Do drums/strings have a pitch bend when they are struck?

[mikejm]

I am a musician trying to develop some physical modelling synthesizers (synthesizers modelling natural instruments). In particular, drums and guitar.

It is my impression from playing drums and guitar that when you strike a drum head or guitar string very aggressively, there is a natural "pitch bend". It sounds as if the note starts slightly sharp from the added tension of the strike. Then rapidly (exponentially) it settles to the resting pitch a little below the pitch during the initial attack.

I am wondering if my ears are wrong though and if perhaps what I perceive as a downward pitch bend is really just rapid decay of high frequency modes/resonances.

It makes sense to me there should be a slight pitch bend based on how much tension is on the membrane/string at any given time but I don't have much physics knowledge so I'm not sure.

Can anyone confirm or refute whether this is actually what's happening?

Thanks a bunch.

 

[Vanadium 50]

Drums don't produce pure tones, so I don't know that describing them in those terms is helpful. (Technically, instead of sines and cosines in the equations you get Bessel functions)

 

[Andy Resnick]

I am a musician trying to develop some physical modelling synthesizers (synthesizers modelling natural instruments). In particular, drums and guitar.

It is my impression from playing drums and guitar that when you strike a drum head or guitar string very aggressively, there is a natural "pitch bend". It sounds as if the note starts slightly sharp from the added tension of the strike. Then rapidly (exponentially) it settles to the resting pitch a little below the pitch during the initial attack.
<snip>

There are ways to generate pitch bends when hitting a drum (especially a tympani), but a natural strike will not result in one. With a drum, pitch bends are produced by varying the head tension- either directly by pressing down on the head or indirectly, either through the frame or tension rods.

I looked on some of the discussion group to see what you are talking about, and there is quite a bit about tuning toms, for example: "[...] the quintessential tom sound is one with a fat pitch bend where the tone drops in pitch after the initial hit. [...] last night, I brought my 10" tom batter up in pitch and tuned the reso as low as possible and voila: a pitch bend! You clearly hear an initial high pitch and then a second lower tone."

But that is not a pitch bend- that is simply different elements tuned to generate different tones.

Similarly, cymbals can appear to generate pitch bends as different parts of the cymbal begin to vibrate, changing the overall tone- this effect is most pronounced in large cymbals and gongs.

@Vanadium 50 : don't confuse 'pitch' and 'tone'. Drums (and most percussion) are unpitched, but when tuned they have definite tones (and tonal relationships). http://www.differencebetween.net/miscellaneous/difference-between-tone-and-pitch/

 

[Vanadium 50]

OK, amended "Drums don't produce pure pitches". That said, I think the point is the same - treating what is a Bessel function like a collection of sine waves may not be the best starting point.

 

[sophiecentaur]

It is also relevant that a drum skin is almost certainly not a linear medium when the initial hit is made. The local displacement can be far too high.

 

[mikejm]

Thanks for the replies guys. I have a few follow up thoughts.

Regarding the pitch bend with drums referenced on other websites, what they're talking about is when the resonant (bottom free head) and batter (struck head) are tuned to different notes, there will be a slow gradual bend over the evolution of the note as one head rings longer than the other.

What I'm referring to seems to me to exist for both a single string instrument and a single head drum. It is also far, far more rapid and really seems to occur over only the very initial PLUCK or STRIKE moment in time.

It is also relevant that a drum skin is almost certainly not a linear medium when the initial hit is made. The local displacement can be far too high.

This is interesting to me. Can you elaborate more on what you mean? This is definitely something I observe only when you really pound the drum or really stretch a string.

My perception is this, using a string as an example (drum is same principle but in 2D):

T = Tension, in pounds;
UW = unit weight of the string, in pounds per linear inch;
L = vibrating length of the string (for an open string, this would be the scale length) in inches;
F = frequency of the note to which you will tune the string, in Hz;

So obviously the frequency of the string correlates with tension on the string. The more tension on the string, the higher the frequency. When you rest a pick against a string, and stretch the string with it, you are increasing tension on the string. Thus for the initial moment when the pick "lets go" of the string and it can ring freely, the tension will be high, and the pitch will be slightly higher.

Rapidly this will settle to a natural vibrating tension which will be closer to its nonvibrating tension (rest tension) and thus "ideal" frequency.

(^ imagine leaning that pick into a string to stretch and increase the tension to it's maximum level before letting go).

This same process of increasing tension on the string to create a "pitch bend" is intentionally performed by guitarists when they perform a note bend, where the length still remains constant (unchanging fret position) but by bending the string, tension is increased and note pitch goes up.

