User:Ganaram inukshuk/Sandbox

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

{{subst:User:Ganaram inukshuk/JI ratios|Int Limit=50|Prime Limit=7|Equave=2/1}}

produces

1/1, 50/49, 49/48, 36/35, 28/27, 25/24, 21/20, 16/15, 15/14, 27/25, 49/45, 35/32, 10/9, 28/25, 9/8, 8/7, 7/6, 32/27, 25/21, 6/5, 49/40, 5/4, 32/25, 9/7, 35/27, 21/16, 4/3, 27/20, 49/36, 48/35, 25/18, 7/5, 45/32, 10/7, 36/25, 35/24, 40/27, 3/2, 32/21, 49/32, 14/9, 25/16, 8/5, 45/28, 49/30, 5/3, 42/25, 27/16, 12/7, 7/4, 16/9, 25/14, 9/5, 49/27, 50/27, 28/15, 15/8, 40/21, 48/25, 27/14, 35/18, 49/25, 2/1

MOS intro

First sentence:

Single-period 2/1-equivalent: xL ys (TAMNAMS name tamnams-name), also called other-name, is an octave-repeating moment of symmetry scale that divides the octave (2/1) into x large and y small steps.
Multi-period 2/1-equivalent: nxL nys (TAMNAMS name tamnams-name), also called other-name, is an octave-repeating moment of symmetry scale that divides the octave (2/1) into nx large steps and ny small steps, with n periods of c cents containing x large and y small steps each.
Single-period 3/1-equivalent: 3/1-equivalent xL ys, also called other-name, is a twelfth-repeating moment of symmetry scale that divides the tritave or perfect 12th (3/1, c cents) into x large and y small steps.
Multi-period 3/1-equivalent: 3/1-equivalent nxL nys, also called other-name, is a twelfth-repeating moment of symmetry scale that divides the tritave or perfect 12th (3/1, nc cents) into nx large steps and ny small steps, with n periods of c cents containing x large and y small steps each.
Single-period 3/2-equivalent: 3/2-equivalent xL ys, also called other-name, is a fifth-repeating moment of symmetry scale that divides the perfect 5th (3/2, c cents) into x large and y small steps.
Multi-period 3/2-equivalent: 3/2-equivalent nxL nys, also called other-name, is a fifth-repeating moment of symmetry scale that divides the perfect 5th (3/2, nc cents) into nx large steps and ny small steps, with n periods of c cents containing x large and y small steps each.

Second sentence:

Generators that produce this scale range from g1 cents to g2 cents, or from d1 cents to d2 cents.

Octave-equivalent relational info:

Parents of mosses with 6-10 steps: xL ys is the parent scale of both child-soft and child-hard.
Children of mosses with 6-10 steps: xL ys expands parent-scale by adding step-count-difference tones.

Rothenprop:

Single-period: Scales of this form are always proper because there is only one small step.
Multi-period: Scales of this form, where every period is the same, are proper because there is only one small step per period.

Sandbox for proposed templates

Cent ruler

50

L

s

L

s

MOS characteristics

NOTE: not suitable for displaying intervals or scale degrees. Repurpose for other content.

Scale degrees of the modes of 5L 2s
UDP	Cyclic order	Step pattern	Scale degree (diadegree)
UDP	Cyclic order	Step pattern	0	1	2	3	4	5	6	7
6\|0	1	LLLsLLs	Perf.	Maj.	Maj.	Aug.	Perf.	Maj.	Maj.	Perf.
5\|1	5	LLsLLLs	Perf.	Maj.	Maj.	Perf.	Perf.	Maj.	Maj.	Perf.
4\|2	2	LLsLLsL	Perf.	Maj.	Maj.	Perf.	Perf.	Maj.	Min.	Perf.
3\|3	6	LsLLLsL	Perf.	Maj.	Min.	Perf.	Perf.	Maj.	Min.	Perf.
2\|4	3	LsLLsLL	Perf.	Maj.	Min.	Perf.	Perf.	Min.	Min.	Perf.
1\|5	7	sLLLsLL	Perf.	Min.	Min.	Perf.	Perf.	Min.	Min.	Perf.
0\|6	4	sLLsLLL	Perf.	Min.	Min.	Perf.	Dim.	Min.	Min.	Perf.

