Interval ratios between adjacent scale notes derive from division of C-based 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 (#expands, via linked claim)

Categorization

• XREF: connects to: Musical scales universally favor intervals with small integer frequency ratios; Adjacent scale intervals are found by dividing note frequency ratios; Musical intervals trace directly to harmonic-series frequency ratios — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 811

Broader Connections

• Adjacent scale intervals are found by dividing note frequency ratios #corroborates (0.95)
• Musical intervals trace directly to harmonic-series frequency ratios #expands (0.80) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 811