I think it is the same phenomenon in both cases.

(^ String length slightly increases during a pitch bend which would lower pitch overall, but mostly tension of the string goes up like crazy during a bend, so the note pitch goes up.)

I think this is the same thing that is happening also with an aggressive pick - just more momentary with the pick.

I think this makes sense, but I'm no physics expert.

Does this make sense? Any further thoughts?

 

[Windadct]

ON a guitar - I think you may be hearing the energy being dispersed into the different natural harmonics. Example - if you pluck a string near at the middle- the initial vibrations will be almost all at the fundamental, but the string will begin to decrease the fundamental and increase the harmonics until it reaches the natural characteristic for that string / instrument.
Conversly - if you pluck the string hard - near a harmonic point, a high percentage of the energy will be in the harmonic and not at the fundamental - like when you pluck near the nut or saddle, you hear a note with a LOT of upper harmonics, this energy will settle to the natural characteristic over time.

Quite sure if you get a PC spectrum analyzer you can see the harmonics change over time.

 

[Andy Resnick]

What I'm referring to seems to me to exist for both a single string instrument and a single head drum. It is also far, far more rapid and really seems to occur over only the very initial PLUCK or STRIKE moment in time.

I can only discuss the case for drums, I have never experienced anything like what you say. It's relevant to mention that frequency and time are related- specifically, if your selected time interval is too short it becomes impossible to assign a pitch. Technically, a single pitch (say 440.00000... Hz) requires an infinite time interval, finite time intervals are associated with pitch ranges/tonal curves. One can't reasonably play 'Flight of the Bumblebee' on a double bass.

In terms of temporal evolution of a struck drum, the initial impact (call it an 'impulse') will generate an broadband 'impulse response' that decays exponentially. For a drum, that impulse response generates an initial broadband frequency sound that decays quickly while the excited resonant tones and overtones decay more slowly. But again, that's not exactly what you are hoping for.

Again, it's easier to demonstrate this with a large cymbal- something with a long decay time- by displaying a 'real-time spectrogram' as the instrument is struck. There's a ton of apps that can be used, for example https://auditoryneuroscience.com/acoustics/spectrogram_software.

To get a sense of the various tone modulations possible with drums, check out Chris Corsano's work, especially:

 

[mikejm]

Thanks again guys. I know some of it is harmonic burst.

But any comment on what I was saying about tension increasing in the string with a pick leaned into it?

Tension is obviously higher at the initial moment of a heavy pick and higher tension should lead to higher pitch (frequency) though just momentarily. That excess tension dispersed in the first moment of release and initial explosion of sound.

The same should apply with a drum head. In the precise moment while the stick is hitting the head tension is higher than it is at rest or during the "sustain" phase of the sound. If tension is higher, this pitch should also be higher momentarily.

 

[sophiecentaur]

This is interesting to me. Can you elaborate more on what you mean?

The 'simple' formula assumes that the modulus of the membrane (or string) remains the same over the whole cycle of any oscillation. If a plastic skin or string is deformed by a strong blow then I would imagine the modulus of the material could well change and so other (non linear) terms would need to be added to that formula. That would have the effect of generating a whole extra set of overtones and side tones. I'm not sure whether or not they would be sustained for long.

 

[Windadct]

I would not call it a burst, but a shift to the natural distribution. Yes the initial pluck will increase the tension - but that is like saying the tone changes on every oscillation, as tension is added, and relaxes. ( basically energy is changing from kinetic in the momentum of the string, to potential in the tension of the string) . So a pluck in the middle - the string will reach the same tension on every oscillation. A pluck "off of center" will have almost no fundamental, so I can understand it seeming like the tone shifts "lower" a moment after it is plucked.

I doubt you are hearing the tone change due to tension of the first few oscillations, more that you are hearing almost random tones ( noise) that are very quickly damped out... found this, you can see the spectra are random and quickly settle into the harmonics.

 

[sophiecentaur]

as tension is added, and relaxes.

And the simple formula assumes that the modulus doesn't change over the cycle. If it does change significantly then the attack will contain many different frequencies. When a drum is hit with a stick the shape of the skin will not be a simple cone (unlike the shape with a plucked string which is pretty well triangular). There will be a single circular wave traveling outwards and hitting the rim etc. etc. I don't think the situation is likely to be analysed at all easily. The normal modes of the drum won't probably be just the modes that the Bessel functions predict.
PS The normal modes of a drum are not 'harmonically' related and neither are the modes of a 'real' guitar string. The term Overtone is best used when discussing this topic and their frequency values can be anyone's guess.

