Subject: arithmetic divisions for 2/7-comma meantone? (Zarlino 1558)

>

Monz/Paul/Gene
Please note that meta-meantone converges on an interval of
695.6304372 cemts which is darn close to 2/7-comma meantone
which is one reason i am posted it!
and it seems that equal beating between the two thirds would make it easier to dial this one in than it might appear!

>
> From: "monz" <monz@attglobal.net>
> Subject: arithmetic divisions for 2/7-comma meantone? (Zarlino 1558)
>
> hold the presses!!
>
>
>
> this procedure would result in the following
> divisions for the "5th":
>
> ratio string ~cents
> length
> 3:2 "perfect 5th" 560 701.9550009
> 3:2 less 1/7-comma 561 698.8662685

>
> 3:2 less 2/7-comma 562 695.7830369

>
> 3:2 less 3/7-comma 563 692.7052867
> 3:2 less 4/7-comma 564 689.6329983
> 3:2 less 5/7-comma 565 686.5661524
> 3:2 less 6/7-comma 566 683.5047298
> 3:2 less 1 comma 567 680.4487113
> 1:1 840 0
>
> if this is how Zarlino calculated his temperament,
> then his 2/7-comma meantone "5th" is ~695.7830369
> cents, and not the ~695.8103467 cents which results
> from the logarithmic division of the comma, and it
> is indeed a rational number: 840/562.
>
> a tempered approximation of this "5th" is 2^(40/69).
>
> -monz
>
>
>
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>

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