Pitch Tuning Timbre Tone
Let's start with the basic idea that percussion drums - with some exceptions, like timpani or tabla - are considered to have an indefinite pitch. But still, musicians are trained to tune their instruments. So...here goes....
The way I see/hear it...pitch is defined by diameter, the length of the longest node- it is physics, like the length of a string on a harp. Each diameter drum has a specific fundamental note. That note can be adjusted by using the "tuning" system, but the ability to change the note is extremely limited - maybe 1 step? Think of drum kit ( or drum kit) - at least 3 drums, maybe 7 or even more. A piccolo snare would be included to provide the high pitch articulate sounds, a standard 14" snare drum would be the workhorse of the mid-range, toms of various sizes to provide in-fill, and then a bass (or kick) drum for the pulsing bass. In a similar way, we think of the 10-13" frame drums as the bright, high end, 14-17" as the mid-range, and the 18"-22" as the bass range.
River Guerguerian plays onstage with large ensembles like Omar Faruk Tekbilek:
BUT, the tightly defined pitch range does not need to be thought of as limiting.
There's also a tonal difference (timbre), that gives each drum a personality, a tonal palette - is the drum crisp and bright and articulate or is it warm, or dark and meditative? does it have complex or controlled overtones? These tonal differences can be manipulated by various construction specifications. For example, we can use different drum shell materials - oak or ash with wider or rounder bearing edges will help to control overtones, whereas tight grained Cherry wood or Maple will make for a more articulate and bright sound. Similarly, the various membrane material (Cooperman uses REMO Weatherking Clear, Renaissance, Ebony Suede, etc.) can make the tone "darker,warmer" (for Ebony), or "brighter" with" complex overtones" (for Renaissance), or "super articulate" and "crisp" for Weatherking Clear. Skins have their own range of tonal qualities - from soft and thuddy to bright and gritty.
John Hadfield extends his creative mix with a SlapBack99 with an REMO Ebony/Black drumhead.
Keita Ogawa's (Snarky Puppy, Bokante) Groove of Day :
Circling back, the pitch of a specific diameter drum is not being changed but its timbre is being changed. The pitch of a 20” is the same regardless of the head material, the shell material, the bearing edge the shell depth, etc.
Here is the link for our notes on tuning - since the issue is not definitive, I gathered notes from several artists we work closely with - Randy Crafton, River Guerguerian, and N. Scott Robinson.
https://www.coopermanframedrums.com/blogs/news/about-tuning-your-cooperman-drums
See too our page on head selections:
https://www.coopermanframedrums.com/blogs/news/comparing-various-synthetic-drumhead-options
Additionially, Yamaha drums has an excellent discussion on their webpages – keep in mind that frame drums are unlike snare drums in that they are single sided drums, hence 100 % vented, so there is not compressed air in the shell of a frame drum.
https://www.yamaha.com/en/musical_instrument_guide/drums/mechanism/mechanism003.html
I do not necessarily mean to validate the claims this blogpost , but I do find it helpful and interesting:
https://www.benjaminwaterson.com/blog/tuning-drums-to-notes/