Blackwood reference

> > > > > http://tonalsoft.com/enc/index2.htm?circle-of-5ths.htm
> > > >
> > A bibliographic reference over to Easley Blackwood's
> > book would also be a nice addition to that page. He
> > presents the theorems so clearly.
> >
>thanks for the suggestion. if you find the citation
>and save me the effort of looking for it, i'll add it
>to the page. thanks.

Blackwood, Easley. The Structure of Recognizable Diatonic Tunings. Princeton University Press, Princeton NJ, 1985. [ISBN 0-691-09129-3]

Many more where that came from:
http://www.xs4all.nl/~huygensf/doc/bib.html

Brad Lehman

hi Brad,

--- In tuning@yahoogroups.com, Brad Lehman <bpl@u...> wrote:
>
> > > > > > http://tonalsoft.com/enc/index2.htm?circle-of-5ths.htm
> > > > >
> > > A bibliographic reference over to Easley Blackwood's
> > > book would also be a nice addition to that page. He
> > > presents the theorems so clearly.
> > >
> > thanks for the suggestion. if you find the citation
> > and save me the effort of looking for it, i'll add it
> > to the page. thanks.
>
> Blackwood, Easley. The Structure of Recognizable Diatonic Tunings.
> Princeton University Press, Princeton NJ, 1985. [ISBN
0-691-09129-3]
>
> Many more where that came from:
> http://www.xs4all.nl/~huygensf/doc/bib.html
>
>
> Brad Lehman

thanks, but ... i had all that. i wanted the specific
page numbers for the theorems you mentioned.

-monz

>Subject: Re: Blackwood reference
> > > > > > > http://tonalsoft.com/enc/index2.htm?circle-of-5ths.htm
> > > > > >
> > > > A bibliographic reference over to Easley Blackwood's
> > > > book would also be a nice addition to that page. He
> > > > presents the theorems so clearly.
> > > >
> > > thanks for the suggestion. if you find the citation
> > > and save me the effort of looking for it, i'll add it
> > > to the page. thanks.
> >
> > Blackwood, Easley. The Structure of Recognizable Diatonic Tunings.
> > Princeton University Press, Princeton NJ, 1985. [ISBN
>0-691-09129-3]
>
>thanks, but ... i had all that. i wanted the specific
>page numbers for the theorems you mentioned.

Chapter 11, section 5, theorems 39 and 40. But, those can hardly be presented outside the context of the whole book, being built upon earlier theorems. You'll be interested especially where he takes it in chapter 12. Unfortunately, since he's concerned with keeping both the fifths and major thirds as nearly pure as possible, he doesn't spend enough time discussing the divisions that 18th century musicians cared most about; neither does Barbour. Ah well. But he does devote a good chunk of chapter 12 to 53edo.

And Friedrich Suppig's "Calculus musicus" of 1722 is about 19edo and 31edo, along with a pretty lousy piece "Labyrinthus musicus" (mostly a bunch of uninspired sequences, sounding like bad imitation Vivaldi). Granted, when I've played through it, it hasn't been in 19edo or 31edo yet; but it's still a piece of music much too long for its content.

Brad Lehman

--- In tuning@yahoogroups.com, Brad Lehman <bpl@u...> wrote:
>
> > Subject: Re: Blackwood reference
> >
> > > > > > > > http://tonalsoft.com/enc/index2.htm?circle-of-5ths.htm
> > > > > > >
> > > > > A bibliographic reference over to Easley Blackwood's
> > > > > book would also be a nice addition to that page. He
> > > > > presents the theorems so clearly.
> > > > >
> > > > thanks for the suggestion. if you find the citation
> > > > and save me the effort of looking for it, i'll add it
> > > > to the page. thanks.
> > >
> > > Blackwood, Easley.
> > > The Structure of Recognizable Diatonic Tunings.
> > > Princeton University Press, Princeton NJ, 1985.
> > > [ISBN 0-691-09129-3]
> >
> > thanks, but ... i had all that. i wanted the specific
> > page numbers for the theorems you mentioned.
>
> Chapter 11, section 5, theorems 39 and 40.

thanks!

> But, those can hardly be presented outside the context
> of the whole book, being built upon earlier theorems.

yes, i realize that this book builds progressively
as it goes along.

> You'll be interested especially where he takes it in
> chapter 12.

i read the book long ago but ought to give it
another look now. so i'll peek at that chapter
especially.

> Unfortunately, since he's concerned with keeping both
> the fifths and major thirds as nearly pure as possible,
> he doesn't spend enough time discussing the divisions
> that 18th century musicians cared most about;
> neither does Barbour. Ah well.

yes, that's something that i've always felt lacking
in Barbour too. he wrote such an encyclopedic work,
which makes it a great reference, but it definitely
has a few strong biases.

> But he does devote a good chunk of chapter
> 12 to 53edo.
>
> And Friedrich Suppig's "Calculus musicus" of 1722 is
> about 19edo and 31edo, along with a pretty lousy piece
> "Labyrinthus musicus" (mostly a bunch of uninspired
> sequences, sounding like bad imitation Vivaldi).
> Granted, when I've played through it, it hasn't been
> in 19edo or 31edo yet; but it's still a piece of music
> much too long for its content.

i'd be very careful about assessing the value of a
piece of music when you've only heard it in a tuning
which you know is not one that was intended for it.

try listening to some of the classics (i.e., meantone-based)
in something like pelogic. Gene Ward Smith just did
this recently with the "Dona Nobis Pacem" from Bach's
_B-minor Mass_. it turns out that i really loved it,
but it doesn't sound anything like the i'm sure Bach
intended it to sound. it's at the bottom of this page:

http://66.98.148.43/~xenharmo/mad.html

and a thread about it on this list begins here:

/tuning/topicId_55446.html#55446

it may be that Suppig's "Labyrinthus" sounds lousy
in 12edo, but would sound fantastic in 19 or 31.
i'd have to at least examine the score (even better,
listen to it) to know how similar or different either
of those would sound from the 12edo version.

-monz