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10L 3s: Difference between revisions

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This is the chromatic scale of the Sephiroth temperament explicated on the page for [[3L_7s|3L 7s]]. However, 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.
{{Infobox MOS}}
{{MOS intro}}


{| class="wikitable"
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" (Hebrew calendar) modes the degrees are to be taken as numbered in 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.  
|-
! | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">(Circle of fifths)</span>
! | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">(ascending scale)</span>
! |
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI-X</span>
| | L L L L s L L L s L L L s
| | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">Mode Tishrei</span>
|-
| | <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>
| | <span style="font-size: 12.8000001907349px;">L L L s L L L s L L L s L</span>
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Cheshvan</span>
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II</span>
| | <span style="font-size: 12.8000001907349px;">L L s L L L s L L L s L L</span>
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Kislev</span>
|-
| | <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>
| | <span style="font-size: 12.8000001907349px;">L s L L L s L L L s L L L</span>
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Tevet</span>
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII</span>
| | <span style="font-size: 12.8000001907349px;">s L L L s L L L s L L L L</span>
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Shvat</span>
|-
| | <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>
| | <span style="font-size: 12.8000001907349px;">L L L s L L L s L L L L s</span>
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Adar minor</span>
|-
| | <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>
| | <span style="font-size: 12.8000001907349px;">L L s L L L s L L L L s L</span>
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Adar major</span>
|-
| | <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>
| | <span style="font-size: 12.8000001907349px;">L s L L L s L L L L s L L</span>
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Nisan</span>
|-
| | <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>
| | <span style="font-size: 12.8000001907349px;">s L L L s L L L L s L L L</span>
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Iyar</span>
|-
| | <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>
| | <span style="font-size: 12.8000001907349px;">L L L s L L L L s L L L s</span>
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Sivan</span>
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX</span>
| | <span style="font-size: 12.8000001907349px;">L L s L L L L s L L L s L</span>
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Tammuz</span>
|-
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V</span>
| | <span style="font-size: 12.8000001907349px;">L s L L L L s L L L s L L</span>
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Av</span>
|-
| | <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>
| | <span style="font-size: 12.8000001907349px;">s L L L L s L L L s L L L</span>
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Elul</span>
|}


{| class="wikitable"
'''Luachoid''' is a proposed name for this scale.
|-
 
| | 3/10
== Modes ==
| |
=== Proposed names ===
| | 360
Names based on the [[wikipedia:Hebrew_calendar|Hebrew calendar]] have been proposed as mode names.
|-
{{MOS modes|Mode Names=Tishrei; Sivan; Adar minor; Cheshvan; Tammuz; Adar major; Kislev; Av; Nisan; Tevet; Elul; Iyar; Shvat}}
| | 16/53
 
| |
=== Degrees ===
| | 362.264
{{MOS mode degrees}}
|-
 
| | 13/43
== Intervals ==
| |
{{MOS intervals}}
| | 362.791
 
|-
== Scale tree ==
| |
{{MOS tuning spectrum}}
| |
 
| | 363.487
[[Category:13-tone scales]]
|-
| | 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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