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When playing an artificial harmonic, does it matter where the stopping finger is placed? Leaving tone quality aside, will the same pitch class be produced regardless the stopping location?

I performed some tests and saw that it seems to be a function of the frequencies that would have been generated in the two points in isolation so there is some interplay.

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    Please consider that your question was not clear to the five highly experienced readers who voted to close it and that additional explanation is required to express how it differs from the referenced duplicates. I've read your recent update, and remain uncertain. Are you just asking, aside from tone quality, whether or not it matters where on the string the stopping finger is placed?
    – Aaron
    Feb 2 at 7:03
  • Yes Aaron. My spectrum app is too poor quality to detect the pitch so I had trouble finding this out on my own.
    – Emil
    Feb 2 at 7:12
  • That is, indeed, clearly a different question. I suggest you re-edit your post to read along the lines of "When playing an artificial harmonic, does it matter where the stopping finger is placed? Leaving tone quality aside, will the same pitch be produced regardless the stopping location?".
    – Aaron
    Feb 2 at 7:21
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    Also, are you talking about guitar? Please add an instrument tag, since just about any stringed instrument can use harmonics (even piano!), and the techniques can vary. Feb 2 at 13:44
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    And I'll try to give you a chance to clarify before giving a full answer, but the short version is yes, it matters a lot. An open string has "natural" harmonics at certain places, like in the middle or at a quarter or its length. An artificial harmonic just uses the stopping finger to "shorten" the string, and then you find harmonics at the same certain places along the now-shorter string, like a quarter of its length. Feb 2 at 13:49

4 Answers 4

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When playing an artificial harmonic, does it matter where the stopping finger is placed?

Absolutely. Artificial harmonics are natural harmonics that simply use a string that has been shortened by stopping it "artificially," so if you move the stopping finger, you alter the length of the string and the placement of all its harmonic nodes.

For example:

  • Say that a violin G string has a sounding length of 60mm (measurements in this example are arbitrary, just for the purposes of illustration).
  • It will have a natural harmonic at exactly half its string length (30mm), producing a pitch one octave above the open string.
  • It will also have harmonic nodes that divide those two halves—one at 15mm and one at 45mm—both producing a pitch of one octave plus a fifth above the open string.
  • Now let's say that you stop the string, raising the pitch by a whole step, to A. The new sounding length is, let's say, 50mm. You will no longer find harmonics at the same spots, because the string is a new length. At the site of the original "octave-higher" harmonic, 30mm up the fingerboard (counting from the nut), there is no harmonic any more. Now, the new "half the string length" node is half of 50mm plus the 10mm of stopped string, so can be found 35mm from the nut.*
  • Similarly, the "one-quarter-string-length" harmonics are now at (50 * 0.25) + 10—22.5mm from the nut—and (50 * 0.75) + 10—47.5mm.
  • Shift the stopping finger, even by a millimeter, and all the harmonic nodes re-distance themselves proportionately. If you do not adjust the "touching finger" to match, you will no longer have a harmonic, unless you happen to move the stopping finger to a spot where the touching finger describes a different harmonic node.

So if you're looking for a formula to express the relationship of the touching finger to the stopping finger, it's not complicated: it is the harmonic series. You will always find harmonics in the same places, relative to the stopping finger, that you find natural harmonics on an open string.

There's a fun "special effect," most effective on cello or bass, in which you play an artificial harmonic, high on the fingerboard, then glissando both fingers downward without adjusting their width as one normally would have to do to preserve an interval of a third. As the fingers slide, they mostly produce a "static-y" shriek of descending, fairly diffuse pitch, but along the way they pass through spots in which they describe other harmonic relationships, which ring out, and the resulting effect suggests a seagull's cry.

This effect basically relies on continuously changing "where the stopping finger is placed," and the fact that only a few spots on that continuum produce harmonics.

* This "counting from the nut" business can be confusing and misleading; I just use it to keep the frame of reference constant. A stopped string "doesn't care" how much string there is behind the stopping finger as long as it doesn't vibrate. If you count "from the stopping finger," then you find harmonics not at set distances but at set proportions, ratios of the string length.

