intonation on the harmonics

[OliverBlackman]

So everything is in tune except for the harmonics on the 4th frets. Is this down to neck relief or the frets? Or is it a common design fault?

[Bilbo]

What are you measuring it with? If everything else is spot on, this is technically impossible

But then again, so is flight in bumble bees!

Actually, major thirds on fretted instruments are generally off (that is why a major third on a distorted guitar sounds so ugly). Are you fretting the note and then playing the harmonic as a comparison? If so, it will always sound marginally different.

[derrenleepoole]

Harmonics, or nodes sound at specific points up and down the strings and when you play them they effective divide the string into equal resonant vibrations along the string length. So if you play the harmonic at the 12th fret, the strings us divided equally at that point. Harmonics have nothing to do with frets or fret positions as they're determined by string length. Is it possible that perhaps the intonation is out on the fretted notes compared with the harmonics as these aer fixed, and not the other way around?

Edited February 3, 2011 by derrenleepoole

[Earbrass]

[quote name='Bilbo' post='1114048' date='Feb 3 2011, 04:03 PM']What are you measuring it with? If everything else is spot on, this is technically impossible

But then again, so is flight in bumble bees![/quote]

Not this old chestnut again!

[url="http://www.straightdope.com/columns/read/1076/is-it-aerodynamically-impossible-for-bumblebees-to-fly"]http://www.straightdope.com/columns/read/1...mblebees-to-fly[/url]

[Bilbo]

Thanks, EB. I should point out that the example was purely a metaphor for illustrative purposes and, in reality, I really coudn't give a rat's

[OliverBlackman]

[quote name='derrenleepoole' post='1114053' date='Feb 3 2011, 04:07 PM']Harmonics, or nodes sound at specific points up and down the strings and when you play them they effective divide the string into equal resonant vibrations along the string length. So if you play the harmonic at the 12th fret, the strings us divided equally at that point. Harmonics have nothing to do with frets or fret positions as they're determined by string length. Is it possible that perhaps the intonation is out on the fretted notes compared with the harmonics as these aer fixed, and not the other way around?[/quote]


Not sure i understand, basically i was playing along to a keyboard and trying out some ideas with harmonics. It sounded fine just when i would go to play the harmonic on/ around the 4th fret. I know its the equivalent to the strings major 3rd.

So i played my bass through the tuner and everything was bang on in tune except for these specific harmonics. The octave harmonics are fine both on the 12th and 5th fret, and the 5th on the 7th fret is fine. Just these major 3rd's are ever so slighty flat on the tuner.

[Earbrass]

[quote name='Bilbo' post='1114071' date='Feb 3 2011, 04:18 PM']Thanks, EB. I should point out that the example was purely a metaphor for illustrative purposes and, in reality, I really coudn't give a rat's [/quote]

Fair enough!

[quote name='blackmn90' post='1114073' date='Feb 3 2011, 04:20 PM']Not sure i understand, basically i was playing along to a keyboard and trying out some ideas with harmonics. It sounded fine just when i would go to play the harmonic on/ around the 4th fret. I know its the equivalent to the strings major 3rd.

So i played my bass through the tuner and everything was bang on in tune except for these specific harmonics. The octave harmonics are fine both on the 12th and 5th fret, and the 5th on the 7th fret is fine. Just these major 3rd's are ever so slighty flat on the tuner.[/quote]

Could this be an equal temperament issue? The harmonic will be a "pure" maj 3rd, while the keyboard will be tuned to equal temperament. Could this account for the discrepancy?

Edited February 3, 2011 by Earbrass

[Bilbo]

[quote name='Earbrass' post='1114091' date='Feb 3 2011, 04:26 PM']Could this be an equal temperament issue? The harmonic will be a "pure" maj 3rd, while the keyboard will be tuned to equal temperament. Could this account for the discrepancy?[/quote]

I think that's what I meant!

