User:Ganaram inukshuk/Sandbox: Difference between revisions
Removed jirined templates (to be moved to a new page) |
Wrote out every possible et/ed intro, based on what already exists on the wiki |
||
| Line 4: | Line 4: | ||
===Generalized ET/ED intro=== | ===Generalized ET/ED intro=== | ||
The intro displayed depends on the equave being divided. | |||
* Common abbreviations | |||
** edo: '''''k'' equal divisions of the octave''' (abbreviated '''''k''edo''' or '''''k''ed2'''), also called '''''k''-tone equal temperament''' ('''''k''tet''') or '''''k'' equal temperament''' ('''''k''et''') when viewed under a regular temperament perspective, is the tuning system that divides the octave into ''k'' equal parts of exactly/about s¢ each. Each step of kedo represents a frequency ratio of 2<sup>1/''k''</sup>, or the ''k''th root of 2. | |||
** edt: '''''k'' equal divisions of the tritave''' or '''twelfth''' (abbreviated '''''k''edt''' or '''''k''ed3''') is a non-octave tuning system that divides the 3rd harmonic, or 3/1, into ''k'' equal parts of exactly/about s¢ each. Each step of ''k''edo represents a frequency ratio of 3<sup>1/''k''</sup>, or the ''k''th root of 3. | |||
** edf: '''''k'' equal divisions of the fifth''' (abbreviated '''''k''edf''' or '''''k''ed3/2''') is a non-octave tuning system that divides the perfect fifth, or 3/2, into ''k'' equal parts of exactly/about s¢ each. Each step of ''k''edo represents a frequency ratio of (3/2)<sup>1/''k''</sup>, or the ''k''th root of 3/2. | |||
* Equal divisions of a harmonic | |||
** ed2: same as edo | |||
** ed3: same as edt | |||
** ed''h'': '''''k'' equal divisions of the ''h''th harmonic''' (abbreviated '''''k''ed''h''''') is a non-octave tuning system that divides the ''h''th harmonic, or ''h''/1, into ''k'' equal parts of exactly/about s¢ each. Each step of ''k''edh represents a frequency ratio of ''h''<sup>1/''k''</sup>, or the ''k''th root of ''h''. | |||
* Equal divisions of an arbitrary ratio ''p''/''q'' | |||
** ed''p''/''q'': '''''k'' equal divisions of ''p''/''q''''' (abbreviated '''''k''ed''p''/''q''''') is a non-octave tuning system that divides ''p''/''q'' into ''k'' equal pieces of exactly/about s¢ each. Each step of ''k''ed''p''/''q'' represents the frequency ratio of (''p''/''q'')<sup>1/''k''</sup>, or the ''k''th root of ''p''/''q''. | |||
* Equal divisions of an arbitrary constant c | |||
** ed''c'': '''''k'' equal divisions of ''c''''' (abbreviated '''''k''edc''') is a non-octave tuning system where the interval of r¢ is divided into ''k'' equal pieces of exactly/about s¢ each. Each step of ''k''ed''c'' represents the frequency ratio of ''c''<sup>1/''k''</sup>, or the ''k''th root of ''c''. | |||
* Equal-step tunings - special cases of the above where there is only one division of the harmonic, ratio, or cent value; more typical of intervals smaller than 2/1. | |||
** 1ed''p''/''q'' - '''1 equal division of ''p''/''q''''' (abbreviated '''1ed''p''/''q'''''), also known as '''ambitonal sequence of ''p''/''q''''' (abbreviated '''AS''p''/''q''''') or '''''p''/''q'' equal-step tuning''', is a non-octave tuning system where adjacent pitches are ''p''/''q'', or exactly/about s¢, apart. | |||
** 1ed''c''¢ - '''1 equal division of ''c''¢''' (abbreviated '''1ed''c''¢''' or '''1ed''c''c'''), also known as '''arithmetic pitch sequence of c¢''' (abbreviated '''APS''c''¢''') or '''''c''cET''', is a non-octave tuning system where adjacent pitches are ''c''¢, apart. | |||
===JI ratio intro=== | ===JI ratio intro=== | ||
Revision as of 03:17, 28 January 2024
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
The intro displayed depends on the equave being divided.
- Common abbreviations
- edo: k equal divisions of the octave (abbreviated kedo or ked2), 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 s¢ each. Each step of kedo represents a frequency ratio of 21/k, or the kth root of 2.
- edt: 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 s¢ each. Each step of kedo represents a frequency ratio of 31/k, or the kth root of 3.
- edf: 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 s¢ each. Each step of kedo represents a frequency ratio of (3/2)1/k, or the kth root of 3/2.
- Equal divisions of a harmonic
- ed2: same as edo
- ed3: same as edt
- edh: k equal divisions of the hth harmonic (abbreviated kedh) is a non-octave tuning system that divides the hth harmonic, or h/1, into k equal parts of exactly/about s¢ each. Each step of kedh represents a frequency ratio of h1/k, or the kth root of h.
- Equal divisions of an arbitrary ratio p/q
- edp/q: 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.
- Equal divisions of an arbitrary constant c
- edc: k equal divisions of c (abbreviated kedc) is a non-octave tuning system where the interval of r¢ is divided into k equal pieces of exactly/about s¢ each. Each step of kedc represents the frequency ratio of c1/k, or the kth root of c.
- Equal-step tunings - special cases of the above where there is only one division of the harmonic, ratio, or cent value; more typical of intervals smaller than 2/1.
- 1edp/q - 1 equal division of p/q (abbreviated 1edp/q), also known as ambitonal sequence of p/q (abbreviated ASp/q) or p/q equal-step tuning, is a non-octave tuning system where adjacent pitches are p/q, or exactly/about s¢, apart.
- 1edc¢ - 1 equal division of c¢ (abbreviated 1edc¢ or 1edcc), also known as arithmetic pitch sequence of c¢ (abbreviated APSc¢) or ccET, is a non-octave tuning system where adjacent pitches are c¢, apart.
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
| 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 |