10L 3s: Difference between revisions

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{| class="wikitable"
{| class="wikitable"
|-
|-
! | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">Circle of fifths</span>
! | Circle of fifths
! | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">Ascending scale</span>
! | Ascending scale
! | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">Mode</span>
! | Mode
|-
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI-X</span>
| | I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI-X
| | L L L L s L L L s L L L s
| | L L L L s L L L s L L L s
| | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">Tishrei</span>
| | Tishrei
|-
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">x-I</span><span style="font-size: 12.8000001907349px;">-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI</span>
| | x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI
| | <span style="font-size: 12.8000001907349px;">L L L s L L L s L L L s L</span>
| | L L L s L L L s L L L s L
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Cheshvan</span>
| | Cheshvan
|-
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II</span>
| | vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II
| | <span style="font-size: 12.8000001907349px;">L L s L L L s L L L s L L</span>
| | L L s L L L s L L L s L L
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Kislev</span>
| | Kislev
|-
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">ii-</span><span style="font-size: 12.8000001907349px;">vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI</span>
| | ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI
| | <span style="font-size: 12.8000001907349px;">L s L L L s L L L s L L L</span>
| | L s L L L s L L L s L L L
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Tevet</span>
| | Tevet
|-
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII</span>
| | xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII
| | <span style="font-size: 12.8000001907349px;">s L L L s L L L s L L L L</span>
| | s L L L s L L L s L L L L
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Shvat</span>
| | Shvat
|-
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">vii-</span><span style="font-size: 12.8000001907349px;">xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III</span>
| | vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III
| | <span style="font-size: 12.8000001907349px;">L L L s L L L s L L L L s</span>
| | L L L s L L L s L L L L s
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Adar minor</span>
| | Adar minor
|-
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">iii-vii</span><span style="font-size: 12.8000001907349px;">-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII</span>
| | iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII
| | <span style="font-size: 12.8000001907349px;">L L s L L L s L L L L s L</span>
| | L L s L L L s L L L L s L
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Adar major</span>
| | Adar major
|-
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">xii-</span><span style="font-size: 12.8000001907349px;">iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII</span>
| | xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII
| | <span style="font-size: 12.8000001907349px;">L s L L L s L L L L s L L</span>
| | L s L L L s L L L L s L L
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Nisan</span>
| | Nisan
|-
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">viii-</span><span style="font-size: 12.8000001907349px;">xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV</span>
| | viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV
| | <span style="font-size: 12.8000001907349px;">s L L L s L L L L s L L L</span>
| | s L L L s L L L L s L L L
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Iyar</span>
| | Iyar
|-
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">iv-</span><span style="font-size: 12.8000001907349px;">viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII</span>
| | iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII
| | <span style="font-size: 12.8000001907349px;">L L L s L L L L s L L L s</span>
| | L L L s L L L L s L L L s
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Sivan</span>
| | Sivan
|-
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX</span>
| | xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX
| | <span style="font-size: 12.8000001907349px;">L L s L L L L s L L L s L</span>
| | L L s L L L L s L L L s L
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Tammuz</span>
| | Tammuz
|-
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V</span>
| | ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V
| | <span style="font-size: 12.8000001907349px;">L s L L L L s L L L s L L</span>
| | L s L L L L s L L L s L L
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Av</span>
| | Av
|-
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">v-</span><span style="font-size: 12.8000001907349px;">ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I</span>
| | v-ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I
| | <span style="font-size: 12.8000001907349px;">s L L L L s L L L s L L L</span>
| | s L L L L s L L L s L L L
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Elul</span>
| | Elul
|}
|}


Revision as of 20:29, 11 April 2021

User:IlL/Template:RTT restriction

↖ 9L 2s ↑ 10L 2s 11L 2s ↗
← 9L 3s 10L 3s 11L 3s →
↙ 9L 4s ↓ 10L 4s 11L 4s ↘
Scale structure
Step pattern LLLLsLLLsLLLs
sLLLsLLLsLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 9\13 to 7\10 (830.8 ¢ to 840.0 ¢)
Dark 3\10 to 4\13 (360.0 ¢ to 369.2 ¢)
TAMNAMS information
Related to 3L 7s (sephiroid)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 3L 7s
Sister 3L 10s
Daughters 13L 10s, 10L 13s
Neutralized 7L 6s
2-Flought 23L 3s, 10L 16s
Equal tunings
Equalized (L:s = 1:1) 9\13 (830.8 ¢)
Supersoft (L:s = 4:3) 34\49 (832.7 ¢)
Soft (L:s = 3:2) 25\36 (833.3 ¢)
Semisoft (L:s = 5:3) 41\59 (833.9 ¢)
Basic (L:s = 2:1) 16\23 (834.8 ¢)
Semihard (L:s = 5:2) 39\56 (835.7 ¢)
Hard (L:s = 3:1) 23\33 (836.4 ¢)
Superhard (L:s = 4:1) 30\43 (837.2 ¢)
Collapsed (L:s = 1:0) 7\10 (840.0 ¢)
View • Talk • Edit

10L 3s or luachoid is scale pattern that expands on sephiroid (3L 7s). A tempered-flat chain of the 13th harmonic really comes into its own as a distinct scale when extended to 13 tones. In these "Luach" modes the degrees are to be taken as numbered is descending order so that the the tempered 13th harmonic is fifth rather than tenth in the scale. This inverts the meaning of major and minor so that the Ionian-like mode reaches its degrees almost exclusively by backtracking.

Circle of fifths Ascending scale Mode
I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI-X L L L L s L L L s L L L s Tishrei
x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI L L L s L L L s L L L s L Cheshvan
vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II L L s L L L s L L L s L L Kislev
ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI L s L L L s L L L s L L L Tevet
xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII s L L L s L L L s L L L L Shvat
vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III L L L s L L L s L L L L s Adar minor
iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII L L s L L L s L L L L s L Adar major
xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII L s L L L s L L L L s L L Nisan
viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV s L L L s L L L L s L L L Iyar
iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII L L L s L L L L s L L L s Sivan
xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX L L s L L L L s L L L s L Tammuz
ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V L s L L L L s L L L s L L Av
v-ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I s L L L L s L L L s L L L Elul
3/10 360
16/53 362.264
13/43 362.791
363.487
10/33 363.818
363.976
27/89 364.045
364.112
17/56 364.286
7/23 365.217
365.904
18/59 366.102
366.256
29/95 366.316
366.414
11/36 366.667
15/49 367.347
19/62 367.742
4/13 369.231
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