:: deftheorem defines pentatonic MUSIC_S1:def 58 :
for MS being MusicSpace
for n being natural Number
for scale being Element of n -tuples_on the carrier of MS holds
( scale is pentatonic iff ( n = 6 & ex frequency being Element of MS ex r1, r2, r3, r4, r5, r6 being positive Real st
( scale . 1 = frequency & scale . 1 = r1 & scale . 2 = r2 & scale . 3 = r3 & scale . 4 = r4 & scale . 5 = r5 & scale . 6 = r6 & r1 < r2 & r2 < r3 & r3 < r4 & r4 < r5 & r5 < r6 & scale . 6 = Octave (MS,frequency) ) ) );