A vibrating bar’s higher modes fall outside the musical scale and harmonic spacing.
Evidence
None of the higher modes is a whole number of equal tempered semi tones above the fundamental and none forms an interval available within a musical scale. The intervals between the modes are very wide compared with harmonic spacing as they are essentially related by the square of odd integers (i.e., 32, 52, 72, 92, …). The relative excitation strength of each mode is in part governed by the point at which the bar is hit. — David Howard, Jamie Angus, coustics and Psychoacoustics, 1309
Categorization
- XREF: Contrasts bar timbre with strings/air columns (harmonic series) — ties to why percussion produces inharmonic, unpitched sounds. — connects to: Bar vibration modes are spaced by squares of odd integers, far apart — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1285; Percussion bars are shaped to tune their modes toward harmonic ratios — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1287; Bars vibrate in modes spaced by squared odd integers, not musical intervals (+2 more)
Broader Connections
- Bars vibrate in modes spaced by squared odd integers, not musical intervals
#corroborates(0.98) - Bar vibration modes are spaced by squares of odd integers, far apart
#corroborates(0.93) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1285 - Struck bars vibrate in non-harmonically related transverse modes
#corroborates(0.90) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1269 - Percussion bars are shaped to tune their modes toward harmonic ratios
#expands(0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1287 - Bending stiffness makes bar vibrations dispersive and inharmonic.
#expands(0.85) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 248