- --- In tuning@yahoogroups.com, "monz" <monz@...> wrote:

> But that's exactly why i want those research notes:

How does he classify 22? Paul Erlich thought his 22 was about the

> Blackwood divides scales into two broad categories,

> diatonic and symmetric, and goes into great detail

> about the types of harmonic progressions he found

> available in each EDO.

weakest of the bunch, because it is a kind of cockeyed diatonic

piece. I thought it was interesting, and amusing in something the way

the Candide Overature is. But things like the recent "Blue Monk" in

22 seem to be more intrinisic to the character of 22. I think maybe

Paul was objecting to the impression he left, that his 22 etude is

what the tuning is *like*, rather than something it makes possible.

> The problem is how to design the Lattice for each EDO.

Interesting questions. For the 23, for instance, I think taking it as

> Having all that info would help me a great deal in

> deciding what to use for the Lattice axes: how many

> dimensions should the Lattice have, which prime-factors

> should define each axis, and in fact are there generators

> other than prime-factors which would be better?

half a 46 might be better. The 16 etude seems to have a diminished

temperament concept to it. What the hell you or anyone can do with 13

is a question. You could look at the chords he was using as, more or

less, consonances to try to sort it out.

> EDO prime-factors

29?? I'd do what I suggested, and look at his chords.

> 13 . 11

> 14 . 29

> Well, it's nice that Blackwood put a legend at the beginning

What do you think of his notations? Scala doesn't use them, but of

> of each Etude which shows the notation *and* the EDO degree

> number!

course it would be relatively easy to produce a Scala version in some

other notation. - Hi Herman,

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

>

> monz wrote:

>

> > I've always thought his notations were a little strange,

> > but given the fact that he did a lot of research into

> > all 11 of these EDOs, i suppose that he put a lot of

> > thought behind them.

>

> I recall thinking that his 16-ET notation was strange,

> but then a while back I realized that the major thirds

> are the best intervals of 16-ET, and with the exception

> of C-E, Blackwood's notation of major thirds is consistent

> with traditional notation. (In that respect it's similar

> to my porcupine-based notations for 15-ET and 22-ET.)

> I still find his 23-ET notation very confusing.

I've read the first 22 pages of Blackwood's

_NEH Research Notes_ so far, and he does go into

some detail about how he devised his notations.

He places a lot of importance on enharmonic equivalence,

drawing parallels to how it works in 12-edo.

So far i've only really read about 15-edo, and the

way he devised his notation for that tuning, he

shows how considering 5-edo as a series of very

sharp 5ths (720 cents) makes a series of five 5ths

upward enharmonically equivalent: thus, in the

sequence C - G - D - A - E - B, the C and B are

the same pitch. Similarly for G/F# in G-D-A-E-B-F#,

F/E in F-C-G-D-A-E, etc. And of course 15-edo

contains 5-edo, so this is significant to him.

He also examines the symmetric modes in detail,

again drawing parallels with how they work in 12-edo.

-monz

http://tonalsoft.com

Tonescape microtonal music software