When we talk about pure octaves we have the distinction between 2:1 octaves (where the 2nd partial of the lower note zero beats with the fundamental of the higher note) and 4:2 octaves (where the 4th partial of the lower note zero beats with the 2nd partial of the higher note. Due to the variability of inharmonicity these two tunings are not necessiarily the same. Doesn't the same consideration hold true for pure 5ths? There can be a 3:2 pure fifth (where the 3rd partial of the lower note zero beats with the 2nd partial of the higher note) or a 6:4 pure fifth (where the 6th partial of the lower note zero beats with the 4th partial of the higher note). I suppose you could even talk about 9:6 and 12:8 pure fifths too, but by the time the partials get that high they are probably too weak to need special attention. How does this impact the discussion of tuning by pure 5ths? Bob Scott Ann Arbor, Michigan
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