User:Ganaram inukshuk/Sandbox

This is a sandbox page for me (Ganaram) to test out a few things before deploying things. (Expect some mess.)

Test area

Expanding the mos intro

Two pieces of additional information that may be worth adding are:

• The specific step pattern for the true mos. (The template will have a link to the page for rotations.)
• Small edos (or ed<p/q>'s) that support the mos.
• For mosses with more than 10 notes, that the mos descends from another, TAMNAMS-named mos and how it relates back to that ancestor mos. This requires standardizing the naming scheme for descendant mosses before it can be added.

The following sections show how these additions may be worded.

Addition of step patterns

xL ys<p/q>, also called mosname, is a moment-of-symmetry scale that consists of x large steps(s) and y small step(s), repeating every equave. Scales of this form have a step pattern of step-pattern or some rotation thereof, with a generator that ranges from g1¢ to g2¢ or from d1¢ or d2¢. Equal divisions of the equave that support this scale's step pattern include (2x+y)ed<p/q> (L = 2 and s = 1), (3x+y)ed<p/q> (L = 3 and s = 1), and (3x+2y)ed<p/q> (L = 3 and s = 2).

nxL nys<p/q>, also called mosname, is a moment-of-symmetry scale that consists of nx large steps(s) and ny small step(s), with a period of x large step(s) and y small steps(s) that repeats every equave-fraction, or n times every equave. Scales of this form have a step pattern of step-pattern or some rotation thereof, with a generator that ranges from g1¢ to g2¢ or from d1¢ or d2¢. Equal divisions of the equave that support this scale's step pattern include (2nx+ny)ed<p/q> (L = 2 and s = 1), (3nx+ny)ed<p/q> (L = 3 and s = 1), and (3nx+2ny)ed<p/q> (L = 3 and s = 2).

Adding mos descendant names

xL ys<p/q>, also called mosname, is a(n) extension scale of the moment-of-symmetry scale zL ws, expanded to x large steps(s) and y small step(s), repeating every equave. Scales of this form have a step pattern of step-pattern or some rotation thereof, with a generator that ranges from g1¢ to g2¢ or from d1¢ or d2¢. Equal divisions of the equave that support this scale's step pattern include (2nx+ny)ed<p/q> (L = 2 and s = 1), (3nx+ny)ed<p/q> (L = 3 and s = 1), and (3nx+2ny)ed<p/q> (L = 3 and s = 2).

nxL nys<p/q>, also called mosname, is a(n) extension scale of the moment-of-symmetry scale nzL nws, expanded to nx large steps(s) and ny small step(s), with a period of x large step(s) and y small steps(s) that repeats every equave-fraction, or n times every equave. Scales of this form have a step pattern of step-pattern or some rotation thereof, with a generator that ranges from g1¢ to g2¢ or from d1¢ or d2¢. Equal divisions of the equave that support this scale's step pattern include (2x+y)ed<p/q> (L = 2 and s = 1), (3x+y)ed<p/q> (L = 3 and s = 1), and (3x+2y)ed<p/q> (L = 3 and s = 2).

Examples

5L 7s, also called (hard) diachromatic or p-chromatic, is a chromatic scale of the moment-of-symmetry scale 5L 2s, expanded to 5 large steps and 7 small steps, repeating every octave. This scale has a step pattern of LssLsLsLssLs, or some rotation thereof, with a generator that ranges from 700¢ to 720¢, or from 480¢ to 500¢. Equal divisions of the octave that support this scale's step pattern include 17edo, 22edo, and 29edo.

Mos degrees template with new code

Template to call module without affecting the current template (fill in arguments as needed):

{{#invoke:MOS_degrees_v2|mos_degrees_frame
|Scale Signature=
|Step Ratio=
|MOS Prefix=
|Show Abbreviations=
|JI Ratios=
|Notation=
|UDP=
}}

Instances of module for testing:

