Equal tempered tuning divides the octave into semitones of the twelfth root of two.
Evidence
Experienced singers are able to vary their intonation (sung pitch) to a very fine degree with respect either to the pitch of any accompanying instrument(s) or, if singing a cappella (unaccompanied), to the pitches of the other singers. If singing with accompaniment that is being provided by a modern piano or pipe organ, then the tuning system will be equal tempered, where all the semitones have a twelfth root of two frequency ratio (see Section 3.4.3). — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1375
Categorization
- DEFINE: Defines equal temperament numerically, the reference tuning system for accompanied singing.
- XREF: Ties to the earlier tuning-systems discussion in Section 3.4.3; needed vocabulary for discussing pitch perception. — connects to: The cent divides the octave into equal logarithmic frequency steps; Each octave rise halves how many hearing-range harmonics a note carries — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 798; A cent is one twelve-hundredth of an octave, or one hundredth of a semitone. — David Howard, Jamie Angus, coustics and Psychoacoustics, 2790 (+2 more)
Broader Connections
- The cent divides the octave into equal logarithmic frequency steps
#expands(0.95) - A cent is one twelve-hundredth of an octave, or one hundredth of a semitone.
#corroborates(0.95) — David Howard, Jamie Angus, coustics and Psychoacoustics, 2790 - Semitones are logarithmically equal steps, not linear ones
#corroborates(0.95) — Eric J. Heller, Why You Hear What You Hear- An…, 2399 - A cent is one hundredth of an equal tempered semitone
#corroborates(0.95) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1064 - Each octave rise halves how many hearing-range harmonics a note carries
#complicates(0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 798