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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?

  • 1
    Yes -- the ratio of their frequencies remains a whole number. – Matthew Read Apr 7 '15 at 14:00
  • In my knowledge, consonant and dissonant notes are not always solely defined by overtones, e.g. the fourth was considered dissonant in some music styles, in modern music the small 9th is considered much more dissonant then the small 2. Also, our ears hearing is not perfectly linear in frequency. Thus, an answer concerning ( historic or biology ) sources would be important. – tommsch May 1 '18 at 19:59
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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.

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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.

  • Except that they don't actually share the same harmonics: the upper member of a perfect octave, for example, will reinforce the root's even-numbered harmonics, but it won't share the root's odd-numbered harmonics. – user16935 Apr 7 '15 at 7:39
  • @Patrx2: All partials of the higher octave are also partials of the lower note, obviously not the other way around. – Matt L. Apr 7 '15 at 7:42
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    It's an important distinction: the higher the octave, the fewer of the root's harmonics in the audible range are reinforced. I think, however, that the idea of "perfect" intervals (because it is really a very old classification) came about because of the lovely simple ratios: 2:1, 4:1, 8:1, etc. for the various octaves, 3:2, etc. for perfect fifths, 4:3, etc. for perfect fourths. I think, however, that it's wiser to treat our naming convention of quality and interval number as just that, a naming convention, considering that we rarely use just intonation anymore. – user16935 Apr 7 '15 at 8:25
  • Are you sure about that Patrix2? Wouldn't each odd harmonic of the upper octave simply be double that of those in the lower octave? The upper octave itself won't consonate with the lower odd harmonics, but it's own harmonics should. Perhaps I don't understand what you were saying. – Kristal McKinstry Apr 8 '15 at 8:23
  • For an octave interval, the 1st harmonic of the root is the fundamental, which the higher note doesn't share; the 2nd is the octave, which is the fundamental of the higher note; the 3rd is the twelfth, which isn't shared; the 4th is the double octave, which is the 2nd harmonic of the higher note; the fifth is a somewhat flat major 17th - unshared; the sixth harmonic is the nineteenth - shared as the 3rd harmonic of the higher note; the seventh is two octaves and a very flat minor seventh - unshared; and so forth. (more...) – user16935 Apr 9 '15 at 17:21
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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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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

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