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  pdftitle={Non-Contact Control of Drumhead Resonance Decay by a Proximity Acoustical Resistor},
  pdfauthor={Calvin D. Rose},
  pdfsubject={Defensive publication / technical disclosure: shortening and tuning the decay time of a drumhead's resonant modes, including selective overtone damping, using an acoustically resistive material held in close proximity to but not touching the drumhead},
  pdfkeywords={drum, drumhead, membrane, overtone damping, acoustic resistance, porous absorber, decay time, RT60, sustain control, non-contact damping, percussion, muffler, defensive publication, prior art}
}

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\lhead{\small\itshape Non-Contact Control of Drumhead Resonance Decay}
\rhead{\small\itshape Defensive publication --- v1.0}
\lfoot{\small Version 1.0 --- \today}
\cfoot{\small\itshape Public domain --- CC0 1.0}
\rfoot{\small\thepage}

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\newcommand{\RT}{\mathrm{RT}_{60}}

\begin{document}

\begin{center}
{\LARGE\bfseries Non-Contact Control of Drumhead Resonance Decay\\[2pt]
by a Proximity Acoustical Resistor}\\[10pt]
{\large A Technical Disclosure with Measured Demonstrations}\\[12pt]
{\large Calvin D. Rose}\\[3pt]
{\normalsize \texttt{calvinrose18938@gmail.com}}\\[9pt]
{\normalsize Version 1.0 --- \today}\\[7pt]
{\small Paper dedicated to the public domain under \textbf{CC0~1.0};
analysis code licensed \textbf{Apache-2.0}.\\
SPDX-License-Identifier: CC0-1.0 (document), Apache-2.0 (code).}
\end{center}

\vspace{4pt}
\noindent\fbox{\parbox{\textwidth}{\small\textbf{Defensive publication.} This
document is released publicly as a \emph{defensive publication} (prior art). The
methods described --- conceived by the author in the late 1970s, reduced to a
detailed design and measured, but never filed as a patent and never previously
disclosed publicly --- are dedicated to the public domain so that anyone may
freely practice them and no party may obtain patents that read on the disclosed
subject matter. This is an intentionally enabling disclosure: it includes the
governing principle, a family of embodiments with the inventor's original
drawings, measured demonstrations, and the complete analysis code. The
authoritative date of public disclosure is the timestamp of the archived record
in which this document appears; see Section~\ref{sec:status}.}}

\vspace{8pt}
\begin{abstract}
\noindent
A method is disclosed for shortening and tuning the decay time of a drumhead's
resonant modes --- including \emph{selectively} shortening the overtones ---
using an acoustically resistive element held in close proximity to, but
\emph{not touching}, the drumhead. A porous or perforated material (open-cell
foam, cloth, fiber, or perforated metal or plastic) is positioned within a
distance small compared with the wavelength of the mode of interest. The
oscillating near-field air motion driven by the vibrating membrane is forced
through the resistive material, where viscous and thermal losses convert modal
energy to heat, raising the modal damping and shortening the decay time. Because
the near field of a membrane mode has a spatial extent and structure set by its
wavelength, the geometry and placement of the resistor --- ring inside diameter,
gap distance, coverage, and orientation --- select which modes are damped,
allowing the fundamental, the overtones, or both to be targeted, either at a
fixed setting or continuously adjustable. Unlike contact mufflers, gels, rings,
and internal dampers, nothing touches or loads the vibrating surface, so the
head's strike response and feel are preserved. The disclosure gives the physical
principle, a family of embodiments (ring, disk, cylinder, adjustable aperture,
pivoting central ``flue,'' near-head pattern, and perimeter blocks) with the
inventor's original drawings, and measured demonstrations on struck toms
(spectrograms, energy-decay curves, and $\RT$ decay times) that confirm strong,
tunable, contact-free decay control that meets or exceeds a commercial contact
muffler. The purpose of the disclosure is to place these methods and their
variants permanently in the public domain.
\end{abstract}

\vspace{2pt}
\noindent\textbf{Keywords:} drumhead; membrane damping; overtone control;
acoustic resistance; porous absorber; decay time; $\RT$; sustain control;
non-contact muffling; percussion; defensive publication; prior art.

