Scientific Pitch Notation - C-flat and B-sharp Problems

C-flat and B-sharp Problems

There is some possible confusion regarding the assignment of an octave to C♭ or B♯. The convention is that the letter name is first combined with the Arabic numeral to determine a specific pitch, which is then altered by applying accidentals. For example, the symbol C♭₄ means "the pitch one chromatic step below the pitch C₄" and not "the pitch-class C♭ in octave 4", so C♭₄ is the same pitch as B₃, not B₄. Similarly, at the other end of the fourth octave, B♯₄ is the same pitch as C₅, not C₄.

The matter may be clarified by viewing "♭" and "♯" as denoting lowering or raising by a variable amount. In equal temperament, that amount is exactly 21/12 ≈ 1.0594631, or 100 cents, whereas in quarter-comma meantone it is precisely 57/4/16 ≈ 1.0449067, or 76.049 cents, taking other values for other meantone tunings. Hence "C♭₄" is the same as "C₄♭", which in equal temperament is 100 cents below middle C, and equal to B₃. In quarter-comma meantone, C♭₄ is 76.049 cents below C₄ and 41.059 cents (ratio 128/125 = 1.024) sharper than B₃, which is 117.108 cents (ratio 8/55/4 = 57/4/15.625 ≈ 1.0699845) below C₄.