--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> > Here's a tally of the 19-limit consonances.
> >
> > 19/18 1
> > 18/17 4
> > 17/16 2
> > 19/17 0
> > 9/8 2
> > 19/16 5
> > 24/19 2
> > 4/3 4
> > 17/12 2
> > ---------
> > 22
> (a,b,c,b,a,b,1,1,b,1,1,b) where a=6137/6144, b=512/513, c=4617/4624.

Hi Carl, Tom & all others,

yours ... 19,17,3 approachs work similar as my older attempts in:
http://launch.groups.yahoo.com/group/clavichord/message/8737
.
That proposal intends to offer an arguable
http://en.wikipedia.org/wiki/Historically_informed_performance
tuning on modern replicas of
http://en.wikipedia.org/wiki/Michael_Mietke
"Clavessin"
"He delivered a harpsichord to the court at Cöthen in 1719 on the
recommendation of Johann Sebastian Bach, which was probably the
instrument for which Bach composed Brandenburg concerto no.5 as a
show-piece."
The scholary literature offers some further details
about Bachs's journey to Berlin for buying there the instrument.
Even the bill is still preserved.
Dated: Cöthen, March 1st 1719,
It lists $130 expenses altogehter.
Reprint in:
Bach-Dokumente, Kassel 1969, Vol.II p.73-74, #95
Translation into english by A.Mendel, Bach reader p.431,490

But when Bach moved in 1723 to Leipzig
that piano remained back in Coethen at least until 1784,
recorded among the court's inventory:
"Specifickation derer Fürstlichen Instrumenten in der
Musikalienkammer"
lists it on March, 8th, 1784 as "defect".

The problem:
Today, nobody knows any more how Bach had tuned that instrument.

But HIPerformers need for Mietke-replicas
adequate modern so called "Bach"-tunings,
preferably in the coeval "Cammerthone"
pitch of a4=(~405+-5)cps
as known from Mietke's others instruments too.

Hence a modern "Bach"-tuning should contain that specification,
in order to represent the state of the art in the research of the
last ~10 years:

New proposal for absolute pitches located at the frequencies:

243 middle_c'
256
272 d'
304
304 e'
312 f'
342
364 g'
392
406 a' cps or Hz
432
456 b'
486 c"

as again obtained from Bach's 1722(1723?) WTC autograph,
when reading the 'squiggle' pattern layout as an instruction
how to temper 5ths the corresponding to the "squiggles"
http://en.wikipedia.org/wiki/Well_Tempered_Clavier

Here an older photo of JSB's "decorative-ornaments" that i do prefer:
http://www.strukturbildung.de/Andreas.Sparschuh/Bach_Handschrift.jpg

That doodle at the top can be interpreted symbolic as:

Concise: start~2~2~2~1-1-1~3-3-3-3-3-3=end

when understood as an cylce 12 times 5ths

Or when labeld with note-names:
start=C~2G~2D~2A~2E-1B-1F#-1C#~3G#-3D#-3A#-3F-3C=end

Or even when expanded into full detailed pitches:
start=C 243 := 3^5 obtained from the last 5 ternary 'squiggles'
~2~ G 91 182 364 728 (<729 :=3^6)
~2~ D 68 136 272 (<273 := 3*G)
~2~ A 203 (<204 := 3*68)
~1- E 19 38 76 152 304 608 (<609 := 3*A) ; 3 single 'squiggles'
-1- B 57
-1~ F# 171
~3- C# 1...512 (<513 := 3*F#) ; the concluding 5 triply 'squiggles'
-3- G# 3
-3- D# 9 := 3^2
-3- A# 27 := 3^3
-3- F 81 := 3^4
-3. C=end 243 := 3^5

That's in today's modern terms of the:
http://www.xs4all.nl/~huygensf/scala/scl_format.html

!Sparschuh_proposal_Mietke.scl
!absolute pitches from the middle_c' on:
c'243#256 d'272#288 e'304 f'324#342 g'364#384 a'406#432 b'456
!
12
!
256/243 ! ~90.22...(cents)
272/243 ! ~195.81... D
32/27 ! ~294.13...
304/243 ! ~387.74... E (5/4)*(1216/1215)
4/3 ! ~498.04... F
38/27 ! ~591.65...
364/243 ! ~699.58... G (3/2)*(728/729)
128/81 ! ~792.18...
406/243 ! ~888.63... A4=406cps ~ Coeval Berlin, Coethen Cammer-thone
16/9 ! ~996.09...
152/81 ! ~1089.69... B
2/1

Attend,
that tuning contains some consecutive partials
out of the overtone-series inbetween the 4 semitones:

16 : 17 : 18 : 19 == C#1 : D1 : Eb1 : E1

in reference to:
http://en.wikipedia.org/wiki/Johann_Gottfried_Walther
specification in his:
"He wrote a handbook for the young Duke with the title Praecepta der
musicalischen Composition, 1708. It remained handwritten until Peter
Benary's edition (Leipzig, 1955)."

in german:
http://de.wikipedia.org/wiki/Johann_Gottfried_Walther
's
"Praecepta der musicalischen Composition, Weimar 1708;
Neu hrsg. von Peter Benary in:
Jenaer Beiträge zur Musikforschung. Band 2,
Breitkopf & Härtel, Leipzig 1955 "

bye
A.S.