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Hanson, kleismic, and catakleismic

🔗Gene Ward Smith <gwsmith@svpal.org>

5/5/2004 12:27:07 PM

Here's the comparison of the 7-limit temperament stemming from 19&34
(kleismic) with that stemming from 53&72 (hanson, as I called it,
formerly catakleismic.)

5-limit hanson has comma 15625/15552 and TOP generators
[1200.291038, 317.0693810]. Compare that with 7-limit hanson and
7-limit kleismic:

hanson
wedgie: <<6 5 22 -6 18 37||
generators: [1200.536355, 316.9063960]

kleismic
wedgie: <<6 5 3 -6 -12 -7||
generators: [1203.187309, 317.8344609]

Clearly the hanson7 generators are much closer to hanson5 than the
kleismic generators are; the name "hanson" therefore attaches to
hanson7 and not to kleismic.

In any case, the 11-limit situation is clear:

wedgie: <<6 5 22 -21 -6 18 -54 37 -66 -135||
generators: [1200.536355, 316.9063960]

The hanson11 generators are exactly the same as the hanson7 generators
and therefore plainly get the same name.

This is simply one instance of a general naming convention you seemed
willing to accept when I proposed it.

🔗wallyesterpaulrus <paul@stretch-music.com>

5/5/2004 4:21:43 PM

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> Here's the comparison of the 7-limit temperament stemming from 19&34
> (kleismic) with that stemming from 53&72 (hanson, as I called it,
> formerly catakleismic.)
>
> 5-limit hanson has comma 15625/15552 and TOP generators
> [1200.291038, 317.0693810]. Compare that with 7-limit hanson and
> 7-limit kleismic:
>
> hanson
> wedgie: <<6 5 22 -6 18 37||
> generators: [1200.536355, 316.9063960]
>
> kleismic
> wedgie: <<6 5 3 -6 -12 -7||
> generators: [1203.187309, 317.8344609]
>
> Clearly the hanson7 generators are much closer to hanson5 than the
> kleismic generators are; the name "hanson" therefore attaches to
> hanson7 and not to kleismic.

It turns out that WRT the list of 23 7-limit 'linear' temperaments I
was going to include in my paper, what you call 'hanson' would have
been #27, while the 10&16 temperament being discussed in another
thread would have been #26. I'm going to stick to 5-limit for my use
of the word 'Hanson', though.

> This is simply one instance of a general naming convention you
>seemed
> willing to accept when I proposed it.

How did I seem willing?