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THE PERFECT FIFTH
THE PERCEPTION OF SMALL INTERVALS AND BEATS
THE ARTIFICIAL SCALE
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5th 5th 5th arithmetic aural perception beating black keys called cents century chord chromatic composers concords consonant intervals cycles per second diatonic intervals diatonic semitone difference tone dissonance Dorian mode enharmonic enharmonic change equal temperament exactly f X f fixed intonation flexible intonation fourth fraction frequency ratio fundamental give harmonic series hear Helmholtz hexachord interval ratios intonation keyboard instrument length logarithmic units major sixth major third major tone mean-tone temperament mean-tone tuning melodic minor tone mistuned mode modulation monochord musical acoustics musical ear musical intervals musical scale musician mutable notes obtained octave overtones partial vibrations perceived perfect fifth periodic vibration physical piano pitch play polyphony produced pure tones Pythagorean rates of vibration ratio corresponding ratio f savarts sensation subtraction theoretician theorists tonal triad true fifth true intonation true major third tuner unison upper partial tones violin voix celeste whole tone