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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
| |
| |
| |
| |
| |
| | 514.286
| |
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 20\47
| | 510.638
| |
|-
| |
| |
| |
| |
| style="text-align:center;" | 17\40
| |
| | 510
| |
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 31\73
| | 509.589
| |
|-
| |
| |
| |
| style="text-align:center;" | 14\33
| |
| |
| | 509.091
| |
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 39\92
| | 508.696
| |
|-
| |
| |
| |
| |
| style="text-align:center;" | 25\59
| |
| | 508.475
| |
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 36\85
| | 508.235
| |
|-
| |
| |
| |
| |
| |
| |
| | 507.934
| style="text-align:center;" | L/s = pi
|-
| |
| |
| style="text-align:center;" | 11\26
| |
| |
| |
| | 507.692
| style="text-align:center;" | Flattone
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 41\97
| | 507.216
| style="text-align:center;" | Flattone
|-
| |
| |
| |
| |
| |
| |
| | 507.151
| style="text-align:center;" | L/s = e
|-
| |
| |
| |
| |
| style="text-align:center;" | 30\71
| |
| | 507.042
| style="text-align:center;" | Flattone
|-
| |
| |
| |
| |
| |
| |
| | 506.9365
| style="text-align:center;" | L/s = phi+1
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 49\116
| | 506.897
| style="text-align:center;" | Flattone
|-
| |
| |
| |
| style="text-align:center;" | 19\45
| |
| |
| | 506.667
| style="text-align:center;" | Flattone
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 46\109
| | 506.422
| style="text-align:center;" | Flattone
|-
| |
| |
| |
| |
| style="text-align:center;" | 27\64
| |
| | 506.25
| style="text-align:center;" | Flattone
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 35\83
| | 506.024
| |
|-
| |
| style="text-align:center;" | 8\19
| |
| |
| |
| |
| | 505.263
| style="text-align:center;" | Boundary of propriety: generators smaller than this are proper.


Meanenneadecal; L/s = 2
== Scale properties ==
|-
{{TAMNAMS use}}
| |
 
| |
=== Intervals ===
| |
{{MOS intervals}}
| |
 
| |
=== Generator chain ===
| style="text-align:center;" | 37\88
{{MOS genchain}}
| | 504.5455
 
| |
=== Modes ===
|-
{{MOS mode degrees}}
| |
 
| |
=== 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 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=
| | 504.507
Mode names<br>(by [[User:Eliora|Eliora]]) $
| style="text-align:center;" | [[Lucy Tuning]]
Mode names<br>(by [[User:Ganaram inukshuk|Ganaram]])
|-
| Table Entries=
| |
July $
| |
Martian $
| |
December $
| |
Aprilian $
| style="text-align:center;" | 29\69
May $
| |
Maian $
| | 504.348
October $
| |
Junian $
|-
March $
| |
Quintillian <br>Julian $
| |
August $
| |
Sextilian <br>Augustan $
| |
January $
| |
Septembian $
| |
June $
| | 504.275
Octobian $
| style="text-align:center;" | L/s = sqrt(3)
November $
|-
Novembian $
| |
April $
| |
Decembian $
| |
September $
| |
Janian $
| |
February $
| style="text-align:center;" | 50\119
Februan $
| | 504.202
}}
| |
 
|-
== Scales ==
| |
* [[Meaneb471a]] – an equal beating tuning of meantone
| |
* [[Meantone12]] – 31edo tuning
| |
* [[Ratwolf]] – 20/13 wolf fifth tuning of meantone
| style="text-align:center;" | 21\50
* [[Meaneb471]] – the other equal beating tuning of meantone
| |
* [[Flattone12]] – 13-limit POTE tuning of flattone
| |
 
| | 504
== Scale tree ==
| style="text-align:center;" | Meantone / Meanpop
{{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]]
| style="text-align:center;" | 55\131
| 13/5 = Golden flattone (506.9365{{c}})
| | 503.817
}}
| style="text-align:center;" | Golden meantone
 
|-
[[Category:12-tone scales]]
| |
[[Category:M-chromatic| ]]<!-- main article -->
| |
[[Category:Chromatic scales]]
| |
| |
| |
| |
| | 503.7855
| style="text-align:center;" | L/s = phi
|-
| |
| |
| |
| |
| style="text-align:center;" | 34\81
| |
| | 503.704
| style="text-align:center;" | Optimal meantone is around here
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 47\112
| | 503.571
| style="text-align:center;" | Meantone / Meanpop
|-
| |
| |
| |
| |
| |
| |
| | 503.5685
| style="text-align:center;" | L/s = pi/2
|-
| |
| |
| style="text-align:center;" | 13\31
| |
| |
| |
| | 503.226
| style="text-align:center;" | Optimal rank range (L/s = 3/2)
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 44\105
| | 502.857
| style="text-align:center;" | Meantone / Huygens
|-
| |
| |
| |
| |
| style="text-align:center;" | 31\74
| |
| | 502.703
| style="text-align:center;" | Meantone / Huygens
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 49\117
| | 502.564
| |
|-
| |
| |
| |
| style="text-align:center;" | 18\43
| |
| |
| | 502.326
| style="text-align:center;" | Meantone / Meridetone
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 41\98
| | 502.041
| |
|-
| |
| |
| |
| |
| style="text-align:center;" | 23\55
| |
| | 501.818
| |
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 28\67
| | 501.493
| |
|-
| style="text-align:center;" | 5\12
| |
| |
| |
| |
| |
| | 500
| |
|}
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