[BottomEndian]

[quote name='Earbrass' post='1114091' date='Feb 3 2011, 04:26 PM']Could this be an equal temperament issue? The harmonic will be a "pure" maj 3rd, while the keyboard will be tuned to equal temperament. Could this account for the discrepancy?[/quote]
Yes. The only harmonic that's genuinely "in tune" (in terms of equal temperament) with the open string is the octave (12th fret). Everything else just gently drifts off from there.

[OliverBlackman]

ahrite well that does make sense. It is a shame though as it would be more useful if if they tuned to the same frequency

[Earbrass]

[quote name='blackmn90' post='1114144' date='Feb 3 2011, 05:06 PM']ahrite well that does make sense. It is a shame though as it would be more useful if if they tuned to the same frequency[/quote]

But if they did that, your bass / keyboard or whatever would only ever be really in tune in one key. The whole point of the equal temperament system is to allow us to play [i]very nearly[/i] in tune in all keys. In return for that, we make do with being [i]very slightly [/i]out of tune in all keys!

[Lfalex v1.1]

[quote name='Earbrass' post='1114152' date='Feb 3 2011, 05:10 PM']But if they did that, your bass / keyboard or whatever would only ever be really in tune in one key. The whole point of the equal temperament system is to allow us to play [i]very nearly[/i] in tune in all keys. In return for that, we make do with being [i]very slightly [/i]out of tune in all keys![/quote]

Or play fretless and be [i]very[/i] out of tune lots of the time!

[chrisba]

[quote]Yes. The only harmonic that's genuinely "in tune" (in terms of equal temperament) with the open string is the octave (12th fret). Everything else just gently drifts off from there.[/quote]

I would argue it's the other way around, the harmonics are always, by definition, "in tune", but won't agree with the fretted notes ( except 12th ) which are always a compromise to some degree.

The whole subject of temperament came as a complete surprise to me. Quick summary, an octave is double the frequency of the root note, and the fifth is 3 times ( or 1.5 if you prefer it in the same octave as the root). If you do the maths on the [url="http://en.wikipedia.org/wiki/Circle_of_fifths"]circle of fifths[/url], from A ( 440hz ) multiplying by 3 each time, and dividing by 2 as required to keep it sensible, you get back to A = 446hz, which is slightly sharp. The different versions of temperament ( [url="http://en.wikipedia.org/wiki/Equal_temperament"]equal temperament is the one commonly used[/url] ) tweak all the intermediate notes slightly so that you get back to 440hz instead. Hence harmonics won't quite match the fretted notes.

I have heard a theory that the reason why choral harmony sounds so "pure", is that they don't have problems with the slightly out of tune notes, as voices would naturally adjust slightly so they sound in tune with the other notes in the chord.

[alim]

About the harmonics being in tune...
I'm not sure that's always exactly the case, even though it seems obvious from basic theory of vibrating strings.
Pianos are tuned using 'stretched octaves', meaning that bottom C fundamental is a little less than half the frequency of the C above it. I think this is because of the effect of harmonics (which may be more dominant in the perception of pitch) being slightly sharper than the a simple fraction multiple of the fundamental frequency. I guess this is to do with the string (particularly very thick piano strings) being constrained at each each, so that they are not free to pivot about the nodes freely.

I don't know how significant this effect is on a bass guitar - not very, probably!

It might well be the equal temperament error that you can hear. This is 13 cents for a major 3rd, i.e. equal temperament gives 554Hz (=440 x 2^(4/12)) instead of the 'harmonically correct' 550Hz (=440 x 5/4). Does that correspond to what the tuner tells you?

[EssentialTension]

[quote name='Lfalex v1.1' post='1114174' date='Feb 3 2011, 05:26 PM']Or play fretless and be [i]very[/i] out of tune lots of the time![/quote]
It's not out of tune, it's just spicy.

