Where does the closing interval go?

Pure fifth = 3/2. For closure across seven octaves, the exceptional ratio is 2⁷/(3/2)¹¹. Cents = 1200 log₂(ratio). Equal-tempered fifth = 2^(7/12). This is the narrowed Pythagorean closure, not the wide quarter-comma-meantone wolf. No real string inharmonicity or octave stretch is modeled.