User:Ganaram inukshuk/Sandbox

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

Sandbox for proposed templates

Generalized ET/ED intro

For nonoctave equaves: k equal divisions of p/q (abbreviated kedp/q) is a non-octave tuning system based on dividing p/q into k equal pieces of exactly/about s¢ each. Each step of kedp/q represents the frequency ratio of (p/q)^1/k or the kth root of p/q.

For edos: k equal divisions of the octave (abbreviated kedo), also called k-tone equal temperament (ktet) or k equal temperament (ket) when viewed under a regular temperament perspective, is the tuning system that divides the octave into k equal parts of exactly/about r¢ each. Each step of kedo represents a frequency ratio of 21/k, or the kth root of 2.

For edts: k equal divisions of the tritave or twelfth (abbreviated kedt or ked3) is a non-octave tuning system that divides the 3rd harmonic, or 3/1, into k equal parts of exactly/about r¢ each. Each step of kedo represents a frequency ratio of 3^1/k, or the kth root of 3.

For edfs: k equal divisions of the fifth (abbreviated kedf or ked3/2) is a non-octave tuning system that divides the perfect fifth, or 3/2, into k equal parts of exactly/about r¢ each. Each step of kedo represents a frequency ratio of (3/2)^1/k, or the kth root of 3/2.

For nonoctave equaves: k equal divisions of p/q (abbreviated kedp/q) is a non-octave tuning system that divides p/q into k equal pieces of exactly/about s¢ each. Each step of kedp/q represents the frequency ratio of (p/q)^1/k or the kth root of p/q.

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
	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

Expanded MOS intro

The following pieces of information may be worth adding:

• Distinguishing between TAMNAMS names from other, noteworthy non-TAMNAMS names. Equave-agnostic names can be treated as TAMNAMS name for appropriate mosses (EG, 4L 1s).
• The specific step pattern for the true mos. (The template will have a link to the page for rotations.)
• Simple edos (or ed<p/q>) that support the mos.
• Support for TAMEX names, or how the mos relates to another, ancestral TAMNAMS-named mos. Extensions include chromatic, enharmonic, subchromatic, and descendant. This requires standardizing the naming scheme for descendant mosses before it can be added.
  • TAMEX is short for temperament-agnostic moment-of-symmetry scale extension naming system.
• Whether the mos exhibits Rothenberg propriety.

Base wording

xL ys<p/q>, named mosname (also called alt-mosname), is a(n) equave-equivalent moment-of-symmetry scale containing x large steps(s) and y small step(s), repeating every equave. Modes of this scale are based on the step pattern of step-pattern. Equal divisions of the equave that support this scale include basic-ed, hard-ed, and soft-ed. Generators that produce this scale range from g1¢ to g2¢, or from d1¢ or d2¢.

nxL nys<p/q>, named mosname (also called alt-mosname), is a(n) equave-equivalent moment-of-symmetry scale, containing 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. Modes of this scale are based on the step pattern of step-pattern. Equal divisions of the equave that support this scale include basic-ed, hard-ed, and soft-ed. Generators that produce this scale range from g1¢ to g2¢, or from d1¢ or d2¢.

Supplemental info

For monosmall and monosmall-per-period mosses: Scales of this form always exhibit Rothenberg propriety because there is only one small step per period.

For mosses that descend from a TAMNAMS-named mos: xL ys<p/q> is a kth-order descendant scale of zL ws<p/q>, an extension of zL ws<p/q> scales with a step-ratio-range step ratio.

Examples

5L 7s, also called p-chromatic, is an octave-equivalent moment of symmetry scale containing 5 large steps and 7 small steps, repeating every octave. 5L 7s is a chromatic scale of 5L 2s, an extension of 5L 2s scales with a hard-of-basic step ratio. Equal divisions of the octave that support this scale's step pattern include 17edo, 22edo, and 29edo. Generators that produce this scale range from 700¢ to 720¢, or from 480¢ to 500¢.

Mbox template test

These would be their own templates.

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