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 I calculate these errors: Sample calculation:
 * 2.14/1.59 = 1.3459 and 7/6 =1.16666. I think the % refers to cents.

https://www.amazon.com/Evans-Strata-Timpani-Drum-Head/dp/B001E4VE88 2pounds

Tipani tension 1500 to 5000 N/m