Mos degrees template (version 2) mockup

Scale degree of 4L 3s

Scale degree	Abbrev.	On J	11edo (Basic, L:s = 2:1)		15edo (Hard, L:s = 3:1)		18edo (Soft, L:s = 3:2)		Approx. JI Ratios
			Steps	Cents	Steps	Cents	Steps	Cents
Perfect 0-smistep	P0md	J	0	0	0	0	0	0	1/1 (exact), 1/1
Augmented 0-smistep	A0md	J&	1	109.1	2	160	1	66.7
Diminished 1-smistep	d1md	K@@	0	0	-1	-80	1	66.7
Minor 1-smistep	m1md	K@	1	109.1	1	80	2	133.3
Major 1-smistep	M1md	K	2	218.2	3	240	3	200
Augmented 1-smistep	A1md	K&	3	327.3	5	400	4	266.7
Diminished 2-smistep	d2md	L@	2	218.2	2	160	4	266.7
Perfect 2-smistep	P2md	L	3	327.3	4	320	5	333.3
Augmented 2-smistep	A2md	L&	4	436.4	6	480	6	400
2× Augmented 2-smistep	AA2md	L&&	5	545.5	8	640	7	466.7
Diminished 3-smistep	d3md	M@@	3	327.3	3	240	6	400
Minor 3-smistep	m3md	M@	4	436.4	5	400	7	466.7
Major 3-smistep	M3md	M	5	545.5	7	560	8	533.3
Augmented 3-smistep	A3md	M&	6	654.5	9	720	9	600
Diminished 4-smistep	d4md	N@	5	545.5	6	480	9	600
Minor 4-smistep	m4md	N	6	654.5	8	640	10	666.7
Major 4-smistep	M4md	N&	7	763.6	10	800	11	733.3
Augmented 4-smistep	A4md	N&&	8	872.7	12	960	12	800
2× Diminished 5-smistep	dd5md	O@@	6	654.5	7	560	11	733.3
Diminished 5-smistep	d5md	O@	7	763.6	9	720	12	800
Perfect 5-smistep	P5md	O	8	872.7	11	880	13	866.7
Augmented 5-smistep	A5md	O&	9	981.8	13	1040	14	933.3
Diminished 6-smistep	d6md	P@	8	872.7	10	800	14	933.3
Minor 6-smistep	m6md	P	9	981.8	12	960	15	1000
Major 6-smistep	M6md	P&	10	1090.9	14	1120	16	1066.7
Augmented 6-smistep	A6md	P&&	11	1200	16	1280	17	1133.3
Diminished 7-smistep	d7md	J@	10	1090.9	13	1040	17	1133.3
Perfect 7-smistep	P7md	J	11	1200	15	1200	18	1200	2/1 (exact)

Step sizes template

User:MOS degrees is deprecated. Please use Template:MOS tunings instead.

Scale degree of 4L 3s

Scale degree	11edo (Basic, L:s = 2:1)		Approx. JI Ratios
	Steps	Cents
Perfect 0-smidegree (unison)	0	0	1/1 (exact)
Minor 1-smidegree	1	109.1
Major 1-smidegree	2	218.2
Perfect 2-smidegree	3	327.3
Augmented 2-smidegree	4	436.4
Minor 3-smidegree	4	436.4
Major 3-smidegree	5	545.5
Minor 4-smidegree	6	654.5
Major 4-smidegree	7	763.6
Diminished 5-smidegree	7	763.6
Perfect 5-smidegree	8	872.7
Minor 6-smidegree	9	981.8
Major 6-smidegree	10	1090.9
Perfect 7-smidegree (octave)	11	1200	2/1 (exact)

3L 4s step sizes

Interval	Basic 3L 4s (10edo, L:s = 2:1)		Hard 3L 4s (13edo, L:s = 3:1)		Soft 3L 4s (17edo, L:s = 3:2)		Approx. JI ratios
	Steps	Cents	Steps	Cents	Steps	Cents
Large step	2	240¢	3	276.9¢	3	211.8¢	Hide column if no ratios given
Small step	1	120¢	1	92.3¢	2	141.2¢
Bright generator	3	360¢	4	369.2¢	5	355.6¢

Notes:

• Allow option to show the bright generator, dark generator, or no generator.
• JI ratios column only shows if there are any ratios to show

Mbox template test

These would be their own templates.

Stub page:

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

Page needs cleanup (with example reason):

This article may require cleanup. Reason: page contains advanced concepts. You can edit this page to improve it.

Page under construction:

This article is being created or in the process of being rewritten, and is not yet ready for use. You are welcome to help with editing this page.

Math symbols test

Isolated symbols

[math]\displaystyle{ T := [ t_1, t_2, ..., t_m ] }[/math] [math]\displaystyle{ S := [ s_1, s_2, ..., s_m ] }[/math] [math]\displaystyle{ P := [ p_1, p_2, ..., p_n ] }[/math]

Sample text

Pulled from muddle page.

Let the target scale T be a sequence of steps [ t1, t2, t3, ... , tm ], the parent scale P be a sequence of steps [ p1, p2, p3, ... , pn ], and the resulting muddle scale S be a sequence of steps [ s1, s2, s3, ... , sm ]. Note that the number of steps in P must be equal to the sum of all ti from T. Also note that both ti and pi are both numeric values, as with si.

The first step s1 of the muddle scale is the sum of the first t1 steps from P, the next step s2 is the sum of the next t2 steps after that (after the previous t1 steps), the next step s3 is the sum of the next t3 steps after that (after the previous t1+t2 steps), and so on, where the last step sm is the sum of the last tm steps from P. For example, if s1 is made from the first 3 steps of P (p1, p2, and p3), then the next step p2 is the sum of the next t2 steps after p3, meaning the sum starts at (and includes) p4.

