For drums with two heads installed, proprietary* research leads to the below relationship-formulae between the fundamental tone and the lug pitches of the batter head and the resonant head.
(*Following estimation methods and formulae are the intellectual property of Bram Van den Broeck and can be used for personal use only.)
Below methods are provided for estimation of some typical tuning cases and can be particularly useful for the tuning of drum types that have two drum heads ("batter head" & "resonant head"), like EG. toms and floor toms.
Generally, drumheads, depending on their construction and diameter, can be tuned to a vast range of pitches.
This doesn't necessarily mean that any acquirable drum head pitch combination for the batter head and the resonant head produces the desired sound.
While these formulae may help to estimate to which pitch ranges the drumheads can be tuned to produce certain fundamental tones at a certain pitch-relationship from a physics viewpoint, from a musical viewpoint it's important to explore different pitch combinations and different fundamentals of a certain drum and drum head combo.
Whether your drums sound fine for your needs, or not when tuned to a certain relationship solely depends on your personal preference, taste judgment and/ musical need.
We'd like to underline the importance of listening to the sound of your drums. Experiment until it feels & sounds good to you!
EG. How to estimate the resulting fundamental tone based upon a chosen batter head lug pitch & a chosen resonant head lug pitch?
EG. How to estimate the resulting fundamental tone and the opposite head pitch, based upon a chosen batter or reso head lug pitch & a chosen interval between both heads?
EG. How to estimate the required opposite head's lug pitch to reach a desired fundamental tone for a chosen batter or reso head lug pitch?
EG. How to estimate the lug pitch required for the opposite head, to tune a drum to chosen fundamental tone with the batter or reso head’s lug pitch tuned to a chosen interval above that chosen fundamental tone?
(In cases other than P1, either the lug pitch of the batter or reso head is tuned to the desired interval with the fundamental tone.
If the batter head lug pitch is higher than the resonant head lug pitch the drum has a more defined attack.)
EG. How to estimate the lug pitches required for the resonant head & the batter head to reach a chosen fundamental tone, with a chosen "pitch interval-relationship" between both heads?
The above proprietary methods and formulae of Bram Van den Broeck generate estimates that are meant to have an accuracy of approx. +/- 10%.
The accuracy of the estimate depends on the applicable deviation of factor 3.46.
The value of 3.46 is an arbitrary factor choice based upon a wide range of tests, in order to have a common starting point that works well and gives reliable estimates for most drums.
Proprietary research showed that factor 3.46 varies slightly for different drums.
Proprietary research showed also that the factor does not seem to remain constant over the tuning range of a drum: it deviates somewhat for the same drum depending on where and how that drum is tuned within its comfort zone/tuning range. The factor itself tends to increase slightly as the fundamental tone increases for a given drum, hereby the amount also depends on how far both heads are tuned apart. (Variations for different drums for factor 3.46 could go from 3.36 to 3.62 for example... With individual fluctuations of approx. 3% +/-3% depending on their tuning.)
The detailed principle behind this 'fluctuation' as understood by the proprietary research, goes beyond the scope of the above simplified 'rules of thumb', which provide estimated starting points as tuning guidance.