hi Graham,

> From: <graham@microtonal.co.uk>

> To: <tuning-math@yahoogroups.com>

> Sent: Wednesday, February 20, 2002 9:12 AM

> Subject: [tuning-math] Re: [tuning] Re: 2401:2400 (was:: Marc Jones EDOs)

> In-Reply-To: <013301c1ba18$428553e0$af48620c@dsl.att.net>

> monz wrote:

>

> > so how about if i write [2 3 5 7]**[-5 -1 -2 4] ?

> >

> > i prefer to keep the prime series in the notation if possible.

>

> There are programming languages that define the usual arithmetic operators

> to be element-wise. Such as Fortran90, Numeric Python and I think

> Matlab. So in such a context your notation would almost work. The only

> thing missing is the implied product to get you from [1/32, 1/3, 1/25,

> 2401] to 2401/2400.

thanks for explaining that ... but ... i don't see how the

"implied product" is "missing". can you explain further?

> You could also write it explicitly as a matrix product

>

> .[log(2) log(3) log(5) log(7)][-5]

> . [-1]

> . [-2]

> . [ 4]

>

> or a wedge product

>

> val([log(2) log(3) log(5) log(7)]) ^ [-5 -1 -2 4]

>

> or even

>

> log(val([2 3 5 7])) ^ [-5 -1 -2 4]

>

> if you decide to define the logarithm of a val. Note that these versions

> all define the relative pitch rather than ratio of the interval.

exactly ... what i'm looking for is a way to simply specify

the r a t i o using the matrix notation.

> You could always define a magic function

>

> Interval([2 3 5 7], [-5 -1 -2 4])

>

> as part of your terminology.

hmmm ... that might work. i'd like to keep using something

of the form [2 3 5 7]**[-5 -1 -2 4] if i can.

-monz

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--- In tuning-math@y..., "monz" <joemonz@y...> wrote:

> hmmm ... that might work. i'd like to keep using something

> of the form [2 3 5 7]**[-5 -1 -2 4] if i can.

Of course the most obvious way to do that is 2^-5 3^-1 5^-2 7^4, but that does not emphasize the vector aspect, and is a little clumbersome. We could steal the idea of bra and ket vectors from the physicists, and write |-5 -1 -2 4> (a ket vector) for the intervals, and <12 19 28 34| (a bra vector) for vals. Then the bra-ket inner product becomes <12 19 28 34|-5 -1 -2 4> = 12*-5 + 19*-1 + 28*-2 + 34*4 = h(12, 2401/2400) = 1.