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Gene wrote:

> Why would I know a definition in a book I havn't read?

I just meant that, you know, it being the first chapter in a book called
"Basic Atonal Theory" suggests that it's a well-known and standard sort of
thing, and so I thought you would have known of the model, not necessarily
from this particular book--which, though it's actually quite carefully put
together and even sufficiently rigorous, was designed as a text-book
palatable to music undergrads, and not for bad-ass PhDs in maths!

> Defining things by means of a map from the integers to a system of
> notation is not the most obvious approach, at least to me. "Integer
> model of pitch", by the way, doesn't exactly sound like this is what
> Rahn does.

Well I'm not sure, either, that he "defines" pitches as integers--that
sounds wrong. He doesn't attempt an ontological examination of what
pitches actually *are*, he assumes you know what pitches are, and starts
by *associating* integers to pitches, then labels pitches by the integer
associated to them, choosing middle C arbitrarily as zero. The pitches of
12-tet are ordered and equally spaced so it seems pretty natural to me
that you'd think of modelling them with integers. Then you can say the
interval between two pitches m and n is the difference |m-n|, etc etc.

And it's not dependent on notation--sing me a song, I'll tell you what the
pcs are, no notation involved.

--- In tuning-math@yahoogroups.com, jon wild <wild@f...> wrote:

> Well I'm not sure, either, that he "defines" pitches as integers--that
> sounds wrong. He doesn't attempt an ontological examination of what
> pitches actually *are*, he assumes you know what pitches are, and starts
> by *associating* integers to pitches, then labels pitches by the integer
> associated to them, choosing middle C arbitrarily as zero.

You know what things are unless you are doing pure math, where you
define what they are. This is applied math, but I think that works
better if you give clean definitions here also. What happens if I make
assumptions about what you mean by "pitch" and they turn out to be
different assumptions that yours? I'm still trying to digest the idea
that "pitch" is a feature of a score, not of any actual sound.

> And it's not dependent on notation--sing me a song, I'll tell you
what the
> pcs are, no notation involved.

What if I'm singing along with Paul and he's playing a 22-et guitar?