Are 2 or more octaves perfect consonant?
According to my knowledge, an octave is considered as a perfect consonant. But are 2 or more octaves considered perfect consonant? For example, is C1 and C5 perfect consonant?
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In theory yes, they should be simple factors of 2 in frequency which is perfectly consonant. In reality, it depends. As an example, pianos are tuned with "stretched octaves". The reason is that the overtones, that in theory should be 2,3,4,5,... times base frequency, are not exactly that on a real world string. In order to reduce interference between overtones, we tune the piano with octaves slightly larger than double frequency. See as example this article
Yes, because the lower note and its octaves, no matter how high, share the same partials. So the quality of the consonance does not change when transposing to a higher octave.
Yes, in the sense that a perfect 15th or 22nd, etc., of C1 will be a C?, not C? (which forms a diminished interval) or C? (which forms an augmented interval). The type of an interval remains the same after octave transposition, e.g., a minor third transposed an octave becomes a minor tenth, a perfect fifth becomes a perfect 12th, etc.
Simple answer - yes. Because our classification of consonance of intervals ignores octave displacements.
Be wary of the 'coinciding harmonics' theory of consonance/dissonance. Apart from the points already made, outside a laboratory a real instrument's harmonics don't fall neatly into the 2X, 3X, 4X etc. pattern. And surely two frequencies NEARLY in tune should sound much more inharmonic than ones in (say) a simpler but 'dissonant' 7:1 ratio? But they don't, do they? Stick to considering the relationship between the fundamental pitches.
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