Sing free/Physics of music
Sometimes I get so involved in the physics that I end up leaving Sing free:
Beat (acoustics) and subpages:
Subpages of Sing free that are more about the physics of music than singing:
- Sing free/Prelude and Fugue in C major (ear training)
- Draft:Sing free/Tables and images
- Draft:Sing free/Physics of music
Timpani (kettledrum)
THE MOST IMPORTANT ARTICLE TO READ IS:
Applied Acoustics 164 (2020) 107284
Sound model of an orchestral kettledrum considering viscoelastic effects
Erik U. Gallardo, Miguel A. Alonso-Arévalo, Eloísa García-Canseco, Carlos Aguilar-Ibáñez
http://hyperphysics.phy-astr.gsu.edu/hbase/Music/timpani.html
Jones, Richard K. (March 2017). "In Search of the Missing Fundamental". The Well-Tempered Timpani. Retrieved September 23, 2018.
- wikipedia uses this reference and it is online at:
- https://wtt.pauken.org/chapter-5/octave-harmonic-effect/2
- https://wtt.pauken.org/chapter-3/preferred-modes
- preferred modes are (1,1), (2,1), (3,1), (4,1), (5,1) and sometimes (6,1).
https://www.acs.psu.edu/drussell/demos/membranecircle/circle.html shows modes with frequencies to 2 sig figs
| mode | frequency |
|---|---|
| 1.1 | 1.59 |
| 2-1 | 2.14 |
| 3-1 | 2.65 |
| 4-1 | 3.16 |
| 5-1 | 3.65 |
I calculate these errors:
Sample calculation:
- 2.14/1.59 = 1.3459 and 7/6 =1.16666. I think the % refers to cents.
| 2 | 1.59 | |||
| 3 | 1.5 | 2.14 | 1.35 | 11.11% |
| 4 | 1.33 | 2.65 | 1.24 | 7.26% |
| 5 | 1.25 | 3.16 | 1.19 | 5.04% |
| 6 | 1.2 | 3.65 | 1.16 | 3.45% |
https://www.amazon.com/Evans-Strata-Timpani-Drum-Head/dp/B001E4VE88 2pounds
Tipani tension 1500 to 5000 N/m