Patent Publication Number: US-9412348-B2

Title: Drum and drum-set tuner

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation patent application of allowed U.S. patent application Ser. No. 14/101,845 filed Dec. 10, 2013, entitled, “DRUM AND DRUM-SET TUNER”, which is a continuation patent application of allowed U.S. patent application Ser. No. 13/004,166, filed on Jan. 11, 2011, now issued as U.S. Pat. No. 8,642,874 entitled, “DRUM AND DRUM-SET TUNER”, which claims priority to expired U.S. Provisional Application No. 61/297,578 filed on Jan. 22, 2010 entitled “DRUM AND DRUM-SET TUNER,” the entireties of which are incorporated by reference herein. 
    
    
     FIELD OF THE INVENTION 
     The invention relates generally to spectral analysis. More specifically, the invention relates to detection of a fundamental frequency to facilitate tuning of a resonant structure. 
     BACKGROUND 
     A variety of structures resonate with a fundamental frequency often combined with a plurality of other frequencies that make detection and analysis of the fundamental frequency problematic. Furthermore, many structures resonant for only a short period of time. A particular example of a resonant structure is a drum. 
     In one example, a drum consists of a hollow cylinder with a circular membrane clamped to either or both ends of the cylinder. A circular membrane that is suspended under tension at its outer perimeter is capable of several modes of vibration including circular symmetric and angular modes. The circular modes are described by a series of first-order Bessel functions for example and are therefore not harmonically related. The frequency of vibration depends, in part, on the radius, tension and density of the membrane. A cylindrical air column also resonates with the frequency of resonance depending on the length of the drum and the speed of sound and whether or not the ends of the cylinder are open or closed. Furthermore, the combination of a cylindrical shell and cylindrical membranes resonates as a system at a variety of frequencies that depend on a number of parameters, such as the dimensions of the drum, the tension and density of the drum-heads and the composition of the shell. 
     In one example, a drum-head is held by a metal or wooden hoop that is attached to a drum shell with several adjustable tension screws. The tension of the drum-head is determined by the force exerted by the tension screws. Tuning involves adjusting the tension screws to achieve a uniform pitch over a drum-head. When the pitch is uniform around the perimeter of the drum, the drum-head is considered to be “cleared” or “in tune with itself.” In addition to being in tune with itself, each drum-head needs to be adjusted to a pitch that produces the desired overall sound. It is sometimes desirable to tune each head separately with the other held damped to prevent vibration. 
     Striking a drum produces a percussive sound that&#39;s shorter in duration than any non-percussive musical instrument. The time-domain response of a typical drum, consists of an oscillatory signal with an abrupt onset followed by a short, approximately exponential, decay. Air pressure acting on the large area of the drum-head limits the duration of the sound. A vibrating string on the other hand has a much smaller area than a drum-head and vibrates much longer in comparison. 
     Tuning a set of drums poses additional challenges for musician. Some drummers tune their drums to a musical chord such as a major chord. Other drummers tune their drums to relative tonic intervals such as thirds or fifths, and still others tune by ear to something suiting their musical taste. The choice of specific drum pitches sometimes depends on the type of music being played. A drum-set might be tuned higher for jazz than for rock, for example, or it might be tuned open to resonate for a live performance or tight for a recording. Tuning also depends on the size and type of drum. A larger diameter drum is usually tuned lower than a smaller diameter drum. Often drummers attempt to copy the pitches used by other drummers from recordings or from memory. In general, the desired tuning of a drum-set depends on the particular sound the drummer is looking for. 
     A drum produces a unique sound when its head is struck resulting from the resonance of the vibrating heads in conjunction with the shell of the drum. Striking a drum excites several rapidly-decaying, non-harmonic modes of vibration resulting in a short, complex burst of sound. Drum tuning, by adjustment of a drum-head tension, to control pitch, tone and timber is essential in establishing a pleasing drum sound. Tuning any musical instrument involves playing a note, measuring or comparing the pitch of the note to some reference and adjusting the instrument&#39;s pitch until it conforms to the reference. However, assessing the pitch of a drum is complicated by the short duration and multiple non-harmonic resonances comprising its sound. Melodic instruments, on the other hand, produce continuous, periodic (harmonic) sounds with easy to measure pitch and are therefore much simpler to tune than a drum. 
