7L 5s: Difference between revisions

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This is the MOS pattern of the [[Meantone_family|meantone]] chromatic scale, which is the only notable harmonic entropy minimum in this range of possible scales. In meantone, "diatonic" semitones (~16/15), such as appear in the [[5L_2s|diatonic scale]], for example B-C, are larger than "chromatic" semitones (~25/24), the intervals by which flats and sharps alter pitches.
{{Infobox MOS}}
{{MOS intro|Other Names=m-chromatic}}


The meantone chromatic scale is [[Rothenberg_propriety|proper]].
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]].


{| class="wikitable"
Meantone is the only notable harmonic entropy minimum.
|-
! colspan="6" | Generator
! | in cents
! | Comments
|-
| style="text-align:center;" | 3\7
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| | 514.286
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 20\47
| | 510.638
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 17\40
| style="text-align:center;" |
| | 510
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 31\73
| | 509.589
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 14\33
| style="text-align:center;" |
| style="text-align:center;" |
| | 509.091
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 39\92
| | 508.696
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 25\59
| style="text-align:center;" |
| | 508.475
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 36\85
| | 508.235
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 507.934
| |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 11\26
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| | 507.692
| style="text-align:center;" | Normal flat-tone.
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | <span style="display: block; text-align: center;">41\97</span>
| | 507.216
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| | 507.151
| style="text-align:center;" | <span style="display: block; text-align: center;">Flattone</span>
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 30\71
| style="text-align:center;" |
| | 507.042
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 506.9365
| |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 49\116
| | 506.897
| style="text-align:center;" | Flattone
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 19\45
| style="text-align:center;" |
| style="text-align:center;" |
| | 506.667
| style="text-align:center;" | Flattone
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 46\109
| | 506.422
| style="text-align:center;" | Flattone
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 27\64
| style="text-align:center;" |
| | 506.25
| style="text-align:center;" | Flattone
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 35\83
| | 506.024
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" | 8\19
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| | 505.263
| style="text-align:center;" | Boundary of propriety: generators smaller than this are proper.


Meanenneadecal
== Scale properties ==
|-
{{TAMNAMS use}}
| style="text-align:center;" |
 
| style="text-align:center;" |
=== Intervals ===
| style="text-align:center;" |
{{MOS intervals}}
| style="text-align:center;" |
 
| style="text-align:center;" |
=== Generator chain ===
| style="text-align:center;" | 37\88
{{MOS genchain}}
| | 504.5455
 
| style="text-align:center;" | LucyTuning
=== Modes ===
|-
{{MOS mode degrees}}
| style="text-align:center;" |
 
| style="text-align:center;" |
=== Proposed names ===
| style="text-align:center;" |
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.
| style="text-align:center;" |
 
| style="text-align:center;" | 29\69
{{MOS modes
| style="text-align:center;" |
| Table Headers=
| | 504.348
Mode names<br>(by [[User:Eliora|Eliora]]) $
| style="text-align:center;" |
Mode names<br>(by [[User:Ganaram inukshuk|Ganaram]])
|-
| Table Entries=
| |
July $
| |
Martian $
| |
December $
| |
Aprilian $
| |
May $
| |
Maian $
| | 504.275
October $
| |
Junian $
|-
March $
| style="text-align:center;" |
Quintillian <br>Julian $
| style="text-align:center;" |
August $
| style="text-align:center;" |
Sextilian <br>Augustan $
| style="text-align:center;" |
January $
| style="text-align:center;" |
Septembian $
| style="text-align:center;" | 50\119
June $
| | 504.202
Octobian $
| style="text-align:center;" |
November $
|-
Novembian $
| style="text-align:center;" |
April $
| style="text-align:center;" |
Decembian $
| style="text-align:center;" |
September $
| style="text-align:center;" | 21\50
Janian $
| style="text-align:center;" |
February $
| style="text-align:center;" |
Februan $
| | 504
}}
| style="text-align:center;" | Meantone/Meanpop
 
|-
== Scales ==
| style="text-align:center;" |
* [[Meaneb471a]] – an equal beating tuning of meantone
| style="text-align:center;" |
* [[Meantone12]] – 31edo tuning
| style="text-align:center;" |
* [[Ratwolf]] – 20/13 wolf fifth tuning of meantone
| style="text-align:center;" |
* [[Meaneb471]] – the other equal beating tuning of meantone
| style="text-align:center;" |
* [[Flattone12]] – 13-limit POTE tuning of flattone
| style="text-align:center;" | 55\131
 
| | 503.817
== Scale tree ==
| style="text-align:center;" | Golden meantone
{{MOS tuning spectrum
|-
| 4/3 = Meantone / [[meridetone]]
| |
| 7/5 = Meantone / [[huygens]] / [[grosstone]]
| |
| 13/8 = [[Golden meantone]] (503.7855{{c}})
| |
| 8/5 = [[Meantone]]
| |
| 5/3 = Meantone / [[meanpop]]
| |
| 5/2 = ↕&nbsp;[[Flattone]]
| |
| 13/5 = Golden flattone (506.9365{{c}})
| | 503.7855
}}
| |
 
|-
[[Category:12-tone scales]]
| style="text-align:center;" |  
[[Category:M-chromatic| ]]<!-- main article -->
| style="text-align:center;" |  
[[Category:Chromatic scales]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 34\81
| style="text-align:center;" |
| | 503.704
| style="text-align:center;" | Optimal meantone is around here
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 47\112
| | 503.571
| style="text-align:center;" | Meantone/Meanpop
|-
| |
| |
| |
| |
| |
| |
| | 503.5685
| |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 13\31
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| | 503.226
| style="text-align:center;" | Optimal rank range (L/s=3/2)
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 44\105
| | 502.857
| style="text-align:center;" | Meantone/Huygens
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 31\74
| style="text-align:center;" |
| | 502.703
| style="text-align:center;" | Meantone/Huygens
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 49\117
| | 502.564
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 18\43
| style="text-align:center;" |
| style="text-align:center;" |
| | 502.326
| style="text-align:center;" | Meantone/Meridetone
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 41\98
| | 502.041
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 23\55
| style="text-align:center;" |
| | 501.818
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 28\67
| | 501.493
| style="text-align:center;" |
|-
| style="text-align:center;" | 5\12
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| | 500
| style="text-align:center;" |
|}

