User:Ganaram inukshuk/Sandbox: Difference between revisions

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→Sandbox for proposed templates: Testing mos interval headers
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Template testing: tamnams use
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== Sandbox for proposed templates ==
== Sandbox for proposed templates ==


=== MOS intervals (headers only) ===
=== TAMNAMS use ===
{| class="wikitable"
<blockquote>''This article assumes [[TAMNAMS]] conventions for naming scale degrees, intervals, and step ratios.''</blockquote>Names for the [[Degree|scale degrees]] of ''x''L ''y''s, the position of the scales tones, are called '''mosdegrees''', or '''''prefix''degrees'''. Its [[Interval|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 '''''prefix''steps'''. 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 only allowed when comparing what diatonic interval category the scale's intervals fall under, rather than the names of the intervals and degrees themselves.
! colspan="2" |Intervals
! colspan="2" |Size in L's and s's
! rowspan="2" |Abbrev.
|-
!Generic
!Specific
!L's and s's
!Cents
|-
|'''0-dicostep (root)'''
|Perfect 0-dicostep
|0
|0¢
|P0ms
|-
| rowspan="2" |1-dicostep
|Minor 1-dicostep
|s
|123¢-456¢
|m1ms
|-
|Major 1-dicostep
|L
|789¢-1011¢
|M1ms
|}
 
===JI ratio intro===


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


Revision as of 22:11, 21 February 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

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 only allowed when comparing what diatonic interval category the scale's intervals fall under, rather than the names of the intervals and degrees themselves.

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

Base wording

scalesig, called mosname in TAMNAMS, (alternatively called alt-mosname), is a(n) equave-equivalent moment-of-symmetry scale containing x large steps(s) and y small step(s), forming a step pattern step-pattern that repeats every equave. Generators that produce this scale range from g1¢ to g2¢, or from d1¢ or d2¢.

scalesig, called mosname in TAMNAMS, (alternatively called alt-mosname), is a(n) equave-equivalent moment-of-symmetry scale containing x large steps(s) and y small step(s), with a period of x/n large and y/n small steps(s) that forms a step pattern step-pattern-per-period that repeats every p¢, or n times every equave. Generators that produce this scale range from g1¢ to g2¢, or from d1¢ or d2¢.

Rothenprop info

Single-period scales: Scales of this form always exhibit Rothenberg propriety because there is only one small step.

Multi-period scales: Scales of this form always exhibit Rothenberg propriety because there is only one small step per period.

Descendant info (descendants of tamnams-named mosses only)

scalesig is a chromatic/enharmonic scale of parent-scalesig, an extension of parent-scalesig scales with a step-ratio-range step ratio.

scalesig is a descendant scale of parent-scalesig.

Full wording

scalesig, called mosname in TAMNAMS, (alternatively called alt-mosname), is a(n) equave-equivalent moment-of-symmetry scale containing x large steps(s) and y small step(s), forming a step pattern step-pattern that repeats every equave. Descendant-info. Generators that produce this scale range from g1¢ to g2¢, or from d1¢ or d2¢. Rothenprop-info.

scalesig, called mosname in TAMNAMS, (alternatively called alt-mosname), is a(n) equave-equivalent moment-of-symmetry scale containing x large steps(s) and y small step(s), with a period of x/n large and y/n small steps(s) that forms a step pattern step-pattern-per-period that repeats every p¢, or n times every equave. Descendant-info. Generators that produce this scale range from g1¢ to g2¢, or from d1¢ or d2¢. Rothenprop-info.

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. Generators that produce this scale range from 700¢ to 720¢, or from 480¢ to 500¢.

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

Navbox MOS

6- to 10-note mosses 1L 5s (selenite) | 2L 4s ( | 3L 3s | 4L 2 | 5L 1s
Monolarge family 1L 5s (selenite) | 1L 6s (onyx) | 1L 7s (spinel) | 1L 8s (agate) | 1L 9s (olivine)
Diatonic mos family
Parent mos 5L 2s (diatonic)
Chromatic scales 7L 5s (soft diatonic chromatic) | 5L 7s (hard diatonic chromatic)
Enharmonic scales 7L 12s (soft diatonic enharmonic) | 12L 7s (hyposoft diatonic enharmonic) | 12L 5s (hypohard diatonic enharmonic) | 5L 12s (hard diatonic enharmonic)
Subchromatic scales 7L 19s and 19L 7s | 19L 12s and 12L 19s | 12L 17s and 17L 12s | 17L 5s and 5L 17s

Scale tree formatting

Proposed changes:

  • Merge step ratio and hardness columns

Advanced table may need custom html?

