One thing is having all the ratios of the Partch 43-tone scale nicely presented with this keyboard layout but how does one get a handle on the ratios *between* the ratios?

In his book Genesis of a Music Partch himself points out that it’s easy to calculate the ratio between two ratios by simply inverting the smaller of the two and using that to multiply the other. So in the case of `4/3`

and `3/2`

we would have `3×3=9`

and `4×2=8`

, which gives us the ratio of `9/8`

, which we know is the major whole tone that we have between a perfectly tuned fourth and fifth.

With some of the more complex ratios, e.g. `81/80:32/31`

, things can get a little more complicated and so I’ve set up a spreadsheet to do the work for me, also including a representation of the interval in terms of cents using the following formula: `1200*log(n/d)/log(2)`

where `n/d`

is your ratio.

And to make things a little more fun I’ve set up a small device using the Audulus 4 beta that uses the same principles to display both the ratio and the cents of any two notes played on the keyboard in real time.

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