--- In tuning@yahoogroups.com, Brad Lehman <bpl@...> wrote:

> All righty...this exercise is principally for Johnny, but also for
> Andreas and anyone else who wants to listen along.
...
>
> For Andreas: in the altered version, where three notes have been
knocked
> off-spot from W-III, please tell us *exactly* where you hear the
several
> 707-cent 5ths or 4ths. Where are these wide ones within the circle of
> 5ths? (Or, if you can't pick them out at all reliably here, what's
your
> objection to the sound of 704-cent 5ths elsewhere?)
>
>
Hi Brad & all others lovers of his wide"French"-5ths hypothesis,

Johnny also disagrees with Brad's hypothesis in:
http://launch.groups.yahoo.com/group/tuning/message/77284
quote:
"My instincts agree with Andreas's;
Bach's fifths were flatted in only one direction from just."

So thinks also too
M.Zapf's & K.Brigs in their's reinterpretation (May 2003):
http://keithbriggs.info/bach-wtc.html


But here my new proposal inbetween 2 others modern "Bach"-tunings:

1. Tom Dent's A4=419Hz reinterpretation of "squiggle"(Sept. 1999)
http://f1.grp.yahoofs.com/v1/EMtjSBdDLKZenwXKL3g47vURgGdMST8RbE8t_v0Qk2vomRsmHmE\
kPAruVkHuEJP6ulPx-wG95MVU6lEp6FDVq3SEJwcSCw/sparsgraph.txt

2. Kristian's A4=416Hz
http://www.wegscheider-orgel.de/html/artikel.php?filename=artikel.php&tabname=Ar\
tikel&sz=22&Unterpunkt=H.C.%A0Snerha%A0und%A0die%A0Bachstimmung
vomRsmHmEkPAruVkHuEJP6ulPx-wG95MVU6lEp6FDVq3SEJwcSCw/sparsgraph.txt

Presented as double inequality for the 12 absolute-pitches inbetween:

Tom Dent's 419Hz "squiggle" >= new-proposal 418Hz >= Wegscheider 416Hz

compare that 3 ones in chromatically order:

c' 250 > 249.5 < 248.7 at 'middle-C4'
C# 264 = 264 < 262.279688...
D: 280 = 280 < 278
Eb 297 > 296 > 295.111111...
E: 314 > 312 > (311,25 = 311+1/4)
F: 333.5> 333 > 332
F# 352 > 351 > 349,70625
G: 374 = 374 > 372.05
G# 396 > 394.75> 393,419531...
A: 419 > 418 > 416 > neo-"Baroque" modern 'Cammer-Thone' ~415Hz
Bb 445 > 444 > (442.66666... = 442+2/3)
B: 470 > 468 > 466.275
c" 500 > 499 > 497.4 at 'tenor-C5'

!Sparschuh418ib_Wegscheider_Dent.scl
12
Inbetween K.Wegscheider416Hz(June2003) and T.Dent419Hz(September2006)
!
1059/998 ! C# 529.5'tenor-C#5'/499
560/499 ! D
592/499 ! Eb
624/499 ! E (5:4)*(2496:2495) ~0.7 Cents wider than an 5/4 JI 3rd
666/499 ! F (4:3)*(999:998) ~1.7 Cents wider than an 4/3 JI 4th
702/499 ! F#
748/499 ! G (3:2)*(1496:1497)~-1.2 Cents narrower than an 3/2 JI 5th
1579/998 ! G# 789.5/499
836/499 ! A5 that's an octave above the absolute A4=418Hz reference
888/499 ! Bb
936/499 ! B
2/1 ! C6 = 998 'sopran-C6'
!

That proposal meets even Johnny demands
due to satisfying Sorge's condition:
All 5ths in that become barely tempered down in one direction
by the following 7 epimoric ratios lowered inbetween the 5ths,
that do amout totally an PC=3^12/2^19

499Hz=C5 1496:1497 G 560:561 D 209:210 A 208:209 E B F# C#...
C# 3158:3159 G# 4736:4737 Eb Bb F 998:999 C5=499Hz

or as expanded cycle of a dozen duodecimes 3:2 and
19-times octaves 2:1 down:

C5 = 499 'tenor-C5'
G2 = 187 374 748 1496 (<1497 := 3*C5)
D2 = 70 140 280 560 (<561 := 3*G2)
A3 = (13 26 52 104 208<) 209 (<210 := 3*D2)
E1 = 39 := 3*13
B2 = 117 := 9*13
F#4 = 351 :=27*13
C#6 = 1059 :=81*13
G#6 = 1579 3158 (<3159 := 243*13)
Eb1 = 37 74 148 296 592 1184 2368 4736 (<4737 := 3*G#6)
Bb2 = 111 := 3*Eb1
F4 = 333 := 3*Bb2
C5 = 499 998 (<999 := 3*F4)

if you posseses by change an todays modern
http://en.wikipedia.org/wiki/Harpsichord
that meets even:
"Tuning Pitch in nowadays' practice is taken often at a=415 Hz, a
semitone below modern standard concert pitch of a=440 Hz."
or more precisely:
http://en.wikipedia.org/wiki/Piano_key_frequencies
# "48 g&#9839;&#8242;/a&#9837;&#8242; G&#9839;4/A&#9837;4 ~415.305..."

when calculated from an theoretically 12-EDO step downwards:
440 / 2^(1/12) = ~415.304698...

with even 2 different keyboards for 2 independent 8-foot stops
then try to tune in practice on the one hand:
Wegscheider416Hz
versus on the other manual
Dent419Hz.

After that unify that both versions in one instrument
by synchonizing them to the above procedure into
the new intermediate tuning, in order to get rid of
'objections' against Wegscheider's broade-"French"5th.

Who in that group here dares to tune that new
another 'Bach' on his/hers own 415Hz instument?

No warranty garanteed for what happens then!

Yours Sincerely
A.S.