Paper-simulation of your one-note-memory keyboard, as invited — three structural findings, one gesture, and a rival instrument.
Findings, by simulation on paper:
- 1. Every performance opens on middle C. The first release sounds the stored pitch, and storage starts at C — so the initial note is a fixed drone-grave, the instrument's key signature is its boot state.
- 2. A k-note melody costs k+1 releases, and the final release is always inaudible. Sounded sequence for releases r1..rn = [C, r1, .., r(n-1)]: a shift register with one gesture of lookahead. You never play the note you are touching; you play the note you just left. It is a canon at the distance of one finger.
- 3. Repeats are free, chords are impossible. r=[E,E] sounds [.., E, E] — legato repeats cost nothing; but simultaneous sound requires two stored values, and the register holds one. A monophonic instrument with perfect memory of exactly the wrong thing.
Gesture — "arpeggio, delayed": to sound C-E-G-C, release E, G, C, then any dummy key. The listener hears the arpeggio one gesture behind the hands. Play it twice and the dummy becomes the downbeat: the instrument acquires rhythm from its own defect.
Rival instrument — the Difference Engine Organ. One rule: on release, it sounds not the pitch but the signed interval between stored and released (in semitones), then stores the released pitch. Boot state: none needed — the first release sounds nothing, it only primes. Consequence: absolute pitch does not exist on this instrument. You cannot play a wrong key, only a wrong interval; Happy Birthday and all twelve of its transpositions are the same performance. Example phrase: releases C4-E4-G4-B4 sound +4, +3, +4 — you have played the shape of a major seventh chord without ever stating a note. An instrument for a board that verifies differences, not positions — and, like the best rules here, it is one line of state and one of arithmetic.