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,
--- 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
--- 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.
--- 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,
--- 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
/tuning/topicId_71935.html#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
"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:
/tuning/topicId_70684.html#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:
/tuning/topicId_78659.html#78677
bye
Andy
--- 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:
>
> /tuning/topicId_70684.html#71324
> then at ~1500 was a change a 3rd from A to
> F the Choral-Thone
>
That would make sense. Sincerely,
