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Meantonic Eb:G:Bb:C#:F = 4: 5*[210/209]: 6*(1880/1881): 7*{232/231}: 9*(512/513)

🔗Andreas Sparschuh <a_sparschuh@...>

2/17/2009 12:50:37 PM

Start in 5ths beginning from Ab,
so that the minor-3rd F-Ab = 13/11 = 6.5/5.5

Ab_-1: 13 26 52 104 208(>209) 416Hz 832Ab_5
Eb_5: 627 [630 315=G_6/5]
Bb_3: 235 470 940Bb_5 1880 (<1881)
F_-1: 11 22 44 88 176 (351<)352*3^0 704F_6 (<705)
C_5 : 526.5 1053 := 351*3^1
G_5 : 787.5 1575 := 350*3^2
D_5 : 588.9375 ... 9423 := 349*3^3
A_5 : 880.875 ... 7047 := 87_174_348*3^4
E_5 : 658.757812... 84321 := 347*3^5
B_5 : 985.757812... 126177 := 173_346*3^6
F#5 : 736.831055... 754515 := 345*3^7(<736 368 184 92 46 23)
C#5 : 551 ..282112(<282123 :=43_86_172_344*3^8)(>552 276 138 69=23*3)
G#-1: 13 26 52 104 208 (<207 = 69*3 = 23*9)

or as concise distribution of the PC over the dozen 5ths

Ab
209/208 ~+8.303
Eb
1880/1881 ~0.921
Bb
704/705 ~-2.457
F
351/352 ~-4.925
C
350/351 ~-4.939
G
349/350 ~-4.953
D
348/349 ~-4.967
A
347/348 ~-4.981
E
346/347 ~-4.996
B
345/346 ~-5.011
F#
(344/345)(282121/282123) ~--5.037
C#
552/551 ~+3.139
G#

Attend and listen the sonorous minor-3rd F-Ab,
that amounts in seize:
13/11 ~280.210...Cents
inbetween the 11th and 13th partial of the overtone-series, or equally
6.5/5.5
(6/5)(65/66) ~-25.432...c ~PC
(32/27)(351/352) ~- 4.925...c ~PC^(1/5)
(7/6)(78/77) ~+22.330...c ~PC

inbetween the 11th and 13th partial of the overtone-series.

Line up the dozen pitches
out of the circle of 5ths
chromatically in ascending order
within the tenor-octave range:

c 526.5 tenor-C_5
# 551
d 787.5
# 627
e 658.757812
f 704
# 736.831055
g 787.5
# 832
a 880.875 Hz ; that's 52.5 Metronome-beats/min above 880 Hz
# 940
b 736.831055
c'1053 sopran-C_6

That's in
http://www.xs4all.nl/~huygensf/scala/scl_format.html

! Spars45679.scl
!
Sparschuh's Eb:G:Bb:C#:F = 4:5*210/209:6*1880/1881:7*232/231:9*512/513
! Deviations in Cents of the chord
! Eb : G : Bb : C# : F = '4':~'5':~'6':~'7':~'9'
!
! Eb '4'
! G_ '5' +~8.264c [210/209]
! Bb '6' -~0.921c (1880/1881)
! C# '7' +~7.478c {232/231}
! F_ '9' -~3.378c (512/513)
!
1102/1053 ! C# (21/20)(1170/1169) ~ 78.743...
349/312 ! D (9/8)(349/351) = (10/9)(1047/1040) ~194.017...
414/351 ! Eb (32/27)(207/208) = (6/5)(114/115) ~285.792...
1041/832 ! E (5/4)(1041/1040) ~387.978...
1408/1053 ! F (4/3)(352/351) ~502.970...
9315/6656 ! F# (45/32)(207/208) ~581.880...
350/234 ! G (3/2)(350/351) ~697.015...
128/81 ! G# (2^7)/(3^4) ~792.180...
87/52 ! A (5/3)(261/260) = (27/16)(116/117) ~891.005...
1880/1053 ! Bb (16/9)(235/234) ~1003.473...
1557/832 ! B (15/8)(520/519) ~1084.936...
2/1
!
!

Try Bach's organ-works canorous sounding in that one.
Have a lot of fun when playing his oeuvre in that mild mean-tonics.
bye
A.S.