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The relative distance along the string from the fretted note to the harmonic note is everything - there are many places where you will get an artificial harmonic. The loudest, and simplest to do are 5th, 7th and 12th fret higher (as well as 12 frets higher than those if you have enough frets), but you will also get one just off the 3rd fret, one around the 9th etc., especially if you use an electric guitar and distortion.

I see you have mentioned various string instruments, but then focus on violin - well, the same holds true for violin, however without frets you just need to focus on distances, and generally when bowing with the right hand you will need to use your left hand to both finger the note and to touch the harmonic node you want - which may limit which harmonics you can reach.

(or use an assistant :-)

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  • But how do you predict which pitch will be sounding? Since I can't do fourier transforms in my head my own answer is not very helpful in this regard, do you have more insight ?
    – Emil
    Feb 14 at 10:38
  • @Emil If you try this on a guitar, using natural harmonics, as you play the harmonic on 12, 7, 5 and 3 fret, you can see how the pitches go up. Example youtu.be/PQi8ZvCyN_0
    – Doktor Mayhem
    Feb 14 at 11:05
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Artificial harmonic is where you fret a note and then play a harmonic with your picking hand 7 or 12 frets higher on the same string. It matters very much where you pick the harmonic. It will only work at very specific places in regards to what note you fret.

This is mainly done in the classical scene where you keep your index finger straight and pick the harmonic with your ring finger. I have also debeloped a way to do it with a pick.

You keep your index finger straight and hold the pick with your middle finger and thumb. This opens up a whole new dimension of harmonics.

The natural harmonics are those that fall natural on the fretboard. Mostly at fret 7 and 12 but on some guitars on fret 5 as well.

You get pinch harmonics or squelies that are made by picking a note and then touching right after you play it on one of the nodes on your guitar.

Lastly, you also get tap harmonics as made popular by Eddy Van Halen. This is a variation on a artificial harmonic. The main difference being you tap the harmonic with your index finger instead of picking it. Something which gives a different sound.

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My unverified theory:

  1. Save the spectrograms of what is produced when you press down your finger at the positions of the artificial harmonic, one finger at a time. You also need to record the sound made with the same distance to the bridge as between your fingers.
  2. Add the spectrograms frequency-wise.
  3. The resulting spectrogram is what will be produced by the artificial harmonic.

NOTE: I have only verified this for three artificial harmonics and one double artificial harmonic where I used three fingers. So it might be bogus. But this is the kind of answer I wanted so I will write it down here anyway. Here is an example from a recording I did today: enter image description here

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  • You're still missing the most fundamental (hehe) point: Not all distances between fingers can generate artificial harmonics. Just as not all points on a string can generate natural harmonics. Artificial harmonics simply stop the string and then make use of the natural harmonic nodes on the (now shortened) string. Feb 14 at 20:47
  • I think this method can be used to compute which sounding pitch will sound. I can make a table for all "overlapping overtones" later in python or something. And I will investigate touching the string in two or more places, perhaps a single sine tone can be produced if you place them just right... but I don't think I will share it here, no point in getting even more downvotes...
    – Emil
    Feb 14 at 21:20
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    See my full answer that I've finally posted. The calculations are not new or complex—it is simply the harmonic series. For what it's worth, there is a table on that page, as well as perhaps a more useful one here. Feb 14 at 21:22
  • Note, the algorithm you propose here is fairly easy to disprove in a couple of ways. 1) After the first node (at the octave), every harmonic node has a mirror image in either half of the string. E.g., if you have a C string, there is a node at the first G and also much higher, 3/4 of the way up the string, at the G an octave higher. Both spots produce the same natural harmonic, even though the fingers "pressed down" will be an octave different. The same holds true if the string is stopped; there are harmonics at the same proportional points. Feb 14 at 21:27
  • And 2) although it's impossible to reach on most string instruments using only one hand, with an assistant one could create an artificial harmonic an octave above the stopped finger. The pitch produced by this is the same as the pitch that the harmonic finger produces when pressed down. Feb 14 at 21:28

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