Thirds and Intonation

cometazzi

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There's something that's bugged me ever since I figured out how to play intervals and what they are- On all my guitars at least, I've noticed this:

Play a major or minor third interval, like E and G# or E and G. As it rings out, start pulling the 3rd sharp. At some point, it will start to sound more 'in tune' or more 'even'. I don't really know how to describe it. This effect is especially enhanced with distortion. Is it like this on your guitars too?

There are plenty of guitar recordings where the the intervals are very 'even' sounding, and have that nice symmetrical texture to them. I know this song won't be everyone's cup of tea here, but I promise it won't hurt you. The intervals played throughout the verse (starts from the beginning) sound 'even' as though they've got the 3rds pulled sharp:



That's two guitarists playing two separate tracks. Do you think they're both masterfully pulling those 3rds sharp with their index finger? Or is this some other form of intonation that I'm not experiencing in the small time at home? The guitars in this recording are perfectly in tune everywhere else.

There are other recordings but this seems to be the best demonstration. Has anyone else noticed this, or am I imagining everything?
 

guitar_paul1

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Pulling could well be right, or fretting just a bit harder.

Sounding "perfectly in tune" is actually a bit off from the actual defined major or minor third, or any other interval except for the octave.. That's because most of us use an "equal tempered" 12 tone scale which causes things to be a bit wonky in spots. It comes from trying to divide an octave up into twelve chunks with the same ratio between each adjacent note frequencies.

If you aren't interested in my typical TMI post, my feelings won't be hurt. But here goes in case anybody cares:

For different intervals, the waves don't line up their zero crossings at quiiiiite the same spot, so it sounds weird. If the waves don't line up perfectly, you can hear the wonkiness, especially with distortion. Some intervals, like the perfect 5th, are really really close to a ratio that can be expressed as a fraction made of two whole numbers.(1.49830707... versus 1.5) so we can't hear much of a difference.

The ratio between two adjacent notes' frequencies in a mathematically perfect equal temperament is the 12th root of 2, which is an irrational number. 1.0594630943592...
If you multiply it by itself 12 times you get the number 2, which is the frequency ratio of an octave.

We hear logarithmically, but the lining up of sine waves would require a rational number for the frequency ratio so it can't be fixed.

And then there's piano tuning, which apparently is all about psychoacoustics and perceived pitch. I don't know anything about that. I just looked at the system of equal temperament as a fun math problem.

Sorry if I bored anybody.

Depending on how it's played, a Buzz Feiten style nut can also help with this.
I've never gone down that road, but some people are into it.
 
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cometazzi

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If you aren't interested in my typical TMI post, my feelings won't be hurt. But here goes in case anybody cares:

No really... this is the sort of thing I was looking for. I figured it had a mathematical basis and that divisions of the octave had something to do with it. The piano definitely sounds different on the intervals to me. Yet, I haven't experienced any deviation between the piano and the guitar when it comes to notes. Maybe i need to listen again...

When it comes to the Buzz Feiten system, it sounds like they move the nut and bridge closer to each other, but that doesn't change the spacing of any of the frets... So other than open, or the ends of the fretboard, I would expect it to still be a compromise near the middle.

Are we just hosed?
 

PhredE

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JS Bach wrote the Well Tempered Clavier 300 years ago. He was keen to the nuances of tempered tuning (of stringed instruments) long, long time ago.

The PBS episode of "Now Hear This" featuring the music of JS Bach, concludes the program with a demonstration of tempered tuning as it applies on the harpsichord.
 

bottlenecker

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There's something that's bugged me ever since I figured out how to play intervals and what they are- On all my guitars at least, I've noticed this:

Play a major or minor third interval, like E and G# or E and G. As it rings out, start pulling the 3rd sharp. At some point, it will start to sound more 'in tune' or more 'even'. I don't really know how to describe it. This effect is especially enhanced with distortion. Is it like this on your guitars too?

There are plenty of guitar recordings where the the intervals are very 'even' sounding, and have that nice symmetrical texture to them. I know this song won't be everyone's cup of tea here, but I promise it won't hurt you. The intervals played throughout the verse (starts from the beginning) sound 'even' as though they've got the 3rds pulled sharp:



That's two guitarists playing two separate tracks. Do you think they're both masterfully pulling those 3rds sharp with their index finger? Or is this some other form of intonation that I'm not experiencing in the small time at home? The guitars in this recording are perfectly in tune everywhere else.

