Full thread (6 messages)
From: ham_45242 (2010-06-16)
Subject: Mersenne Chromatic Scale Diagram
Hello, all. I've been studying a diagram from Marin Mersenne's Harmonicorum Libri (the diagram may be seen at http://pythagoraspoetry.blogspot.com/2009/11/modern-understanding-of-key-center.html) and was wondering if anyone else in the group had looked at it in depth. A few observations:
1. It's definitely not a circle of 5ths (I don't know why one would conclude this.)
2. From the ratios presented the tuning appears to consist of 3 chains (separated by just thirds) of just (3/2) fifths: Eb (labelled as D#)-Bb-F-C-G, D-A-E-B and F#-C#-G#
3. There is at least one penmanship error: The C-F# tritone ratio should be 25/18 vice 35/18 as shown.
4. This tuning appears to be one of the tunings (after transposition) for the lute described by Mersenne in his Harmonie Universelle.
5. I've no clue as to the "7 1/2" value shown by the note F.
6. The solfege appears to be that used with hexachords and thus appropriate to the period.
Your time and comment is greatly appreciated. Sincerely,
From: Andy (2010-06-16)
Subject: Re: Mersenne Chromatic Scale Diagram
--- In tuning@yahoogroups.com, "ham_45242" <arl_123@...> wrote:
>
>...Marin Mersenne's Harmonicorum Libri, diagram may be seen at
> http://pythagoraspoetry.blogspot.com
> /2009/11/modern-understanding-of-key-center.html
Hi Ham,
in order to view it more precisely change to high-resultion as GIF:
http://3.bp.blogspot.com/_WAOQD2JSStc/SxA5Dk6CRSI/AAAAAAAAACw/BmaisJ5D5uQ/s1600/mersennestar.gif
then consider just only the 12 outer ratios in clockwise direction:
C 25/24 C# 16/15 D 16/15 Eb 135/128 E 16/15 F 25/24 F#....
...F# 27/25 G 25/24 G# 16/15 A 16/15 Bb 135/128 B 16/15 C
! MersenneStar.scl
Marin Mersenne's dodecatonic 5-limit Star compiled by A.Sparschuh
! from source
! http://3.bp.blogspot.com
! /_WAOQD2JSStc/SxA5Dk6CRSI/AAAAAAAAACw/BmaisJ5D5uQ/s1600
! /mersennestar.gif
!
12
!
25/24 ! C#
10/9 ! D
32/27 ! Eb
5/4 ! E
4/3 ! F
25/18 ! F#
3/2 ! G
25/16 ! G#
5/3 ! A
16/9 ! Bb
15/8 ! B
2/1
!
![eof]
bye
Andy
From: genewardsmith (2010-06-16)
Subject: Re: Mersenne Chromatic Scale Diagram
--- In tuning@yahoogroups.com, "Andy" <a_sparschuh@...> wrote:
> ! MersenneStar.scl
A transposition is already in the Scala directory as mersen_12.scl. You can obtain the scale by nibbling a corner off of the duodene and moving it to extend one of the chains of fifths.
From: ham_45242 (2010-06-17)
Subject: Re: Mersenne Chromatic Scale Diagram
--- In tuning@yahoogroups.com, "Andy" <a_sparschuh@...> wrote:
> 25/24 ! C#
> 10/9 ! D
> 32/27 ! Eb
> 5/4 ! E
> 4/3 ! F
> 25/18 ! F#
> 3/2 ! G
> 25/16 ! G#
> 5/3 ! A
> 16/9 ! Bb
> 15/8 ! B
> 2/1
> !
> ![eof]
>
>
> bye
> Andy
>
Thanks, Andy, and to the others who replied. The above is what I obtained as well. The Eb seems to stand out as a lone note (I probably would have used a 75/64 D# in this tuning.). Perhaps it's appropriate for a lute. Further errors in the diagram are the labelling of the Bb as "B" and no note indicated at the actual B location. Still don't know about that "7 1/2". Maybe it's an unrelated scribbling.
