Octaves are doublings

Jump 12 keys and the frequency doubles — every time. The A's climb 27.5, 55, 110, 220, 440… a live powers-of-two table your ear already knows.

every A on the keyboard is lit — tap them low to high

Same letter, same feeling — just twice as fast each time you go up.

the doubling table — every A is 27.5 × a power of two

note	27.5 × 2^	frequency
A₀	2⁰	27.5 Hz	off keys
A₁	2¹	55 Hz	off keys
A₂	2²	110 Hz
A₃	2³	220 Hz
A₄	2⁴	440 Hz
A₅	2⁵	880 Hz
A₆	2⁶	1760 Hz
A₇	2⁷	3520 Hz	off keys

Double it, same note

Jump twelve keys — one octave — and the frequency doubles. 220 becomes 440 becomes 880. Your ear hears these as the “same note, higher,” which is the wonder: a plain ×2 is the most natural sound in music.

Read the middle column down and you get the powers of two — 2⁰, 2¹, 2², 2³… the fastest-growing pattern most kids ever meet, sitting quietly inside a piano.

lowest A = 27.5 Hz → seven doublings → 27.5 × 2⁷ = 3520 Hz

For the classroom

Learning goals

Going up one octave multiplies frequency by 2 — an octave is a doubling, no exceptions.
The same note across octaves forms a geometric sequence: 55, 110, 220, 440, 880 … = 55 × 2ⁿ.
The frequencies of every A are 27.5 × 2ⁿ — a concrete, audible table of the powers of two.

Try this

1.Play the A's low to high; have students call out the next frequency before each note (they're doubling). Then go high to low and halve.
2.Ask: the A above middle C is 440 Hz — what is the A two octaves above it? (Two doublings: ×4 = 1760.) Check it on the table, then find it on the keyboard.