User:Ganaram inukshuk/Sandbox: Difference between revisions

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→Scale tree formatting: binary tree in-table?
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Advanced table may need custom html?
Advanced table may need custom html?
 
{| class="wikitable center-all"
{| class="wikitable"
! colspan="7" rowspan="2" |Generator (in steps of [[edo]])
! rowspan="2" |Steps of ED
! colspan="2" |Cents
! colspan="2" |Generator in cents
! colspan="2" |Step ratio
! colspan="2" |Step ratio
! rowspan="2" |Comments
! rowspan="2" |Comments
Line 167: Line 166:
!Dark
!Dark
!L:s
!L:s
!Ranges
!Hardness
|-
|-
|[[7edo|4\7]]
|[[7edo|4\7]]
|
|
|
|
|
|
|685.714
|685.714
|514.286
|514.286
|1:1
|1:1
|Equalized
|1.000
|Equalized 5L 2s
|-
|
|
|
|
|
|
|-
|┌
|[[47edo|27\47]]
|[[47edo|27\47]]
|689.362
|689.362
|510.638
|510.638
|7:6
|7:6
| rowspan="7" | <div style="writing-mode: vertical-rl; text-orientation: mixed;">Ultrasoft range</div>
|1.167
|
|
|-
|-
|
|
|
|
|┌
|[[40edo|23\40]]
|[[40edo|23\40]]
|690
|
|510
|690.000
|510.000
|6:5
|6:5
|1.200
|
|
|-
|-
|
|
|
|
|│
|└
|[[73edo|42\73]]
|[[73edo|42\73]]
|690.411
|690.411
|509.589
|509.589
|11:9
|11:9
|1.222
|
|
|-
|-
|
|
|
|┌
|[[33edo|19\33]]
|[[33edo|19\33]]
|
|
|690.909
|690.909
|509.091
|509.091
|5:4
|5:4
|1.250
|
|
|-
|-
|
|
|
|│
|
|┌
|[[92edo|53\92]]
|[[92edo|53\92]]
|691.304
|691.304
|508.696
|508.696
|14:11
|14:11
|1.273
|
|
|-
|-
|
|
|
|│
|
|[[59edo|34\59]]
|[[59edo|34\59]]
|
|691.525
|691.525
|508.475
|508.475
|9:7
|9:7
|1.286
|
|
|-
|-
|
|
|
|│
|
|└
|[[85edo|49\85]]
|[[85edo|49\85]]
|691.765
|691.765
|508.235
|508.235
|13:10
|13:10
|1.300
|
|
|-
|-
|
|
|┌
|[[26edo|15\26]]
|[[26edo|15\26]]
|
|
|
|692.308
|692.308
|507.692
|507.692
|4:3
|4:3
|Supersoft
|1.333
| Supersoft 5L 2s
|-
|
|
|│
|│
|
|
|-
|┌
|[[97edo|56\97]]
|[[97edo|56\97]]
|692.784
|692.784
|507.216
|507.216
|15:11
|15:11
| rowspan="7" | <div style="writing-mode: vertical-rl; text-orientation: mixed;">Parasoft range</div>
|1.364
|
|
|-
|-
|
|
|│
|│
|┌
|[[71edo|41\71]]
|[[71edo|41\71]]
|
|692.958
|692.958
|507.042
|507.042
|11:8
|11:8
|1.375
|
|
|-
|-
|
|
|│
|│
|│
|└
|[[116edo|67\116]]
|[[116edo|67\116]]
|693.103
|693.103
|506.897
|506.897
|18:13
|18:13
|1.385
|
|
|-
|-
|
|
|│
|└
|[[45edo|26\45]]