% =====================================================================
\section{Introduction and motivation}

Players of drums and tuned percussion routinely need to control the
\emph{sustain} and \emph{overtone content} of a drumhead: a tom or snare that
rings too long or sings unwanted high partials must be tamed for the room, the
microphone, or the musical context. The established ways of doing this all share
one property: they \emph{touch the vibrating head}. Adhesive gel pads, felt or
foam strips, ``O-ring'' and control-ring dampers laid on the head, internal
mufflers pressed against the underside, and external arm dampers all add mass and
mechanical loading directly to the membrane. That contact does shorten the decay,
but it also alters the very thing the drummer feels and hears: the attack, the
rebound, the pitch, and the touch response of the head change together with the
sustain, and the effect is difficult to adjust in a graded, repeatable way.

This disclosure describes a different approach, conceived by the author in the
late 1970s and subsequently reduced to a detailed set of embodiments and
supported by acoustic measurements. Instead of loading the membrane, an
acoustically \emph{resistive} element is held in the air \emph{near} the head but
not touching it. The near-field air motion that the vibrating head necessarily
drives is made to pass through the resistive material, which dissipates the
modal energy. Because nothing contacts the head, the strike response and feel are
preserved; and because the coupling is through the mode's near field, the
\emph{geometry} of the element can be used to choose which modes are damped ---
in particular, to shorten the long-ringing overtones while leaving the
fundamental comparatively intact, or to do the reverse, or both. The method was
never patented and never publicly disclosed; it is published here as prior art.

% =====================================================================
\section{Relationship to prior work}
\label{sec:prior}

Drum damping is a crowded field, but the relevant prior art is almost entirely
\emph{contact} based. Representative categories include: rings or discs of film
or foam laid on the head (control rings); adhesive gel or moongel pads; felt or
foam ``tone control'' mufflers mounted inside the shell and pressed against the
underside of the head by a lever or spring; external adjustable arms that bring a
felt pad down onto the head; and pillows or foam placed inside bass drums in
contact with the head. The author compiled an extensive collection of such
patents and products during the development of this work (including, e.g., U.S.
Patent 4{,}254{,}685 and numerous later muffling and impact-pad patents), and in
every case the damping element makes mechanical contact with, and adds mass or a
compliant load to, the vibrating membrane.

The distinguishing element disclosed here is that the damping element is
\emph{non-contacting}: it is held in acoustically close proximity to the head and
removes energy through the air, by acoustic resistance, rather than by touching
or loading the membrane. The physics of porous acoustic absorbers and acoustic
resistance is classical~\cite{morse,ingard}, and the modal acoustics of drum
membranes is well
described~\cite{rossingperc,fletcher}; what is disclosed here is the application
of a proximity acoustic resistor to selectively and adjustably control the decay
of drumhead modes without contact, together with the specific family of
embodiments and mounting geometries of Section~\ref{sec:embod}. No proprietary
claim is made to the underlying acoustics, which is classical.

% =====================================================================
\section{Physical principle}
\label{sec:principle}

\subsection{Near-field coupling and acoustic resistance}

A drumhead vibrating in one of its membrane modes moves the air immediately
adjacent to it. Within roughly one wavelength of the surface, most of this motion
is a reactive, largely incompressible ``sloshing'' of air back and forth (the
evanescent near field) rather than radiated sound; it carries oscillating kinetic
energy that is normally returned to the mode each cycle. If an acoustically
resistive layer --- a porous or perforated material with a real flow resistance
--- is placed in this near field, the oscillating air is forced through its
narrow channels, and viscous and thermal losses convert part of that kinetic
energy irreversibly to heat. The layer presents a specific acoustic resistance
\begin{equation}
R_a \;\approx\; \sigma\,t ,
\end{equation}
where $\sigma$ is the flow resistivity of the material and $t$ its thickness (for
a thin layer, below the regime where reactance dominates). Introducing $R_a$ into
the near field of a mode adds a dissipative term to that mode's dynamics.

