Pythagorean scales are constructed by stacking perfect fifths
Evidence
Pythagorean scale can be built up on the starting note C by making F and G an exact perfect fourth and perfect fifth respectively (maintaining a perfect relationship for the subdominant and dominant respectively) … The frequency ratios for the other notes of the scale are found by ascending in perfect fifths from G and, when necessary, bringing the result down to be within an octave of the starting note. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1017
Categorization
Category: Definitional Content
- DEFINE: Clarifies the generative rule of the Pythagorean tuning system as a foundational psychoacoustics/music theory concept.
Related
- Pythagorean tuning generates scales purely from whole-number ratios of the fifth (similarity 0.86)
- Twelve stacked perfect fifths fail to close the octave exactly (similarity 0.84)
- The Pythagorean comma requires redistribution across fifths for multi-key tuning (similarity 0.80)
- Designing scales from upper harmonics yields ratios no Pythagorean scheme can reach (similarity 0.80)
- Pythagorean tuning generates all notes from factors 3 and 2 alone. (similarity 0.79)
- Twelve stacked fifths slightly overshoot seven octaves by the Pythagorean comma (similarity 0.79)