Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Conversion: Cent Deviations to Pythagorean comma fractions

Dear friends,

I tune historical temperaments by ear but I am occasionally asked to tune according to a list of cent deviations which are entered in an electronic device. Do you have a calculation (formula) or template from which I can convert the cent deviations to Pythagorean comma fractions of fifths? I mean from C -1 C#+3 etc to C-G -1/6 G-D -1/6 etc?

Your help would be much appreciated.

Narrowness of fifth in cent offsets plus 2 divided by 24.
Eg C +2 G -2: (4+2) cent narrow = 1/4 Pyth comma narrow.

Super. Thanks so much!!!

...and any idea how to do the opposite i.e. from Pythagorean comma fraction to cent deviation?

A fifth that is 1/12 comma = 2 cent narrow has both notes same offset, so if it was say 1/4' narrow it is 6 cent narrow, so the upper note would be -4 flat offset relative to the lower (eg C+2 G-2)

Brilliant. You made my day! Thanks so much. I need the second conversion when I tune the harpsichord by ear and the organ technician tunes the organ electronically.