billhails / MuseScore-plugins

Various MuseScore2 plugins that people might find useful
GNU General Public License v3.0
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normalise Bach/Lehman 1722 and add Bach/Lehman Chorale #4

Closed mirabilos closed 6 years ago

mirabilos commented 6 years ago

See also: https://github.com/gstlaurent/ttuner/pull/3

My notes on this (in case it interests someone):

Offsets keeping A4 constant:
  C (+5.9), C♯ (+3.9), D (+2), E♭ (+3.9), E (-2), F (+7.8),
   F♯ (+2), G (+3.9), G♯ (+3.9), A (0), B♭ (+3.9), B (0).
You end up with: F-C-G-D-A-E as they are in Vallotti ("1/6 comma" each);
 E-B-F♯-C♯ pure; C♯-G♯-D♯-A♯ very gently tempered ("1/12 comma" each);
 A♯-F leftover is also gently tempered, but happens to be wide.
  (pythagoräïsches Komma: 23.46 cent)
   Vallottis Temperatur besteht aus sechs um 1/6 pythagoräisches Komma
   temperierten Quinten von 698 Cent (F–C–G–D–A–E–H) und aus sechs
   reinen Quinten, die 702 Cent entsprechen (H–Fis–Cis–Gis/As–Es–B–F).
Chorale: 1 Ton hoch, also: G-D-A-E-B-F♯ 1/6 comma each; F♯-C♯-G♯-D♯ pure;
 E♭-B♭-F-C 1/12 comma each; very slightly wide (but nearly pure) C-G resulting.
 Offsets from A:
  C (0), C♯ (-3.9), D (+2), E♭ (0), E (-1.9), F (0),
   F♯ (-5.9), G (+3.9), G♯ (-1.9), A (0), B♭ (0), B (-3.9).

F   -2792.2     F-C   698.1     698 (-⅙,)                       -2800   +7.8
C   -2094.1     C-G   698       698 (-⅙,)                       -2100   +5.9
G   -1396.1     G-D   698.1     698 (-⅙,)                       -1400   +3.9
D   -698        D-A   698       698 (-⅙,)                       -700    +2.0
A   0           A-E   698       698 (-⅙,)                       0       ±0.0
E   698         E-B   702       702 (reine Stimmung)            700     -2.0
B   1400        B-F♯  702       702 (reine Stimmung)            1400    ±0.0
F♯  2102        F♯-C♯ 701.9     702 (reine Stimmung)            2100    +2.0
C♯  2803.9      C♯-G♯ 700       700 (-1/12,)                    2800    +3.9
G♯  3503.9      G♯-D♯ 700       700 (gleichstufige Stimmung)    3500    +3.9
D♯  4203.9      D♯-A♯ 700       700 (-1/12,)                    4200    +3.9
A♯  4903.9      B♭-F  703.9     704 (+1/12,)                    4900    +3.9
(F) 5607.8, ab initio 8400 = 7 Oktaven

Chorale konstruïert:

G   -1396.1     G-D   698.1     698 (-⅙,)                       -1400   +3.9
D   -698        D-A   698       698 (-⅙,)                       -700    +2.0
A   0           A-E   698.1     698 (-⅙,)                       0       ±0.0
E   698.1       E-B   698       698 (-⅙,)                       700     -1.9
B   1396.1      B-F♯  698       698 (-⅙,)                       1400    -3.9
F♯  2094.1      F♯-C♯ 702       702 (reine Stimmung)            2100    -5.9
C♯  2796.1      C♯-G♯ 702       702 (reine Stimmung)            2800    -3.9
G♯  3498.1      G♯-D♯ 701.9     702 (reine Stimmung)            3500    -1.9
D♯  4200        E♭-B♭ 700       700 (-1/12,)                    4200    ±0.0
B♭  4900        B♭-F  700       700 (gleichstufige Stimmung)    4900    ±0.0
F   5600        F-C   700       700 (-1/12,)                    5600    ±0.0
C   6300        C-G   703.9     704 (+1/12,)                    6300    ±0.0
(G) 7003.9, ab initio 8400 = 7 Oktaven
mirabilos commented 6 years ago

As discussed in https://github.com/billhails/MuseScore-plugins/issues/5 we’ll likely need a rules-based system instead, to support different base pitches.

Furthermore, my Maths was slightly off: to divide an interval like 531441/524288 does not mean (524288 + (531441 - 524288)/6)/524288 but to use the sixth root of (531441/524288), even if the resulting numbers are close enough together to make the difference look like a rounding issue…

I’m closing this and will later provide a new PR with a rules-based system.

billhails commented 6 years ago

Thanks for your attention, for some reason I missed your previous PR, I don't watch these repositories very closely but I do normally get e-mails. I await your rule-based system with interest.