     Drum tuning is typically done by ear, which is an art subject to the skill and taste of an individual musician. In addition, tuning by ear is inaccurate and has poor repeatability of results. Moreover, it is increasingly difficult to tune by ear when tuning a drum-set where each drum typically is tuned to a different pitch or to tune the drum-set to a variety of popular drum-set sounds varying based on style of music or the acoustic properties of the physical environment within which the drum-set will be used. 
     Existing tuners for melodic instruments such as guitars and pianos are unsuitable for drum or drum-set tuning. They require a sustained tone duration that is longer than the duration of a drum sound and only operate correctly on a periodic signal consisting of a single fundamental and associated harmonics, not on the transient sound produced by a drum. Drums typically create overtones unlike harmonics that are more easily distinguished from the fundamental frequency. Overtones are typically related to the fundamental frequency by a product of it π (pi), being related to the area and circumference of the drum-head. 
     Mechanical tuning devices exist that measure the tension of the drum-head by measuring the deflection of the head for a given force but do not measure the pitch produced by a drum and thus suffer from a variety of inaccuracies due to drum skin thickness and temperature variations for example. 
     BRIEF SUMMARY 
     In one aspect, the invention features a method for resonance tuning comprising receiving an analog signal in response to a resonance of a structure. The analog signal is digitized to create a plurality of time samples. A burst of the time samples is detected, enabling a trigger thereby. A series of time samples is buffered from the plurality of time samples in response to the trigger being enabled. A power spectrum is estimated by computing a Time-To-Frequency-Transform of the series of time samples to create a series of frequency samples and squaring a magnitude of each of the frequency samples. One or more subsets of frequency samples from the series of frequency samples is selected. Each subset is associated with one or more spectral peaks and each spectral peak includes at least one of the frequency samples having a first magnitude exceeding a first threshold and being spectrally adjacent to any other of the frequency samples in any other spectral peak within the same subset by less than a second threshold. A fundamental spectral peak in a fundamental subset is determined. The fundamental subset includes the spectral peak having the frequency sample at the lowest frequency greater than zero. The fundamental spectral peak has the frequency sample with the largest first magnitude within the fundamental subset. 
     In another aspect, the invention features a resonance tuner comprising a receiver configured to generate an analog signal in response to a resonance of a structure. An analog to digital converter is in communication with the receiver and is configured to generate a plurality of time samples of the analog signal. A pitch estimator is in communication with the analog to digital converter and is configured to calculate a fundamental spectral peak of the resonance of the structure from the plurality of time samples. A display module is in communication with the pitch estimator and is configured to display information to a user based on a fundamental spectral peak of the structure. 
     In another aspect, the invention features a drum-set tuner comprising a receiver configured to generate an analog signal in response to a resonance of a membrane of a drum. The analog to digital converter is in communication with the receiver and is configured to generate a plurality of time samples of the analog signal. A pitch estimator is in communication with the analog to digital converter and is configured to calculate a fundamental spectral peak of the resonance of the membrane of the drum from the plurality of time samples. A user interface module is in communication with the pitch estimator. The user interface module includes a one or more input controls configured to accept user inputs and a display configured to display information to a user based on a fundamental spectral peak of the membrane of the drum. A pitch-set processor is in communication with the pitch estimator and the user interface module. The pitch-set processor specifies the pitches of the various drum-heads in a set of drums. 
     In another aspect, the invention features a method for automatic drum tuning comprising measuring a plurality of pitches. Each measurement is made after striking the drum-head proximal to a respective tuning lug in a plurality of tuning lugs of a drum-head. The lowest pitch lug associated with the lowest pitch of the plurality of pitches is determined. A location of the lowest pitch lug and a deviation of the pitch of the lowest pitch lug from a selected pitch is displayed on a user interface. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       The above and further advantages of this invention may be better understood by referring to the following description in conjunction with the accompanying drawings, in which like numerals indicate like structural elements and features in various figures. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. 