|[[45edo|26\45]]
|
|
|693.333
|693.333
|506.667
|506.667
|7:5
|7:5
|1.400
|[[Flattone]] is in this region
|-
|
|
|
|-
|│
|
|│
|┌
|[[109edo|63\109]]
|[[109edo|63\109]]
|693.578
|693.578
|506.422
|506.422
|17:12
|17:12
|1.417
|
|
|-
|-
|
|
|│
|
|└
|[[64edo|37\64]]
|[[64edo|37\64]]
|693.75
|
|506.25
|693.750
|506.250
|10:7
|10:7
|1.429
|
|
|-
|-
|
|
|│
|
|
|└
|[[83edo|48\83]]
|[[83edo|48\83]]
|693.976
|693.976
|506.024
|506.024
|13:9
|13:9
|1.444
|
|
|-
|-
|
|┌
|[[19edo|11\19]]
|[[19edo|11\19]]
|
|
|
|
|694.737
|694.737
|505.263
|505.263
|3:2
|3:2
|Soft
|1.500
|Soft 5L 2s
|-
|
|│
|│
|
|
|
|-
|┌
|[[88edo|51\88]]
|[[88edo|51\88]]
|695.455
|695.455
|504.545
|504.545
|14:9
|14:9
| rowspan="7" |
|1.556
|
|
|-
|-
|
|│
|│
|
|┌
|[[69edo|40\69]]
|[[69edo|40\69]]
|
|695.652
|695.652
|504.348
|504.348
|11:7
|11:7
|1.571
|
|
|-
|-
|
|│
|│
|
|│
|└
|[[119edo|69\119]]
|[[119edo|69\119]]
|695.798
|695.798
|504.202
|504.202
|19:12
|19:12
|1.583
|
|
|-
|-
|
|│
|│
|┌
|[[50edo|29\50]]
|[[50edo|29\50]]
|696
|
|504
|
|696.000
| 504.000
|8:5
|8:5
|1.600
|
|
|-
|-
|
|│
|│
|│
|│
|┌
|[[131edo|76\131]]
|[[131edo|76\131]]
|696.183
|696.183
|503.817
|503.817
|21:13
|21:13
|1.615
|[[Golden meantone]] (696.2145¢)
|-
|
|
|-
|│
|│
|│
|└
|[[81edo|47\81]]
|[[81edo|47\81]]
|
|696.296
|696.296
|503.704
|503.704
|13:8
|13:8
|1.625
|
|
|-
|-
|
|│
|│
|│
|
|└
|[[112edo|65\112]]
|[[112edo|65\112]]
|696.429
|696.429
|503.571
|503.571
|18:11
|18:11
|1.636
|
|
|-
|-
|
|│
|└
|[[31edo|18\31]]
|[[31edo|18\31]]
|
|
|
|696.774
|696.774
|503.226
|503.226
|5:3
|5:3
|Semisoft
|1.667
|Semisoft 5L 2s
[[Meantone]] is in this region
|-
|
|│
|
|│
|
|
|-
|┌
|[[105edo|61\105]]
|[[105edo|61\105]]
|697.143
|697.143
|502.857
| 502.857
|17:10
|17:10
| rowspan="7" |Minisoft range
|1.700
|
|
|-
|-
|
|│
|
|│
|┌
|[[74edo|43\74]]
|[[74edo|43\74]]
|
|697.297
|697.297
|502.703
|502.703
|12:7
|12:7
|1.714
|
|
|-
|-
|
|│
|
|│
|│
|└
|[[117edo|68\117]]
|[[117edo|68\117]]
|697.436
|697.436
|502.564
|502.564
|19:11
|19:11
|1.727
|
|
|-
|-
|
|│
|
|└
|[[43edo|25\43]]
|[[43edo|25\43]]
|
|
|697.674
|697.674
|502.326
|502.326
|7:4
|7:4
|1.750
|
|
|-
|-
|
|│
|
|
|│
|
|[[98edo|57\98]]
|[[98edo|57\98]]
|697.959
|697.959
|502.041
|502.041
|16:9
|16:9
|1.778
|
|
|-
|-
|
|│
|
|
|└
|[[55edo|32\55]]
|[[55edo|32\55]]
|
|698.182