Interval and degree tables

The following two tables were made using a custom program (dubbed Moscalc and Modecalc) whose output is formatted for use with MediaWiki.

Intervals of 2L 5s for each mode

Mode	UDP	Rotational order	mosunison	1-mosstep	2-mosstep	3-mosstep	4-mosstep	5-mosstep	6-mosstep	mosoctave
LssLsss	6|0	0	0	L	L+s	L+2s	2L+2s	2L+3s	2L+4s	2L+5s
LsssLss	5|1	3	0	L	L+s	L+2s	L+3s	2L+3s	2L+4s	2L+5s
sLssLss	4|2	6	0	s	L+s	L+2s	L+3s	2L+3s	2L+4s	2L+5s
sLsssLs	3|3	2	0	s	L+s	L+2s	L+3s	L+4s	2L+4s	2L+5s
ssLssLs	2|4	5	0	s	2s	L+2s	L+3s	L+4s	2L+4s	2L+5s
ssLsssL	1|5	1	0	s	2s	L+2s	L+3s	L+4s	L+5s	2L+5s
sssLssL	0|6	4	0	s	2s	3s	L+3s	L+4s	L+5s	2L+5s

Degrees of 2L 5s for each mode

Mode	UDP	Rotational order	0-mosdegree	1-mosdegree	2-mosdegree	3-mosdegree	4-mosdegree	5-mosdegree	6-mosdegree	7-mosdegree
LssLsss	6|0	0	perfect	major	major	perfect	augmented	major	major	perfect
LsssLss	5|1	3	perfect	major	major	perfect	perfect	major	major	perfect
sLssLss	4|2	6	perfect	minor	major	perfect	perfect	major	major	perfect
sLsssLs	3|3	2	perfect	minor	major	perfect	perfect	minor	major	perfect
ssLssLs	2|4	5	perfect	minor	minor	perfect	perfect	minor	major	perfect
ssLsssL	1|5	1	perfect	minor	minor	perfect	perfect	minor	minor	perfect
sssLssL	0|6	4	perfect	minor	minor	diminished	perfect	minor	minor	perfect

Note: don't merge cells on a table with sorting.

Intervals of 2L 5s for each mode (with mode names)

Mode	Mode name	UDP	Rotational order	mosunison	1-mosstep	2-mosstep	3-mosstep	4-mosstep	5-mosstep	6-mosstep	mosoctave
LssLsss	antilocrian	6|0	0	0	L	L+s	L+2s	2L+2s	2L+3s	2L+4s	2L+5s
LsssLss	antiphrygian	5|1	3	0	L	L+s	L+2s	L+3s	2L+3s	2L+4s	2L+5s
sLssLss	anti-aeolian	4|2	6	0	s	L+s	L+2s	L+3s	2L+3s	2L+4s	2L+5s
sLsssLs	antidorian	3|3	2	0	s	L+s	L+2s	L+3s	L+4s	2L+4s	2L+5s
ssLssLs	antimixolydian	2|4	5	0	s	2s	L+2s	L+3s	L+4s	2L+4s	2L+5s
ssLsssL	anti-ionian	1|5	1	0	s	2s	L+2s	L+3s	L+4s	L+5s	2L+5s
sssLssL	antilydian	0|6	4	0	s	2s	3s	L+3s	L+4s	L+5s	2L+5s

Degrees of 2L 5s for each mode (with mode names)

Mode	Mode name	UDP	Rotational order	0-mosdegree	1-mosdegree	2-mosdegree	3-mosdegree	4-mosdegree	5-mosdegree	6-mosdegree	7-mosdegree
LssLsss	antilocrian	6|0	0	perfect	major	major	perfect	augmented	major	major	perfect
LsssLss	antiphrygian	5|1	3	perfect	major	major	perfect	perfect	major	major	perfect
sLssLss	anti-aeolian	4|2	6	perfect	minor	major	perfect	perfect	major	major	perfect
sLsssLs	antidorian	3|3	2	perfect	minor	major	perfect	perfect	minor	major	perfect
ssLssLs	antimixolydian	2|4	5	perfect	minor	minor	perfect	perfect	minor	major	perfect
ssLsssL	anti-ionian	1|5	1	perfect	minor	minor	perfect	perfect	minor	minor	perfect
sssLssL	antilydian	0|6	4	perfect	minor	minor	diminished	perfect	minor	minor	perfect