         FIG. 1  is a perspective view of a drum usable with an embodiment of the invention. 
         FIG. 2  is graphical view of a measured time-domain response of one embodiment of a drum when struck. 
         FIG. 3  is a graphical view of a calculated power-spectrum of the time-domain response as illustrated in  FIG. 2  and according to an embodiment of the invention. 
         FIG. 4  is schematic view of an embodiment of a Drum-Tuner according to the invention. 
         FIG. 5  is a schematic view of an embodiment of the Pitch Estimator shown in  FIG. 4 . 
         FIG. 6  is a schematic view of an embodiment of the Power-Spectral Estimator shown in  FIG. 5 . 
         FIG. 7  is a schematic view of an embodiment of the Burst Detector shown in  FIG. 5 . 
         FIG. 8  is a schematic view of an embodiment of a Drum-Set Tuner according to the invention. 
         FIG. 9  is a schematic view of an embodiment of a Pitch-Set Processor shown in  FIG. 8 . 
         FIG. 10  is a top view of the drum shown in  FIG. 1 . 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of resonance tuners described herein provide for the measurement of a fundamental frequency of a structure from a short duration transient signal that typically includes other frequencies. In one embodiment, the resonant structure is a vibrating blade in a turbine engine. The signal is measured by acoustic emissions from the blade. In another embodiment, the signal from the blade is measured with an interferometer. In another embodiment, the resonant structure is a vocal cord from a person practicing musical scales. A microphone measures the signal from the vocalist. 
     In a preferred embodiment, the resonant structure is a drum-head, with a signal measured by a receiver or sensor. The fundamental pitch of a drum is measured to facilitate drum tuning. A receiver produces an electrical signal corresponding to the sound or vibration produced by the drum, after the drum is struck. 
       FIG. 1  shows a perspective view of a typical “tom-tom” drum  10   a , which in one example, is used with the invention. The drum  10   a  includes a circular membrane (drum-head)  12  suspended under tension on top of the drum shell  14  by a hoop  16 . The tension of the membrane  12  is adjusted by tightening the hoop  16  with a plurality of lugs  20   b ,  21   b ,  22   b    23   b  and  27   b  (not shown in  FIG. 1 ) and lugs  23   b ,  24   b ,  25   b  and  26   b . Each lug is affixed to the drum shell  14  by an attachment  18 . The drum shown in  FIG. 1  shows a single membrane  12 , although in other embodiments a second membrane is present on the opposing side of the drum. In one embodiment, when an opposing membrane is present, the opposing membrane is “damped” or put on a towel or cushion to substantially prevent the opposing membrane from interacting with the membrane  12  during the tuning of membrane  12 . Subsequent to tuning the membrane  12 , the opposing membrane is tuned with membrane  12  damped. In another embodiment, the membrane  12  is tuned without damping the opposing membrane. 
     Adjusting the tension of the membrane  12  requires adjusting each of the lugs to “clear” the drum and adjusting all of the lugs to achieve a desired pitch. Each lug is adjusted by imparting energy to the membrane  12  in the vicinity of the lug. For example, to adjust lug  24   b , a musician would tap the membrane  12  near location  24   a . Similarly, to adjust lug  25   b , the musician would tap the membrane  12  near location  25   a . Tapping is typically performed by striking the membrane  12  with a drum stick, although approaches where an impulse of energy is delivered to the membrane  12  are envisioned. 