 

[lesaid]

Just a quick aside - I don't know much about drums, but the 'pitch bend' you describe, if I understand your meaning properly, is a very real effect on clavichords - which strike the string with a metal edge (that also defines the 'end' of the vibrating string) when a key is pressed. Not only does it happen, but it is exploited by the performer to create a vibrato, by varying the pressure on the key. Example at

 

[mikejm]

Ha! I'm not crazy!

You guys were seriously making me question my sanity. But perhaps you should be questioning your own instead ...

"When a tom-tom is struck a hard blow, the deflection of the drumhead may be great enough to cause a significant change in the tension, which momentarily raises the frequencies of all modes of vibration and thus the apparent pitch. The fundamental frequency in a 33-cm (13-in.) tom-tom, for example, was found to be about 8% (slightly more than a semitone) greater during the first 0.2 s after the strike than after a second or more (Rose, 1978), resulting in a perceptible pitch glide. An even greater pitch change of 160c (about 10%) was observed by Bork and Meyer in a 32-cm tom-tom (Bork, 1983)."

From:
The Physics of Musical Instruments
By Neville H. Fletcher, Thomas Rossing
https://books.google.ca/books?id=gvDSBwAAQBAJ&pg=PA515&lpg=PA515&dq=tom+drum+modes&source=bl&ots=nl_8knGute&sig=-LNpxzZvoaO3UMlEW8NBUczXRbY&hl=en&sa=X&ved=0ahUKEwik4831q4XVAhUi_IMKHRNoDwcQ6AEIQjAG#v=onepage&q=tom drum modes&f=false

 

[lesaid]

ON a guitar - I think you may be hearing the energy being dispersed into the different natural harmonics. Example - if you pluck a string near at the middle- the initial vibrations will be almost all at the fundamental, but the string will begin to decrease the fundamental and increase the harmonics until it reaches the natural characteristic for that string / instrument.
Conversly - if you pluck the string hard - near a harmonic point, a high percentage of the energy will be in the harmonic and not at the fundamental - like when you pluck near the nut or saddle, you hear a note with a LOT of upper harmonics, this energy will settle to the natural characteristic over time.

This made me wonder. Does the energy distribution into different harmonics actually cause us to perceive a change in pitch at all? Plucking a guitar string at different points certainly changes the harmonic distribution and the audible tone, but not the perceived pitch. To get a 'harmonic' from a guitar or violin say, you have to suppress all but the desired harmonic by touching the string at an appropriate point. As soon as many other harmonics are present, I think the fundamental itself would be perceived.

I am under the impression that if you hear a collection of related harmonics in almost any distribution, the ear/brain 'reconstructs' the fundamental, even if it might be completely absent, so that the perceived pitch is unaffected.

I have no reference for this - the conclusion came from a sixth form school physics project that I did, many many years ago. Anyone know if it is true?

 

[sophiecentaur]

This made me wonder. Does the energy distribution into different harmonics actually cause us to perceive a change in pitch at all? Plucking a guitar string at different points certainly changes the harmonic distribution and the audible tone, but not the perceived pitch. To get a 'harmonic' from a guitar or violin say, you have to suppress all but the desired harmonic by touching the string at an appropriate point. As soon as many other harmonics are present, I think the fundamental itself would be perceived.

I am under the impression that if you hear a collection of related harmonics in almost any distribution, the ear/brain 'reconstructs' the fundamental, even if it might be completely absent, so that the perceived pitch is unaffected.

I have no reference for this - the conclusion came from a sixth form school physics project that I did, many many years ago. Anyone know if it is true?

As I mentioned before, the sound from many / most musical instruments does not actually consist of Harmonics. The Overtones from a brass instrument are very much not inherently harmonically related and the bores of a trumpet (conical) and a Cornet (cylindrical) give them each a different characteristic sound because of the different overtones they produce. Brass players have to bend the notes in the higher registers to pull the overtones to nearer to the harmonic frequencies to stay in tune with the music.
Yes, I have heard of this. It must be why tiny loudspeakers on smart phones and small radios sound better than you would ever expect.

 

[Andy Resnick]

Ha! I'm not crazy!

You guys were seriously making me question my sanity. But perhaps you should be questioning your own instead ...

Thanks for the link- this book looks awesome, I now have a 'summer beach read' :)

I'll start closely reading Chapter 18, but in the meantime, I caution you about your conclusion. The two references you quoted may not be relevant. For example, Rose (1978) could be a study that relies on a bizarro drumhead that is highly non-standard.

