7L 5s: Difference between revisions

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Added intervals heading and intervals template, added MOS mode degrees template, added "proposed names" subheading
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→Proposed Names: clarify that it's cyclic order
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{{MOS mode degrees}}
{{MOS mode degrees}}
=== Proposed Names ===
=== Proposed Names ===
Both [[User:Eliora|Eliora]] and [[User:Ganaram inukshuk|Ganaram]] have independently proposed mode names based on names of the months. The former scheme uses mode names from the Gregorian calendar, starting with January assigned to the step pattern LsLsLsLLsLsL, with successive rotations assigned to successive months. The latter scheme is based on month names from the Roman calendar, starting with Mensis Martius as the brightest mode, with successive month names for each mode by descending brightness.
Both [[User:Eliora|Eliora]] and [[User:Ganaram inukshuk|Ganaram]] have independently proposed mode names based on names of the months. The former scheme uses mode names from the Gregorian calendar using cyclic order, starting with January assigned to the step pattern LsLsLsLLsLsL due to positioning of 31-day and 30-day months, with successive rotations assigned to successive months. The latter scheme is based on month names from the Roman calendar, starting with Mensis Martius as the brightest mode, with successive month names for each mode by descending brightness.
{{MOS modes|Table Headers=Mode names<br>(by [[User:Eliora|Eliora]]); Mode names<br>(by [[User:Ganaram inukshuk|Ganaram]])|Table Entries=July; Martian; December; Aprilian; May; Maian; October; Junian; March; Quintillian <br>Julian; August; Sextilian <br>Augustan; January; Septembian; June; Octobian; November; Novembian; April; Decembian; September; Janian; February; Februan}}
{{MOS modes|Table Headers=Mode names<br>(by [[User:Eliora|Eliora]]); Mode names<br>(by [[User:Ganaram inukshuk|Ganaram]])|Table Entries=July; Martian; December; Aprilian; May; Maian; October; Junian; March; Quintillian <br>Julian; August; Sextilian <br>Augustan; January; Septembian; June; Octobian; November; Novembian; April; Decembian; September; Janian; February; Februan}}


Revision as of 14:18, 30 September 2024

↖ 6L 4s ↑ 7L 4s 8L 4s ↗
← 6L 5s 7L 5s 8L 5s →
↙ 6L 6s ↓ 7L 6s 8L 6s ↘ 
┌╥╥┬╥┬╥╥┬╥┬╥┬┐
│║║│║│║║│║│║││
││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLLsLsLs
sLsLsLLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\12 to 3\7 (500.0 ¢ to 514.3 ¢)
Dark 4\7 to 7\12 (685.7 ¢ to 700.0 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 5L 2s
Sister 5L 7s
Daughters 12L 7s, 7L 12s
Neutralized 2L 10s
2-Flought 19L 5s, 7L 17s
Equal tunings
Equalized (L:s = 1:1) 5\12 (500.0 ¢)
Supersoft (L:s = 4:3) 18\43 (502.3 ¢)
Soft (L:s = 3:2) 13\31 (503.2 ¢)
Semisoft (L:s = 5:3) 21\50 (504.0 ¢)
Basic (L:s = 2:1) 8\19 (505.3 ¢)
Semihard (L:s = 5:2) 19\45 (506.7 ¢)
Hard (L:s = 3:1) 11\26 (507.7 ¢)
Superhard (L:s = 4:1) 14\33 (509.1 ¢)
Collapsed (L:s = 1:0) 3\7 (514.3 ¢)

7L 5s, also called m-chromatic, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 5 small steps, repeating every octave. 7L 5s is a child scale of 5L 2s, expanding it by 5 tones. Generators that produce this scale range from 500 ¢ to 514.3 ¢, or from 685.7 ¢ to 700 ¢. 7L 5s represents the chromatic scale of meantone, or meantone chromatic scale. Such scales are characterized by having a small step (diatonic semitone) that is larger than the chroma (chromatic semitone), the reverse of 5L 7s.

Meantone is the only notable harmonic entropy minimum.

