January 31, 2019, 8:13 AM · Could someone please explain to me how fundamentals/partials/harmonics work, and what they mean?

A specific scenario I would like to understand... If I compare playing on the fingerboard using lots of bow, with playing at the bridge with slow bow, both at the SAME decibel level: which will give me what combination/level of fundamental and harmonics?

## Replies (12)

January 31, 2019, 8:39 AM · This is a question you can answer for your self. Put a "spectrum analyzer" app on your smart phone and do the experiments.
January 31, 2019, 9:41 AM · A vibrating string (or column of air, in the case of a wind player), has the tendency to break itself into multiple parts, with each part vibrating like an entirely separate string. For example, the string will split in two and one can hear the octave, in 6 parts and one will hear an octave and a 5th, and so on. This series of tones produced is call the "harmonic series." Theoretically, it's infinite as the string divides and subdivides itself into smaller and smaller parts, but in reality the stiffness of the string interferes and the string can no longer divide itself. Thus, an upper limit is reached.

The first few partials (you can call them overtones) look like this, from low to high:
1st partial: the string vibrates as a whole (also called the "fundamental," for which the string is named)
2nd partial: one octave up
3rd partial: Octave and a 5th
4th partial: 2 octaves and a 3rd up
5th partial: 2 octaves and a 5th up

The terms "partial" and "overtone" mean the same thing but use a different numbering system.

Every violin (or instrument) has its unique sound, called the "timbre," due to the relative loudness of the partials. That's what Andrew's spectrum analyzer will show you. You can "encourage" a string to produce louder high partials or low partials. As James points out, bowing near the bridge helps bring out the higher partials. Different bows or strings will emphasize different partials. Bouncing the bow off the string quickly will let higher partials ring. Keeping it one the string dampens them.

When we play harmonics, we are forcing the string to divide itself in certain ways as well, and those points on the string correspond to the harmonic series on each string: 8ctave, 5th, 3rd, etc.

One would assume that the vibration of the string as a whole, and for which the string is named--the fundamental (or 1st partial)--is the strongest tone. Not true. If you use a spectrum analyzer, you see that actually lower strings on the violin and supposedly low notes on other instruments have a weak fundamental and are actually producing a stronger 2nd partial (the octave). Our ear is being fooled into thinking it hears the lower tone. True also on the bass of a piano, especially smaller pianos.

James, you're asking about specific combinations and strengths. I'm not sure there's an answer to that question except "it depends." There are too many variables. In this case, the ear is the best judge: what sound are you trying to achieve?

January 31, 2019, 11:01 AM · Thanks for that information Scott!

The sound I am trying to achieve is one which carries and projects the most. I am a big fan of Zukerman and Gautier Capucon's right hand technik, and they often use less bow, slower bow, right at the bridge, and with lots of audible scratching up close. I also play very much in this style because I like the concentration of the sound but many people encourage me to use more bow. If playing closer to the bridge brings out higher partials better, is there a trade off? Does this mean that playing with more bow speed and further from the bridge brings out more fundamentals instead?

January 31, 2019, 12:44 PM · The reason the fundamental pitch of low tones is dwarfed by higher partials is because the instrument corpus and/or air-cavity cannot support vibrations of the low tones.

Another thing that happens when you bow close to the bridge is that you are creating vibrations on the string that can add audible anharmonicity that can enhance projection, especially when supported by skillful vibrato. I think the sound produced this way also depends very strongly on the resonances of the particular instrument - some can support it and some cannot.

Edited: January 31, 2019, 1:11 PM · Mr. Dong,

Do remember too that Mr. Zukerman and most others do use synthetics. Not a problem, but those do sound better being played in the aforementioned, concentrated manner. You can do it with your gut strings too, but do not *need* to do so all the time (I am not implying-or complaining-that these soloists do it "all the time", however.)

Many synthetics force me to bow in a more forceful, "weighty" way in order to pull the tone. I find that, perhaps ironically, the violin is so much simpler to play with gut strings, despite the more nuanced bowing often required.