Rose, C.D. (1978). "A New Drumhead Design: An Analysis of the Nonlinear Behavior of a Compound Membrane." M.S. thesis, Northern Illinois University, DeKalb, Illinois.
Bork, I. (1983). "Entwicklung von akustischen Optimierungsverfahren fiir Stabspiele und Membraninstrumente." PTB report, Project 5267, Braunschweig, Germany (unpublished).

Regardless, I look forward to reading this book- thanks!

Edit: It seems that the pitch glide is indeed caused by the change in membrane tension generated by finite-amplitude displacement (pg, 602):

"The average surface tension of a membrane increases when it vibrates at finite amplitude. The increase in the average surface tension ΔT is proportional to the square of the displacement amplitude d, and the frequency is proportional to the square root of To + ΔT:
(insert equation) (18.25)
Thus, each mode will have a greater frequency just after the drum is struck, decreasing as the amplitude dies down. When a bass drum is struck a full blow, a typical value for the initial amplitude is 6 mm, which results in an upward frequency shift of about 10%, or nearly a whole tone on the musical scale (Cahoon, 1970). Of course, the pitch shift is made less noticeable by the downward pitch shift with increasing sound intensity, a well-known psychoacoustical effect that is especially strong at low frequency [see, for
example, Chapter 7 in Rossing (1982b)]."

Edit #2: the pitch glide effect diminishes when the (resting?) head tension increases. You need to tune those toms low and sloppy to generate a pitch glide. (pg. 608).

 

[lesaid]

Brass players have to bend the notes in the higher registers to pull the overtones to nearer to the harmonic frequencies to stay in tune with the music.

I'm not a brass player and had never heard of this but I find it intriguing! My understanding (based partly on that old school project) is that in general, the sound from an instrument (after any initial concussion) is made up of a collection of related harmonics alongside a collection of overtones. And that in most cases, brass instruments (along with the flute flamily) have a relatively low harmonic content, unlike, for example, the oboe or violin in their lower registers. So - it would seem plausible that the pitch we perceive is due to the related harmonics and the tone, to a mixture of the harmonics and the overtones.

For a brass player to have to bend the pitch to stay in tune due to overtones in high registers - would this become significant because in the higher registers, there will be fewer harmonics of the fundamental note within whatever frequency range plays a part in this kind of pitch perception and brass instruments generally have relatively low harmonic levels anyway. The overtones could then become more prominent and be able to 'confuse' the ear in a way that wouldn't happen in lower registers or other instruments richer in harmonic content? This would also presume that the overtones would not disappear up into high frequencies at the same rate that harmonics do as the pitch goes up? And perhaps that the overtones might themselves contain harmonically related components to be able to fool the ear? And the this pitch effect might also apply to flautists too, more than other woodwind and strings?

I think I need to do some reading! Thank you for kicking off this train of thought :)

 

[Andy Resnick]

The Physics of Musical Instruments
By Neville H. Fletcher, Thomas Rossing

Whoa- this book is incredible. Whatever my plans were for today is out the window- I'm spending it reading chapters 18-21 because, as we all know, percussion is where it's at. :)

 

[sophiecentaur]

the sound from an instrument (after any initial concussion) is made up of a collection of related harmonics

We'll. . . . if the natural modes are not harmonically related (and they seldom are) and the system is reasonably linear (air is a pretty linear medium) then what would generate harmonics of the fundamental and overtones? So I would say that has to imply that we hear the overtones.
The non-linearity I started off with would only be caused by extreme stretching of a medium past its linear range.
Incidentally, if you listen to music played on ancient brass (type) instruments like Roman horns etc, a chord played by two or three horns sounds really horrible because the techniques and the tube shapes play merry hell with the overtones. Try to play an arpeggio on a piece of plumbing pipe; the high orders are really bad and even using a proper mouthpiece makes it hard for a beginner to pull the notes right. An expert can even play in tune on a teapot!

 

[sophiecentaur]

percussion is where it's at. :)

No need to bang on about it!

 

[calvinrose]

Hi All, I just noticed this forum and I wrote the 1978 paper on pitch bend in drum heads referenced in my friend Thomas Rossing's book. If you want to try something really cool and useful, put some open cell foam (preferably 1" thick) on the inside of your tom-tom, bass drum, or snare rims 1/8" away from the drum head. It will kill the overtones without touching the drum head. In the attached photo, the distance "d" should be about 1/8 inch. I was going to patent this idea, but decided to publish it instead so people would hopefully use it. The benefit is it dampens out the overtones without killing the stick or pedal strike on the head.

 

[jedishrfu]

Muffled drums rolls on...