|698.182
|501.818
|501.818
|9:5
|9:5
|1.800
|
|
|-
|-
|
|│
|
|
|
|└
|[[67edo|39\67]]
|[[67edo|39\67]]
|698.507
|698.507
|501.493
| 501.493
|11:6
|11:6
|1.833
|
|
|-
|-
|
|[[12edo|7\12]]
|[[12edo|7\12]]
|700
|
|500
|
|
|
|
|700.000
|500.000
|2:1
|2:1
|Basic
|2.000
|Basic 5L 2s
|-
|
|│
|
|
|
|
|-
|┌
|[[65edo|38\65]]
|[[65edo|38\65]]
|701.538
|701.538
|498.462
|498.462
|11:5
|11:5
| rowspan="7" |Minihard range
|2.200
|
|
|-
|-
|
|│
|
|
|┌
|[[53edo|31\53]]
|[[53edo|31\53]]
|
|701.887
|701.887
|498.113
|498.113
|9:4
|9:4
|2.250
|The generator closest to a just [[3/2]] for EDOs less than 200
|-
|
|│
|
|
|
|-
|│
|└
|[[94edo|55\94]]
|[[94edo|55\94]]
|702.128
|702.128
|497.872
|497.872
|16:7
|16:7
|2.286
|[[Garibaldi]] / [[Cassandra]]
|-
|
|│
|
|
|-
|┌
|[[41edo|24\41]]
|[[41edo|24\41]]
|
|
|702.439
|702.439
|497.561
|497.561
|7:3
|7:3
|2.333
|
|
|-
|-
|
|│
|
|│
|│
|┌
|[[111edo|65\111]]
|[[111edo|65\111]]
|702.703
|702.703
|497.297
|497.297
|19:8
|19:8
|2.375
|
|
|-
|-
|
|│
|
|│
|└
|[[70edo|41\70]]
|[[70edo|41\70]]
|
|702.857
|702.857
|497.143
|497.143
|12:5
|12:5
|2.400
|
|
|-
|-
|
|│
|
|│
|
|└
|[[99edo|58\99]]
|[[99edo|58\99]]
|703.03
|703.030
|496.97
|496.970
|17:7
|17:7
|2.429
|
|
|-
|-
|
|│
|┌
|[[29edo|17\29]]
|[[29edo|17\29]]
|
|
|
|703.448
|703.448
|496.552
|496.552
|5:2
|5:2
|Semihard
|2.500
|Semihard 5L 2s
|-
|
|│
|│
|│
|
|
|-
|┌
|[[104edo|61\104]]
|[[104edo|61\104]]
|703.846
|703.846
|496.154
|496.154
|18:7
|18:7
| rowspan="7" |Quasihard range
|2.571
|
|
|-
|-
|
|│
|│
|│
|┌
|[[75edo|44\75]]
|[[75edo|44\75]]
|704
|
|496
|704.000
|496.000
|13:5
|13:5
|2.600
|
|
|-
|-
|
|│
|│
|│
|│
|└
|[[121edo|71\121]]
|[[121edo|71\121]]
|704.132
|704.132
|495.868
|495.868
|21:8
|21:8
|2.625
|Golden neogothic (704.0956¢)
|-
|
|
|-
|│
|│
|└
|[[46edo|27\46]]
|[[46edo|27\46]]
|
|
|704.348
|704.348
|495.652
|495.652
|8:3
|8:3
|2.667
|[[Neogothic]] is in this region
|-
|
|│
|│
|
|
|
|-
|┌
|[[109edo|64\109]]
|[[109edo|64\109]]
|704.587
|704.587
|495.413
|495.413
|19:7
|19:7
|2.714
|
|
|-
|-
|
|│
|│
|
|
|[[63edo|37\63]]
|[[63edo|37\63]]
|
|704.762
|704.762
|495.238
|495.238
|11:4
|11:4
|2.750
|
|
|-
|-
|
|│
|│
|
|
|└
|[[80edo|47\80]]
|[[80edo|47\80]]
|705
|705.000
|495
|495.000
|14:5
|14:5
|2.800
|
|
|-
|-
|
|└
|[[17edo|10\17]]
|[[17edo|10\17]]
|
|
|
|
|705.882
