Questions and answers
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An octave spans twelve half steps, from one note to the next note with the same name, for example C up to the next C. Counted in letter names, C D E F G A B C, the upper note is the eighth, which is where the name comes from.
Two notes an octave apart share a name and almost merge into one sound; the upper note vibrates exactly twice as fast as the lower one. Octaves double a line to make it fuller, especially in the bass, and an octave leap is one of the clearest gestures a melody can make.
On the keyboard both notes are always the same color, with eleven keys between them, so the octave has two shapes: from a white key, or from a black key.
Each shape sits a little differently under the hand, so it is worth knowing them all. Under each keyboard, the same notes are on the staff: played together, then up, then down.
Octaves that share this same shape start on C, D, E, F, G, A, and B. Eleven keys lie in between, six white keys and five black keys.
Octaves that share this same shape start on D♭, E♭, G♭, A♭, and B♭. Eleven keys lie in between, seven white keys and four black keys.
An octave goes from a line to a space, or from a space to a line, with three lines and three spaces in between.
This is what makes intervals so useful for reading. Rather than naming every note from the clef, we read from one note to the next: once we know where we are, the shape on the staff tells us how far to move. Reading this way is relational rather than absolute, and it is much faster.
It works the same in the treble and bass clef, and at any height on the staff, so a reader who knows the look of an octave recognizes it everywhere.
Octaves are played 1 and 5 on white keys, and if it’s comfortable to reach, 1 and 4 on black keys. The hand holds one shape, and the arm carries it. For a smaller finger span, we need to relax and let the hand contract after playing octaves to avoid holding tension and getting tired.
The spacing on the staff and the spacing in the hand belong together. Beyond a fifth the fingers no longer map one to one onto the notes, so it helps to know the span as a whole hand shape: we see the distance on the staff, and the hand opens to it.
Moving the lower note of an octave up an octave puts both notes on the same pitch: the octave inverts to a unison. The numbers still add up to nine (8 + 1).
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