       FIG. 2  shows a measured time-domain response of an example embodiment when the membrane  12  is struck, at location  24   a  for example.  FIG. 3  shows a calculated power-spectrum of  FIG. 2  according to an embodiment of the invention. Multiple spectral peaks  36 ,  38 ,  40  and  42  are calculated from the time-domain response shown in  FIG. 1 . The spectral peaks are further grouped into subsets  32  and  34  based on their spectral proximity. For example, spectral peaks  36  and  38  are grouped into the same subset  32  because they are sufficiently related based on frequency separation. Similarly, spectral peaks  40  and  42  are grouped into subset  34 . In the example shown in  FIG. 2 , spectral peaks  36  and  38  each correspond to a fundamental frequency of one of two lugs, which are out of tune with respect to each other. In one example, spectral peak  36  corresponds a fundamental frequency associated with lug  24   b , and spectral peak  38  corresponds to a fundamental frequency associated with nearby lug  25   b . The subset  32  is a “fundamental subset” because it contains a spectral peak with the lowest frequency, excluding zero Hz. (D.C.). The spectral peaks  40  and  42  correspond to “overtones,” which are undesirable higher frequency byproducts of the fundamental spectral peak produced when the initial impulse travels across the circular drum and around the periphery of the drum, in addition to other complex propagation paths. The highest amplitude spectral peak  36  within the fundamental subset  32  is chosen as the “fundamental spectral peak” associated with the lug  24   b  being tuned. Subsequently, lug  24   b  is tuned so that the fundamental spectral peak  36  matches a selected pitch. Each lug of the drum  10   a  is tuned in the manner described above until all lugs are “cleared” and tapping the drum  10   a  at any location  20   a ,  21   a ,  22   a ,  23   a ,  24   a ,  25   a ,  26   a  or  27   a  produces substantially the same fundamental pitch, which also corresponds to the selected pitch. 
       FIG. 4  shows an example embodiment of a Drum Tuner  50   a  according to the invention. In one example, the Drum Tuner  50   a  is positioned over the drum  10   a  close enough (e.g. several inches) to detect the resonance of the membrane  12 . The Drum Tuner need not be positioned near the lug being tuned. In one embodiment, the Drum Tuner is attached to the hoop  16  and remains stationary throughout the entire tuning process of one drum-head. 
     A receiver  52  detects a signal corresponding to a sound or vibration from a resonant structure, the drum  10   a  in  FIG. 1  for example. In one embodiment, the receiver includes a sensor  54 , a microphone for example, and a preliminary amplifier (Preamp)  56 . The Preamp  56  includes a low pass filter to limit aliasing of subsequently sampled data. The signal received by the sensor  54  is amplified by the Preamp  56  and converted to a representative digital signal by an analog to digital convertor (ADC)  58 . In one non-limiting embodiment the ADC  58  includes a 12 bit successive approximation register (SAR) operating at 8 k samples/sec with 8× decimation. The ADC  58  has a clock  60  with sufficient accuracy to determine the fundamental spectral peak  36 . In one embodiment, the clock  60  is a crystal oscillator. For example, a clock  60  with 0.01 Hz accuracy for a sample rate of 1 k samples/sec is sufficient. The digital signal from the ADC  58  is processed by a Pitch Estimator  62  that estimates the fundamental spectral peak  36  from the signal received by the receiver  52 . In one embodiment, each of the functions performed by the Pitch Estimator  62  are implemented with circuits. In another embodiment, each of the functions performed by the Pitch Estimator  62  are performed with one or more processors. In yet another embodiment, the Pitch Estimator  62  uses a combination of circuits and processors to perform its function. The frequency estimate is provided to a User Interface  64  that in turn displays at least one of the fundamental spectral peak  36 , a nearest musical note and the deviation of the fundamental spectral peak  36  from the selected pitch. The user provides a variety of inputs to the Drum Tuner  50   a  with controls  68  on the User Interface  64 . For example, inputs provided by the user include the selected pitch, type of drum and what type of information should be displayed. In addition, the User Interface provides controls for storing and recalling specified and measured pitches. Other user inputs are also envisioned within the scope of adjusting parameters of a resonant system in response to detection of a fundamental frequency. 
       FIG. 5  shows an embodiment of the Pitch Estimator  62  as referenced in  FIG. 4 . The Pitch Estimator  62  stores a series of time samples from the ADC  58  in a buffer  70 . In one embodiment the Buffer stores 1024 time samples. The number of samples stored in the Buffer is chosen to achieve a sufficient sample size for accurate measurement, to store sufficient samples for the duration of a drum burst, (e.g. 1 second) and to reduce the time required between successive measurements based on typical user expectations. A Burst Detector  72  detects the start of a signal burst typically corresponding to the beginning of the resonance of a structure after the structure has received an impulse of energy, a drum strike for example. In a preferred embodiment, the burst detection occurs after the cumulative energy of the digitized signal exceeds a pre-determined threshold. In another embodiment, the burst detector  72  determines when the digitized signal exceeds a threshold by a hysteresis value. In another embodiment, the burst detector  72  determines when a sum of a plurality of absolute values of the digitized signal exceeds a threshold, (or also a threshold value with hysteresis). 