|705.882
|494.118
|494.118
|3:1
|3:1
|Hard
|3.000
|Hard 5L 2s
|-
|
|
|-
|
|│
|
|
|┌
|[[73edo|43\73]]
|[[73edo|43\73]]
|706.849
|706.849
|493.151
|493.151
|13:4
|13:4
| rowspan="7" |Superhard range
|3.250
|
|
|-
|-
|
|
|│
|
|┌
|[[56edo|33\56]]
|[[56edo|33\56]]
|
|707.143
|707.143
|492.857
|492.857
|10:3
|10:3
|3.333
|
|
|-
|-
|
|
|│
|
|│
|└
|[[95edo|56\95]]
|[[95edo|56\95]]
|707.368
|707.368
|492.632
|492.632
|17:5
|17:5
|3.400
|
|
|-
|-
|
|
|│
|┌
|[[39edo|23\39]]
|[[39edo|23\39]]
|
|
|707.692
|707.692
|492.308
|492.308
|7:2
|7:2
|3.500
|
|
|-
|-
|
|
|│
|│
|│
|┌
|[[100edo|59\100]]
|[[100edo|59\100]]
|708
|708.000
|492
|492.000
|18:5
|18:5
|3.600
|
|
|-
|-
|
|
|│
|│
|└
|[[61edo|36\61]]
|[[61edo|36\61]]
|
|708.197
|708.197
|491.803
|491.803
|11:3
|11:3
|3.667
|
|
|-
|-
|
|
|│
|│
|
|└
|[[83edo|49\83]]
|[[83edo|49\83]]
|708.434
|708.434
|491.566
|491.566
|15:4
|15:4
|3.750
|
|
|-
|-
|
|
|└
|[[22edo|13\22]]
|[[22edo|13\22]]
|
|
|
|709.091
|709.091
|490.909
|490.909
|4:1
|4:1
|Superhard
|4.000
|Superhard 5L 2s
[[Archy]] is in this region
|-
|
|
|
|
|-
|│
|
|┌
|[[71edo|42\71]]
|[[71edo|42\71]]
|709.859
|709.859
|490.141
|490.141
|13:3
|13:3
| rowspan="7" |Ultrahard range
|4.333
|
|
|-
|-
|
|
|
|│
|┌
|[[49edo|29\49]]
|[[49edo|29\49]]
|
|710.204
|710.204
|489.796
|489.796
|9:2
|9:2
|4.500
|
|
|-
|-
|
|
|
|│
|│
|└
|[[76edo|45\76]]
|[[76edo|45\76]]
|710.526
|710.526
|489.474
|489.474
|14:3
|14:3
|4.667
|
|
|-
|-
|
|
|
|└
|[[27edo|16\27]]
|[[27edo|16\27]]
|
|
|711.111
|711.111
|488.889
|488.889
|5:1
|5:1
|5.000
|
|
|-
|-
|
|
|
|
|│
|┌
|[[59edo|35\59]]
|[[59edo|35\59]]
|711.864
|711.864
|488.136
|488.136
|11:2
|11:2
|5.500
|
|
|-
|-
|
|
|
|
|└
|[[32edo|19\32]]
|[[32edo|19\32]]
|712.5
|
|487.5
|712.500
|487.500
|6:1
|6:1
|6.000
|
|
|-
|-
|
|
|
|
|
|└
|[[37edo|22\37]]
|[[37edo|22\37]]
|713.514
|713.514
|486.486
|486.486
|7:1
|7:1
|7.000
|
|
|-
|-
|[[5edo|3\5]]
|[[5edo|3\5]]
|720
|
|480
|
|
|
|
|
|720.000
|480.000
|1:0
|1:0
|Collapsed
|→ ∞
|
|Collapsed 5L 2s
|}
|}

Revision as of 08:43, 16 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

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

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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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