Latest revision as of 12:36, 28 April 2025

↖ 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.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

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 ¢

Generator chain

Generator chain of 7L 5s
Bright gens Scale degree Abbrev.
18 Augmented 6-mosdegree A6md
17 Augmented 1-mosdegree A1md
16 Augmented 8-mosdegree A8md
15 Augmented 3-mosdegree A3md
14 Augmented 10-mosdegree A10md
13 Augmented 5-mosdegree A5md
12 Augmented 0-mosdegree A0md
11 Augmented 7-mosdegree A7md
10 Major 2-mosdegree M2md
9 Major 9-mosdegree M9md
8 Major 4-mosdegree M4md
7 Major 11-mosdegree M11md
6 Major 6-mosdegree M6md
5 Major 1-mosdegree M1md
4 Major 8-mosdegree M8md
3 Major 3-mosdegree M3md
2 Major 10-mosdegree M10md
1 Perfect 5-mosdegree P5md
0 Perfect 0-mosdegree
Perfect 12-mosdegree		 P0md
P12md
−1 Perfect 7-mosdegree P7md
−2 Minor 2-mosdegree m2md
−3 Minor 9-mosdegree m9md
−4 Minor 4-mosdegree m4md
−5 Minor 11-mosdegree m11md
−6 Minor 6-mosdegree m6md
−7 Minor 1-mosdegree m1md
−8 Minor 8-mosdegree m8md
−9 Minor 3-mosdegree m3md
−10 Minor 10-mosdegree m10md
−11 Diminished 5-mosdegree d5md
−12 Diminished 12-mosdegree d12md
−13 Diminished 7-mosdegree d7md
−14 Diminished 2-mosdegree d2md
−15 Diminished 9-mosdegree d9md
−16 Diminished 4-mosdegree d4md
−17 Diminished 11-mosdegree d11md
−18 Diminished 6-mosdegree d6md

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		 Mode names
(by Eliora)		 Mode names
(by Ganaram)
11|0 1 LLsLsLLsLsLs July Martian
10|1 6 LLsLsLsLLsLs December Aprilian
9|2 11 LsLLsLsLLsLs May Maian
8|3 4 LsLLsLsLsLLs October Junian
7|4 9 LsLsLLsLsLLs March Quintillian
Julian
6|5 2 LsLsLLsLsLsL August Sextilian
Augustan
5|6 7 LsLsLsLLsLsL January Septembian
4|7 12 sLLsLsLLsLsL June Octobian
3|8 5 sLLsLsLsLLsL November Novembian
2|9 10 sLsLLsLsLLsL April Decembian
1|10 3 sLsLLsLsLsLL September Janian
0|11 8 sLsLsLLsLsLL February Februan

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

Scale tree and tuning spectrum of 7L 5s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\12 500.000 700.000 1:1 1.000 Equalized 7L 5s
28\67 501.493 698.507 6:5 1.200
23\55 501.818 698.182 5:4 1.250
41\98 502.041 697.959 9:7 1.286
18\43 502.326 697.674 4:3 1.333 Supersoft 7L 5s
Meantone / meridetone
49\117 502.564 697.436 11:8 1.375
31\74 502.703 697.297 7:5 1.400 Meantone / huygens / grosstone
44\105 502.857 697.143 10:7 1.429
13\31 503.226 696.774 3:2 1.500 Soft 7L 5s
47\112 503.571 696.429 11:7 1.571
34\81 503.704 696.296 8:5 1.600 Meantone
55\131 503.817 696.183 13:8 1.625 Golden meantone (503.7855 ¢)
21\50 504.000 696.000 5:3 1.667 Semisoft 7L 5s
Meantone / meanpop
50\119 504.202 695.798 12:7 1.714
29\69 504.348 695.652 7:4 1.750
37\88 504.545 695.455 9:5 1.800
8\19 505.263 694.737 2:1 2.000 Basic 7L 5s
Scales with tunings softer than this are proper
35\83 506.024 693.976 9:4 2.250
27\64 506.250 693.750 7:3 2.333
46\109 506.422 693.578 12:5 2.400
19\45 506.667 693.333 5:2 2.500 Semihard 7L 5s
↕ Flattone
49\116 506.897 693.103 13:5 2.600 Golden flattone (506.9365 ¢)
30\71 507.042 692.958 8:3 2.667
41\97 507.216 692.784 11:4 2.750
11\26 507.692 692.308 3:1 3.000 Hard 7L 5s
36\85 508.235 691.765 10:3 3.333
25\59 508.475 691.525 7:2 3.500
39\92 508.696 691.304 11:3 3.667
14\33 509.091 690.909 4:1 4.000 Superhard 7L 5s
31\73 509.589 690.411 9:2 4.500
17\40 510.000 690.000 5:1 5.000
20\47 510.638 689.362 6:1 6.000
3\7 514.286 685.714 1:0 → ∞ Collapsed 7L 5s
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