Generator (in steps of edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\7 685.714 514.286 1:1 1.000 Equalized 5L 2s
╭ 27\47 689.362 510.638 7:6 1.167
╭ 23\40 690.000 510.000 6:5 1.200
┆ ╰ 42\73 690.411 509.589 11:9 1.222
╭ 19\33 690.909 509.091 5:4 1.250
┆ ┆ ╭ 53\92 691.304 508.696 14:11 1.273
┆ ╰ 34\59 691.525 508.475 9:7 1.286
┆ ╰ 49\85 691.765 508.235 13:10 1.300
╭ 15\26 692.308 507.692 4:3 1.333 Supersoft 5L 2s
┆ ┆ ╭ 56\97 692.784 507.216 15:11 1.364
┆ ┆ ╭ 41\71 692.958 507.042 11:8 1.375
┆ ┆ ┆ ╰ 67\116 693.103 506.897 18:13 1.385
┆ ╰ 26\45 693.333 506.667 7:5 1.400 Flattone is in this region
┆ ┆ ╭ 63\109 693.578 506.422 17:12 1.417
┆ ╰ 37\64 693.750 506.250 10:7 1.429
┆ ╰ 48\83 693.976 506.024 13:9 1.444
╭ 11\19 694.737 505.263 3:2 1.500 Soft 5L 2s
┆ ┆ ╭ 51\88 695.455 504.545 14:9 1.556
┆ ┆ ╭ 40\69 695.652 504.348 11:7 1.571
┆ ┆ ┆ ╰ 69\119 695.798 504.202 19:12 1.583
┆ ┆ ╭ 29\50 696.000 504.000 8:5 1.600
┆ ┆ ┆ ┆ ╭ 76\131 696.183 503.817 21:13 1.615 Golden meantone (696.2145¢)
┆ ┆ ┆ ╰ 47\81 696.296 503.704 13:8 1.625
┆ ┆ ┆ ╰ 65\112 696.429 503.571 18:11 1.636
┆ ╰ 18\31 696.774 503.226 5:3 1.667 Semisoft 5L 2s

Meantone is in this region

┆ ┆ ╭ 61\105 697.143 502.857 17:10 1.700
┆ ┆ ╭ 43\74 697.297 502.703 12:7 1.714
┆ ┆ ┆ ╰ 68\117 697.436 502.564 19:11 1.727
┆ ╰ 25\43 697.674 502.326 7:4 1.750
┆ ┆ 57\98 697.959 502.041 16:9 1.778
┆ ╰ 32\55 698.182 501.818 9:5 1.800
┆ ╰ 39\67 698.507 501.493 11:6 1.833
7\12 700.000 500.000 2:1 2.000 Basic 5L 2s
┆ ╭ 38\65 701.538 498.462 11:5 2.200
┆ ╭ 31\53 701.887 498.113 9:4 2.250 The generator closest to a just 3/2 for EDOs less than 200
┆ ┆ ╰ 55\94 702.128 497.872 16:7 2.286 Garibaldi / Cassandra
┆ ╭ 24\41 702.439 497.561 7:3 2.333
┆ ┆ ┆ ╭ 65\111 702.703 497.297 19:8 2.375
┆ ┆ ╰ 41\70 702.857 497.143 12:5 2.400
┆ ┆ ╰ 58\99 703.030 496.970 17:7 2.429
┆ ╭ 17\29 703.448 496.552 5:2 2.500 Semihard 5L 2s
┆ ┆ ┆ ╭ 61\104 703.846 496.154 18:7 2.571
┆ ┆ ┆ ╭ 44\75 704.000 496.000 13:5 2.600
┆ ┆ ┆ ┆ ╰ 71\121 704.132 495.868 21:8 2.625 Golden neogothic (704.0956¢)
┆ ┆ ╰ 27\46 704.348 495.652 8:3 2.667 Neogothic is in this region
┆ ┆ ┆ ╭ 64\109 704.587 495.413 19:7 2.714
┆ ┆ ╰ 37\63 704.762 495.238 11:4 2.750
┆ ┆ ╰ 47\80 705.000 495.000 14:5 2.800
╰ 10\17 705.882 494.118 3:1 3.000 Hard 5L 2s
┆ ╭ 43\73 706.849 493.151 13:4 3.250
┆ ╭ 33\56 707.143 492.857 10:3 3.333
┆ ┆ ╰ 56\95 707.368 492.632 17:5 3.400
┆ ╭ 23\39 707.692 492.308 7:2 3.500
┆ ┆ ┆ ╭ 59\100 708.000 492.000 18:5 3.600
┆ ┆ ╰ 36\61 708.197 491.803 11:3 3.667
┆ ┆ ╰ 49\83 708.434 491.566 15:4 3.750
╰ 13\22 709.091 490.909 4:1 4.000 Superhard 5L 2s

Archy is in this region

┆ ╭ 42\71 709.859 490.141 13:3 4.333
┆ ╭ 29\49 710.204 489.796 9:2 4.500
┆ ┆ ╰ 45\76 710.526 489.474 14:3 4.667
╰ 16\27 711.111 488.889 5:1 5.000
┆ ╭ 35\59 711.864 488.136 11:2 5.500
╰ 19\32 712.500 487.500 6:1 6.000
╰ 22\37 713.514 486.486 7:1 7.000
3\5 720.000 480.000 1:0 → ∞ Collapsed 5L 2s
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