I have scoured through the SGF archives looking up all the old topics about just intonation vs. equal temparament. I think I understand the basics, and have used JT with much success on my pedal steel. But let me now take the discussion to 6-string guitars....

After purchasing a new electric guitar, I took it to my guitar tech for some minor adjustments to the neck and bridge. Upon picking it up, I was amazed at how good it sounded.....he had used a strobe tuner to tune it up for me. Every open and barred chord I played sounded in perfect tune.....wonderful!

Now I should say that I generally use a chromatic digital tuner to tune all strings to 440 (equal temperament), though for other instruments I use just intontation (specifically, my pedal steel). However, I always felt that my other 6-strings sounded a bit "off"...especially the G string.

Anyhow, when I got the guitar home, I immediately hooked it up to my digital tuner to determine how it was tuned on the Hz scale. Specifically, the EBGDAE strings were tuned to 440Hz, 438Hz, 437Hz, 439Hz, 439Hz, 436Hz respectively.

So, my question is this: does a strobe tuner tune all open strings to 440Hz (meaning that my digital tuner needs calibration)? Or, does it tune all strings to a reference of A=440Hz (which I presume means that, say, the D-string would not tune to 440Hz, but rather, as in this case, 439Hz)? I presume that if the latter case was true, a stobe tuner is NOT used for equal temparament?

I'm certain that some of this sounds foolish to those of you with very advanced musc theory....I am hoping that you can help to get me to understand WHY my guitar sounds better when all the strings are NOT tuned to 440.....and why MOST guitarists DO tune their open strings to 440.

Looking forward to your responses....thanks!

Confused in Indianapolis....

Joe

[This message was edited by Joe Alterio on 20 May 2002 at 08:03 AM.]

440Hz is a specific note which vibrates 440 times a second (a synonym for Hz or Hertz is cycles/sec). ONLY that note, which happens to be A below middle C, vibrates at 440Hz.

Here's the confusing part . . .
On most tuners, there is a Hertz scale that makes it look like you are tuning everything to 440. NOT TRUE. In that case, all strings would be tuned to the SAME NOTE. What turning the dial or switch to A440 will do is to calibrate all notes to be in tune with that note. In other words, the A note is part of the C scale, so the C is not tuned TO 440 it is tuned RELATIVE TO 440.

IF YOU TUNE EVERY STRING OF ANY GUITAR (Spanish, lap, pedal, whatever) RELATIVE TO A440, your open tuning is in Equal Temperament. The most notable objections your ear will make is the thirds and, to some extent, sixths. So, in an EMajor-based tuning, G#s and C#s will sound sharp to your ear, which likes to hear JUST INTONATION.

Now for the Spanish guitar, specifically. . .
How you tune a six-string depends on how you're gonna use it. What the guitar tech did was probably tune with equal emphasis on all of the typical positions and found the happy medium. This is the only way that, for example, an open E, open G, open D, open A, and barred chords can all be (almost) in tune. If you use all those positions in a given song or in a given session, that may be a good solution for tuning your guitar. If you're playing Rocky Top on an acoustic, you may want to optimize the open G chord (assuming you're playing in G).
The answer to your question about why your guitar sounds best tuned like it came from your technician is that it's WHAT YOUR EAR LIKES TO HEAR. (Just Intonation)

Guitarists who tune all notes relative to 440 are only perfectly in tune for that one open chord -- which nobody ever really uses. Most guitarists that I work with generally tune into the 'ballpark' with the tuner and do the rest by ear. That is also the way I tune a guitar (and my steel, for that matter).

Hope this doesn't just muddy the waters further.

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Larry Bell - email: larry@larrybell.org - gigs - Home Page
2000 Fessenden S-12 8x8, 1969 Emmons S-12 6x6, 1971 Emmons D-10 9x9, 1971 Dobro

[This message was edited by Larry Bell on 20 May 2002 at 08:48 AM.]

Here is the way it works out in real frequencies as opposed to "relative" frequencies.

Using the A note as a reference, the following is the actual frequency of each of the 12 notes from A to octave A (880 down to (440).

A--880
G#830.6093952
G--783.9908720
F#739.9888454
F--698.4564629
E--659.2551138
D#622.2539674
D--587.3295358
C#554.3652620
C-523.2511306
B--493.8833013
A#466.1637615
A--440

Now, when your meter shows a C# as "440" it is referenced to the bottom A note. However the actually frequency is NOT 440 cycles per second (HZ), but actually 554.3652620 cycles per second. It just makes it easier to say 440 rather than to try and quote those awful frequencies above and below 440 (octaves excluded).