\subsection{Decay time and damping}

A struck mode of natural frequency $\omega_0=2\pi f_0$ and damping ratio $\zeta$
rings down with an amplitude envelope $\propto e^{-\zeta\omega_0 t}$. Its
$60$\,dB decay time is
\begin{equation}
\RT \;=\; \frac{3\ln 10}{\zeta\,\omega_0}
       \;=\; \frac{60\ \text{dB}}{\text{(decay slope, dB/s)}},
\label{eq:rt60}
\end{equation}
the right-hand operational form (sixty decibels divided by the measured decay
slope) being the one used for the data below. Adding acoustic resistance in the
mode's near field increases $\zeta$ and therefore shortens $\RT$. The amount of
shortening grows with how strongly the resistor couples to that particular mode.

\subsection{Mode selectivity through geometry}

The key to selective control is that different modes present different near
fields. A higher-order mode (an overtone) has a shorter wavelength and a finer
spatial pattern of antinodes; its reactive near field is correspondingly
\emph{thinner} and more sharply localized against the head. A resistor placed at
a small gap distance $d$ from the head therefore couples strongly to the thin,
high-wavenumber near field of the overtones, damping them heavily, while a
resistor withdrawn to larger $d$ reaches only the broader near field of the
low-order fundamental. Likewise, the lateral coverage of the element selects
modes by their antinodal pattern: a ring with a given inside diameter (ID)
overlaps the fundamental's central antinode differently than it overlaps the
ring-shaped antinodes of the overtones. In qualitative summary, and consistent
with the measurements below,
\begin{center}
\emph{smaller gap $d$ $\Rightarrow$ shorter overtone decay;\qquad
smaller ring ID $\Rightarrow$ shorter fundamental decay.}
\end{center}
A special case is a resistive disc placed on a pivot at the \emph{center of the
shell}, far from the head: it is too distant to reach the overtones' near field
and instead acts as an adjustable ``flue'' throttling the bulk air exchange of
the enclosed cavity, controlling mainly the fundamental. For two-headed drums the
shell and heads form a coupled (Helmholtz-like) cavity resonator; resistance
placed within the cavity or near the resonant head damps the coupled system.
These distinctions are what allow one design family to target the fundamental,
the overtones, or both.

% =====================================================================
\section{The device and its embodiments}
\label{sec:embod}

The acoustic resistor is a ring, disc, cylinder, volume, or pattern of
perforated, porous, or open-cell material --- foam, cloth, fiber, perforated
metal, or plastic --- held in acoustically close proximity to the drumhead by a
fixed or adjustable frame, without touching the head except, optionally, at the
extreme edge (shell or rim) for mounting. It may be mounted on the shell, on the
rim, or on the head near the rim, on either the inner (preferred) or outer
surface, and on the batter head, the resonant head, or both. ``Acoustically
close'' means a gap small compared with the wavelength of the mode to be damped.
The principal embodiments, shown in the author's original drawings in
Appendix~\ref{app:figs}, are:

\begin{itemize}[leftmargin=1.4em,itemsep=2pt]
\item \textbf{Ring} (Fig.~\ref{fig:ring}) --- a ring of resistor material of a
chosen inside diameter held at gap $d$; ID and $d$ set the balance of fundamental
versus overtone damping.
\item \textbf{Disc or cylinder} --- a solid resistive shape in close proximity;
damps both fundamental and overtones.
\item \textbf{Adjustable aperture} (Fig.~\ref{fig:aperture}) --- an iris-like
element whose effective ID is varied to tune the fundamental/overtone balance on
the fly.
\item \textbf{Pivoting central ``flue''} (Fig.~\ref{fig:flue}) --- a resistive
disc on a central pivot in the shell, adjusted by a control knob; from open
(little effect) to closed (shortest fundamental), it controls mainly the
fundamental.
\item \textbf{Near-head pattern} (Fig.~\ref{fig:perp}) --- a pattern of resistor
material with its long dimension perpendicular to and acoustically close to the
head; targets overtones with little effect on the fundamental.
\item \textbf{Perimeter blocks} (Fig.~\ref{fig:foam}) --- small blocks of
open-cell foam attached to the shell at a small gap $d$ (e.g.\ $\sim$5\,mm) from
the head; shorten the overtones while affecting the fundamental only slightly.
\end{itemize}

