User:Ganaram inukshuk/Sandbox

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

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

SB tree

Ratios
1/1
7/6
6/5
5/4
4/3
7/5
3/2
8/5
5/3
7/4
2/1
7/3
5/2
8/3
3/1
7/2
4/1
5/1
6/1
7/1
1/0

Arguments

The template currently supports the following arguments:

Argument	Required?	Description
Tuning	No (optional)	"xL ys" (for 2/1-equivalent mosses), "xL ys<p/q>" or "xL ys⟨p/q⟩" (for non-2/1 mosses), or "xL ys (p/q-equivalent)" (if the tuning is specified in the page's title). If left blank, then the page's title will be used instead, or if not on a mos page, then 5L 2s will be used instead.
ModeNames	No (optional)	A list of names delimited using semicolons. The number of names must match the number of modes or names will not be added. If the tuning is "5L 2s", then mode names (Lydian, Ionian, etc) are automatically added.

Typical use

For most mos pages, simply include the code below. If included on any other page, the template will default to the modes of 5L 2s, including mode names. The number of names must match the number of modes or they won't be included.

{{#invoke:MOS_modes|modes_table}}

Usage with a different tuning

To specify a tuning, include it as shown below. Non-octave tunings are supported.

{{MOS modes|Tuning=5L 3s}}

{{MOS modes|Tuning=4L 5s <3/1>}}

Usage with mode names

Names for each mode are separated by semicolons, as shown below. A mode may have multiple names or a name consisting of multiple words.

{{MOS modes|Tuning=5L 3s|ModeNames=Dylathian, Dylian; Ilarnekian; Celephaïsian; Ultharian; Mnarian; Kadathian, Kadian; Hlanithian, Hlanian; Sarnathian, Sarnian, Sarn}}

{{MOS modes|Tuning=4L 5s <3/1>|ModeNames=Walker I; Walker II; Moll I (Delta); Lambda; Moll II (Pierce); Harmonic; Dur I; Walker A; Walker B}}

Mos intro text

nxL nys <p/q> is a p/q-equivalent moment-of-symmetry (or mos) consisting of x large step and y small steps that repeats n times per equivalence interval. This mos is generated using an interval ranging from g_equalized to g_collapsed cents.

The wording is meant to be as general as possible. Possible changes and additions are made based on the mos and equivalence interval.

• Changes according to the mos:
  • If the mos nxL nys <p/q> is a multi-period mos (n is greater than 1):
    • The words multi-period are added after a p/q-equivalent.
    • The words repeats n times per equivalence interval continues with the words , or once at the period of period_cents.
    • The words repeats n times has n be replaced by the value of n itself.
      • If n is 2, then the wording becomes repeats twice.
  • If the mos nxL nys <p/q> is a single-period mos (n is exactly 1):
    • The words repeats n times is replaced with repeats at the.
• Changes according to the equivalence interval:
  • If the equivalence interval p/q is 2/1:
    • The mos nxL nys <p/q> is replaced with nxL nys, as the absence of an equivalence interval typically refers to an octave-equivalent scale.
    • The words a p/q-equivalent are replaced with octave-equivalent.
    • The words per equivalence interval is replaced with every octave.
• Values:
  • period_cents is the cent value of the period and is expressed both as edsteps and cent values. This value is added only for multi-period mosses.
  • g_equalized and g_collapsed refer to the sizes of the generator, expressed both as edsteps and cent values. These should be calculated using the mos module.
• Links to other pages should also be included, mainly "moment-of-symmetry".