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Linear temperament consistency?

🔗genewardsmith <genewardsmith@juno.com>

1/25/2002 1:00:09 PM

Does anyone apply the consistency concept to linear temperaments, or even to higher dimensions? It seems like that would make sense also.

🔗graham@microtonal.co.uk

1/26/2002 5:32:00 AM

genewardsmith wrote:

> Does anyone apply the consistency concept to linear temperaments, or
> even to higher dimensions? It seems like that would make sense also.

I've thought about it. You'd have to confine it to a particular scale,
because any non-just interval can be approximated better with enough steps
of an irrational generator.

One detail is that the 31 note MOS of 1/4 comma meantone would be
inconsistent. The unofficial fifth is tuned better than the official one.

Linear mappings of equal temperaments will tend to be ambiguous, because
you can get to the same intervals by going round the circle in the other
direction.

Graham