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PitchNote NameHarmonic SeriesRegisterPerfect Intervals

The octave is the one concept in music theory that belongs to physics and psychology at once: physically it is a doubling of frequency, perceptually it sounds like "the same note, one level up". That double identity explains why seven letters are enough for an entire naming system.

A doubling of frequency

Take a tone and place another at exactly twice its frequency: the two are an octave apart. A4 is 440 Hz, so A5 is 880 Hz and A3 is 220 Hz.

Double again for the next octave up, halve for the next down. Strictly speaking, then, an octave is not only "the neighbouring pair": A2 and A6 are four octaves apart and still stand in an octave relationship.

Why it sounds like "the same note"

Because the two tones' harmonic series overlap heavily. Give the lower tone a fundamental of 100 Hz; its harmonics are 200, 300, 400, 500 and so on. The upper tone's fundamental at 200 Hz lands exactly on the lower tone's first harmonic, and the upper tone's own harmonics — 400, 600, 800 — are all members of the lower set.

Hearing so much shared material, the ear concludes "same family". A perfect fifth (ratio 3:2) also overlaps strongly and sounds clean for the same reason, but nobody mistakes a fifth for one note, because its overlap is less complete than the octave's.

The octave is the most complete overlap any interval can have.

Diagram: where octaves meet in the harmonic series

Why seven letters are enough

Because above an octave the names repeat unchanged: C D E F G A B runs out and the next note is called C again. Without this convention the alphabet would have been exhausted long ago. Strictly, a note name needs an octave number to pin down a single pitch (C4 and C5 are different pitches), but there is still only one name for the letter.

This is also why keys, chords and scales are normally named without octave numbers: they describe structure, and structure holds at any octave.

Three uses of the octave in writing

• Thickening: doubling a melody at the octave (piano hands an octave apart, string sections in parallel).

The volume grows while the melodic outline stays identical — the most common device of all.

• Layering: giving a melody to different octaves to distinguish who is speaking — the lower octave reads

as narration, the upper as a question.

• Pushing the limits: at extreme registers the octave is the only way to expand, because higher than that

the ear stops hearing a definite pitch at all.

Listen: the octave

Hear the lower tone, then the tone an octave above, then both together. The third one sounds emptiest, because there is almost nothing between the two tones that needs blending.

Common misconceptions

• "The octave is the farthest interval." It is the largest simple interval, yet one of the easiest to identify — precisely because it sounds like the same note.
• "All octaves sound alike." Same structure, different impression. Low octaves are thick and smear together easily; high octaves thin out into two fine lines.
• "There is only one kind of octave interval." There is only one perfect octave, but "spanning an octave" can describe any pair in that relationship; they all belong to perfect intervals.
• "An octave is twelve semitones." Only in twelve-tone equal temperament. The octave is always the 2:1 ratio; twelve semitones are one way of slicing it up.

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Sources

• {'八度频率比 2': '1、泛音列中八度重合、八度叠奏的用法，属通行乐理与配器常识'}
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