What's the difference between two notes played on strings of different thickness?

Question

I'm working on this piece of music on a sequencer, and I'm trying to emulate the effect of playing the same note on different strings of a guitar, say, an E3 on the 5th fret of the B string and an open E3 on the E (first) string.

Obviously, only repeating the exact same note doesn't work, so I figured I could achieve this by introducing a small difference in frequency between the notes played. But this is not a general solution, since the higher you go on the fingerboard the higher is the difference between frequencies.

So what is the difference in timbre between any two notes, with the same pitch, played in strings of different thickness?

Answer 1

Technically speaking two notes with the same pitch have the same frequency as the fundamental.

However this does not explain why two notes of the same frequency also called unisons, sound different on strings of different diameters or lengths or both. The guitar and the entire orchestra string family as you may know have numerous unisons (unlike the piano).

For instance on the guitar, E4 can be played on 5 different strings.

As shown in the diagram below.

So the key question is why and how do these sound different although they are the same pitch?

Largely because each one of these unisons differs in the amplitudes of each harmonic. This is due to the change of thickness of the strings and the length of the string as in where the string is 'stopped' (fretted).

Conversely if you had two identical gauge strings tuned exactly the same as in the two upper E strings on a standard 12 string guitar, then the only difference would be phase related as to when the strings were struck. If the these two strings were engaged at the same time they would sound the same.

To understand why two unisons may sound different (thickness and/or length), you need to make a study of how a thick string playing say E4 vs. a thinner string playing E4 has differing strengths for the harmonics. One way would be to look at each waveform using an oscilloscope or an audio spectrum analyzer or software that would take your audio inputs and render a Fourier transform.

Wiki on Harmonics:

http://en.wikipedia.org/wiki/Harmonic_series_%28music%29

Answer 2

All else being equal, a thicker string will damp out transverse vibrations more rapidly because it experiences more drag (inter-molecular deformation) per unit length. (See section 4.6 of [not my work] http://www.people.fas.harvard.edu/~djmorin/waves/transverse.pdf.) (If we consider strings made of different materials or under different tensions, this rule may or may not apply.)

As noted in some other answers (for various correct and incorrect reasons), the spectrum of harmonics will also be different between the two strings. However, while this is true, my own experience is that the difference in tone produced by this effect is usually smaller than what can be achieved with other performance techniques. For example, by moving the bow closer to the bridge when playing on the heavier string, the difference between the overtone spectra may become negligible or even inverted, or acquire totally different characteristics like the noise of attacking each string from an angle. Thus, getting your sequencer to sound like a human musician may be somewhat counterintuitive, and you should play around with different ideas.

In addition to adjusting the rate of decay of one of your enharmonic notes, I also suggest you try adding vibrato (finger-speed frequency fluctuations) to one of them, since that is what a real player's finger would be doing on the fingered string, but obviously not on the open string.

As far as shifting the center of each pitch, which is also a realistic idea, you would simply need to scale the pitch difference logarithmically with frequency, as @BenKushigian suggests. I also like @smiley's idea of adding a very slight phasor over the entire waveform, to enhance the effect of beating between the strings.

Please let us know what you find sounds best!

Answer 3

The other two answers are true however it seems your question is about sounding a unison as opposed to replicating one sound on a different string, even though you pointed out string thickness as a possible reason for the sound you are noticing. What happens when a string vibrates is that it actually stretches from side to side or up and down depending on which way it was plucked or snapped. This causes a slight warble in pitch which is almost unnoticeable. Depending on how hard the string is attacked this warble will become noticeable and will confuse your electronic tuner. When unison strings are sounded at the same time each one has its own warble pattern and the effect is somewhat akin to chorusing. I have a twelve string guitar that I keep strung with same octave strings so I can get this effect. It sounds amazing but don't try bending the strings. The minute difference in the amount each string gets bent sends the notes out of sink with each other. It makes a ring modulator sound harmonic!

Answer 4

Some additional details.

There is a very small change in pitch due to the change in tension that occurs when the string is fretted. This change in tension varies along the neck, generally larger changes further up (away from the nut) the neck. This change is small enough that it is usually imperceptible in single note playing; however this difference does contribute to the chorusing type of sound that you hear when playing unisons.

Changing the length of the vibrating string also has effects on the inharmonicities in the overtones of the note; in general, the shorter the string the greater the change in frequency of the higher overtones away from their ideal values (this has to do with the fact that real strings have non-zero transverse stiffness). In addition, thicker strings (of a given material) will have greater degree of inharmonicities in the overtones. These effects will shift the locations of the harmonics in frequency.

I suspect that the relative strengths of the harmonics, as indicated in Filzilla's answer is the dominant effect, and would be what I'd look at trying to modify first, possibly by just applying different EQ curves to the differently fretted notes; however, if you are going into excruciating detail, there is a physical basis for incorporating effects that shift the frequencies of the harmonics, including the fundamental.

One point which is implicit in some of the other answers but not spelled out in detail is that when modifying pitches you usually want to shift them multiplicatively, something like F' = (1+df)*F where df is a fractional change in the pitch. My read of this question is that the OP tried doing the pitch shifts by F'=F+dF where dF is a frequency shift in Hertz, which does not produce uniform changes in perceived pitch as the original pitch is varied.

Answer 5

So the difference between the quality of two notes that are the same pitch (two different strings, or even with two different instruments) is not in the frequency necessarily (though my guitar is always a bit out of tune...) but rather the overtones each string produces. I don't know exactly how to mimic that but read into the overtone series - maybe bassier strings should have more emphasis on the lower end of the overtone series (just a hair, too much and it would be too drastic!)

Also, as far as changing the frequencies are concerned, look into cents ( a logarithmic division of semitones in equal-temperment) instead of constant numerical changes. If I had an A440 and added 2Hz to it and wanted to mimic this at A880 then I would want to add 4Hz to it. The best way to do this is to automate the process (if you have any programing skills). I did up a little Python script, I can send it along if you want it - you input your first frequency, your second frequency (adjusted a few Hz) and then a third frequency. The script outputs a fourth frequency that is logarithmically proportional to the third frequency as the second is to the 1st.

Answer 6

There's a key difference in string gauges. Under the same tension, a thinner gauge has less mass and it can move more easily when it receives an impulse, as opposite to a thicker gauge. In thinner strings, more harmonics are generated because, aside from the fundamental vibration, smaller harmonic vibrations occur on the string more easily. That makes for a "brighter" sound to our minds, as opposite from the "darker" sound on thicker strings. There's also other things involved, as noted in Dave's answer.

You won't be able to generate this on a computer so easily, by just changing frequencies, it's not a matter of frecuencies, but physics. If you still want to try, you need to have a variable amount of harmonics (hint: can be achieved with a low-pass filter).

Those subtle differences are what make electronic generated music sound so artificial.

https://en.wikipedia.org/wiki/Harmonic#Harmonics_and_overtones

Answer 7

I think you'll find the difference in timbre is less about the gauge of string, more about the difference in sound between an open string and a fretted one. And possibly about the different plucking position relative to the string's effective length.

So how to do this in a sequencer? For a start, don't just introduce 'random wrongness' to the tuning. It's not desirable for one string to be out of tune, even if it does sometimes happen accidentally in practice.

I suggest you don't worry too much about WHAT the difference in timbre is, just make sure there IS one. This means choosing a sample set that doesn't merely repeat the same sample for each note, but rotates between a selection of samples. And remember, guitarists spend money to minimise the sort of difference we're talking about!