and step ratio information occurred mid-editing.

Deployed examples can be found under 17edo mos scales and 31edo mos scales.

Mos Family Tree (single-period only), with TAMNAMS Names italics denote 1L ns scales (named for completeness); asterisks denote non-official names (from my own notes)
Progenitor scale		1st-order child mosses		2nd-order child mosses		3rd-order child mosses		4th-order child mosses		5th-order child mosses
Steps	Scale name	Steps	Scale name	Steps	Scale name	Steps	Scale name	Steps	Scale name	Steps	Scale name
1L 1s	prototonic*	1L 2s	antideuteric*	1L 3s	antitetric*	1L 4s	antimanic	1L 5s	antimachinoid	1L 6s	anti-archeotonic

										6L 1s	archeotonic

								5L 1s	machinoid	5L 6s

										6L 5s

						4L 1s	manic	4L 5s	orwelloid	4L 9s

										9L 4s

								5L 4s	semiquartal	5L 9s

										9L 5s

				3L 1s	tetric*	3L 4s	mosh	3L 7s	sephiroid	3L 10s

										10L 3s

								7L 3s	dicotonic	7L 10s

										10L 7s

						4L 3s	smitonic	4L 7s	kleistonic	4L 11s

										11L 4s

								7L 4s	suprasmitonic	7L 11s

										11L 7s

		2L 1s	deuteric*	2L 3s	pentic	2L 5s	antidiatonic	2L 7s	joanatonic	2L 9s

										9L 2s

								7L 2s	superdiatonic	7L 9s

										9L 7s

						5L 2s	diatonic	5L 7s	p-chromatic	5L 12s	p-superchromatic*

										12L 5s

								7L 5s	m-chromatic	7L 12s

										12L 7s	m-superchromatic*

				3L 2s	antipentic	3L 5s	sensoid	3L 8s		3L 11s

										11L 3s

								8L 3s		8L 11s

										11L 8s

						5L 3s	oneirotonic	5L 8s		5L 13s

										13L 5s

								8L 5s		8L 13s

										13L 8

Family tree limited to 10 notes and with up to 5 periods

Mosses whose children exceed 10 notes are shown in bold. (Stars indicate mosses whose descendants now bear at least a mos intro and infobox mos template. Double stars indicate mosses whose descendants already had those templates. Triple stars indicate that the mos's descendants lack a page.)

Family tree of single-period mosses, limited to 10-note scales
Root		1st-order child scales		2nd-order child scales		3rd-order child scales		4th-order child scales		5th-order child scales		6th-order child scales		7th-order child scales		8th-order child scales
Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name	Mos	Name
1L 1s	trivial	1L 2s	antrial	1L 3s	antetric	1L 4s	pedal	1L 5s	antimachinoid	1L 6s	onyx	1L 7s	antipine	1L 8s	antisubneutralic	1L 9s	antisinatonic *
														1L 8s	antisubneutralic	9L 1s	sinatonic *
														8L 1s	subneutralic **
												7L 1s	pine *
										6L 1s	archaeotonic **
								5L 1s	machinoid *
						4L 1s	manual	5L 4s	semiquartal *
						4L 1s	manual	4L 5s	gramitonic *
				3L 1s	tetric	4L 3s	smitonic *
						3L 4s	mosh	7L 3s	dicoid *
						3L 4s	mosh	3L 7s	sephiroid *
		2L 1s	trial	3L 2s	antipentic	3L 5s	checkertonic *
				3L 2s	antipentic	5L 3s	oneirotonic **
				2L 3s	pentic	5L 2s	diatonic *
						2L 5s	antidiatonic	7L 2s	armotonic **
						2L 5s	antidiatonic	2L 7s	balzano *
Family tree of 2-period mosses, limited to 10-note scales
Root		1st-order child scales		2nd-order child scales		3rd-order child scales
Mos	Name	Mos	Name	Mos	Name	Mos	Name
2L 2s	biwood	2L 4s	malic	2L 6s	subaric	2L 8s	jaric *
				2L 6s	subaric	8L 2s	taric ***
				6L 2s	ekic **
		4L 2s	citric	6L 4s	lemon *
		4L 2s	citric	4L 6s	lime *
Family tree of 3-period mosses, limited to 10-note scales
Root		1st-order child scales
Mos	Name	Mos	Name
3L 3s	triwood	3L 6s	tcherepnin *
3L 3s	triwood	6L 3s	hyrulic *
Family tree of 4-period mosses, limited to 10-note scales
Root
Mos	Name
4L 4s	tetrawood **
Family tree of 5-period mosses, limited to 10-note scales
Root
Mos	Name
5L 5s	pentawood *

Mos Family Tree for an Edo

The basis of this diagram is simple: take the infinite mos family tree and only show the scales that are available for a specific edo.

19edo Example

The table shown below is the mos family tree for 19edo.

