Stiff strings => sharp harmonics, but some are flat! Explain?

[LetItGrowTone]

All observations are with iStroboSoft tuner on iPhone with the "harmonic tuning" add-in.

There's this theory that stiff construction tends to cause a string's higher harmonics to go sharp. It seems to be true and I think I understand it. But I looked into this for the first time with this app and was surprised to see that some are flat; often the 2nd harmonic is flat while the 3rd is sharp.

Can anyone explain that?

**
I finally found a case where all harmonics were sharp: La Bella 760FS on a short scale, at the 12th fret. This was as expected, but it wasn't as bad as expected.

 

[HaphAsSard]

often the 2nd harmonic is flat

1st of all...which "2nd harmonic" do you mean?
(There's a reason for my question.)

 

[LetItGrowTone]

1st of all...which "2nd harmonic" do you mean?
(There's a reason for my question.)

Oh, I think I know your reason.
Open E is about 41Hz. Pluck it. Another component of the vibrations on the string is the 2nd harmonic at 82Hz. Third is at about 123Hz, etc.

These were the names as I learned them, and also the way the app labels them.

 

[LetItGrowTone]

That second harmonic is also an E; the third is not an E, and some strangeness could be caused by the equal temperament thingie and how the app handles that. Don't really want to talk about that here.

It's ok if the thread just focuses on how in the world that 2nd harmonic E at about 82Hz could be flat.

 

[HaphAsSard]

Oh, I think I know your reason.
Open E is about 41Hz. Pluck it. Another component of the vibrations on the string is the 2nd harmonic at 82Hz. Third is at about 123Hz, etc.

These were the names as I learned them, and also the way the app labels them.

Good, we're on the same page then.

[To anyone else perplexed by the exchange:
a harmonic is not necessarily an overtone. The latter term excludes fundamentals by definition, unlike "harmonic", which means "fundamental frequency times a positive integer": since 1 is an integer, the first harmonic is fundamental x1 = the fundamental itself; the second is the fundamental x2 = one octave up (lowest overtone); the 3rd is the overtone at an interval of perfect twelfth (octave+perfect fifth) from the fundamental; 4th is the second octave; and so on.]

That second harmonic is also an E; the third is not an E, and some strangeness could be caused by the equal temperament thingie and how the app handles that. Don't really want to talk about that here.

It's ok if the thread just focuses on how in the world that 2nd harmonic E at about 82Hz could be flat.

But the question was germane to the thread topic: had you thought of the octave+fifth overtone as the "2nd harmonic", the reason for its flatness was to be found precisely on the fact that digital tuners/apps do not recognise it as an equal temperament note (it is indeed flatter).

Since that's not the case - as in, no you don't miscount harmonics, and yeah, it is the octave harmonic that is flat - I'm afraid I got nothing. Quite the puzzle in fact.