There are other recordings but this seems to be the best demonstration. Has anyone else noticed this, or am I imagining everything?


12 equal divisions of an octave produces intervals that are only close to naturally consonant intervals. No temper fixes this, it just moves problems around.
The third is the worst offender. Any major third in twelve tone equal temperament is 14 cents sharp from the perfectly consonant interval your ear wants to hear.
I used to drive myself crazy tuning my guitar by ear to get chords to sound right before I understood this. (I would tune a G to sound perfect, then C sounded like crap.)
Some things I do with this information: Leave the third out of the chord when a singer's melody is landing on the third.
Invert the third to soften the blow.
Play fretless guitar.
Laugh when guitarists say they like 6 saddle bridges for "perfect intonation".

Some other related bits:
1. A fifth is only 2 cents from perfect. This is why "power chords" sound smooth with distortion, and thirds don't.

2. A dominant 7th chord can be played with heavy distortion and sound as smooth as a power chord, if you tune all of the intervals by ear to their "just intonation" (perfectly consonant) counterparts. And then your guitar can't play any other chord, but it's an interesting experiment.

3. There's a natural harmonic a little behind the 4th fret on the low E string that is a perfect just intoned major third above your open high E string. Compare it to the 4th fret note on your high E to hear how off it is, or just listen to it ring with the high E to hear the sweetness.
 

cometazzi

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12 equal divisions of an octave produces intervals that are only close to naturally consonant intervals. No temper fixes this, it just moves problems around.
The third is the worst offender. Any major third in twelve tone equal temperament is 14 cents sharp from the perfectly consonant interval your ear wants to hear.
I used to drive myself crazy tuning my guitar by ear to get chords to sound right before I understood this. (I would tune a G to sound perfect, then C sounded like crap.)
Some things I do with this information: Leave the third out of the chord when a singer's melody is landing on the third.
Invert the third to soften the blow.
Play fretless guitar.
Laugh when guitarists say they like 6 saddle bridges for "perfect intonation".

Some other related bits:
1. A fifth is only 2 cents from perfect. This is why "power chords" sound smooth with distortion, and thirds don't.

2. A dominant 7th chord can be played with heavy distortion and sound as smooth as a power chord, if you tune all of the intervals by ear to their "just intonation" (perfectly consonant) counterparts. And then your guitar can't play any other chord, but it's an interesting experiment.

3. There's a natural harmonic a little behind the 4th fret on the low E string that is a perfect just intoned major third above your open high E string. Compare it to the 4th fret note on your high E to hear how off it is, or just listen to it ring with the high E to hear the sweetness.

Interesting... I'll need to try the Dominant 7th chord tuned with crushing distortion.

So this brings up another question- un-fretted instruments... say a brass section, or (especially) a string section. Violins, violas, and cellos each playing a single note at a time, stacking up intervals and building chords. Do those end up sounding more 'pure' because each musician is rolling their finger on the string to sharpen or flatten their note to sit in the sweet spot? Or are they robotically bringing their finger down and intonating the note in a mildly-dissonant way because that's what they've practiced a bajillion times? If they all hit their notes by ear and form a perfectly 'even' chord, does that beat against other fixed-note instruments like pianos, organs, or guitars?

Maybe the vibrato is a coping mechanism... egadzooks!

I'll have to find an appropriate symphony and listen again.
 

bottlenecker

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Interesting... I'll need to try the Dominant 7th chord tuned with crushing distortion.

So this brings up another question- un-fretted instruments... say a brass section, or (especially) a string section. Violins, violas, and cellos each playing a single note at a time, stacking up intervals and building chords. Do those end up sounding more 'pure' because each musician is rolling their finger on the string to sharpen or flatten their note to sit in the sweet spot? Or are they robotically bringing their finger down and intonating the note in a mildly-dissonant way because that's what they've practiced a bajillion times? If they all hit their notes by ear and form a perfectly 'even' chord, does that beat against other fixed-note instruments like pianos, organs, or guitars?