Alternate mos tables

Pattern	Number of notes	Number of periods	Name	Prefix
1L 1s	2	1	trivial	triv-
1L 1s	2	1	monowood	monowd-
1L 2s	3	1	antrial	atri-
2L 1s	3	1	trial	tri-
1L 3s	4	1	antetric	atetra-
2L 2s	4	2	biwood	biwd-
3L 1s	4	1	tetric	tetra-
1L 4s	5	1	pedal	ped-
2L 3s	5	1	pentic	pent-
3L 2s	5	1	antipentic	apent-
4L 1s	5	1	manual	manu-
1L 5s	6	1	antimachinoid	amech-
2L 4s	6	2	anticitric	acitro-
3L 3s	6	3	triwood	triwd-
4L 2s	6	2	citric	citro-
5L 1s	6	1	machinoid	mech-
1L 6s	7	1	onyx	on-
2L 5s	7	1	antidiatonic	pel-
3L 4s	7	1	mosh	mosh-
4L 3s	7	1	smitonic	smi-
5L 2s	7	1	diatonic	none
6L 1s	7	1	arch(a)eotonic	arch-
1L 7s	8	1	antipine	apine-
2L 6s	8	2	antiekic	anek-
3L 5s	8	1	checkertonic	check-
4L 4s	8	4	tetrawood; diminished	tetwd-
5L 3s	8	1	oneirotonic	neiro-
6L 2s	8	2	ekic	ek-
7L 1s	8	1	pine	pine-
1L 8s	9	1	antisubneutralic	ablu-
2L 7s	9	1	balzano	bal- /bæl/
3L 6s	9	3	tcherepnin	cher-
4L 5s	9	1	gramitonic	gram-
5L 4s	9	1	semiquartal	cthon-
6L 3s	9	3	hyrulic	hyru-
7L 2s	9	1	superdiatonic	arm-
8L 1s	9	1	subneutralic	blu-
1L 9s	10	1	antisinatonic	asina-
2L 8s	10	2	jaric	jara-
3L 7s	10	1	sephiroid	seph-
4L 6s	10	2	lime	lime-
5L 5s	10	5	pentawood	penwd-
6L 4s	10	2	lemon	lem-
7L 3s	10	1	dicoid /'daɪkɔɪd/	dico-
8L 2s	10	2	taric	tara-
9L 1s	10	1	sinatonic	sina-

Scale trees of 1L 1s, 1L 2s, and 2L 1s (sandbox)

Generator						Bright gen.	Dark gen.	L	s	L/s	Ranges of mosses
1\2						600.000	600.000	1	1	1.000
					6\11	654.545	545.455	6	5	1.200	2L 5s range (includes 2L 7s and 7L 2s)
				5\9		666.667	533.333	5	4	1.250
					9\16	675.000	525.000	9	7	1.286
			4\7			685.714	514.286	4	3	1.333	Basic 2L 3s
					11\19	694.737	505.263	11	8	1.375	5L 2s range (includes 7L 5s and 5L 7s)
				7\12		700.000	500.000	7	5	1.400
					10\17	705.882	494.118	10	7	1.429
		3\5				720.000	480.000	3	2	1.500	Basic 2L 1s
					11\18	733.333	466.667	11	7	1.571	5L 3s range
				8\13		738.462	461.538	8	5	1.600
					13\21	742.857	457.143	13	8	1.625
			5\8			750.000	450.000	5	3	1.667	Basic 3L 2s
					12\19	757.895	442.105	12	7	1.714	3L 5s range
				7\11		763.636	436.364	7	4	1.750
					9\14	771.429	428.571	9	5	1.800
	2\3					800.000	400.000	2	1	2.000	Basic 1L 1s (dividing line between 2L 1s and 1L 2s)
					9\13	830.769	369.231	9	4	2.250	3L 4s range (includes 3L 7s and 7L 3s)
				7\10		840.000	360.000	7	3	2.333
					12\17	847.059	352.941	12	5	2.400
			5\7			857.143	342.857	5	2	2.500	Basic 3L 1s
					13\18	866.667	333.333	13	5	2.600	4L 3s range
				8\11		872.727	327.273	8	3	2.667
					11\15	880.000	320.000	11	4	2.750
		3\4				900.000	300.000	3	1	3.000	Basic 1L 2s
					10\13	923.077	276.923	10	3	3.333	Range of 1L 4s (includes 4L 5s and 5L 4s)
				7\9		933.333	266.667	7	2	3.500
					11\14	942.857	257.143	11	3	3.667
			4\5			960.000	240.000	4	1	4.000	Basic 1L 4s
					9\11	981.818	218.182	9	2	4.500	Range of 4L 1s (includes 5L 1s and 1L 5s)
				5\6		1000.000	200.000	5	1	5.000
					6\7	1028.571	171.429	6	1	6.000
1\1						1200.000	0.000	1	0	→ inf

Module and template sandbox

Mos ancestors and descendants

2nd ancestor	1st ancestor	Mos	1st descendants	2nd descendants
uL vs	zL ws	xL ys	xL (x+y)s	xL (2x+y)s
				(2x+y)L xs
			(x+y)L xs	(2x+y)L (x+y)s
				(x+y)L (2x+y)s