The secor: an exact definiton

Hello, there, everyone, and George Secor has suggested that I share
his revised value for the interval now known here as a 'secor,' the
generator for a near-just approximation of Harry Partch's "monophonic
fabric" of just intonation (JI) based on a generator of around 7/72
octave.

After his initial article "A New Look at the Partch Monophonic Fabric"
in _Xenharmonikon_ 3 (Spring 1975), describing the generator as
"116.69 cents," George Secor issued a correction in _Xenharmonikon_ 5
(Spring 1976), on page 2 of his first article in that issue, offering
a definition and a revised value for this interval.

As he explained, the generator is defined as precisely (18:5)^(1/19),
so that 19 generators would yield a just 5:18, i.e. an interval equal
to a pure 5:9 minor seventh plus an octave.

The result in cents is

"(1017.596288 + 1200)/19 = 116.7155941. This makes
the intervals 8:9 and 4:5 false by 3.323 cents;
altering the value slightly will improve one and
worsen the other. No other primary interval in
Partch's 11-limit has a greater error, making this
the optimum value for the generating interval.
(Graphing the error of each interval against the
generating interval value on a single graph bears
this out.)"

As George Secor pleasantly notes, we now have an exact definition for
the interval called a "secor."

Most appreciatively,

Margo Schulter
mschulter@value.net

Very nice, Margo! Thanks. It's so neat that there can be something
that powerfully unifying underlying all that just diversity.

--- In tuning@y..., mschulter <MSCHULTER@V...> wrote:
> Hello, there, everyone, and George Secor has suggested that I share
> his revised value for the interval now known here as a 'secor,' the
> generator for a near-just approximation of Harry Partch's
"monophonic
> fabric" of just intonation (JI) based on a generator of around 7/72
> octave.
>
> After his initial article "A New Look at the Partch Monophonic
Fabric"
> in _Xenharmonikon_ 3 (Spring 1975), describing the generator as
> "116.69 cents," George Secor issued a correction in _Xenharmonikon_
5
> (Spring 1976), on page 2 of his first article in that issue,
offering
> a definition and a revised value for this interval.
>
> As he explained, the generator is defined as precisely (18:5)^
(1/19),
> so that 19 generators would yield a just 5:18, i.e. an interval
equal
> to a pure 5:9 minor seventh plus an octave.
>
> The result in cents is
>
> "(1017.596288 + 1200)/19 = 116.7155941. This makes
> the intervals 8:9 and 4:5 false by 3.323 cents;
> altering the value slightly will improve one and
> worsen the other. No other primary interval in
> Partch's 11-limit has a greater error, making this
> the optimum value for the generating interval.
> (Graphing the error of each interval against the
> generating interval value on a single graph bears
> this out.)"
>
> As George Secor pleasantly notes, we now have an exact definition
for
> the interval called a "secor."
>
> Most appreciatively,
>
> Margo Schulter
> mschulter@v...

--- In tuning@y..., mschulter <MSCHULTER@V...> wrote:
> Hello, there, everyone, and George Secor has suggested that I share
> his revised value for the interval now known here as a 'secor,' the
> generator for a near-just approximation of Harry
Partch's "monophonic
> fabric" of just intonation (JI) based on a generator of around 7/72
> octave.

Excellent. Have you shared with George much of the work that we've
done since we rediscovered his generator?

> After his initial article "A New Look at the Partch Monophonic
Fabric"
> in _Xenharmonikon_ 3 (Spring 1975), describing the generator as
> "116.69 cents," George Secor issued a correction in _Xenharmonikon_
5
> (Spring 1976), on page 2 of his first article in that issue,
offering
> a definition and a revised value for this interval.

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.

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