% =====================================================================
\section{Experimental demonstration}
\label{sec:exp}

\subsection{Method}

A tom (one-headed, and a two-headed 13-inch drum) was struck and recorded under a
series of conditions: the naked head; a commercial contact muffler (Remo
Muff'ls); and the acoustical resistor in several configurations (full-coverage
resistor, resistor rings of two inside diameters, a small perimeter gap, and an
adjustable element set to ``small,'' ``medium,'' and ``full''). Decay was
characterized three ways: short-time spectrograms; the broadband energy-decay
envelope; and the $60$\,dB decay time $\RT$ of individual partials, obtained by
fitting the decay slope in decibels per second per
Eq.~\eqref{eq:rt60}. The complete analysis code is given in
Appendix~\ref{app:code}; it uses only \texttt{numpy}, \texttt{scipy}, and
\texttt{matplotlib}, and reproduces every figure and number below from the
recordings.

\subsection{Results}

\textbf{Spectrograms.} Figure~\ref{fig:spec} shows the qualitative effect. On the
naked head, overtone bands at roughly $200$, $400$, $600$, and $800$\,Hz ring for
one to two seconds; the commercial muffler and every acoustical-resistor
configuration collapse these overtones quickly. The two ring configurations show
the geometry dependence directly.

\begin{figure}[t]
\centering
\includegraphics[width=\textwidth]{fig1_spectrograms.png}
\caption{Spectrograms of a struck one-headed tom under six conditions (shared
level scale). The naked head sustains strong overtone bands for seconds; the
non-contact acoustical resistor collapses them, comparably to a commercial
\emph{contact} muffler, with the ring inside diameter and coverage controlling
the result.}
\label{fig:spec}
\end{figure}

\textbf{Decay times.} Figure~\ref{fig:decay} quantifies it. Panel (A) shows the
broadband energy envelope: the naked head reaches $-20$\,dB only after several
tenths of a second and rings well beyond a second, whereas the acoustical
resistor brings the decay down to, or below, that of the commercial contact
muffler. Panel (B) reproduces the author's own $\RT$ measurements on the
13-inch drum for the fundamental ($110$\,Hz) and the first overtone ($220$\,Hz).
The single most striking number is that on the naked head the \emph{overtone}
rings longest of all, $\RT\!\approx\!2.3$\,s, far longer than the fundamental's
$\approx\!1.0$\,s; the non-contact resistor reduces that overtone to
$0.2$--$0.6$\,s depending on setting. Table~\ref{tab:rt60} lists the values.

\begin{figure}[t]
\centering
\includegraphics[width=\textwidth]{fig2_decay_rt60.png}
\caption{(A) Measured broadband energy decay of a struck one-headed tom: the
acoustical resistor decays as fast as or faster than the commercial contact
muffler. (B) The inventor's measured $\RT$ decay times on a 13-inch drum for the
$110$\,Hz fundamental and the $220$\,Hz overtone. The naked overtone rings
longest ($\approx2.3$\,s) and is strongly suppressed by the non-contact device.}
\label{fig:decay}
\end{figure}

\begin{table}[t]
\centering
\caption{Inventor's measured $\RT$ decay times (seconds), 13-inch drum, from the
decay-slope method of Eq.~\eqref{eq:rt60}.}
\label{tab:rt60}
\begin{tabular}{@{}lcc@{}}
\toprule
Condition & Fundamental, 110\,Hz & Overtone, 220\,Hz \\
\midrule
Naked head                       & 0.98 & 2.33 \\
Commercial contact muffler (Remo) & 0.51 & 0.29 \\
Acoustical resistor --- small     & 0.60 & 0.65 \\
Acoustical resistor --- medium    & 0.52 & 0.29 \\
Acoustical resistor --- full      & 0.31 & 0.21 \\
\bottomrule
\end{tabular}
\end{table}

