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Sing free/Physics of music

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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:

Timpani (kettledrum)

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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.

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