Topic: Re: [tuning] From Descartes-12-tone to Newton-53-tone diagramms

1 scales

File	Description	Notes	Period (¢)	Limit
Descartes_Hexa	Descartes 3 nested ~1650 hexachords:voices(B)-flat,naturall and in [B]	12	1200.0	5

Thread (4 messages)

From: Graham Breed (2009-04-15)
Subject: Re: [tuning] From Descartes-12-tone to Newton-53-tone diagramms

Andreas Sparschuh wrote:
> Hi all,
> 
> here the *.pdf file:
> http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6WG9-4NS2GPC-2-1&_cdi=6817&_user=2717328&_orig=search&_coverDate=02%2F29%2F2008&_sk=999649998&view=c&wchp=dGLbVzb-zSkzV&md5=52ea534852cf87238f69b44dfa2b8e44&ie=/sdarticle.pdf
> the *.html link:
> http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WG9-4NS2GPC-2&_user=2717328&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000056831&_version=1&_urlVersion=0&_userid=2717328&md5=6cc6ad7161746a29dd61f7a618ebdc16

This mentions another chart from Newton:

"Next there are several versions, two quite large, of a 
chart in which the notes of the just scale are correlated 
with their approximations in various different equal 
divisions of the octave. Altogether, the equal divisions 
that were tried out were those into 12, 20, 24, 25, 29, 36, 
41, 51, 53, 59, 100, 120, and 612: the apparently most final 
version of the table shows those into 53, 612, 100, 36, 29, 
and 120 (in that order) [Cambridge, University Library, Add 
MS. 4000, ff. 108r\ufffd108v]."

                            Graham

From: Andreas Sparschuh (2009-04-17)
Subject: Re: From Descartes-12-tone to Newton-53-tone diagramms

--- In [email protected], Graham Breed <gbreed@...> wrote:
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WG9-4NS2GPC-2&_user=2717328&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000056831&_version=1&_urlVersion=0&_userid=2717328&md5=6cc6ad7161746a29dd61f7a618ebdc16
> 
> This mentions another chart.... 
of Descartes's
http://www.sciencedirect.com/science?_ob=MiamiCaptionURL&_method=retrieve&_udi=B6WG9-4NS2GPC-2&_image=fig002&_ba=2&_user=2717328&_rdoc=1&_fmt=full&_orig=search&_cdi=6817&view=c&_acct=C000056831&_version=1&_urlVersion=0&_userid=2717328&md5=c2fa8edb2aeea631f259b011ff4f50d5

Read his stringlenghts in clockwise direction

C 360 sol|ut|fa
d 324 la|re|__
D 320 __|__|sol
e 288 __|mi|la 
F 540 ut|fa|__ 270
g 486 re|__|__
G 480 __|sol|ut
a 432 mi|la|re
(A later added)
b(b) 405 fa|__|__
?B(b) ??? probably meant ?
h 384 __|__|mi or [B]
C'360 sol|ut|fa

or when expressed in 
http://www.xs4all.nl/~huygensf/scala/scl_format.html
terms as JI-ratios with some 81/80 comma-shifts

!Descartes_Hexa.scl
!
Descartes 3 nested ~1650 hexachords:voices(B)-flat,naturall and in [B]
!
12
!
10/9 !_ d
9/8 !__ D
5/4 !__ e
4/3 !__ F
40/27 ! g
3/2 !__ G
5/3 !__ a
27/16 ! A later added in order to yield totally a dozen pitches
16/9 !_ b(b) round
9/5 !__ B(b) ? probably meant ?
15/8 !_ h or [B] quadratic
2/1 !__ C'
!
!

Quest:
Is that interpretation correct so?

bye
A.S.

From: Claudio Di Veroli (2009-04-17)
Subject: RE: [tuning] Re: From Descartes-12-tone to Newton-53-tone diagramms

Most interesting Andreas!
Just added a missing detail:

________________
Read his stringlenghts in clockwise direction

C 360 sol|ut|fa
d 324 la|re|__
D 320 __|__|sol
e 288 __|mi|la 
>>> should add here E 276
F 540 ut|fa|__ 270
g 486 re|__|__
G 480 __|sol|ut
a 432 mi|la|re
(A later added)
b(b) 405 fa|__|__
?B(b) ??? probably meant ?
h 384 __|__|mi or [B]
C'360 sol|ut|fa
_________________

As you know very well, it is worth noting that, as much as extant tuning
instructions for practical musicians - and the musical scores -  show, in
the Baroque period where those writings were produced and published,
performing musicians used meantone temperament, circular temperaments and
occasionally equal temperament, but not JI in any of its variants, except
for very isolated cases, unrelated to the work of any major composer, and
related instead to experimental instruments (such as Ban's keyboard,
triple-fretboard guitars and the like). 

Kind regards

Claudio

http://temper.braybaroque.ie/

From: Andreas Sparschuh (2009-04-18)
Subject: Re: From Descartes-12-tone to Newton-53-tone diagramms

--- In [email protected], "Claudio Di Veroli" <dvc@...> wrote:
agreed Claudio,

> Just added a missing detail:
that there should 

5/4 > e 288 __|mi|la 
81/64 > >>> should add here E 276

also appeat the ditone
http://de.wikipedia.org/wiki/Ditonus
too.


> Baroque period...:  
> used meantone temperament, circular temperaments and
> occasionally equal temperament, but not JI ...
> for very isolated cases,
> related to experimental instruments: such as Ban's keyboard,
http://www.xs4all.nl/~huygensf/pics/ban2.png


http://en.wikipedia.org/wiki/Joan_Albert_Ban
http://www.xs4all.nl/~huygensf/ban.html
http://www.hbdirect.com/browse_classical.php?v%5B0%5D=composer&composer=B&do=specific_composer&specific_composer=Ban%2C%20Joan%20Albert
http://www.dbnl.org/auteurs/auteur.php?id=ban_001

Ban teached that to Weckmeister.

bye
A.S.