Mos Family Tree for 19edo
Generator Pair	18\19 - 1\19	17\19 - 2\19	16\19 - 3\19	15\19 - 4\19	14\19 - 5\19	13\19 - 6\19	12\19 - 7\19	11\19 - 8\19	10\19 - 9\19
Gen. 1	1L 1s
Gen. 2	1L 2s						2L 1s
Gen. 3	1L 3s				3L 1s		3L 2s	2L 3s
Gen. 4	1L 4s			4L 1s	4L 3s	3L 4s	3L 5s	5L 2s	2L 5s
Gen. 5	1L 5s			5L 4s	4L 7s	3L 7s	8L 3s	7L 5s	2L 7s
Gen. 6	1L 6s		6L 1s	5L 9s	4L 11s	3L 10s			2L 9s
Gen. 7	1L 7s		6L 7s			3L 13s			2L 11s
Gen. 8	1L 8s								2L 13s
Gen. 9	1L 9s								2L 15s
Gen. 10	1L 10s
Gen. 11	1L 11s
Gen. 12	1L 12s
Gen. 13	1L 13s
Gen. 14	1L 14s
Gen. 15	1L 15s
Gen. 16	1L 16s
Gen. 17	1L 17s

This tree can be thought of as a pruned mos family tree, where every leaf node corresponds to a mos available to 19edo with a step ratio of 2:1. To conceptualize this tree better, consider the leaf node 7L 5s. Since the entire structure is a binary tree (that is, there are no loopy paths), there is one and only one unique path that starts from 1L 1s and ends at 7L 5s. Likewise, all other leaf nodes have a unique path that, when traversed backwards, merges back with 1L 1s.

Note that all of these paths inevitably overlap. It's important to note that these overlaps are due to each path having multiple mosses in common with one another; for a node with two child nodes, the two child scales don't share the same generator pair, only a common mos from the parent node. Pruning a mos tree by generator pair isolates a single linear path between 1L 1s and the leaf node with the step ratio of 2:1; put another way, the tree would be pruned down to a single, finite branch.

Note the curious case of 1L 7s in this example. It should be the leaf node for the generator pair 17\19 and 2\19, but since that scale is also available to the generator pair of 18\19 and 1\19, it's not and that branch continues to 1L 17s. Technically speaking, the branches for the generator pairs of 18\19-1\19 and 17\19-2\19 coincide.

Mos-edo table

This table shows what edos are possible for a given mos; in other words, given a mos xL ys (where x and y are fixed), L and s can vary to produce different edos (where L > s). The example below is for 12edo. Degenerate cases lie along the edges of the triangle, with the diagonal (in bold) are for edos where L:s = 1:1.

Edos of 5L 2s		Small step size (s)
Edos of 5L 2s		0	1	2	3	4	5	6	7	8	9	10
Large step size (L)	0	0
	1	5	7
	2	10	12	14
	3	15	17	19	21
	4	20	22	24	26	28
	5	25	27	29	31	33	35
	6	30	32	34	36	38	40	42
	7	35	37	39	41	43	45	47	49
	8	40	42	44	46	48	50	52	54	56
	9	45	47	49	51	53	55	57	59	61	63
	10	50	52	54	56	58	60	62	64	66	68	70

An alternate table shows mosses where L:s = 2:1 is on the diagonal, dividing the table into a soft half and a hard half. Here, two additional diagonals are shown in bold, one each for L:s = 3:1 and L:s = 3:2. Rows represent chroma size rather than large step size.

Edos of 5L 2s		Small step size (s)
Edos of 5L 2s		0	1	2	3	4	5	6	7	8	9	10
Chroma size \|L-s\|	0	0	7	14	21	28	35	42	49	56	63	70
	1	5	12	19	26	33	40	47	54	61	68	75
	2	10	17	24	31	38	45	52	59	66	73	80
	3	15	22	29	36	43	50	57	64	71	78	85
	4	20	27	34	41	48	55	62	69	76	83	90
	5	25	32	39	46	53	60	67	74	81	88	95
	6	30	37	44	51	58	65	72	79	86	93	100
	7	35	42	49	56	63	70	77	84	91	98	105
	8	40	47	54	61	68	75	82	89	96	103	110
	9	45	52	59	66	73	80	87	94	101	108	115
	10	50	57	64	71	78	85	92	99	106	113	120

User:Ganaram inukshuk/Tables

Contents

Golden ratio tunings of mosses

Scale Table

Family tree limited to 10 notes and with up to 5 periods

Mos Family Tree for an Edo

19edo Example

Mos-edo table

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User:Ganaram inukshuk/Tables

Golden ratio tunings of mosses

Scale Table

Family tree limited to 10 notes and with up to 5 periods

Mos Family Tree for an Edo

19edo Example

Mos-edo table

Navigation menu

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