--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > my whole idea of "xenharmonic bridging" is based on the
> > fact that certain lower-prime-limit pitches emulate those
> > which *define* higher-prime-limit pitches.
>
> Here are some xenharmonic bridges:
>
> 5-limit
>
> 16/15, 135/128, 81/80, 32805/32768
>
> 7-limit
>
> 200/189, 28/27, 36/35, 525/512, 64/63, 875/864, 126/125,
> 225/224, 5120/5103, 65625/65536, 4375/4374
>
> 11-limit
>
> 77/75, 45/44, 55/54, 56/55, 99/98, 100/99, 176/175, 896/891,
> 385/384, 441/440, 1375/1372, 6250/6237, 540/539, 5632/5625
>
> We might call a temperament "brigable" if it can be defined in terms
> of xenharmonic bridges. The classic example would be meantone,
where
> 81/80 bridges 3 to 5, 126/125 or 225/224 bridges 5 to 7, and 99/98
or
> 385/384 (depending on which version we want) bridges 7 to 11.
>
> 5 ~ 3^4/2^4
>
> 7 ~ 5^3/2 3^2
>
> 11 ~ 2^7 3 / 5 7 (385/384) or
>
> 11 ~ 2 7^2 / 3^2 (99/98)

So pajara, defined in terms of 64/63 and 225/224, would
be "bridgable", right? Or do you need to modify your definition?

> A bridgable temperament has a fifth as a generator and an octave as
a
> period, which makes it of a rather particular kind.

Pajara has a half-octave period.