(No debate of synthetics vs gut intended above-just that I know from previous posts that Mr. Dong uses-or has used, at any rate-many sorts of pure gut and wound gut strings. What is "best" is ultimately a personal choice.)

Edited: January 31, 2019, 1:15 PM · If you listen to a clarinet, the sound you are hearing is probably as close to a perfect sine wave (a single frequency) of any of the common orchestral instruments.

If you play a "single note" on a violin into an oscilloscope, you'll see a horribly jagged-looking waveform -- nothing like a sine wave. But if you add together sine waves of different frequencies and amplitudes, you can reconstruct the jagged wave of the violin. The mathematical process is called Fourier analysis. Generally speaking these different component frequencies will be overtones. But because the bow contact is not an infinitely small point, and because the string is not infinitely thin and flexible, etc., there are non-ideal features of the sound too -- and these are the features that are difficult to model but important to your overall sound. ("Non-ideal" doesn't mean your violin sounds bad -- it means the math is much more difficult.)

I read somewhere that "projection" has been associated with prominence (i.e., volume) in a certain range of frequencies, and while my recollection is not always the best, I thought that was in the range of 3-4 kHz.

January 31, 2019, 3:05 PM · To me, a clarinet's sound is closer to a square wave than a sine wave. It has a good dollop of third harmonic in there, and if you listen closely you can hear a tone an octave and a fifth above the fundamental. Still, you're right that it doesn't have a lot of those higher harmonics that give a violin its characteristic sound.

As for projection, I know what you mean about that 3-4 kHz range. The human ear seems to be quite sensitive to those frequencies. I suspect that we evolved that way so as to able to readily hear the screams of a child in distress, which happen to be in exactly that range.

January 31, 2019, 3:54 PM · James,
I'd simply say, for the purpose of projection and clarity, be as close to the bridge as possible until you can't stand the sound quality. I don't know what level you are, but the primary fault of most students is that their first-position contact point remains even while they are in the upper positions.

As close to the bridge as possible...

January 31, 2019, 6:25 PM · To get that dense tone you need to load the weight of the hand onto the fingers, and onto the bow. Weight will be transferred through the middle fingers, rather than first finger, and distributed more evenly across all four fingers. And of course you adjust the sound point appropriately.
January 31, 2019, 9:49 PM · This is actually a rather complex topic.

A sustained note on a violin string is actually a shallow triangular looking bump of length much shorter than the length of the string. This bump travels up and down the string simultaneously and is reflected and inverted when each bump encounters the bridge and nut.

Playing closer to the bridge changes the shape of the bump because the physics of the string sticking to the drawn bow and then slipping, forming the bump, varies. Much less deflection of the string is needed at the bridge to get it to slip off the bow hairs and form the bump.

This change in shape accounts for the change in timbre of the note.

The harmonics that people talk about, in this case, is a theoretical, mathematical game. It turns out any complex shape, such as the bump traveling along the violin string, can be represented as the sum of sine and cosine functions whose frequencies are all integer multiples of some base frequency.

But the bump shape can also be represented as the sum of polynomials that have no frequency terms. In fact, there are many strange functions that can be summed up to represent the shape of the traveling bump. These sets of functions form a special class of functions called orthogonal functions.

There are various theoretical advantages to representing sound and sound-causing waves as the sum of sines and cosines that I won't go into here. But there is nothing inherent in the shape of the vibrating string that requires us to view them as the sum of harmonics.

February 1, 2019, 6:42 AM · Charlie yes the clarinet is the classic square wave but at least that's conceptually simple. The square wave actually should be an infinite series of overtones if I remember correctly.
February 1, 2019, 6:56 AM · A square wave only contains the odd-numbered harmonics, giving that warm, slightly hollow tone.
The flute has them all, but in very small quantity.

Both anharmonicity (e.g. a pendulum) and inharmonicity (e.g. a bell) give charm to violin string tone, especially at the start of a note. Which is why synthesised violins sound...synthetic!

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