Interval consonance ranking derives from critical-bandwidth proximity between harmonics
Evidence
Musical intervals can be ordered by decreasing consonance on this psycho acoustic basis. To determine the degree of consonance of a musical interval consisting of two complex tones, each with all harmonics present, the fre quencies up to the frequency of the seventh harmonic of the lower notes are found. Then the critical bandwidth at each frequency midway between harmonics of each note that are closest in frequency is found to establish whether or not they are within 5 to 50% of a critical bandwidth and there fore adding a dissonance contribution to the overall perception when the two notes are played together. If the harmonic of the upper note is midway between harmonics of the lower note, the test is carried out with the higher frequency pair since the critical bandwidth will be larger and the positions of table entries indicate this. — David Howard, Jamie Angus, coustics and Psychoacoustics, 958
Musical intervals can be ordered by decreasing consonance on this psychoacoustic basis. To determine the degree of consonance of a musical interval consisting of two complex tones, each with all harmonics present, the frequencies up to the frequency of the seventh harmonic of the lower notes are found. Then the critical bandwidth at each frequency midway between harmonics of each note that are closest in frequency is found to establish whether they are within 5 to 50% of a critical bandwidth and therefore adding a dissonance contribution to the overall perception when the two notes are played together. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 944
Categorization
- DEFINE: Explains the operational procedure for computing consonance on a psychoacoustic basis via critical bandwidths.
- corroborated: 2 independent passages support this claim — David Howard, Jamie Angus, coustics and Psychoacoustics, 958; David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 944
- XREF: connects to: Consonance and dissonance judgments stem from critical bandwidth mechanics — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 934; Chord consonance is computed from individual harmonic proximity across the notes — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 943