Re: [LAU] Chord finder

On Thu, Jul 12, 2012 at 7:21 PM, Rustom Mody <rustompmody@email-addr-hidden> wrote:

>
> The pythagorean comma is (by definition??) the gap between B# and C where
> by B# means the 12th in a circle of perfect fifths starting at C.
>
>
I would say "a possible gap". It depends on the used temperament, in this
case Pythagorean (perfect fifth: 3/2). For example mean tone temperament
doesn't care that much about fifths and uses 5/4 for major thirds.

Going from C to B# takes only three major thirds: C-E, E-G#, G#-B#.

(5/4)^3 = 125/64;

C to C':
2/1 = 128/64;

128/125 != (3/2)^2 / 2^7 (does not equal Pythagorean comma).

Because on an acoustic piano with 12 keys per octave the same frequency is
used for C and B# at least one of those three major thirds cannot be
exactly 5/4 and will be transformed into a diminished fourth (E-Ab or
G#-C). On a computer we don't have this problem if we enable ourselves to
recalculate each frequency by one simple action (e.g. hit one button) or
even write an algorithm that does that for us.

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Received on Fri Jul 13 12:15:02 2012