14L 1s: Difference between revisions

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Mos intro
Ganaram inukshuk (talk | contribs)
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Replaced scale tree, populated tree with entries for nautilus and sextilififths
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{{Infobox MOS}}
{{Infobox MOS}}
{{MOS intro}}
{{MOS intro}}
This scale is notable for corresponding to 15-note scales of temperaments like [[nautilus]] and [[sextilififths]].
This scale is notable for corresponding to 15-note scales of temperaments like [[nautilus]] and [[sextilififths]]. 6 steps of the scale cover a diatonic fourth, and they also go from the lower bound to upper bound of diatonic fourths (3\7 to 2\5) over the course of the entire step ratio spectrum, corresponding to going from 14edo perfect fourth to 15edo pefect fourth.
 
==Scale tree==
6 steps of the scale cover a diatonic fourth, and they also go from the lower bound to upper bound of diatonic fourths (3\7 to 2\5) over the course of the entire step ratio spectrum, corresponding to going from 14edo perfect fourth to 15edo pefect fourth.
{{Scale tree|Comments=3/2: [[Nautilus]];
 
9/4: ↕ [[Sextilififths]]}}
 
== Scale tree ==
{| class="wikitable"
! colspan="8" | generator
! L
! s
! L/s
! gen (cents)
! comment
|-
| 1\14
|
|
|
|
|
|
|
| 1
| 0
|
| 85.714
|
|-
|
|
|
|
|
|
|
| 8\113
| 8
| 1
| 8.000
| 84.956
|
|-
|
|
|
|
|
|
| 7\99
|
| 7
| 1
| 7.000
| 84.848
|
|-
|
|
|
|
|
| 6\85
|
|
| 6
| 1
| 6.000
| 84.706
|
|-
|
|
|
|
| 5\71
|
|
|
| 5
| 1
| 5.000
| 84.507
|
|-
|
|
|
| 4\57
|
|
|
|
| 4
| 1
| 4.000
| 84.211
|
|-
|
|
| 3\43
|
|
|
|
|
| 3
| 1
| 3.000
| 83.721
|
|-
|
|
|
| 5\72
|
|
|
|
| 5
| 2
| 2.500
| 83.333
|
|-
|
| 2\29
|
|
|
|
|
|
| 2
| 1
| 2.000
| 82.759
|
|-
|
|
|
| 5\73
|
|
|
|
| 5
| 3
| 1.667
| 82.192
|
|-
|
|
| 3\44
|
|
|
|
|
| 3
| 2
| 1.500
| 81.818
| Nautilus is around here
|-
|
|
|
| 4\59
|
|
|
|
| 4
| 3
| 1.333
| 81.356
|
|-
|
|
|
|
| 5\74
|
|
|
| 5
| 4
| 1.250
| 81.081
|
|-
|
|
|
|
|
| 6\89
|
|
| 6
| 5
| 1.200
| 80.899
|
|-
|
|
|
|
|
|
| 7\104
|
| 7
| 6
| 1.167
| 80.769
|
|-
|
|
|
|
|
|
|
| 8\119
| 8
| 7
| 1.143
| 80.672
|
|-
| 1\15
|
|
|
|
|
|
|
| 1
| 1
| 1.000
| 80.000
|
|}
 
[[Category:15-tone scales]]
[[Category:15-tone scales]]

Revision as of 05:32, 29 February 2024

← 13L 1s 14L 1s 15L 1s →
↙ 13L 2s ↓ 14L 2s 15L 2s ↘
Scale structure
Step pattern LLLLLLLLLLLLLLs
sLLLLLLLLLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 1\15 to 1\14 (80.0 ¢ to 85.7 ¢)
Dark 13\14 to 14\15 (1114.3 ¢ to 1120.0 ¢)
TAMNAMS information
Related to 1L 9s (antisinatonic)
With tunings 5:1 to 6:1
Related MOS scales
Parent 1L 13s
Sister 1L 14s
Daughters 15L 14s, 14L 15s
Neutralized 13L 2s
2-Flought 29L 1s, 14L 16s
Equal tunings
Equalized (L:s = 1:1) 1\15 (80.0 ¢)
Supersoft (L:s = 4:3) 4\59 (81.4 ¢)
Soft (L:s = 3:2) 3\44 (81.8 ¢)
Semisoft (L:s = 5:3) 5\73 (82.2 ¢)
Basic (L:s = 2:1) 2\29 (82.8 ¢)
Semihard (L:s = 5:2) 5\72 (83.3 ¢)
Hard (L:s = 3:1) 3\43 (83.7 ¢)
Superhard (L:s = 4:1) 4\57 (84.2 ¢)
Collapsed (L:s = 1:0) 1\14 (85.7 ¢)
View • Talk • Edit

14L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 14 large steps and 1 small step, repeating every octave. 14L 1s is related to 1L 9s, expanding it by 5 tones. Generators that produce this scale range from 80 ¢ to 85.7 ¢, or from 1114.3 ¢ to 1120 ¢. Scales of this form are always proper because there is only one small step. This scale is notable for corresponding to 15-note scales of temperaments like nautilus and sextilififths. 6 steps of the scale cover a diatonic fourth, and they also go from the lower bound to upper bound of diatonic fourths (3\7 to 2\5) over the course of the entire step ratio spectrum, corresponding to going from 14edo perfect fourth to 15edo pefect fourth.

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 14L 1s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\15 80.000 1120.000 1:1 1.000 Equalized 14L 1s
6\89 80.899 1119.101 6:5 1.200
5\74 81.081 1118.919 5:4 1.250
9\133 81.203 1118.797 9:7 1.286
4\59 81.356 1118.644 4:3 1.333 Supersoft 14L 1s
11\162 81.481 1118.519 11:8 1.375
7\103 81.553 1118.447 7:5 1.400
10\147 81.633 1118.367 10:7 1.429
3\44 81.818 1118.182 3:2 1.500 Soft 14L 1s
11\161 81.988 1118.012 11:7 1.571
8\117 82.051 1117.949 8:5 1.600
13\190 82.105 1117.895 13:8 1.625
5\73 82.192 1117.808 5:3 1.667 Semisoft 14L 1s
12\175 82.286 1117.714 12:7 1.714
7\102 82.353 1117.647 7:4 1.750
9\131 82.443 1117.557 9:5 1.800
2\29 82.759 1117.241 2:1 2.000 Basic 14L 1s
9\130 83.077 1116.923 9:4 2.250
7\101 83.168 1116.832 7:3 2.333
12\173 83.237 1116.763 12:5 2.400
5\72 83.333 1116.667 5:2 2.500 Semihard 14L 1s
13\187 83.422 1116.578 13:5 2.600
8\115 83.478 1116.522 8:3 2.667
11\158 83.544 1116.456 11:4 2.750
3\43 83.721 1116.279 3:1 3.000 Hard 14L 1s
10\143 83.916 1116.084 10:3 3.333
7\100 84.000 1116.000 7:2 3.500
11\157 84.076 1115.924 11:3 3.667
4\57 84.211 1115.789 4:1 4.000 Superhard 14L 1s
9\128 84.375 1115.625 9:2 4.500
5\71 84.507 1115.493 5:1 5.000
6\85 84.706 1115.294 6:1 6.000
1\14 85.714 1114.286 1:0 → ∞ Collapsed 14L 1s
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