Musical intervals trace directly to harmonic-series frequency ratios
Evidence
These ratios can also be inferred from knowledge of the musical intervals and the harmonic series. Figure 3.3 shows that the major sixth is the interval between the fifth and third harmonics—in this example, these are G4 and E5—and therefore their frequency ratio is 5:3. Similarly, the interval of a minor sixth is the interval between the fifth and eighth harmonics, in this case E5 and C6; therefore, the frequency ratio for the minor sixth is 8:5. Knowledge of the notes of the harmonic series is both musically and acoustically useful and is something that all brass players and organists who understand mutation stops (see Section 5.4) are particularly aware of. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 811
Categorization
- DEFINE: Explains why the major sixth ratio is 5:3 and minor sixth 8:5 via harmonic positions—a concrete grounding of interval theory.
- corroborated: 3 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 811
- XREF: connects to: Harmonic complex tones dominate daily life through speech and music; Siren hole geometry directly determines pitch and tuned intervals.; String length ratios explain musical intervals since Pythagoras (+16 more)