\textbf{Tunability.} Figure~\ref{fig:tune} shows the adjustable embodiment set to
three positions. A single non-contact device produces a smooth family of decay
curves spanning from near the naked head down to, and beyond, the commercial
contact muffler --- graded, repeatable control that contact dampers achieve only
awkwardly.

\begin{figure}[t]
\centering
\includegraphics[width=0.92\textwidth]{fig3_tunability.png}
\caption{Continuous, contact-free control of sustain (13-inch drum, single
strike): one adjustable acoustical resistor spans from the naked head to beyond a
commercial contact muffler as it is opened from ``small'' to ``full.''}
\label{fig:tune}
\end{figure}

\subsection{Interpretation and honest limits}

The recordings establish, unambiguously, that a material held \emph{near but not
touching} the head strongly shortens the decay of its modes, that the effect is
continuously adjustable, and that it can meet or exceed a commercial contact
muffler --- all without loading the membrane. They also show the expected
geometry dependence (ring ID, gap, coverage). Two honest caveats: first, in the
particular configurations recorded, the resistor shortens \emph{both} the
fundamental and the overtones, with the long-ringing overtones reduced at least
as much as the fundamental; a claim of leaving the fundamental wholly untouched
is design- and setting-dependent and is not asserted from these specific
recordings. Second, the measurements are single-drum demonstrations, not a
controlled parametric study across drum sizes, materials, and gaps; the disclosed
principle and embodiments are intended to enable such optimization rather than to
report it exhaustively.

% =====================================================================
\section{Enumerated variants}
\label{sec:variants}

For breadth of disclosure the following non-exhaustive variants, and any workable
combination of them, are expressly included.

\begin{enumerate}[leftmargin=1.4em,itemsep=2pt]
\item Resistive material of any perforated, porous, or open-cell type: foam,
cloth, felt, fiber, woven or sintered metal, or perforated/louvered plastic or
metal.
\item Element geometry: ring, disc, cylinder, tube, volume, aperture/iris,
louver, pivoting flue, or a discrete or continuous near-head pattern.
\item Fixed or continuously adjustable gap distance $d$, inside diameter, or
coverage, by manual, mechanical, or motorized means.
\item Mounting on the shell, the rim, or the head near the rim; on the inner
(preferred) or outer surface; on the batter head, the resonant head, or both.
\item Targeting of mainly the fundamental, mainly the overtones, or both, by
choice of the above.
\item Combination with cavity/Helmholtz tuning in single- or double-headed drums,
including resistance placed within the enclosed cavity.
\item Application to any struck membranophone --- toms, snare, bass drum,
timpani, congas, and the like --- and to other membrane or plate resonators where
selective, non-contact decay control is desired.
\item Integration with sensing or with a remote/automated control of the
adjustable element.
\end{enumerate}

% =====================================================================
\section{Publication status and establishing priority}
\label{sec:status}

