drumhead pitch relationship

DRUMHEAD

PITCH RELATIONSHIP DEMYSTIFIED


For drums with two heads installed, proprietary research of Bram Van den Broeck 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 particularly useful for the tuning of EG. toms and floor toms.


General relationship =>  [(Batter Lug Pitch + Reso Lug Pitch) : 2] * 1.73 = Fundamental Tone +/- 10%




1. ESTIMATE RESULTING FUNDAMENTAL TONE BASED UPON LUG PITCHES OF BOTH HEADS.

EG. How to estimate the resulting fundamental tone based upon a chosen batter head lug pitch & a chosen resonant head lug pitch?


CHOSEN VALUES

  • Batter Lug Pitch
  • Reso Lug Pitch

 

RESULTING ESTIMATE

  • Estimated Fundamental tone = (Batter Lug Pitch + Reso Lug Pitch) : 3.46






2. ESTIMATE RESULTING FUNDAMENTAL TONE AND OPPOSITE HEAD LUG PITCH BASED UPON A CHOSEN INTERVAL BETWEEN BOTH HEADS AND ONE 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?


CHOSEN VALUES

  • Batter or Reso Lug Pitch
  • Desired Interval Ratio. DIR between both heads = ( P1= 1, m3= 6/5, M3=5/4, P4= 4/3, P5= 3/2, m6= 8/5, M6= 5/3, P8= 2)

 

RESULTING ESTIMATE

  • Estimated Fundamental tone = [(Batter or Reso Lug Pitch + (DIR *Batter or Reso Lug Pitch)] : 3.46
  • Estimated Opposite Head Lug Pitch = DIR * Batter or Reso Lug Pitch




3. ESTIMATE OPPOSITE HEAD LUG PITCH REQUIRED TO REACH A TARGET FUNDAMENTAL TONE AT A GIVEN TUNING OF ONE HEAD.

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?


CHOSEN VALUES

  • Batter or Reso Lug Pitch
  • Desired Fundamental Tone

 

RESULTING ESTIMATE

  • Estimated Opposite Head Lug Pitch = (3.46 * Fundamental Tone) - Batter or Reso Lug Pitch



 

4. ESTIMATE BOTH HEAD PITCHES NEEDED TO REACH A FUNDAMENTAL TONE, WITH ONE HEAD TUNED IN A CHOSEN INTERVAL RELATIONSHIP TOWARDS THE FUNDAMENTAL TONE.

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.)


CHOSEN VALUES

  • Desired Fundamental Tone
  • Desired Interval Ratio. DIR between batter or reso head and fundamental tone = ( P1= 1, m3= 6/5, M3=5/4, P4= 4/3, P5= 3/2, m6= 8/5, M6= 5/3, P8= 2)

 

RESULTING ESTIMATE

  • Estimated Opposite Head Lug Pitch = 3,46*Fundamental Tone - DIR*Fundamental Tone
  • Estimated Batter or Reso Head Lug Pitch = DIR*Fundamental Tone

 

 


5. ESTIMATE BOTH HEAD PITCHES NEEDED TO REACH A FUNDAMENTAL TONE, WITH BOTH HEADS TUNED IN A CHOSEN INTERVAL RELATIONSHIP TOWARDS EACH OTHER.

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?


CHOSEN VALUES

  • Desired Fundamental Tone
  • Desired Interval Ratio. DIR between both heads = ( P1= 1, m3= 6/5, M3=5/4, P4= 4/3, P5= 3/2, m6= 8/5, M6= 5/3, P8= 2)

 

RESULTING ESTIMATE

  • Estimated Batter or Reso Lug Pitch =[3,46:(1+DIR)]*Fundamental Tone
  • Estimated Opposite Head Lug Pitch = [3,46:(1+DIR)]*Fundamental Tone*DIR




NOTE:

The above proprietary methods and formulae generate estimates that are meant to have an accuracy of approx. +/- 10%.

The accuracy of the estimate depends on the applicable deviation of factor 1.73.

The value of 1.73 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 1.73 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. (Variations for different drums for factor 1.73 could go from 1.68 to 1.81 for example...)

The factor itself tends to increase slightly as the fundamental tone increases for a given drum, thus when the applied head tension increases. (approx. 3% +/-3)

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 good starting points as tuning references. 

  

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