[EssentialTension]

If anyone's interested in the history of this problem, I recommend [url="http://www.amazon.co.uk/Temperament-Stuart-Isacoff/dp/0571234461/ref=sr_1_1?ie=UTF8&qid=1297627397&sr=8-1"]Stuart Isaacoff, [i]Temperament: How Music Became the Battleground for the Great Minds of Western Civilisation[/i], Faber , 2002[/url].

Edited February 13, 2011 by EssentialTension

[skej21]

Just because it's related and usually quite an eye-opener, have a watch of this!

*be warned, you will hear lots of things out of tune immediately after listening to this and/or if exposed to it on a regular basis *

[u][b]ALSO, DO NOT PLAY ALONG WITH IT OR YOU WILL MAKE YOUR EARS BLEED! [/b][/u]lol

Edited February 13, 2011 by skej21

[markstuk]

Most modern keyboards allow ths use of different temperaments.. Last time I bothered to look on my Motif ES I had over 20 different types... And I can create custom ones as well :-)

Mark

[quote name='alim' post='1124344' date='Feb 11 2011, 08:52 PM']About the harmonics being in tune...
I'm not sure that's always exactly the case, even though it seems obvious from basic theory of vibrating strings.
Pianos are tuned using 'stretched octaves', meaning that bottom C fundamental is a little less than half the frequency of the C above it. I think this is because of the effect of harmonics (which may be more dominant in the perception of pitch) being slightly sharper than the a simple fraction multiple of the fundamental frequency. I guess this is to do with the string (particularly very thick piano strings) being constrained at each each, so that they are not free to pivot about the nodes freely.

I don't know how significant this effect is on a bass guitar - not very, probably!

It might well be the equal temperament error that you can hear. This is 13 cents for a major 3rd, i.e. equal temperament gives 554Hz (=440 x 2^(4/12)) instead of the 'harmonically correct' 550Hz (=440 x 5/4). Does that correspond to what the tuner tells you?[/quote]

[tauzero]

[quote name='EssentialTension' post='1126350' date='Feb 13 2011, 08:04 PM']If anyone's interested in the history of this problem, I recommend [url="http://www.amazon.co.uk/Temperament-Stuart-Isacoff/dp/0571234461/ref=sr_1_1?ie=UTF8&qid=1297627397&sr=8-1"]Stuart Isaacoff, [i]Temperament: How Music Became the Battleground for the Great Minds of Western Civilisation[/i], Faber , 2002[/url].[/quote]
A few minutes ago there were two brand-new copies of this on That Ebay for the princely sum of about three and a half quid delivered. Now there's just one.

[philw]

I went to a classical gig once (although I seem to remember Andy Shepherd was playing so maybe it was a jazz gig) where the pianist, Joanna McGregor, had two nominally identical grand pianos, one tuned to equal temperament and one tuned to an alternative temperament – they sounded utterly different.

P

[ead]

[quote name='Bilbo' post='1114048' date='Feb 3 2011, 04:03 PM']Actually, major thirds on fretted instruments are generally off[/quote]

I believe this to be the case. I find a major 3rd on my fretless sounds better when the 3rd in question slightly flattened and vice versa for the minor 3rd.

[Earbrass]

[quote name='philw' post='1129913' date='Feb 16 2011, 05:17 PM']... the pianist, Joanna McGregor, had two nominally identical grand pianos, one tuned to equal temperament and one tuned to an alternative temperament – they sounded utterly different.

P[/quote]

I briefly shared a house in Clapham with her (and several others), back in the mid 80's. Not relevant, but I thought I'd throw it in for luck.

[philw]

[quote name='Earbrass' post='1130938' date='Feb 17 2011, 01:05 PM']I briefly shared a house in Clapham with her (and several others), back in the mid 80's. Not relevant, but I thought I'd throw it in for luck.[/quote]

About the same time I was sharing a house in Petersfield with Erica Roe (if you can't remember or are too young, Google is your friend) then. Don't think Erica was quite as good a pianist as Joanna McGregor, but still, there weren't too many dull moments.

P