Quote:
Originally Posted by Gardener
That is totally correct, but note that I didn't -only- say that the majority of listeners would classify it as atonal, but also that such randomly generated music wouldn't have a tonal centre. Would you classify totally random music as tonal, yourself?
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The devil is in the details. Consider a more simple situation in which you pick at random three tones, and ascertain if they form a recognizable triad (certainly having a tonal center).
Without sacrificing generality, we can fix the first tone as C (generalizable because scale degrees are preserved upon transposition). Total possible outcome = (1)(12)(12) = 144 sets of threes (any one tone may be non-unique)
The following 12 triads are possible:
C E G
C Eb G
C Eb Gb
C E G#
A C E
A C Eb
Ab C Eb
Ab C E
F A C
F Ab C
F# A C
E G# B# (= E G# C)
Therefore the probability of finding any of these relative triads in 3 randomly picked tones is 12/144 or 1/12
But if a 'piece' consists of at least 12 triads (or 36 notes), statistically there is at least (12)(1/12) = 1 recognizable triad. Does it make the 'piece' tonal? The devil is in the details.