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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.

Emil
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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 02 '22 at 07:03
  • 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 02 '22 at 07:12
  • 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 02 '22 at 07:21
  • I am guessing maybe it will only be same if the frequency if it has a high component in the stopping tone but not sure, I am at a loss here. – Emil Feb 02 '22 at 07:46
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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. – Andy Bonner Feb 02 '22 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. – Andy Bonner Feb 02 '22 at 13:49
  • My spectrogram app noticed the pitch when I did it on the thickest string on the guitar (was a good idea to try it on a thicker stringed instrument!) and unfortunately the stopping location seemed to dictate what was the most prominent pitch, keeping the harmonic finger stationary. I got a ratio of 3 instead of a multiple of 2. So obviously my mental model is lacking somehow, it just felt like the waves between the bridge and the harmonic finger should still be there but I guess its more complicated somehow. – Emil Feb 02 '22 at 17:24
  • Looks more like a frequency-wise AND operation between the harmonic finger position and the stopping finger position in my tests so far... seems complicated... – Emil Feb 02 '22 at 17:51
  • [This might help](https://en.wikipedia.org/wiki/String_harmonic). Meanwhile, I'm confused; you added the tag "violin" but say you've been playing guitar. If your question is about how to play artificial harmonics on guitar, then we can talk in terms of frets. Meanwhile, try to make sure that your edits clarify one question (and how it's different from the proposed duplicates); some of the recent edits seem to instead mix other questions in. – Andy Bonner Feb 02 '22 at 20:04
  • Yes, I am learning artificial harmonics on all my stringed instruments, I have quite a few at home. The violin was the hardest to do it on so that's what I am most interested in. I removed my guesswork now. – Emil Feb 02 '22 at 20:09
  • I think it is related to the convolution theorem somehow, because of the and-ish behavior I saw. I think I might be able to figure out the answer on my own if I think about it long and hard enough but I'm getting a bit tired of this question now so might not want to spend more energy right now. – Emil Feb 02 '22 at 20:23
  • @Emil Fair enough. I'm pretty sure we can give you an answer, though, if you can make the question clear. It's really not a complicated topic; mathematically it's a simple series of ratios. As it stands, if your question is "does it matter where you stop the string" the answer is "Oh my gosh yes; it makes as much difference for harmonics as it does for normal notes. You get a different string length, ergo a different note." You're going about it strangely by "leaving the harmonic finger stationary" and moving the stopping finger. The nodes are *proportional* to the string length... – Andy Bonner Feb 02 '22 at 21:10
  • ... not to the neck of the instrument. E.g., on violin, the most common artificial harmonic is to put the harmonic finger a perfect fourth above the stopping finger. Move the stopping finger, even slightly, and you'll have to move the harmonic finger as well to keep a distance of a perfect fourth. – Andy Bonner Feb 02 '22 at 21:12
  • I think it is somehow like multiplying the waves that would have existed if you had stopped the string in either of the two positions. If you go even further it should be possible to use two or more "harmonic fingers" but I don't even know if that has a name. – Emil Feb 02 '22 at 21:19
  • @Emil - no, it doesn't multiply anything. It stops all harmonics that don't have a node where your finger is. – Doktor Mayhem Feb 14 '22 at 17:00
  • @Doktor Mayhem how is that different from multiplying? X*0=0 after all. Have you tried looking at the spectrograms? – Emil Feb 14 '22 at 18:23
  • Yes I have Emil - I did extensive work in this field when I used to design audio effects. It doesn't add or multiplyu any harmonics, it simply subtracts harmonics from the range that exists. – Doktor Mayhem Feb 15 '22 at 16:16
  • Well, 1+-1 is also zero. Like noise cancelling headphones. The sine signal is both positive and negative at different time positions, not sure why you are so anti. I just made the decibels to be the difference from the baseline by exponentiating them. – Emil Feb 15 '22 at 18:19
  • Sure, I probably should have summed in complex space, but I think the difference doesn't matter too much. – Emil Feb 15 '22 at 18:34
  • I think three strings of same material with same length as between your fingers, between your finger and the bridge and between your other finger and the bridge, played simultaneously, would sound very similar. But I am not a researcher for goodness sake. – Emil Feb 15 '22 at 18:48
  • Yup, just tried it with a capo on the second fret and playing the low E string super high. It definitely sounds similar, although I think some bassy notes came too strong, so they are probably dampened more than 50%. – Emil Feb 15 '22 at 19:10
  • @Emil - I'm not anti. This subject has been extensively researched so it is well known. The played string has the fundamental and a wide number of harmonics. Touching the string at any point simply removes any harmonics that don't have a node at that point. No multiplication or summing required. Your finger just stops vibrations for all harmonics that don't already have a stationary node at that point. – Doktor Mayhem Feb 16 '22 at 19:29
  • And you find which ones belong to them by summing the waves on the subdivisions and look at which ones are in common with the harmonics of the untouched string. So summing and finding peaks and comparing is necessary. Unless you have a magical alternative. – Emil Feb 16 '22 at 19:44
  • Which is similar to summing them, because the shared frequencies will have constructive interference. It will be a lot of buzzing nonrelated frequencies but it's good enough for a mental model for me. – Emil Feb 16 '22 at 19:57

4 Answers4

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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.

Andy Bonner
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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 :-)

Doktor Mayhem
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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 '22 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 https://youtu.be/PQi8ZvCyN_0 – Doktor Mayhem Feb 14 '22 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.

Neil Meyer
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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

Emil
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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. – Andy Bonner Feb 14 '22 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 '22 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](https://en.wikipedia.org/wiki/Harmonic_series_(music)). For what it's worth, there is a table on that page, as well as perhaps a more useful one [here](https://en.wikipedia.org/wiki/String_harmonic). – Andy Bonner Feb 14 '22 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. – Andy Bonner Feb 14 '22 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. – Andy Bonner Feb 14 '22 at 21:28
  • I guess my recording misses out on the waves having nodes "between the fingers" and only includes the waves "between the finger and bridge" or something like that. – Emil Feb 14 '22 at 21:51
  • Oh yeah, that would matter a lot. Also, there *is* some math at work for the "things that aren't harmonics," and I'm not sure how that works. For instance, just sticking with natural harmonics to keep things simple: You can find harmonics a fifth, a fourth, and a (sort of) major third above the open string. If you lightly touch the string *between* these nodes, e.g. "a slightly out of tune 4th" etc., you get a sort of diffuse sound that is analogous to the same pitch you would get if pressing the finger in the same spot, but with a different timbre, "breathier" (which of course means... – Andy Bonner Feb 14 '22 at 21:56
  • ... means different overtone blend). What principles govern this sound production, I'm not sure; maybe there's an algorithm for it? What *is* true is that harmonics work specifically because they set up standing waves on either side of the touched finger. – Andy Bonner Feb 14 '22 at 21:58
  • Major d'oh moment, the log of a multiplication is a sum. – Emil Feb 15 '22 at 16:07