On the Origins of Harmony – Sound Examples

Sound samples from On the Origins of Harmony.

Chapter 3 – Harmonic Relationships

Sound 3.1: Two complex tones, the first at A3 (220 Hz), the second an octave higher at A4 (440 Hz). Played separately, then together. Then the lower tone is played, joined by the upper tone.

Sound 3.2: A demonstration of octave equivalence. A chord is played, then each note of the chord is moved down by an octave then up by an octave. Then each note of the chord is moved down by a fifth then up by a fifth. The chords with octave transpositions do not fundamentally change, but most of the chords with fifth transpositions do fundamentally change. This demonstrates how equivalence is maintained with octave transposition but not with non-octave transpositions.

Sound 3.3: Two complex tones, first at a unison A3 (220 Hz) with one drifting sharp then back to unison, then at a unison A4 (440 Hz) with one drifting sharp then back to unison, then at an octave (A3 and A4) with the upper pitch drifting sharp then back to the octave.

Sound 3.4: Demonstration of difficulty of tuning 16:1 without, then with, intervening octaves.

Sound 3.5: Two complex tones, the first at A3 (220 Hz), the second a twelfth higher at E5 (660 Hz). Played separately, then together. Then the lower tone is played, joined by the upper tone.

Sound 3.6: The first five perfect consonances: 2:1, 3:1, 4:1, 5:1, 6:1. For each interval, first the lower note is played, then the upper note, then both notes simultaneously.

Sound 3.7: First A3 (220 Hz) followed by several 3:1-related pitches (6:1, 3:1, 3:2, 3:4, 3:8, 3:16)—notice how each of these 3:1-related pitches are the same, just in different octaves. Then A3 by itself; then A3 with E6 (1320 Hz) which together form the ratio 6:1; then A3 with E5 (660 Hz), forming the ratio 3:1; A3 with E4 (330 Hz) forming 3:2; A3 with E3 (165 Hz) forming 3:4; A3 with E2 (82.5 Hz) forming 3:8; and A3 with E1 (41.25 Hz) forming 3:16.

Sound 3.8a: A3 and E4, then A3 and E4 with the implied tone (A2) reinforced, and then just A3 and E4 again.

Sound 3.8b: A4 and E5, then A4 and E5 with the implied tone (A3) reinforced, and then just A4 and E5 again.

Sound 3.9: First A3 (220 Hz) by itself, then the pitches generated by 5:1, 5:2, 5:4, 5:8 by themselves (so we can hear they are the same note C#). Then A3 (220 Hz) by itself; then A3 with C#6 (1100 Hz) which together form the ratio 5:1; then A3 with C#5 (550 Hz), forming the ratio 5:2; then A3 with C#4 (275 Hz), forming 5:4; A3 with C#3 (137.5 Hz), forming 5:8; and A3 with C#2 (68.75 Hz), forming 5:16.

Sound 3.10: Comparison of the two kinds of major thirds (A3 and C#4). First the 5:4 major third, then 81:64 major third. Repeated three times.

Sound 3.11: Comparison of the two kinds of major thirds (A3 and C#4). First the 5:4 major third, then 81:64 major third. Then both intervals played with their difference tones reinforced. Finally the two intervals played again.