     When a burst is detected by the Burst Detector  72 , a Trigger signal  74  is enabled. The enabling of the Trigger signal  74  initiates several operations. A pre-determined number of samples of digitized data from the ADC  58  are stored in the Buffer  70  for subsequent processing. In one embodiment, the Power-Spectral Estimator  78  computes the power spectrum of the buffered data by transforming the samples into the frequency domain and computing the magnitude-squared value of the samples. After transformation from the time domain to the frequency domain, the data are generally complex and computing the magnitude-squared value of each sample consists of summing the squares of the real and imaginary values. 
     The Peak Selector  80  then identifies the spectral peaks of the power spectrum. In a preferred embodiment, the spectral peaks are calculated by first storing the magnitude-squared frequency domain samples in a “power array.” The power array is searched to identify the “maximum value power sample.” A “minimum peak power threshold” is then defined as a constant value below the maximum value power sample, typically 18 dB lower than the value of the maximum value power sample. The power array is then searched starting at the lowest frequency location and stopping at the highest frequency location and storing the magnitude and frequency of all the spectral peaks that are greater than the minimum peak power threshold in a “peak array.” The spectral peaks are defined as samples from the power array with a zero value first derivative and a negative value second derivative when the power array is differentiated with respect to frequency. Typically, only the 10 lowest frequency spectral peaks identified in the ascending search are stored in the “peak array.” The peak array will thus contain the first 10 spectral peaks in ascending order of frequency all of which will exceed the minimum power threshold. 
     In a preferred embodiment, the opposing membrane to the membrane  12  in  FIG. 1  is damped. The Frequency Estimator  82  searches through the peak array and where any two successive spectral peaks are spectrally adjacent within a limited frequency bandwidth (or threshold) of 10 Hz for example, if the second spectral peak has a larger magnitude than the first spectral peak, the sequential position of the second spectral peak will be swapped with the first spectral peak. After these steps, the first entry in the peak array corresponds to the estimate of the frequency and magnitude (or power) of the fundamental spectral peak (or fundamental component) of the measure signal. This sorting of the spectral peaks results in a number of subsets, each with at least one spectral peak, where every spectral peak in a subset is spectrally adjacent to another spectral peak within a limited bandwidth (or threshold; e.g. 10 Hz). The spectral peak ordering method determines the fundamental subset having the spectral peak with the lowest frequency and selects the spectral peak with the largest magnitude in the fundamental subset as the fundamental spectral peak. 
     In another preferred embodiment, the opposing membrane to the membrane  12  in  FIG. 1  is not damped (also referred to as “open”) and is allowed to couple resonant energy to the membrane  12  when the drum is struck. This coupling of resonant energy introduces a lower frequency spectral peak below the frequency of the fundamental spectral peak generated when tuning with the opposing membrane damped. An open drum is tuned by altering the tuning method used to tune a drum with the opposing membrane damped to exclude the lowest frequency subset and choosing the fundamental spectral peak in the next highest frequency subset. 
       FIG. 6  shows an embodiment of the Power-Spectral Estimator  78  as referenced in  FIG. 5 . The Power-Spectral Estimator  78  receives a series of buffered time samples from the Buffer  70  in  FIG. 5  and optionally conditions the samples with Zero-padding  84  and Windowing  86  prior to converting the time samples to the frequency domain with a Fast Fourier Transform (FFT)  88 . Zero-padding  84  refers to adding zero-value samples to the predominately non-zero value series of time samples to increase the size of the FFT and hence the resulting frequency resolution. For an FFT with N samples, (an “N point FFT”), with sample rate Fs, the frequency resolution is given by the equation ΔFs=Fs/N, so with a larger sample size N, finer frequency resolution is obtained. For example, in one embodiment, the Buffer  70  stores 1024 samples. By appending 3072 zero-value samples a 4096-point FFT is performed thereby increasing frequency resolution by a factor of 4. Although the buffer could optionally store 4096 samples and zero-padding could be avoided, at an effective 1 khz ADC sampling rate (or 8 kHz with 8 times decimation) the user would have to wait four seconds to fill the buffer while the typical drum burst only last one second as shown in  FIG. 2 . 