Maybe the vibrato is a coping mechanism... egadzooks!

I'll have to find an appropriate symphony and listen again.

Classical musicians, including vocalists, seem to be pretty rigidly trained to adhere to the 12 tone octave. The best example I can think of, of just intonation used to sweeten chords in a progression, would be a capella singing groups. A good barbershop quartet, or west african singing groups like ladysmith black mambazo. It takes a very sophisticated computer, like the human brain, to sweeten intervals on the fly, but maintain common tonal reference. What singers do when they do this is amazing.

I've always meant to try recording a song with each chord recorded seperately and sweetened to just intonation, but I've never gotten around to it.
 
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cometazzi

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Get a fretless guitar? I mean there is always going to be a give and take with the frets. Plus, fret size also can impact it. Lots of variables to consider.

lol... I doubt I'd be able to play a fretless guitar with any level of intonation.

Well, maybe if I really tried and spent a lot of time on it, but I don't know if I've got that much time left. I have seen some videos of people playing fretless guitars, but it's mostly just done as a joke. One of them also had a double-locking trem on it too. weird.

Fretlessly though, I kinda wish I had access to a cello. I think they're really neat.
 

Edgar Allan Presley

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Interesting... I'll need to try the Dominant 7th chord tuned with crushing distortion.

So this brings up another question- un-fretted instruments... say a brass section, or (especially) a string section. Violins, violas, and cellos each playing a single note at a time, stacking up intervals and building chords. Do those end up sounding more 'pure' because each musician is rolling their finger on the string to sharpen or flatten their note to sit in the sweet spot? Or are they robotically bringing their finger down and intonating the note in a mildly-dissonant way because that's what they've practiced a bajillion times? If they all hit their notes by ear and form a perfectly 'even' chord, does that beat against other fixed-note instruments like pianos, organs, or guitars?

Maybe the vibrato is a coping mechanism... egadzooks!

I'll have to find an appropriate symphony and listen again.

We string players definitely think about and practice this. If a violin or other bowed string instrument is playing with a piano, for example, it has to stick with equally tempered intonation. But a string quartet, being all unfretted strings, can be more expressive with it. Major thirds and sevenths are raised a bit and minor thirds lowered for expressive intonation, basically pushing leading tones a little closer to the landing tone to create greater tension and resolution. Or a string quartet or soloist can play closer to just intonation, which would pull the major third a bit lower than it would be in equal tempering.
 
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Blue Bill

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I remember the famous studio players, Tom Tedesco, etc., in magazine interviews, discussing how they continuously are correcting the pitch of each string, as part of their playing. I guess, once you develop the ear and skills to micro-bend any string that sounds flat, it just comes naturally. They say Hendrix was a master at it, probably because he honked on his whammy bar so much.
 

klasaine

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I pull (or push) minor thirds in particular a little 'sharp'. Personally, that's how I hear them.
Guitar is probably the least in tune of all modern instruments and because it's fretted you don't really have the ability to flatten anything. You can only make stuff sharper. Having said that, at this point in my music listening and music playing life - I'm really lenient with slightly out of tune. I don't have perfect pitch. I don't care about perfect pitch and a little out of tune doesn't bug me at all.
 

AJBaker

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Tuning is unfortunately an imprecise science. As others have pointed out, you're fighting a few factors:

- Equal tempered tuning: it's mathematically impossible to have all 12 notes be in tune with each other, so we made a system where all the notes are slightly out of tune in order to make the whole thing work. The thirds are the notes that are the furthest from being in tune.
This means that if you tune your (perfectly intonated) guitar perfectly with a digital tuner, certain notes will still sound a bit off.

- Guitar intonation is approximate:
With straight frets and a straight nut, it isn't possible to perfectly intonate a guitar. Some notes will just be a bit off no matter what you adjust. I usually end up intonating to have frets 1-5 sound as good as possible, which often means the higher frets sounding a touch flat (which I compensate for with bending and vibrato).
 

JIMMY JAZZMAN

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Intonation is give and take to begin with. Your in open and out at the 12th fret. You compromise the
best you can. Yes, sometimes you pull your string, to be dead on (if need be) and on some solos
that's necessary, but other times it actually sounds better (blues, jazz) to be a couple "cents" off.
 




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