BTW, there hasn't been a lot of activity lately over at the bach_tunings group. Sincerely,
From: Andy (2010-06-17)
Subject: Re: Mersenne Chromatic Scale Diagram
--- In tuning@yahoogroups.com, "ham_45242" <arl_123@...> wrote:
> Further errors in the diagram are the labelling
> of the Bb as "B" and no note indicated at the actual B location.
Hi Ham,
just attend
http://launch.groups.yahoo.com/group/tuning/message/72095
for discernig inbetween the both variants of labeling the note "B":
ancient_round(b) = todays_english(Bb) = later_german(B) note-name
and
ancient_quadratic(b) = todays_enlish(B) = later_german(H) respectively.
alike used in Mersenne's other graphic in:
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WG9-4NS2GPC-2&_user=2717328&_rdoc=1&_fmt=full&_orig=search&_sort=d&view=c&_acct=C000056831&_version=1&_urlVersion=0&_userid=2717328&md5=5ff04abd46a359eda81dbd0b40a39c4b#bib002
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&_issn=03150860&_pii=S0315086007000341&view=c&_acct=C000056831&_version=1&_urlVersion=0&_userid=2717328&md5=a803e41e97c93821530901708fc11240
"Fig. 2. Descartes' representation in the English translation (Walter Charleton, Trans., William Brouncker, Ed.), Renatus Des-Cartes Excellent Compendium of Musick, 35. By permission of the Bodleian Library, University of Oxford (shelfmark: 4o R4 Art B5, 3).
> Still don't know about that "7 1/2".
> Maybe it's an unrelated scribbling.
I suppose, that means on monochord-string-length for F of 7.5 foots,
or an corresponding organ-pipe of 7.5" hight,
in the old sense of Arnold Schlick's tretaise on organ-building:
http://launch.groups.yahoo.com/group/tuning/message/71324
then at ~1500 was a change a 3rd from A to
F the Choral-Thone
> BTW, there hasn't been a lot of activity lately over at the
> bach_tunings group.
In deed, but that do appear here in that group for instance under:
http://launch.groups.yahoo.com/group/tuning/message/78677
bye
Andy
From: ham_45242 (2010-06-18)
Subject: Re: Mersenne Chromatic Scale Diagram
--- In tuning@yahoogroups.com, "Andy" <a_sparschuh@...> wrote:
> alike used in Mersenne's other graphic in:
> http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WG9-4NS2GPC-2&_user=2717328&_rdoc=1&_fmt=full&_orig=search&_sort=d&view=c&_acct=C000056831&_version=1&_urlVersion=0&_userid=2717328&md5=5ff04abd46a359eda81dbd0b40a39c4b#bib002
Hi, Andy and all. The above is a reference to an excellent paper IMO that I downloaded a while back but I don't see any diagrams by Mersenne, who isn't the subject of this paper.
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&_issn=03150860&_pii=S0315086007000341&view=c&_acct=C000056831&_version=1&_urlVersion=0&_userid=2717328&md5=a803e41e97c93821530901708fc11240
>
> "Fig. 2. Descartes' representation in the English translation (Walter Charleton, Trans., William Brouncker, Ed.), Renatus Des-Cartes Excellent Compendium of Musick, 35. By permission of the Bodleian Library, University of Oxford (shelfmark: 4o R4 Art B5, 3).
>
OK, the Descartes diagram shows the B with the flat and natural notes clearly marked. Both Descartes and Mersenne show the B "Fa" note, which would correspond to the 4th note (Bb) in a "hexachordum molle".
>
> > Still don't know about that "7 1/2".
> > Maybe it's an unrelated scribbling.
>
> I suppose, that means on monochord-string-length for F of 7.5 foots,
> or an corresponding organ-pipe of 7.5" hight,
> in the old sense of Arnold Schlick's tretaise on organ-building:
>
> http://launch.groups.yahoo.com/group/tuning/message/71324
> then at ~1500 was a change a 3rd from A to
> F the Choral-Thone
>
That would make sense. Sincerely,