To explain WHY JI (Just Intonation) sounds better than ET (Equal Temperament) check out the following scenario:

Look at 2 of the above notes. The bottom A and the E notes. Notice their relation to each other. Obviously the A at 440 is easy to see. Now look at E. The ear WANTS to hear 660!!. Why? (*See below)

IF it had worked out in the "physical" world that our E notes tuned to ET were in fact 660, this thread and all related threads would never have surfaced. But in life, things are NOT that simple. The E note is NOT 660. Rather it is a part of a cycle less than 660.

What this says is, when tuning the A and the E to a "perfect fifth", we can get away with it pretty much, BECAUSE we are still so very close.

NOW lets look at a much more serious situation. Compare the A note with the C# note. As the Wizard of OZ said to Dorothy when she asked about the purple horse,
"That's a horse of a different color!!"

Notice if you will, the C# is NOT 550. NO where near it. The C# note (ET) is over 5 cycles sharp of 550, which the ear loves to hear. This is why the thirds sound soooooo bad to most ears.

So, most steel players flatten their thirds approaching more or less that magic 550 HZ. By the way, 550 HZ relates to 440 in this way. If you take 440 and divide it in half and then in half again you get 110. If you add that back to 440, you have 550. This means C# (JI) is the 2nd subharmonic of A.

The same holds true for the E note. If you divide 440 in half (220) and add it back to 440 you get 660. So the E note (JI) is the first subharmonic to 440.

It is interesting to note that when we tune for perfect 5ths (or 4ths) we are actually tuning JI. Because in ET they are NOT perfect.

If the above is confusing, don't give it a second thought. ONLY us technical nuts crave it anyway Just tune and play your guitar the way YOU want to and be happy.

May God richly bless you all,

carl

* Most ears love harmonics and subharmonics. They do NOT like any other blends.

[This message was edited by C Dixon on 20 May 2002 at 09:25 AM.]

If the E note is tuned to 330 Hz, the G# would be 330 X 5/4 = 412.5 Hz.

All of this is why a lot of us prefer to use the cents scale instead of Hz. The cents scale tells you how far from ET you are. A just major third is 15 cents flat of ET, no matter what frequency it is.

As for your guitar question, Joe, I think Larry really summed it up nicely. Write down those numbers if you like them. But listen carefully to what that tuning does to unusual chord positions first. You might find that some jazz chords (esp. diminished) really sound "odd" with this tempering.

quote:

---

ONLY that note, which happens to be A below middle C, vibrates at 440Hz.

---

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Larry Bell - email: larry@larrybell.org - gigs - Home Page
2000 Fessenden S-12 8x8, 1969 Emmons S-12 6x6, 1971 Emmons D-10 9x9, 1971 Dobro

Ahhh....you all are great! Thanks so much for spending some time clearing this up for me. Special tip of the hat to Larry

I'm curious, though....has anyone actually come up with a Newman-type chart for 6-string acoustic/electric guitars that would get you in the ballpark for JI? (i.e. A at 440, low E at 437, etc.)

One thing I've noticed....now having tuned my electric 6-string with JI, I sound very much in tune with the records I play along with. Is it possible that MOST pro musicians tune their instruments with JI and not ET?

Thanks again for your insights....

Joe

[This message was edited by Joe Alterio on 20 May 2002 at 08:48 PM.]

If it sounds right, it is right.

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Larry Bell - email: larry@larrybell.org - gigs - Home Page
2000 Fessenden S-12 8x8, 1969 Emmons S-12 6x6, 1971 Emmons D-10 9x9, 1971 Dobro

As I was watching the tech tune the guitar with his strobe tuner, he did nothing more than turn the switch to the note he was playing...nothing else. In other words, he wasn't adjusting the Hz for each string to tune it to, say, 438 instead of 440 like we do with our chromatic tuners for the steel. My thought was that a stobe tuner performed the same function as a digital chromatic tuner....if you want everything set to reference 440Hz, just the dial set at 440, and only change the note dial while you are tuning. Since my digital tuner was reading different Hz for each note, could it be that the tech and his strobe tuner truly WERE referencing one specific Hz (and my own tuner needs calibration)? Or does a strobe tuner work differently than a digital one?

