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4.3.8Definition of an Octave (and the Meaning of Tyrannical!)
You don’t have to think of the octave (by definition, the irreducibly simple 2-to-1 frequency ratio) as tyrannical. But, like other natural phenomena (gravity, for instance), it is. As Figure 20 above illustrates, all arrows curve to the octave notes. In music, you can’t break free of the tyrannical octave.
No matter how hard your tune may try to break the chains of 1 and 1 (8), there’s just no escaping. Your tune merrily leaves home, lights out for the territory, and ends up ... where? Strangely, back home. Without having turned back. Without having gone in a circle.
The irreducible simplicity of the 2:1 (octave) frequency ratio induces a feeling of balance or repose. All other pitches arise from more complex frequency ratios such as 3:2, 4:3, 5:4, and so on.