     The FFT is a specific implementation of a Time-To-Frequency-Transform, defined herein to refer to the conversion of time samples to the frequency domain irrespective of the algorithm used. For example, in other embodiments the Time-To-Frequency-Transform uses either a Discrete Fourier Transform (DFT), a Discrete Cosine Transform (DCT), a Fast Cosine Transform, a Discrete Sine Transform (DST) or a Fast Sine Transform (FST). 
     In a preferred embodiment Zero-padding  84  is used with Windowing  86 . Because the series of time samples, with or without the Zero-padding  84 , only represents a finite observation window, the resulting spectral information will be distorted after performing an FFT due to the ringing or sin(f)/f spectral peaks of the rectangular window. This is also referred to as “spectral leakage.” To correct for this, each sample in a series of time samples is multiplied by a sample from a fixed waveform such as a Hanning, Bartlett or Kaiser window. In this embodiment these window functions have the same number of samples as the FFT (e.g. 4096), have symmetry about N/2 and increase in value from close to zero at the beginning and end of the time series to a maximum value at the center of the time series. In a preferred embodiment, a Blackman-Harris window function is used. 
     In a preferred embodiment the time samples are preconditioned with Zero-padding  84  and Windowing  86  and are subsequently converting to the frequency domain with an FFT processor. It is envisioned that any Discrete Fourier Transform (DFT) can be used to perform the frequency conversion without being limited to using an FFT. Following the FFT  88 , the series of frequency samples forming an estimate of the frequency spectrum is converted into a power-spectral estimate by squaring each of the frequency samples with a Magnitude Squared function  90 . 
     The Drum Tuner  50   a  operates on either isolated drum strikes or on a series of repetitive drum strikes. For repetitive drum strikes, the Burst Detector  72  re-triggers prior to the requisite number of time samples (e.g. less than 1024 samples in one embodiment) and the shorter series of time samples is zero-padded to the same length as an isolated burst. For example, an isolated burst has 1024 samples and is zero-padded to 4096 samples by adding an additional 3072 zero value samples. A repetitive strike occurring every 500 ms only has 512 samples in one example and would be extended to 4096 samples by adding 3584 zero value samples. In one embodiment, the Zero-Padding  84  detects the number of samples stored in the Buffer  70  and adjusts the number of zero value samples to be added accordingly, such that 4096 time samples result. 
     Spectral averaging is performed with an Averager  100  on the estimated power spectrum output for each successive burst thereby increasing the precision of the Power-Spectral Estimator  78  and the resulting estimate of the fundamental spectral peak. Spectral averaging is performed by taking the average of the magnitude-squared value of each frequency sample of the series of frequency samples with the magnitude-squared value of a corresponding previously stored frequency sample. For example, the 2nd frequency sample of a new burst is averaged with the second frequency sample of a previous burst. Zero padding occurs at the end of a shortened burst of time samples, so the proper alignment of time samples from current and previous bursts is maintained. 
     In one embodiment, the Burst Detector  72  of  FIG. 5  includes a comparator that compares the digitized data from the ADC  58 , or it&#39;s absolute value, to a threshold to enable the burst-detected Trigger  74 . In a preferred embodiment shown in  FIG. 7 , energy detection is used. Energy detection is more complex but offers more reliable burst detection in the presence of noise sources and glitches. The energy of several consecutive samples (e.g. 8 samples in one embodiment) is calculated by squaring and summing the samples together. Specifically, a plurality of sample and hold circuits  102   a ,  102   b  through  102   n  (generally  102 ) hold the time samples from the ADC  58 . In the example where the ADC  58  uses 12 bit resolution, each sample and hold circuit  102  is a 12 bit register in one embodiment. In another embodiment, the sample and hold circuit  102  is a First In First Out (FIFO) memory. Each time delayed sample from each sample and hold circuit  102  including a time sample without a delay is squared with circuits  104   a ,  104   b ,  104   c  through  104   n  (generally  104 ). Specifically, a sample with no delay is squared with circuit  104   a , a previous sample held by sample and hold  102   a  is squared with circuit  104   b , and so on. Each squared sample is summed with a summing circuit  106 , compared to a Threshold  110  with a subtraction circuit  108 , and activates a Trigger  74  if the value is positive as determined by a comparator  112 . In a preferred embodiment, the value of the Threshold  110  is 5% of the peak burst energy. In an alternative embodiment using voltage level detection the threshold is 20% of the peak voltage. 
