Musical sequence

[David Wilson]

In general music theory, we hold to the concept of an octave, specifically, that 
if a musical scale includes a tone of frequency f, it also includes a tone of 
frequency 2f.

What if we abandon the notion of octave, but keep the idea of equally spaced 
tones, so that our scale can be described by base tone frequency b and a ratio r 
between adjacent tones on the scale.

Is there a measure of goodness of r that would rate r = 2^(1/12) high? 
Presumably this rating would be based on the closeness of tone ratios to simple 
rationals which represent pleasing harmonies.  Given this rating, what would be 
the best r?  If we return to octave-based scales, could be construct a sequence 
of t with increasingly better ratings of 2^(1/t), which would represent 
increasingly good choices for number of tones in an octave?

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- David Wilson