Robert Kelley

Robert Kelley is an academic music theorist who ties
diatonic scale theory to just intonation. The best
introduction is his PhD thesis:

http://www.robertkelleyphd.com/Mod7Transformations.pdf

The idea is that, contrary to what Agmon said, tuning
theory is relevant to diatonic spelling. However, there's
still no mention of meantone temperament. But diatonic
spelling is the first step to resolving intervals in just
intonation, so tuning is still relevant.

The mathematics gets complicated because of the way he
applies octave equivalence. He uses scale-based just
intonation so that there's no pitch drift, but some
intervals will be wrong.

He identifies tonal function with just intonation, because
the two tunings of D in C major correspond to chords of
different function. He doesn't seem to do much with this
revelation, though. The musical analyses are all in terms
of the meantone spellings. Not that I pretend to
understand them in detail.

He cites Karp for the matrix operations that were
uncredited in an earlier paper. He also has Fokker in the
bibliography, but missed the citation for "periodicity
block". There are other citations for related concepts,
and the early chapters are useful for collecting them.

Note that on page 137 (or 145 of the PDF) he acknowledges
that "tuning theory has progressed apart from academic
music theory."

A more recent paper, here, has some other details:

http://www.robertkelleyphd.com/AMathematicalModelOfTonalFunction.pdf

He calls the threefold division of an octave "arp number".
The way he describes the arp number, "counting the number
of consonant skips", is similar to how I describe the wheels
of tricycle notation. They are essentially the same.

I don't know if there's a deep reason why there should be
three wheels to the octave for 5-limit just intonation.
The three comes out because periodicity blocks will add
three syntonic commas to the octave to move from meantone
to the full 5-limit. Adding three divisions to a meantone
EDO will tend to give you something good in the 5-limit.
19 and 22 are an example of this, hence the threeness
applies to Magic. But the wheels really come from
augmented triads with the 5-limit application an accident.
I believe 2 or 4 wheels to the octave would also
disambiguate 5-limit intervals.

Graham

Thanks for checking into this, Graham. He cites Euler,
Eskelin, Fokker, Gann, Monzo, Partch, Soderberg, and Tenney.
It's almost as if he checked the internet before finalizing
his paper. :)

-Carl

At 11:22 AM 8/26/2011, you wrote:
>Robert Kelley is an academic music theorist who ties
>diatonic scale theory to just intonation. The best
>introduction is his PhD thesis:
>
>http://www.robertkelleyphd.com/Mod7Transformations.pdf
>
>The idea is that, contrary to what Agmon said, tuning
>theory is relevant to diatonic spelling. However, there's
>still no mention of meantone temperament. But diatonic
>spelling is the first step to resolving intervals in just
>intonation, so tuning is still relevant.
>
>The mathematics gets complicated because of the way he
>applies octave equivalence. He uses scale-based just
>intonation so that there's no pitch drift, but some
>intervals will be wrong.
>
>He identifies tonal function with just intonation, because
>the two tunings of D in C major correspond to chords of
>different function. He doesn't seem to do much with this
>revelation, though. The musical analyses are all in terms
>of the meantone spellings. Not that I pretend to
>understand them in detail.
>
>He cites Karp for the matrix operations that were
>uncredited in an earlier paper. He also has Fokker in the
>bibliography, but missed the citation for "periodicity
>block". There are other citations for related concepts,
>and the early chapters are useful for collecting them.
>
>Note that on page 137 (or 145 of the PDF) he acknowledges
>that "tuning theory has progressed apart from academic
>music theory."
>
>A more recent paper, here, has some other details:
>
>http://www.robertkelleyphd.com/AMathematicalModelOfTonalFunction.pdf
>
>He calls the threefold division of an octave "arp number".
>The way he describes the arp number, "counting the number
>of consonant skips", is similar to how I describe the wheels
>of tricycle notation. They are essentially the same.
>
>I don't know if there's a deep reason why there should be
>three wheels to the octave for 5-limit just intonation.
>The three comes out because periodicity blocks will add
>three syntonic commas to the octave to move from meantone
>to the full 5-limit. Adding three divisions to a meantone
>EDO will tend to give you something good in the 5-limit.
>19 and 22 are an example of this, hence the threeness
>applies to Magic. But the wheels really come from
>augmented triads with the 5-limit application an accident.
>I believe 2 or 4 wheels to the octave would also
>disambiguate 5-limit intervals.
>
>
> Graham
>
>
>------------------------------------
>
>Yahoo! Groups Links
>
>
>

On Sat, Aug 27, 2011 at 4:56 AM, Carl Lumma <carl@lumma.org> wrote:
>
> Thanks for checking into this, Graham. He cites Euler,
> Eskelin, Fokker, Gann, Monzo, Partch, Soderberg, and Tenney.
> It's almost as if he checked the internet before finalizing
> his paper. :)
>
> -Carl

Would somebody mind referencing me to this mysterious Agmon paper
where he trashes tuning theory? All I know is that everyone hates him,
and he hates all of us, but if his basic gist is that scale cognition
isn't dependent on intonation, then I have to agree.