This device was conceived by the author in the late 1970s, developed into the
detailed embodiments and measurements presented here, but \emph{never filed as a
patent and never previously disclosed publicly}. It is published now as a
defensive publication: an enabling, dated, public description whose purpose is to
place the methods and their variants in the public domain, so that anyone may use
them and no party may later obtain a patent that reads on the disclosed subject
matter. The authoritative date of public disclosure is the timestamp of the
archived record in which this document appears (for example, a DOI-bearing
repository deposit), not any date printed on this page. For the disclosure to
function as prior art it must be public, dated, and discoverable; to that end it
is deposited in venues that provide an authoritative timestamp and indexing that
patent examiners search. A defensive publication is effective only to the extent
it is \emph{enabling}: the principle of Section~\ref{sec:principle}, the
embodiments and original drawings of Section~\ref{sec:embod} and
Appendix~\ref{app:figs}, the measured demonstrations of Section~\ref{sec:exp},
and the complete analysis code of Appendix~\ref{app:code} are included to meet
that bar for the disclosed methods and their enumerated variants. Publication is
deliberate and, by design, places the methods in the public domain; it is
generally irreversible with respect to the author's own patent rights, which the
author knowingly forgoes.

\vspace{4pt}
\noindent\emph{This draft was prepared with computational assistance for the
acoustic analysis and typesetting. The invention, drawings, and measurements are
the author's; nothing here is legal advice.}

% =====================================================================
\begin{thebibliography}{9}
\small
\bibitem{rossingperc} T.~D.~Rossing. \emph{Science of Percussion Instruments.}
World Scientific, 2000.
\bibitem{fletcher} N.~H.~Fletcher and T.~D.~Rossing. \emph{The Physics of
Musical Instruments,} 2nd ed. Springer, 1998 (membranes and drums).
\bibitem{morse} P.~M.~Morse and K.~U.~Ingard. \emph{Theoretical Acoustics.}
McGraw-Hill, 1968 (acoustic impedance and dissipation).
\bibitem{ingard} U.~Ingard. \emph{Noise Reduction Analysis.} Jones \& Bartlett,
2010 (flow resistance and porous acoustic resistance).
\bibitem{p685} U.S. Patent 4{,}254{,}685 and related drum-muffling patents,
collected by the author as prior-art context (contact-type dampers).
\end{thebibliography}

% =====================================================================
\newpage
\appendix
\section{Inventor's original drawings}
\label{app:figs}

The following are the author's original design drawings for the principal
embodiments (headers cropped). They date from the development of the device and
are reproduced here as part of the enabling disclosure.

\begin{figure}[h]
\centering
\begin{minipage}[t]{0.48\textwidth}\centering
\includegraphics[height=6.2cm]{fig_ring.png}
\caption{Ring embodiment: a ring of resistor material of inside diameter ID held
at gap $d$ from the head.}\label{fig:ring}
\end{minipage}\hfill
\begin{minipage}[t]{0.48\textwidth}\centering
\includegraphics[height=6.2cm]{fig_aperture.png}
\caption{Adjustable-aperture embodiment: the effective inside diameter is varied
to tune the fundamental/overtone balance.}\label{fig:aperture}
\end{minipage}
\end{figure}

\begin{figure}[h]
\centering
\begin{minipage}[t]{0.48\textwidth}\centering
\includegraphics[height=6.2cm]{fig_flue.png}
\caption{Pivoting central ``flue'': a resistive disc on a central pivot, adjusted
by a knob, controlling mainly the fundamental.}\label{fig:flue}
\end{minipage}\hfill
\begin{minipage}[t]{0.48\textwidth}\centering
\includegraphics[height=6.2cm]{fig_perp.png}
\caption{Near-head pattern: resistor material acoustically close to the head,
targeting overtones.}\label{fig:perp}
\end{minipage}
\end{figure}

\begin{figure}[h]
\centering
\includegraphics[height=6.6cm]{fig_foam.png}
\caption{Perimeter-block embodiment: small open-cell foam blocks attached to the
shell at a small gap $d$ from the head, shortening the overtones while affecting
the fundamental only slightly.}\label{fig:foam}
\end{figure}

\newpage
\section{Analysis code (complete)}
\label{app:code}
The following reproduces the spectrograms, decay curves, and figures from the
recordings using only \texttt{numpy}, \texttt{scipy}, and \texttt{matplotlib}.
\lstinputlisting[style=py]{analyze.py}

\end{document}