Intervals

Intervals of 7L 5s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 100.0 ¢
Major 1-mosstep M1ms L 100.0 ¢ to 171.4 ¢
2-mosstep Minor 2-mosstep m2ms L + s 171.4 ¢ to 200.0 ¢
Major 2-mosstep M2ms 2L 200.0 ¢ to 342.9 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 171.4 ¢ to 300.0 ¢
Major 3-mosstep M3ms 2L + s 300.0 ¢ to 342.9 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 342.9 ¢ to 400.0 ¢
Major 4-mosstep M4ms 3L + s 400.0 ¢ to 514.3 ¢
5-mosstep Diminished 5-mosstep d5ms 2L + 3s 342.9 ¢ to 500.0 ¢
Perfect 5-mosstep P5ms 3L + 2s 500.0 ¢ to 514.3 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 514.3 ¢ to 600.0 ¢
Major 6-mosstep M6ms 4L + 2s 600.0 ¢ to 685.7 ¢
7-mosstep Perfect 7-mosstep P7ms 4L + 3s 685.7 ¢ to 700.0 ¢
Augmented 7-mosstep A7ms 5L + 2s 700.0 ¢ to 857.1 ¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 685.7 ¢ to 800.0 ¢
Major 8-mosstep M8ms 5L + 3s 800.0 ¢ to 857.1 ¢
9-mosstep Minor 9-mosstep m9ms 5L + 4s 857.1 ¢ to 900.0 ¢
Major 9-mosstep M9ms 6L + 3s 900.0 ¢ to 1028.6 ¢
10-mosstep Minor 10-mosstep m10ms 5L + 5s 857.1 ¢ to 1000.0 ¢
Major 10-mosstep M10ms 6L + 4s 1000.0 ¢ to 1028.6 ¢
11-mosstep Minor 11-mosstep m11ms 6L + 5s 1028.6 ¢ to 1100.0 ¢
Major 11-mosstep M11ms 7L + 4s 1100.0 ¢ to 1200.0 ¢
12-mosstep Perfect 12-mosstep P12ms 7L + 5s 1200.0 ¢

Modes

Scale degrees of the modes of 7L 5s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12
11|0 1 LLsLsLLsLsLs Perf. Maj. Maj. Maj. Maj. Perf. Maj. Aug. Maj. Maj. Maj. Maj. Perf.
10|1 6 LLsLsLsLLsLs Perf. Maj. Maj. Maj. Maj. Perf. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
9|2 11 LsLLsLsLLsLs Perf. Maj. Min. Maj. Maj. Perf. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
8|3 4 LsLLsLsLsLLs Perf. Maj. Min. Maj. Maj. Perf. Maj. Perf. Maj. Min. Maj. Maj. Perf.
7|4 9 LsLsLLsLsLLs Perf. Maj. Min. Maj. Min. Perf. Maj. Perf. Maj. Min. Maj. Maj. Perf.
6|5 2 LsLsLLsLsLsL Perf. Maj. Min. Maj. Min. Perf. Maj. Perf. Maj. Min. Maj. Min. Perf.
5|6 7 LsLsLsLLsLsL Perf. Maj. Min. Maj. Min. Perf. Min. Perf. Maj. Min. Maj. Min. Perf.
4|7 12 sLLsLsLLsLsL Perf. Min. Min. Maj. Min. Perf. Min. Perf. Maj. Min. Maj. Min. Perf.
3|8 5 sLLsLsLsLLsL Perf. Min. Min. Maj. Min. Perf. Min. Perf. Min. Min. Maj. Min. Perf.
2|9 10 sLsLLsLsLLsL Perf. Min. Min. Min. Min. Perf. Min. Perf. Min. Min. Maj. Min. Perf.
1|10 3 sLsLLsLsLsLL Perf. Min. Min. Min. Min. Perf. Min. Perf. Min. Min. Min. Min. Perf.
0|11 8 sLsLsLLsLsLL Perf. Min. Min. Min. Min. Dim. Min. Perf. Min. Min. Min. Min. Perf.

Proposed Names

Both Eliora and Ganaram have independently proposed mode names based on names of the months. The former scheme uses mode names from the Gregorian calendar using cyclic order, starting with January assigned to the step pattern LsLsLsLLsLsL due to positioning of 31-day and 30-day months, with successive rotations assigned to successive months. The latter scheme is based on month names from the Roman calendar, starting with Mensis Martius as the brightest mode, with successive month names for each mode by descending brightness.

Modes of 7L 5s
UDP Cyclic
order		 Step
pattern
11|0 1 LLsLsLLsLsLs
10|1 6 LLsLsLsLLsLs
9|2 11 LsLLsLsLLsLs
8|3 4 LsLLsLsLsLLs
7|4 9 LsLsLLsLsLLs
6|5 2 LsLsLLsLsLsL
5|6 7 LsLsLsLLsLsL
4|7 12 sLLsLsLLsLsL
3|8 5 sLLsLsLsLLsL
2|9 10 sLsLLsLsLLsL
1|10 3 sLsLLsLsLsLL
0|11 8 sLsLsLLsLsLL

Scales

  • Meaneb471a – an equal beating tuning of meantone
  • Meantone12 – 31edo tuning
  • Ratwolf – 20/13 wolf fifth tuning of meantone
  • Meaneb471 – the other equal beating tuning of meantone
  • Flattone12 – 13-limit POTE tuning of flattone

Scale tree

Template:Scale tree

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