Here, Lauren Pierce claims that she doesn't use harmonics to tune because they are "slightly flat". Why is this? Is she referring to just intonation vs equal temperament, or inharmonicity, or something else?

I'm even more confused because she also demonstrates by playing the 3rd harmonic (8va + 5th) and 4th harmonic (8va + 8va). To my knowledge, compared to ET the octaves are in tune, and the 5th is slightly sharper. So why would she say the harmonics are flat?

  • Something related, if you want a little more info. – user45266 Mar 22 at 23:44

If you're using a tuner, then you can safely use the octave harmonic to tune. She is wrong in saying blanketly that "the harmonics are slightly flat". Some are flat, some are sharp, some match equal temperament exactly*. This page has a figure that shows the relative sharpness and flatness of the first several harmonics.

Often people use "tuning with harmonics" on an instrument tuned in fourths usually means matching the "7th fret" harmonic of the higher string (a perfect fifth + an octave above the open string) with the "5th fret" harmonic of the lower string (2 octaves above the open string).

The problem is that the 7th fret harmonic is 2 cents sharper than an equal tempered fifth , so if you make these harmonics match then your open higher string will be 2 cents flatter than an equal tempered fourth above the lower string (or depending on your perspective, your lower string is 2 cents sharp).

If you start on the low E and tune all your strings in order, you end up with the G string being 6 cents flat (+- 3 human errors). If you start on the high G and tune them top down, the low E ends up 6 cents sharp (again +- 3 human errors). Perhaps this is a source of confusion that it relevant here.

*The asterisk is for inharmonicity, which is a problem with stringed instruments and not the harmonic series. Harmonics tend to go sharp, not flat, but the first few harmonics should be close enough to tune with.

  • Isn't that 2 cent difference considerably smaller than most people can discern in normal circumstances? – Karl Knechtel Mar 23 at 8:13
  • I've always found it's not that it's a couple of cents out each time but more that you have 5 chances to get it wrong in the same direction. I've always found the same with fret/open tuning. I learned 30 years ago to just listen to the open strings. You just learn what they should sound like after a while. – Tetsujin Mar 23 at 9:21
  • @KarlKnechtel If you hear the 2 pitches one after the other, you won't hear the difference. But if you play them together, you may notice some beating. (a gradual wah-wahhhh) – Bennyboy1973 Mar 23 at 10:48
  • 2
    @KarlKnechtel On a 5 string instrument those 2 cents x 4 intervals add up to 8 cents. (on a 4 string, 6 cents.) To put it another way, on a 5 string violin (tuned in fifths) it gives you a pythagorean (3/2)^4 = 81/16 = 5.0625 ratio between your lowest and highest string, which differs significantly from the equal tempered 2^(28/12)=5.0397, and is further from the just ratio of exactly 5 (which would be the most pleasing if the two strings were played together.) On a 5 string bass (tuned in fourths) same is true but in reverse (but I showed the violin example because math is easier to follow.) – Level River St Mar 23 at 13:53
  • @JirkaHanika I addressed that tuning method in my answer, even though I don't think it is being referred to in the video. Nonetheless, the harmonic is not flat, it's sharp- see the table. You're right that inharmonicity affects higher harmonics more, but we see this effect for both flageolets and the open string, so I don't really see the relevance here. Also, when the string is bowed, the harmonics end up being perfectly harmonic, since the bowing action locks the harmonics' phases together. – Edward Mar 23 at 19:59

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