The Cent Ledger

7:4 · 10 semitones

Harmonic seventh. Billed for a note it never delivers.

Pure
968.83¢
Tempered
1000¢
Charge
+31.17¢
Beat
7.00 Hz

Lower note 220 Hz. Pure upper 385.00 Hz. Tempered upper 392.00 Hz.

The ratio 7:4 is the seventh harmonic over the fourth. A keyboard has no key for it, so it plays the minor seventh at 1000 cents instead, 31.2 cents sharp of 7:4.

That is the largest charge in this ledger. The cited source says barbershop singers are expected to tune this interval in dominant seventh chords, and also that empirical data (Hagerman and Sundberg, 1980) challenges how accurately they do. Harmonic seventh (Wikipedia, CC BY-SA).

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