       FIG. 8  shows a Drum-Set Tuner  50   b  as an alternative embodiment to the Drum Tuner of  FIG. 4  including an additional Pitch-Set Processor  120  to facilitate tuning of multiple drums. The Pitch-Set Processor  120  selects the pitches (e.g. the desired fundamental spectral peak) of each drum-head in the drum-set based on criteria provided by the user via a User Interface  64 . For example, the user will specify the sizes and number of drums in the drum-set and the type of tuning desired, such as a chord, interval, type of sound, or a famous drummer&#39;s tuning. The Pitch-Set Processor  120  then indicates the selected pitch for each drum-head in the drum set thereby assisting the user in tuning each head of each drum to the correct pitch. In addition, the user can store specific or measured drum-set tunings in the Pitch-Set Processor  120  to be recalled at a later time. This storage mode includes pitches or musical notes entered by the user with controls  68  and communicated to the Pitch-Set Processor at  124  or pitches measured with the Drum Tuner by the user and communicated to the Pitch-Set Processor at  122 . The Selected Pitch calculated by the Pitch-Set Processor  120  is communicated to the Display  66  at  126 . 
       FIG. 9  shows a preferred embodiment of the Pitch-Set Processor  120  that determines the Selected Pitch  126   b  for tuning each of the drums in a set of drums to pitches comprising the notes in an extended Major chord. For example, the Major chord has pitches that are in increasing order relative to the lowest or Base Pitch  124   a  are 1, 5/4, 3/2, 2, 5/2 and 3, shown collectively as Pitch Multiples  136 . The Base Pitch  124   a  and the Selected Drum  124   b  from the drum-set are supplied from the User Interface  64 . The Selected Pitch  126   b  is computed according to its position in the chord as a product  132  of the Base-Pitch  124   a  and the selected Pitch Multiple  134 , the Pitch Multiple  136  being selected by Multiplexor  134  controlled by the Selected Drum  124   b . In addition to computing the Selected Pitch  126   b , the Deviation  126   a  of the Selected Pitch  126   b  from the Pitch Estimate  122 , (e.g. the fundamental spectral peak) is calculated by subtracting the Selected Pitch  126   b  from the Pitch Estimate  122  with the subtraction circuit  130 . The Selected Pitch  126   b  and the Deviation  126   a  are both conveyed to the Display  66  at  126  shown in  FIG. 8 . 
       FIG. 10  is top view of the drum  10   a  shown in  FIG. 1  illustrating an automatic tuning method according to a preferred embodiment of the invention. The Drum Tuner of  FIG. 4  enables a user to tune a drum by measuring the individual pitches (e.g. the fundamental spectral peak) near each tuning lug and making corresponding adjustments to the lug tensions until the pitches are uniform. However, this is an iterative approach involving repeated pitch measurements and lug adjustments because the tension and pitch of the drum-head adjacent to a tuning lug depends not only on the tension of the closest lug but also to a lesser extent on the tension of all the other lugs. Consequently, there is an interaction between the tensioning of each lug. 
     For example, tightening a lug to raise the nearby drum-head pitch will also raise the pitch near the two adjacent lugs and the opposite lug to some extent. This inherent interaction between the tension of a single lug and the pitch of other lugs complicates drum-head tuning and increases the number of iterations that are required before uniformity is achieved. It would therefore be advantageous to automate the drum-head tuning process to account for the tension lug interaction and thereby minimize the number of iterations to simplify and speed up the tuning of a drum-head. This would also save the user the task of remembering the various pitches around the drum-head. 
