HEWM notation calculator (was: help with ratio/vector algorithm)

----- Original Message -----
From: <graham@microtonal.co.uk>
To: <tuning-math@yahoogroups.com>
Sent: Monday, March 04, 2002 3:34 AM
Subject: [tuning-math] Re: help with ratio/vector algorithm

> In-Reply-To: <004101c1c32d$603c6540$af48620c@dsl.att.net>
> monz wrote:
>
> > > ratio r = 2^p * 3^q
> > >
> > > if q < 0
> > > then p = int((log(3^abs(q)) / log(2)) + 0.5)
> > > else p = (int((log(3^abs(q)) / log(2)) + 1.5)) * -1
> > > end if
> > >
> > > but it's not foolproof: sometimes the exponent of 2 is
> > > one less or one more than it should be. i've tried
> > > setting up further nested if-statements, to check if
> > > the absolute value of p is greater than that of q and
> > > adjust accordingly, but there's always an error somewhere.
> >
> >
> > the errors are occurring because the spreadsheet has to
> > check to see if n > d, and i can't figure out how to
> > implement that without getting a circular reference.
>
> I think =MOD(N20, 1)-N20 does it where N20 is the magnitude of the
> original interval in octaves. So you have to substitute that with
> log(3^abs(q)) / log(2).

thanks, Graham! (duh... of course i have to use MOD!)

i've implemented this in an Excel spreadsheet that assists
in finding the HEWM notation of a ratio:
http://www.ixpres.com/interval/dict/hewm.xls

color LEGEND:

cyan = data to be input by user
magenta = constants, used in calculations
orange = results of calculations on user data

at the top are a bunch of constants that i use in the
calculations.

below those...

on the left side, the user inputs the exponents of the
target ratio first, and then the exponent of 3 which gets
near it. the spreadsheet subtracts that, and indicates
the letter-name and any sharp or flat. (there's still
a bug here -- i don't know how to generate the negative
numbers when using MOD.) then the the user enters the
exponents of the notational "commas" from the magenta
table above until all exponents are zero. eventually,
i want to be able to have the spreadsheet determine all
of the accidental symbols from the exponents entered by
the user... but this is not implemented fully yet.

on the right side, the user inputs the exponents of the
target ratio, then directly enters the notational symbols
which eventually reduce all exponents to zero. the only
thing to be aware of here is that an apostrophe (') must
precede the minus and plus signs when entering them.

-monz

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