Adjacent harmonics of a fundamental produce every familiar musical interval
Evidence
The musical intervals of adjacent harmonics in the natural harmonic series starting with the fundamental or first harmonic, illustrated on a musical stave and as notes on a keyboard in Figure 3.3, are: octave (2:1), perfect fifth (3:2), perfect fourth (4:3), major third (5:4), minor third (6:5), flat minor third (7:6), sharp major second (8:7), a major whole tone (9:8) and a minor whole tone (10:9). … The frequency ratios for intervals between nonadjacent harmonics in the series can also be inferred from the figure. For example, the musical interval between the fourth harmonic and the fundamental is two octaves, and the frequency ratio is 4:1, equivalent to a doubling for each octave. Similarly, the frequency ratio for three octaves is 8:1 and for a twelfth (octave and a fifth) is 3:1. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 803
Categorization
- DEFINE: Maps each named interval to its exact ratio in the harmonic series — a clean reference table for the field’s core vocabulary.
- XREF: Connects to how just intonation and Pythagoras’ ratios describe consonance, and to the equal-temperament comparison likely elsewhere in the book. — connects to: Sinusoidal vibration is the fundamental atom of all sound; Musical scales universally favor intervals with small integer frequency ratios; Harmonic tones are integer multiples of a fundamental frequency — Jennifer Lentz, Psychoacoustics- Perception of Normal…, 1180 (+2 more)
- corroborated: 2 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 803
Broader Connections
- Musical intervals trace directly to harmonic-series frequency ratios
#corroborates(0.95) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 811 - Musical intervals between adjacent harmonics shrink as harmonic number rises
#qualifies(0.90)