Meantone and "starling" scale with slightly stretched octaves

I've got another interesting kind of scale to play with. I was trying to
optimize the "starling" scale (the one based on major and minor thirds of
388 and 312 cents that I described in a previous thread), and it occurred
to me that there was another interval I could tweak, one that I hadn't even
considered before: the octave. It turns out that making the octave 2 cents
sharp (without affecting the thirds or the fifth) improves the augmented
sixth, so that instead of 964 cents, it ends up as 966 cents, only 2.8
cents flat! A slightly better result is achieved with a major third of
388.3 cents and a minor third of 311.7 cents, which leaves the fifth the
same (700 cents), but results in an augmented sixth of 966.9 cents (1.9
cents flat). So the 2/1, 3/2, 5/4, and 7/4 are all within about 2 cents of
being perfectly tuned!

Slightly stretched octaves can also be applied to meantone scales. A
1/7-comma meantone sounds pretty good with the octave stretched by 1/7 of a
comma. The D a fifth above G is only 2/7-comma flat, which makes for good
ninth chords, but the D an octave lower is 3/7-comma flat, which is good as
a meantone major second, the best of both worlds (the major third thus ends
up being 1/7-comma sharp). The augmented sixth in this scale is 973.5
cents, or about 4.6 cents sharp.
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