Re: consistency up and down

Welcome back Paul! You wrote :

> Hi Kraig.
>
> Yes, and that, again, is the point of consistency. In 24-tET, the 5th
> harmonic is sharp by 0.27 step, and the 7th harmonic is flat by 0.37 step.
> Since these errors are in opposite directions, 24-tET is considered
> inconsistent in the 7-limit.

Isn't it "since the sum of these errors (-.27 + .37 ) is greater than
1/2 a step, 24-tET is considered inconsistent in the 7-limit." This
specific case exactly says that the best 5/4 connects to the best 7/4
NOT by the best 7/5, but by the best 7/5 + one step. Opposite signs
is necessary but not sufficient to produce a sum > 1/2 step.

Bob Valentine

You mean -.27 - .37. But right, necessary but not sufficient. In terms of
replying to Kraig, the relevant part of this example is that, if these size
errors were in the same direction, the tuning would be considered
consistent, since the .37 - .27 = .1 < .5.

-----Original Message-----
From: Robert C Valentine [mailto:BVAL@IIL.INTEL.COM]
Sent: Wednesday, April 04, 2001 4:30 AM
To: tuning@yahoogroups.com
Subject: [tuning] Re: consistency up and down

Welcome back Paul! You wrote :

> Hi Kraig.
>
> Yes, and that, again, is the point of consistency. In 24-tET, the 5th
> harmonic is sharp by 0.27 step, and the 7th harmonic is flat by 0.37 step.
> Since these errors are in opposite directions, 24-tET is considered
> inconsistent in the 7-limit.

Isn't it "since the sum of these errors (-.27 + .37 ) is greater than
1/2 a step, 24-tET is considered inconsistent in the 7-limit." This
specific case exactly says that the best 5/4 connects to the best 7/4
NOT by the best 7/5, but by the best 7/5 + one step. Opposite signs
is necessary but not sufficient to produce a sum > 1/2 step.

Bob Valentine

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