Friday, September 21, 2012

[snqashfg] Arpeggiated keyboard

It is easier to play arpeggios than arbitrary sequences of keys. 

Consider a 10-button one-handed keyboard with two keys per finger.  How many arpeggios are there?

2^5 = 32 5 finger upward arpeggios
2^4 * 5c4 = 16*5=80
2^3 * 5c3 = 8*10=80
2^2 * 5c2 = 4*10=40

232 total, *2 for downward arpeggios = 464
2*5 = 10 single button presses.
474 total.

It is tricky to distinguish consecutive separate arpeggios from a single longer one, for example, two single-button presses.

Previously, enumerating arbitrary chords and arpeggiations.

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