Calculator - Tune Smithy - Windows Software

You can use this as a normal calculator - just enter any sum, or formula and it will instantly calculate the result. But it's strong point is that it is particularly designed for use with scale calculations involving cents, ratios etc.

This shows some example ratios, and some values in the special // notation where 1//31 means an equal thirty first part of an octave. I've chosen to show the results as cents.

You can have as many individual expressions as you like - they are comma separated. This means you can have spaces within the expressions (in the other fields in tune smithy permitting several values to a line, normally the expressions have to be without spaces to make it clear where one value ends and the next begins).

Results can be shown in the current scale notation, so that includes for instance the option to show the factorisation of any ratio, to show it in lattice notation, and to show the nearest approximate ratios to any number.

One of the options lets you show the entries as ratios, lattice notation, and cents all in one go (the results are shown one to a line) - like this:

The calculator can show ratios exactly with up to nineteen digits above and below - higher precision than is possible in most programs though not arbitrarily large. This covers with just about all of the ratios most frequently needed by microtonalists, though if you are interested in investigating xenharmonic bridges you may go over the limit.

It can also accept g for the golden ratio, PI, SIN, COS, etc, the usual mathematical formulae and expressions. The golden ratio is often used in scale construction - it is in a sense "as far as possible" away from a pure just intonation ratio - the continued fraction for g converges more slowly than for any other number. PI is also used, e.g. for Lucy Tuning.