Intervals of 5L 2s
Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.	Steps subtended	Range in cents
0-diastep	Perfect 0-diastep	P0dias	0	0.0¢
1-diastep	Minor 1-diastep	m1dias	s	0.0¢ to 171.4¢
1-diastep	Major 1-diastep	M1dias	L	171.4¢ to 240.0¢
2-diastep	Minor 2-diastep	m2dias	L + s	240.0¢ to 342.9¢
2-diastep	Major 2-diastep	M2dias	2L	342.9¢ to 480.0¢
3-diastep	Perfect 3-diastep	P3dias	2L + s	480.0¢ to 514.3¢
3-diastep	Augmented 3-diastep	A3dias	3L	514.3¢ to 720.0¢
4-diastep	Diminished 4-diastep	d4dias	2L + 2s	480.0¢ to 685.7¢
4-diastep	Perfect 4-diastep	P4dias	3L + s	685.7¢ to 720.0¢
5-diastep	Minor 5-diastep	m5dias	3L + 2s	720.0¢ to 857.1¢
5-diastep	Major 5-diastep	M5dias	4L + s	857.1¢ to 960.0¢
6-diastep	Minor 6-diastep	m6dias	4L + 2s	960.0¢ to 1028.6¢
6-diastep	Major 6-diastep	M6dias	5L + s	1028.6¢ to 1200.0¢
7-diastep	Perfect 7-diastep	P7dias	5L + 2s	1200.0¢

Tamnams suggests the name NAME for this scale, which comes from ORIGIN. Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.

4

5

6

7

8

9

MOS intervals (using large/small instead of MmAPd)

Intervals of 5L 2s
Interval	Size(s)	Steps	Range in cents	Abbrev.
0-diastep (root)	Perfect 0-diastep	0	0.0¢	P0ms
1-diastep	Small 1-diastep	s	0.0¢ to 171.4¢	s1ms
1-diastep	Large 1-diastep	L	171.4¢ to 240.0¢	L1ms
2-diastep	Small 2-diastep	L + s	240.0¢ to 342.9¢	s2ms
2-diastep	Large 2-diastep	2L	342.9¢ to 480.0¢	L2ms
3-diastep	Small 3-diastep	2L + s	480.0¢ to 514.3¢	s3ms
3-diastep	Large 3-diastep	3L	514.3¢ to 720.0¢	L3ms
4-diastep	Small 4-diastep	2L + 2s	480.0¢ to 685.7¢	s4ms
4-diastep	Large 4-diastep	3L + s	685.7¢ to 720.0¢	L4ms
5-diastep	Small 5-diastep	3L + 2s	720.0¢ to 857.1¢	s5ms
5-diastep	Large 5-diastep	4L + s	857.1¢ to 960.0¢	L5ms
6-diastep	Small 6-diastep	4L + 2s	960.0¢ to 1028.6¢	s6ms
6-diastep	Large 6-diastep	5L + s	1028.6¢ to 1200.0¢	L6ms
7-diastep (octave)	Perfect 7-diastep	5L + 2s	1200.0¢	P7ms

MOS mode degrees (using large/small instead of MmAPd)

