Fifive, an untempered sequence of pitches

Some time ago, Mike was interested to know more about the half-octave temperament I called "fifive". As an example, here I'm listing a sequence of pitches leading to one untempered period. You may notice that the pitch changes go in steps of alternating 5/1s and 1/3s. If you multiplied both of these by the 24th root of 9565938/9765625, you would end up with sqrt(2) instead of 3125/2187.

BTW: In a couple of days, I'm planning to make a comma pump example using the tempered version of this sequence.

Petr

----------

! fifiveseq.scl

!

A prime sequence leading to the untempered "fifive" period

12

!

1/3

5/3

5/9

25/9

25/27

25/81

125/81

125/243

625/243

625/729

625/2187

3125/2187

2011/6/12 Petr Pařízek <petrparizek2000@...>
>
> Some time ago, Mike was interested to know more about the half-octave
> temperament I called "fifive". As an example, here I'm listing a sequence of
> pitches leading to one untempered period. You may notice that the pitch
> changes go in steps of alternating 5/1s and 1/3s. If you multiplied both of
> these by the 24th root of 9565938/9765625, you would end up with sqrt(2)
> instead of 3125/2187.
>
> BTW: In a couple of days, I'm planning to make a comma pump example using
> the tempered version of this sequence.

Very neat, I look forward to the comma pump! PS, still slowly working
my way through your comma pump paper - sorry it's taking so long, my
life is completely upside down right now.

-Mike