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7L 5s: Difference between revisions

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{{interwiki
| de =
| en = 7L 5s
| es =
| ja = 7L 5s
}}
{{Infobox MOS}}
{{Infobox MOS}}
{{MOS intro|Other Names=m-chromatic}}


'''7L 5s''' is the MOS pattern of the [[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.
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]].


The meantone chromatic scale with generator between 5\12 (500 cents) and 8\19 (505.263 cents) is [[Rothenberg propriety|proper]].
Meantone is the only notable harmonic entropy minimum.


== Modes ==
== Scale properties ==
Eliora proposes mode names based on the layout of the Gregorian calendar. For example, since starting with January months are 31-28*-31-30-31-30-31-31-30-31-30-31, making a LsLsLsLLsLsL pattern, the associated mode is named January.
{{TAMNAMS use}}


* 11|0 LLsLsLLsLsLs - July
=== Intervals ===
* 10|1 LLsLsLsLLsLs - December
{{MOS intervals}}
* 9|2 LsLLsLsLLsLs - May
 
* 8|3 LsLLsLsLsLLs - October
=== Generator chain ===
* 7|4 LsLsLLsLsLLs - March
{{MOS genchain}}
* 6|5 LsLsLLsLsLsL - August
 
* 5|6 LsLsLsLLsLsL - January
=== Modes ===
* 4|7 sLLsLsLLsLsL - June
{{MOS mode degrees}}
* 3|8 sLLsLsLsLLsL - November
 
* 2|9 sLsLLsLsLLsL - April
=== Proposed names ===
* 1|10 sLsLLsLsLsLL - September
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.
* 0|11 sLsLsLLsLsLL - February
 
{{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 $
}}


== Scales ==
== Scales ==
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== Scale tree ==
== Scale tree ==
Generator ranges:
{{MOS tuning spectrum
* Chroma-positive generator: 500 cents (5\12) to 514.2857 cents (3\7)
| 4/3 = Meantone / [[meridetone]]
* Chroma-negative generator: 685.7143 cents (4\7) to 700 cents (7\12)
| 7/5 = Meantone / [[huygens]] / [[grosstone]]
 
| 13/8 = [[Golden meantone]] (503.7855{{c}})
{| class="wikitable center-all"
| 8/5 = [[Meantone]]
! colspan="6" | Generator
| 5/3 = Meantone / [[meanpop]]
! Cents
| 5/2 = ↕&nbsp;[[Flattone]]
! L
| 13/5 = Golden flattone (506.9365{{c}})
! s
}}
! L/s
! Comments
|-
| 5\12 || || || || || || 500.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 28\67 || 501.493 || 6 || 5 || 1.200 ||
|-
| || || || || 23\55 || || 501.818 || 5 || 4 || 1.250 ||
|-
| || || || || || 41\98 || 502.041 || 9 || 7 || 1.286 ||
|-
| || || || 18\43 || || || 502.326 || 4 || 3 || 1.333 || [[Meantone]] / [[meridetone]]
|-
| || || || || || 49\117 || 502.564 || 11 || 8 || 1.375 ||
|-
| || || || || 31\74 || || 502.703 || 7 || 5 || 1.400 || [[Meantone]] / [[huygens]] / [[grosstone]]
|-
| || || || || || 44\105 || 502.857 || 10 || 7 || 1.428 ||
|-
| || || 13\31 || || || || 503.226 || 3 || 2 || 1.500 ||
|-
| || || || || || 47\112 || 503.571 || 11 || 7 || 1.571 ||
|-
| || || || || 34\81 || || 503.704 || 8 || 5 || 1.600 || [[Meantone]]
|-
| || || || || || 55\131 || 503.817 || 13 || 8 || 1.625 || [[Golden meantone]] (503.7855¢)
|-
| || || || 21\50 || || || 504.000 || 5 || 3 || 1.667 || [[Meantone]] / [[meanpop]]
|-
| || || || || || 50\119 || 504.202 || 12 || 7 || 1.714 ||
|-
| || || || || 29\69 || || 504.348 || 7 || 4 || 1.750 ||
|-
| || || || || || 37\88 || 504.545 || 9 || 5 || 1.800 ||
|-
| || 8\19 || || || || || 505.263 || 2 || 1 || 2.000 || Basic m-chromatic <br>(Generators smaller than this are proper)
|-
| || || || || || 35\83 || 506.024 || 9 || 4 || 2.250 ||
|-
| || || || || 27\64 || || 506.250 || 7 || 3 || 2.333 ||
|-
| || || || || || 46\109 || 506.422 || 12 || 5 || 2.400 ||
|-
| || || || 19\45 || || || 506.667 || 5 || 2 || 2.500 || [[Flattone]]
|-
| || || || || || 49\116 || 506.897 || 13 || 5 || 2.600 || Golden flattone (506.9365¢)
|-
| || || || || 30\71 || || 507.042 || 8 || 3 || 2.667 ||
|-
| || || || || || 41\97 || 507.216 || 11 || 4 || 2.750 ||
|-
| || || 11\26 || || || || 507.692 || 3 || 1 || 3.000 ||
|-
| || || || || || 36\85 || 508.235 || 10 || 3 || 3.333 ||
|-
| || || || || 25\59 || || 508.475 || 7 || 2 || 3.500 ||
|-
| || || || || || 39\92 || 508.696 || 11 || 3 || 3.667 ||
|-
| || || || 14\33 || || || 509.091 || 4 || 1 || 4.000 ||
|-
| || || || || || 31\73 || 509.589 || 9 || 2 || 4.500 ||
|-
| || || || || 17\40 || || 510.000 || 5 || 1 || 5.000 ||
|-
| || || || || || 20\47 || 510.638 || 6 || 1 || 6.000 ||
|-
| 3\7 || || || || || || 514.286 || 1 || 0 || → inf ||
|}


[[Category:12-tone scales]]
[[Category:12-tone scales]]
[[Category:M-chromatic| ]] <!-- main article -->
[[Category:M-chromatic| ]]<!-- main article -->
[[Category:Chromatic scales]]
[[Category:Chromatic scales]]
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