Scale degree qualities of 5L 2s modes
Mode names		Ordering		Step pattern	Scale degree
Default	Names	Bri.	Rot.	Step pattern	0	1	2	3	4	5	6	7
5L 2s 6\|0	Lydian	1	1	LLLsLLs	Perf.	Lg.	Lg.	Lg.	Lg.	Lg.	Lg.	Perf.
5L 2s 5\|1	Ionian (major)	2	5	LLsLLLs	Perf.	Lg.	Lg.	Sm.	Lg.	Lg.	Lg.	Perf.
5L 2s 4\|2	Mixolydian	3	2	LLsLLsL	Perf.	Lg.	Lg.	Sm.	Lg.	Lg.	Sm.	Perf.
5L 2s 3\|3	Dorian	4	6	LsLLLsL	Perf.	Lg.	Sm.	Sm.	Lg.	Lg.	Sm.	Perf.
5L 2s 2\|4	Aeolian (minor)	5	3	LsLLsLL	Perf.	Lg.	Sm.	Sm.	Lg.	Sm.	Sm.	Perf.
5L 2s 1\|5	Phrygian	6	7	sLLLsLL	Perf.	Sm.	Sm.	Sm.	Lg.	Sm.	Sm.	Perf.
5L 2s 0\|6	Locrian	7	4	sLLsLLL	Perf.	Sm.	Sm.	Sm.	Sm.	Sm.	Sm.	Perf.

KB vis

Type

Visualization

Individual steps

Notes

Start

Large step

Small step

End

Small vis

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Not enough room for note names.

Large vis

┌──┬─┬─┬─┬─┬─┬──┬──┬─┬─┬─┬──┬───┐
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Black squares indicate notes one equave apart.

Contains shading characters, meant for spacing.

Type

Visualization

Individual steps

Notes

Start

Size 1

Size 2

Size 3

Size 4

Size 5

End

Multisize vis (large)

┌────┬───┬──┬───┬──┬─┬─┬────┬────┬─┬─┬──┬─┬─┬────┬──────┐
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└──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘

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──┐
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──┘

X's are placeholders for note names.

Naturals only, as there is not enough room for accidentals.

May not display correctly on some devices.

Testing with unintrusive filler characters

TAMNAMS use

This article assumes TAMNAMS conventions for naming scale degrees, intervals, and step ratios.

Names for the scale degrees of xL ys, the position of the scales tones, are called mosdegrees, or prefixdegrees. Its intervals, the pitch difference between any two tones, are based on the number of large and small steps between them and are called mossteps, or prefixsteps. Both mosdegrees and mossteps use 0-indexed numbering, as opposed to using 1-indexed ordinals, such as mos-1st instead of 0-mosstep. The use of 1-indexed ordinal names is discouraged for nondiatonic MOS scales.

JI ratio intro

For general ratios: m/n, also called interval-name, is a p-limit just intonation ratio of exactly/about r¢.

For harmonics: m/1, also called interval-name, is a just intonation ration that represents the mth harmonic of exactly/about r¢.

MOS step sizes

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
Interval	Steps	Cents	Steps	Cents	Steps	Cents	Approx. JI ratios
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

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
			xL (x+y)s	(2x+y)L xs
			(x+y)L xs	(2x+y)L (x+y)s
			(x+y)L xs	(x+y)L (2x+y)s

Encoding scheme for module:mos

Mossteps as a vector of L's and s's

For an arbitrary step sequence consisting of L's and s's, the sum of the quantities of L's and s's denotes what mosstep it is. EG, "LLLsL" is a 5-mosstep since it has 5 L's and s's total. This can be expressed as a vector denoting how many L's and s's there are. EG, "LLLsL" becomes { 4, 1 }, denoting 4 large steps and 1 small step.

Alterations by adding a chroma always adds one L and subtracts one s (or subtracts one L and adds one s, if lowering by a chroma), so the sum of L's and s's, even if one of the quantities is negative, will always denote what k-mosstep that interval is. EG, raising "LLLsL" by a chroma produces the vector { 5, 0 }, and raising it by another chroma produces the vector { 6, -1 }.

Through this, the "original size" of the interval can always be deduced.