     In the process of tuning a drum-head, it is possible to either increase the tension of the lugs corresponding to lowest pitch, or to lower the tension of the lugs corresponding to highest pitch, the former being preferable. Lowering the tension of a lug results in a partial de-seating of the lug screw and a less predictable or stable tension setting. As such, the following description is based on increasing tuning lug tension to raise the pitch of the lower pitched sections of the drum-head to match the pitch of the higher pitched sections. 
     Referring to  FIG. 10 , an embodiment of a drum  10   a  has 8 lugs  20   b ,  21   b ,  22   b ,  23   b ,  24   b ,  25   b ,  26   b  and  27   b  (generally “lugs”). Each lug has a corresponding location  20   a ,  21   a ,  22   a ,  23   a ,  24   a ,  25   a ,  26   a  and  27   a  (generally “tap location”) where the drum-head is struck during tuning. The automatic tuning process begins by tuning each of the lugs as previously described and saving the pitch estimate proximal to each lug. A plurality of pitch-pairs is then calculated by averaging the pitch proximal to each lug with the pitch proximal to a diametrically opposed lug. For example, the pitch  20   a  proximal to lug  20   b  is averaged with the pitch  24   a  proximal to  24   b , and similarly for lug  21   b  with  25   b ,  22   b  with  26   b , and  23   b  with  27   b  resulting in four pitch-pairs. For each of the four resulting pitch-pairs, the pitch-pair with the lowest average pitch is chosen as a “primary pitch-pair.” 
     For example, in the embodiment shown in  FIG. 10  the average pitch associated with lugs  20   b  and  24   b  has the lowest average pitch and the primary pitch-pair is as shown based on pitch measurements at  20   a  and  24   a . The primary pitch-pair has a first lug,  20   b  and a second lug  24   b . Adjusting the pitch associated with the first lug  20   b  will affect the pitch associated with all lugs, however the greatest effect will be with respect to the adjacent lugs  27   b  and  21   b  due to the forces from the hoop  16 , and also with respect to the diametrically opposed lug  24   b.    
     After establishing which of the four pitch-pairs is the primary pitch-pair, if either the first lug  20   b  or the second lug  24   b  have substantially different pitches associated with them (e.g. a 0.25 Hz difference) then the lower pitch of the two lugs will be adjusted first, then the other lug will be adjusted. Subsequently, the next lowest pitch-pair will be chosen as the primary pitch-pair and a similar adjustment made until all pitches associated with each lug are adjusted. 
     If the pitch associated with the first lug  20   b  and the second lug  24   b  of the primary pitch-pair are not substantially different then the determination of which of the first lug  20   b  and the second lug  24   b  is to be adjusted next then depends on the secondary effects on the adjacent lugs. A first adjacent pitch-pair is determined by averaging the pitch associated with the lugs  27   b  and  21   b  adjacent to the first lug  20   b . A second adjacent pitch-pair is determined by averaging the pitch associated with the lugs  25   b  and  23   b  adjacent to the second lug  24   b . If the first adjacent pitch-pair has a lower average pitch than the second adjacent pitch-pair then the first lug  20   b  is adjusted before the second lug  24   b , otherwise the second lug  24   b  is adjusted first. Subsequently, the next lowest pitch-pair will be chosen as the primary pitch-pair and a similar adjustment made until all pitches associated with each lug are adjusted. In the example embodiment of a drum  10   b , eight lugs are shown. It should be appreciated that the automatic tuning method similarly applies to other drum embodiments. 
     As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method, or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a “circuit,” “module” or “system.” Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon. 
     Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. 
     A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. 
     Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wire-line, optical fiber cable, RF, etc., or any suitable combination of the foregoing. 
     Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The program code may execute entirely on the user&#39;s computer, partly on the user&#39;s computer, as a stand-alone software package, partly on the user&#39;s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user&#39;s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). 
     Aspects of the present invention are described below with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks. 
     The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions. 
     While the invention has been shown and described with reference to specific preferred embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the following claims.