Re: A Pythagorean "shift of gears"? -- for Joseph Pehrson

Hello, there, Joseph Pehrson, and I've been very intently following
the discussions on notations and on your own dilemmas in choosing
keyboard tuning schemes for your own music.

Curiously, a few technical complications regarding Internet e-mail and
the like may have paradoxically given me the opportunity, catching up
with the List, to read the fully matured threads before offering my
own responses.

Now in the middle of the process of writing the second part of my
article on the e-based tuning, I'm inclined to take a break to say a
bit about the 24-note tunings and notational approach I find myself
using. To borrow from one thread, at least, this discussion might
involve a bit of Pythagorean "two-gear biking" assuming neither
circularity nor lots of _small_ integer ratios.

Reading your posts with great interest, one question has captured my
imagination over the last couple of days: how might my approach to
tuning and notation be made more understandable to a composer and
musician with your kind of lively historical interest, so that people
can feel free to borrow or adapt what might seem helpful and may take
it as a starting point for some radical new direction?

Your mention of Nicola Vicentino might be especially relevant here
because Vicentino introduced a basic notational tool -- the use of a
dot above a note -- which together with the five-line staff and the
conventional accidentals Eb-G# makes it possible for me to notate any
of my "usual" 24-note tunings. (A 17-note Pythagorean tuning or
complete 17-tET circle calls for Gb-A# without dots getting involved.)

I wonder how my approach might look from your perspective as someone
evidently most familiar with 12-tET -- indeed a common _conceptual_
element in the training of many musicians, whatever may be the
realities of psychoacoustical perception or flexible-pitch intonation.

Please let me reassure you that my purpose here is not to persuade you
to take up a neo-Gothic style, but just to toss out some ideas which
might have a certain entertainment value, and possibly could suggest
some ideas for your own creative dilemmas in following your own
musical and intonational style on a fixed-pitch keyboard.

Of course, I must also emphasize that you would be bestowing me with a
great benefit in such a dialogue: feedback which at once might help me
to articulate my ideas more clearly, and give me some insights into
how other musicians look at things.

For now, I would say that _two_ 12-note keyboards seem a very pleasant
arrangement for me, with a typical 24-note notation which really needs
to indicate only two "variables" or "parameters," so to speak:

(1) Which note is it (Eb-G#)?
(2) Which of the two keyboards is it on (lower/upper)?

Of course, this is a much simpler problem than either the 72-tET
situation or the n-limit JI situation: we're dealing here primarily
with regular tunings having fifths ranging from Pythagorean to
17-tET.

Interestingly, the same principles can nicely apply to what I'd call
two historical 20th-century tunings when used for a neo-Gothic kind of
style: 24-tET, and 24-of-36-tET (yes, the regular thirds and sixths
are a bit subdued, but there's room for some variation and diversity
here).

Anyway, thank you and others for a most fascinating thread which has
lent energy both to my own musicmaking, and to the project of trying
to explain some notational aspects here, however partially and
imperfectly.

Most appreciatively,

Margo

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:

/tuning/topicId_21720.html#21720

> Hello, there, Joseph Pehrson, and I've been very intently following
> the discussions on notations and on your own dilemmas in choosing
> keyboard tuning schemes for your own music.
>
> Your mention of Nicola Vicentino might be especially relevant here
> because Vicentino introduced a basic notational tool -- the use of a
> dot above a note -- which together with the five-line staff and the
> conventional accidentals Eb-G# makes it possible for me to notate
any of my "usual" 24-note tunings.
>
> I wonder how my approach might look from your perspective as someone
> evidently most familiar with 12-tET -- indeed a common _conceptual_
> element in the training of many musicians, whatever may be the
> realities of psychoacoustical perception or flexible-pitch
intonation.
>

> For now, I would say that _two_ 12-note keyboards seem a very
pleasant arrangement for me, with a typical 24-note notation which
really needs to indicate only two "variables" or "parameters," so to
speak:
>
> (1) Which note is it (Eb-G#)?
> (2) Which of the two keyboards is it on (lower/upper)?
>

Thank you very much, Margo, for this clear restatement of your
present keyboard arrangement. You had mentioned these two
Pythagorean keyboards before, and I knew that they differed from one
another by a Pythagorean comma, but I never knew precisely how you
used your notation.

Why of course, this seems like a VERY simple and straightforward
method of notating! It would seem that a musician familiar with 12-
tET could probably read the notation with the Vicentino dots "right
off" without even all that much extensive practice!

It's great that you were able to reduce some of these complex
concepts to a simple physical model that a conventionally-trained
musician could immediately grasp and play.

Might I urge you to, someday, make a presentation at a gathering such
as the MicroFest (in CALIFORNIA, of course!) where, possibly, people
could try these keyboards out for themselves??

(I did get a copy of the paper that you had delivered there!)

Thanks so much!

_______ ______ _______
Joseph Pehrson