[I wrote:]

>>>Oh, I meant that, despite fewer words. Although, I see that Herman

>>>is saying "1/7-comma meantone with 1/7-comma tempered octaves";

>>>perhaps if the word "tempered" were changed to "stretched", it'd be

>>>clearer...

[Herman Miller:]

>>Done.

[Dave Keenan:]

>No. I think maybe John still doesn't get it. It's definitely "with

>octaves tempered 1/7-comma wide" and _not_ "with a stretch of 1/7

>comma per octave". These are very different things.

You're right, Dave! I'm gonna study the rest of what you wrote and try

to clear up my understanding. Thanks!

JdL

[Dave Keenan wrote:]

>Here are the three scales to the nearest cent

>1. Ordinary 1/7 comma meantone

>2. 1/7 comma meantone with a stretch of 1/7 comma per octave

>3. 1/7 comma meantone with octaves tempered 1/7 comma wide.

>

>Name Octaves Fifths 1/7 with with

> comma stretch tempered octaves

>-----------------------------------------------

>C 0 0 0 0 0

>C# -4 7 92 92 80

>D -1 2 198 198 195

>Eb 2 -3 303 304 309

>E -2 4 396 397 389

>F 1 -1 501 502 504

>F# -3 6 593 595 584

>G 0 1 699 701 699

>G# -4 8 791 793 779

>A -1 3 897 899 894

>Bb 2 -2 1002 1005 1008

>B -2 5 1094 1097 1088

>C 1 0 1200 1203 1203

>

>Look at E. Notice how stretch makes the major thirds (4:5 = 386c)

>slightly worse, but wide-tempered-octaves makes them significantly

>better.

Thanks again, Dave, for the clear and detailed explanation. So... the

tempered octave tuning _could_ be reformulated as an octave stretch,

howbeit the scale to be stretched would be arrived at in a convoluted

manner.

JdL

> Thanks again, Dave, for the clear and detailed explanation. So...

the

> tempered octave tuning _could_ be reformulated as an octave stretch,

> howbeit the scale to be stretched would be arrived at in a

convoluted

> manner.

Er, yes. _Very_ convoluted.

Instead the final scale is arrived at by (for each note) multiplying

the number in the "Octaves" column by the size of the tempered

octave (1200c plus 1/7 comma) and multiplying the number in the

"Fifths" column by the size of the tempered fifth (701.955c minus 1/7

comma) and adding these together.

-- Dave Keenan

[I wrote:]

>>Thanks again, Dave, for the clear and detailed explanation. So... the

>>tempered octave tuning _could_ be reformulated as an octave stretch,

>>howbeit the scale to be stretched would be arrived at in a convoluted

>>manner.

[Dave Keenan:]

>Er, yes. _Very_ convoluted.

Oh c'mon, Dave; it's only _fairly_ convoluted. ;->

>Instead the final scale is arrived at by (for each note) multiplying

>the number in the "Octaves" column by the size of the tempered

>octave (1200c plus 1/7 comma) and multiplying the number in the

>"Fifths" column by the size of the tempered fifth (701.955c minus 1/7

>comma) and adding these together.

Yes, I think I could finally pass a test on it... My interest in

conceptualizing this kind of scale in a reformulated way has to do with

comparing apples to apples against about-to-be stretched tunings.

Certainly the direct route you outline is the one that would normally be

followed.

JdL