And why is his paper a refutation of Agmon? Is Agmon some kind of
mysterious driving force in academia? I don't get it.

-Mike

Mike wrote:

>Would somebody mind referencing me to this mysterious Agmon paper
>where he trashes tuning theory? All I know is that everyone hates him,
>and he hates all of us, but if his basic gist is that scale cognition
>isn't dependent on intonation, then I have to agree.

We don't hate him, but he's highly invested in a body of
work that is basically incompatible with intonation theory.
I don't know of a paper where he trashes tuning theory.

>And why is his paper a refutation of Agmon? Is Agmon some kind of
>mysterious driving force in academia?

Yes.

-Carl

On Sat, Aug 27, 2011 at 5:09 AM, Carl Lumma <carl@lumma.org> wrote:
>
> Mike wrote:
>
> >Would somebody mind referencing me to this mysterious Agmon paper
> >where he trashes tuning theory? All I know is that everyone hates him,
> >and he hates all of us, but if his basic gist is that scale cognition
> >isn't dependent on intonation, then I have to agree.
>
> We don't hate him, but he's highly invested in a body of
> work that is basically incompatible with intonation theory.
> I don't know of a paper where he trashes tuning theory.

OK, and it's commonly accepted even on this list that scale cognition
involves factors separate from intonation, yes? That's why we all talk
about Rothenberg so much. So what specifically is it that Agmon
believes that everyone disagrees with, what aspect of his theory...?

-Mike

Mike wrote:
>OK, and it's commonly accepted even on this list that scale cognition
>involves factors separate from intonation, yes? That's why we all talk
>about Rothenberg so much. So what specifically is it that Agmon
>believes that everyone disagrees with, what aspect of his theory...?

Rothenberg is very intonation-oriented compared to mainstream
theory. Among mainstream theorists, Agmon is too

http://www.biu.ac.il/HU/mu/Prof_EYTAN%20AGMON.htm

which is probably why he made his famous visit to the list way
back in the dusty year of '03. -Carl

On Sat, Aug 27, 2011 at 5:28 AM, Carl Lumma <carl@lumma.org> wrote:
>
> Mike wrote:
> >OK, and it's commonly accepted even on this list that scale cognition
> >involves factors separate from intonation, yes? That's why we all talk
> >about Rothenberg so much. So what specifically is it that Agmon
> >believes that everyone disagrees with, what aspect of his theory...?
>
> Rothenberg is very intonation-oriented compared to mainstream
> theory. Among mainstream theorists, Agmon is too
>
> http://www.biu.ac.il/HU/mu/Prof_EYTAN%20AGMON.htm
>
> which is probably why he made his famous visit to the list way
> back in the dusty year of '03. -Carl

I'm going through the archives now - can't seem to find his posts, but
it looks like the gist of it is he likes the 3L2s, 5L2s, 7L2s, 9L2s
series, corresponding to father, meantone, mavila, and avila,
respectively, and because it allows for diatonic scales with one
ambiguous tritone.

Tangentially, I saw this comment of yours from back in the day and
laughed out loud -

> > The final speaker in the first presentation session was Jonathan
> > Wild (wild@fas.harvard.edu), a graduate student at Harvard
> > University. His talk, "Tessellating the Chromatic," dealt with
> > concepts related to combinatoriality as applied to pitch-space,
> > rather than pitch-class space.
>
> Whoa, stop the press! Pitch space? How trendy, how neo-neo.
> My, pitch space and music. Dear me.
>
> -Carl

LMAO. Every AES or ASA convention has to have at least 2 to 3 papers
on some sort of "pitch space," usually some kind of higher-dimensional
manifold that spirals back into itself to represent
octave-equivalence, and then shows how the whole thing is generated by
the circle of fifths, or maybe fifths and major thirds if they really
dig deep. I've stopped going to them because they tend to generate too
much existential angst.

-Mike

Mike wrote:
>I'm going through the archives now - can't seem to find his posts, but
>it looks like the gist of it is he likes the 3L2s, 5L2s, 7L2s, 9L2s
>series, corresponding to father, meantone, mavila, and avila,
>respectively, and because it allows for diatonic scales with one
>ambiguous tritone.

Most of the action took place in an offlist CC list. That's
because academic types - especially in Ricebowl Championship
fields like music theory - are paranoid about damaging the
smarter-than-you reputations they build through carefully-
controlled publications. For senior people in such fields,
even talking to undergrads in other groups is an honor doled
out miserly. This is why most academic music theorists won't
set foot on an open mailing list like this one, where somebody
like Gene is liable to expose the fact that they don't really
know much group theory, or someone like Paul that their system
for explaining common practice theory falls apart when applied
to quarter-comma meantone.

-Carl