Topic: G66600011111C1G.scl as Bach's loops in an scala-file

2 scales

Thread (3 messages)

From: Andreas Sparschuh (2009-02-07)
Subject: G66600011111C1G.scl as Bach's loops in an scala-file

1. On the one hand:
Bach's famous drawing in:
http://www.strukturbildung.de/Andreas.Sparschuh/Bach_Handschrift.jpg
allows to regard the frist initial loop on the left 
as an lowercase Greek "phi"
http://en.wikipedia.org/wiki/Phi_(letter)
or similar as an German handwritten serif 
"G/g"
http://en.wikipedia.org/wiki/G

Already Simon Stevin also choosed that 'G' as root too.
http://www.xs4all.nl/~huygensf/doc/singe.html
"...g (from groot = large). Starting the scale with ut on G,..."
as remarked by the physicist A.D.Fokker
http://www.xs4all.nl/~huygensf/doc/stevinsp.html
"...It is curious to see that in certain diagrams he assigns the vocables

       ut  re  mi  fa  sol  la  sa  ut

to the letters

       -g- -a- -b- -c- -d- -e- -f- -g-  .... "

Attend that Bach refers in his introduction to the hexachords.
http://www.celestialmonochord.org/log/images/celestial_monochord.jpg


2. On the other hand:
Consider also Werckmeister's#3 PC^(1/4) ~6cents 
"C~G~D~A-E-B~F#...C" concept with '~'5ths := 696cents

C -6 G -6 D -6 A E B -6 F# C# G# Eb Bb F C.

That both components result in an corresponding scala-file:

! G66600011111C1G.scl 
! or expanded
G -6 D -6 A -6 E B F# -1 C# -1 G# -1 Eb -1 Bb -1 F -1 C -1 G.  
!
12
!
95
197
297
389
499
593
701
796
893
998
1091
2/1
!
!

Obtained from the tuning-procedure in a dozen 5ths and 7 octaves:

C 000
+ 701
G 701
+ 696 - 1200
D 197
+ 696 
A 893
+ 696 - 1200
E 389
+ 702
B1091
+ 702 - 1200
F#593
+ 702 - 1200
C# 95
+ 701
G#796
+ 701 - 1200
Eb297   
+ 701
Bb998
+ 701 - 1200
F 499
+ 701
C1200

Have a lot of fun when playing Bach's works in the above tuning.
bye
A.S.

From: Petr Parízek (2009-02-08)
Subject: Re: [tuning] G66600011111C1G.scl as Bach's loops in an scala-file

Andreas wrote:

> That both components result in an corresponding scala-file:

With the exception that cent values need to have a decimal point in them otherwise Scala treats them as frequency ratios. 

Petr

From: Andreas Sparschuh (2009-02-08)
Subject: G55500011111C4G.scl  SC  vs.  G66600011111C1G.scl PC as possible  Bach  variants

--- In [email protected], Petr Par�zek  wrote:

> With the exception that cent values need to have a decimal point in 
> them otherwise Scala treats them as frequency ratios. 

Sorry Peter,

in deed i really forgot all the required decimal dots "."
for indicating the pitches distinctively as cent-values,
as clearly demanded in the:
http://www.xs4all.nl/~huygensf/scala/scl_format.html
Many thanks for the kind advise.

Hence, here comes the now corrected version:

! G66600011111C1G.scl
! that's when expanded inbetween the corresponding 5ths
G -6 D -6 A -6 E B F# -1 C# -1 G# -1 Eb -1 Bb -1 F -1 C -1 G.scl
! PC variant
!
12
!
95.  ! C#
197. !PC! D > [195. SC]
297. ! Eb
389. ! E
499. ! F
593. ! F#
701. !PC! G < [699. SC] 
796. ! G#
893. !PC! A > [892, SC]
998. ! Bb
1091.! B
2/1
!
!

Alternative try the SC interpretation instead of the PC variant.

Replace the 3 Werckmeisterian G~D~A~E 5ths each of ~696c from the
http://en.wikipedia.org/wiki/Werckmeister_temperament
They amount more precisely in seize accurately:

1200c * ln(1.5 / ((3^12)/(2^19))^(1/4))) / ln(2) = ~696.089998...c
or
~-23.46...c/4 = ~5.87...c below just 3/2

inbetween the empty strings of the violin: G ~-6 D ~-6 A ~-6 E

by it's "regular" meantonic counterpart: (81/80)^(1/4)
http://launch.dir.groups.yahoo.com/group/tuning/message/79641

1200c * ln(1.5 / (81/80)^(1/4)) / ln(2) = ~696.578428...c ~697c
or
1200c * ln(80/81))/ln(2) / 4 = ~-5.3765724...c below just 3/2

Round that intermediate-extension downwards to integral ~-5c finally.

Attend the little differences
that arises from distinguishing
inbetween the PC and SC variants
@ the three pitches D, G & A in: 

! G55500011111C4G.scl
! or that's expanded inbetween the dozen of 5ths
G -5 D -5 A -5 E B F# -1 C# -1 G# -1 Eb -1 Bb -1 F -1 C -4 G.scl
! SC variant
!
12
!
95.  ! C#
195. !SC!  D < [197. PC]
297. ! Eb
389. ! E
499. ! F
593. ! F#
699. !SC! G > [701. PC]
796. ! G#
892. !SC! A < [893. PC] 
998. ! Bb
1091.! B
2/1
!
!

Speculative quest when compareing them both:
Which of that two above variants (PC or SC?) would had presumably
confused Bach's consort string-players less than the other one?
when considering that conservative guys had still persisted in tuning 
the empty strings G~D~A~E in meantonics furthermore...

Are there any suggestions or improvements that do sound even better 
as well-temperament that preserves an meantonic kernel on G~D~A~E 
as practical condition for coeval Baroque performance?

Who knows more?

Concluding remark:
Against the both above PC&SC variants, K3 
http://harpsichords.pbwiki.com/f/Kirn_1871.html
http://harpsichords.pbwiki.com/f/K_III.html
contains i.m.h.o. simply to many
http://de.wikipedia.org/wiki/Ditonus
http://en.wikipedia.org/wiki/Pythagorean_interval
" major third ditone 	81/64 	407.82"
as the initial W3 had all to much already once before.

bye
A.S.