All common Western scales are built on the octave ratio of two to one
Evidence
Musical scales are basic to most Western music. Modern keyboard instruments have 12 notes per octave, with a musical interval of one semitone between adjacent notes. All common Western scales incorporate octaves whose frequency ratios are (2:1). Therefore, it is only necessary to consider notes in a scale over a range of one octave, since the frequencies of notes in other octaves can be found from them. Early scales were based on one or more of the musical intervals found between members of the natural harmonic series (e.g., see Figure 3.3). — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1011
Categorization
- XREF: connects to: Musical scales are exponential, so changing the octave needs logarithmic scaling