Re: The secor: an exact definition

Hello, there, Paul, and thank you for your response to my post on
George Secor's exact definition of what we now call a "secor."

To this point, what I've mainly done is mentioned the excitement about
the "rediscovery" of both the tuning and his first _Xenharmonikon_
article about it here. Of course, I could try to explain a bit about
some of the subsets, and so forth.

Also, I now find that the "Wonder Tuning" included by Manuel Op de
Coul in the Scala archive based on (3:2)^(1/3), or ~233.985 cents,
uses a generator equal to approximately 2.00474497 secors. Maybe I
should mention this to George Secor.

> This is good -- Dave Keenan had calculated the the generator meeting
> Secor's specifications would in fact be 116.72 cents, not 116.69
> cents -- so it's good to know that George had already made this
> correction.

Yes, it's nice that the results agree, showing that the true value of
a secor is a bit further from 7/72 octave than the initial
approximation in his first article on the temperament, or maybe
microtemperament.

> Note that, with this definition, the Secorian temperaments can be
> safely said to consitute a "Middle Path", and not an ET.

Yes, it's a "middle path" temperament which can be approximated by
certain ET's as discussed in some of these threads, just as JI systems
can be approximated by certain ET's also.

Of course, since George Secor's temperament is presented as an
approximation of Partch's "monophonic fabric," we might say that a
similar scheme using something like 7/72 octave as a generator is an
ET (or subset) approximating a "middle path" temperament approximating
a JI system.

By the way, while a Secorian temperament isn't an eventone, maybe it
represents a broader category of "evenstep" tunings where we have
relationships analogous to "four equal fifths make a major third."
Here, for example, we have "three near-7:8's of two secors each make a
near-2:3 of six secors," or "three near-5:7's of five secors each make
a near-4:11 of 15 secors."

The term "evenstep," by the way, came up in a dialogue where someone
(or maybe more than one person) pointed out that there are tunings
with these kind of relationships that don't fit a usual eventone
pattern; so eventone tunings might be considered that subset of
evenstep tunings where the generator is more specifically a fifth of
which two form a regular whole-tone and four a regular major third.

A final point occurs to me: might the largest variation in George's
temperament from just, approximately 3.323 cents (with GNU Emacs Calc,
I get ~3.3228725522864030398 cents), be considered as a definition for
one kind of "near-just" standard? As he notes, this is the variation
for either the 4:5 or the 8:9.

By the way, Paul, as someone who has done such an immense amount along
with Dave Keenan and Graham Breed and Joe Pehrson and others to
"rediscover" and promote the Secorian temperaments, you're helping to
build a bridge between the exciting era that produced the Scalatron
and today's era of global tuning technologies and dialogue via the
Internet. Now, as then, the challenge is to see if we can get the
options -- acoustical or electronic -- more widely appreciated,
especially in cultures where mass standardization has replaced variety
and choice.

Most appreciatively,

Margo Schulter
mschulter@value.net