EG, the vector { 6, -2 } is given, assuming a mos of 5L 2s. Adding 6 and -2 shows that the interval is a 4-mosstep. Taking the brightest mode of 5L 2s (LLLsLLs) and truncating it to the first 4 steps (LLLs), the corresponding vector is { 3, 1 }. This is the vector to compare to. Subtracting the given vector from the comparison vector ( as { 6-3, -2-1 }) produces the vector { 3, -3 }, meaning that { 6, -2 } is the large 4-mosstep raised by 3 chromas. (A shortcut can be employed by simply subtracting only the L-values.) The decoding scheme below shows how the "large 4-mosstep plus 3 chromas" can be decoded into more familiar terms. In this example, since the large 4-mosstep is the perfect bright generator, adding 3 chromas makes it triply augmented.

Encoding scheme
Value	Encoded		Decoded
Value	Intervals with 2 sizes	Intervals with 1 size	Nonperfectable intervals	Bright gen	Dark gen	Period intervals
2	Large plus 2 chromas	Perfect plus 2 chromas	2× Augmented	2× Augmented	3× Augmented	2× Augmented
1	Large plus 1 chroma	Perfect plus 1 chroma	Augmented	Augmented	2× Augmented	Augmented
0	Large	Perfect	Major	Perfect	Augmented	Perfect
-1	Small	Perfect minus 1 chroma	Minor	Diminished	Perfect	Diminished
-2	Small minus 1 chroma	Perfect minus 2 chromas	Diminished	2× Diminished	Diminished	2× Diminished
-3	Small minus 2 chromas	Perfect minus 3 chromas	2× Diminished	3× Diminished	2× Diminished	3× Diminished

Rationale:

Vectors of L's and s's can always be translated back to the original k-mosstep, no matter how many chromas were added. The "unmodified" vector (the large k-mosstep, or perfect k-mosstep for period intervals) can be compared with the mosstep vector to produce the number of chromas.
- Alterations by entire large steps or small steps is considered interval arithmetic.

Easy to translate values to number of chromas for mos notation. Best done with notation assigned to the brightest mode, but can be adapted for arbitrary notations by adjusting the approprite chroma offsets.

Examples of encodings for 5L 2s

Interval encodings for 5L 2s
Interval in mossteps	Encoding		Decoding	Standard notation in the key of F
Interval in mossteps	Mossteps	Chroma	Decoding	Standard notation in the key of F
0	0	0	Perfect 0-diastep	F
s	1	-1	Minor 1-diastep	Gb
L	1	0	Major 1-diastep	G
L + s	2	-1	Minor 2-diastep	Ab
2L	2	0	Major 2-diastep	A
2L + s	3	-1	Perfect 3-diastep	Bb
3L	3	0	Augmented 3-diastep	B
2L + 2s	4	-1	Diminished 4-diastep	Cb
3L + s	4	0	Perfect 4-diastep	C
3L + 2s	5	-1	Minor 5-diastep	Db
4L + s	5	0	Major 5-diastep	D
4L + 2s	6	-1	Minor 6-diastep	Eb
5L + s	6	0	Major 6-diastep	E
5L + 2s	7	0	Perfect 7-diastep	F

Mode names		Ordering		Step pattern
Default	Names	Bri.	Rot.	Step pattern	1	2	3	4	5	6	7
5L 2s 6\|0	Lydian	1	1	LLLsLLs	0	0	0	0	0	0	0
5L 2s 5\|1	Ionian (major)	2	5	LLsLLLs	0	0	-1	0	0	0	0
5L 2s 4\|2	Mixolydian	3	2	LLsLLsL	0	1	-1	0	0	-1	0
5L 2s 3\|3	Dorian	4	6	LsLLLsL	0	-1	-1	0	0	-1	0
5L 2s 2\|4	Aeolian (minor)	5	3	LsLLsLL	0	-1	-1	0	-1	-1	0
5L 2s 1\|5	Phrygian	6	7	sLLLsLL	-1	-1	-1	0	-1	-1	0
5L 2s 0\|6	Locrian	7	4	sLLsLLL	-1	-1	-1	-1	-1	-1	0