Thanks yet again

I don't think it's as much the fact that it's a strobe vs a standard digital tuner (I could be wrong and suspect the Peterson folks might disagree) as it is the ability to store the fact that you want E's and B's at 0 cents and G#s at -14 cents and all the other temperament data. Once it's stored you recall the data and it automatically uses the deflections you set. Most of the high end tuners allow you to store multiple temperaments -- so that would allow you to use different numbers for steel and guitar.

Maybe I'm a curmudgeon (or a tightwad), but most any tuner that's accurate and roadworthy will work ok for me.

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Larry Bell - email: larry@larrybell.org - gigs - Home Page
2000 Fessenden S-12 8x8, 1969 Emmons S-12 6x6, 1971 Emmons D-10 9x9, 1971 Dobro

I don't know about the tech's strobe tuner. BUT, several strobe tuners on the market today, have adjustments to shift certain notes AWAY from 440 reference even though the strobe says 440.

Could it be that is what happened here? It occurs to me that IF his tuner was calibrated to pure ET, your readings at home would have ALL been 440 (excluding some temp changes between his place and yours.

Anyway interesting,

I DON'T expect a tuner to
* know what sounds good
* make any decisions/judgements

A tuner is nothing more than an electronic measuring device that inputs a complex analog signal (a vibrating string) and does the best it can to home in on the predominant fundamental frequency and compare it to a standard. As my friend, Sir Richard, so astutely points out in a slightly different context, buying a new tuner will do very little to help one play in tune (a separate issue ENTIRELY from tuning).

I use a tuner for two things:
* a glorified, electronic tuning fork to get ONE NOTE to tune by
* a tuning aid for use in noisy situations where I don't have the luxury of carefully tuning by ear

The first use allows me to find 'concert pitch' and create or tweak my tuning chart, which I use for the second application. I choose not to carry headphones -- just my own choice -- so I need to be able to see my tuning in certain venues, like noisy clubs with loud jukeboxes or dinner establishments where we've been asked to avoid disturbing the audience before the show starts.
The ability to store temperament information in the tuner only makes use #2 a bit easier -- you don't have to bring your chart with you or memorize it.

I also believe that the place to tune one's pedal and lever pulls is AT HOME. Only tuning open strings, plus necessary minor tweaks to the string pulls should be necessary on the bandstand, IMHO.

Truth be known, my favorite way to tune is #1: "gimme an E".

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Larry Bell - email: larry@larrybell.org - gigs - Home Page
2000 Fessenden S-12 8x8, 1969 Emmons S-12 6x6, 1971 Emmons D-10 9x9, 1971 Dobro

[This message was edited by Larry Bell on 21 May 2002 at 11:44 AM.]

The following is a reprint of THE GUILD OF AMERICAN LUTHIERS data sheet #45.

Many guitarists are frustrated because of their attempts to tune the guitar to pure chords (free of beats). These particular players have very sensitive ears that prefer pure intervals and reject the mandatory equal temperament. They tune their guitar beautifully pure on one chord only to discover that the next chord form is unacceptable. In too many instances they assume that there must be a flaw in the workmanship on the fingerboard. Their problem is not in the construction of the guitar. It is one of pure tuning verses equal temperament.

You must accept this compromise because the guitar is an instrument of fixed pitch and the strings must be tuned to tempered intervals, not pure. Equal temperament is the name given to a system of dividing the chromatic scale into 12 equal half steps. Guitarists who have been trying to tune to one or another pure chord form must learn to understand and accept equal temperament. (They might be interested to know that to approximate pure chords on all forms would require about three dozen frets within the octave.) The system of equal temperament reduces the number to twelve, thereby making manageable all instruments of fixed pitch.

Here is what all of this means to the guitarist: You must not, at any time, use harmonic tones at the 7th fret as a point of reference (skilled piano tuners could use them because they know how many beats to introduce between 4th and 5th). Harmonic tones at the 7th fret are pure 5ths, while in equal temperament each 5th must be lowered slightly. To tune by harmonics at the 7th fret (as occasionally ill-advised) will make the guitar sound entirely unacceptable on some chord forms.

On the other hand, all harmonics at the 12th and 5th frets, being one and two octaves above the open strings, are immediately useful as explained below. All octaves and unisons are pure on all instruments of fixed pitch.
Therefore, you may use harmonics at 12th and 5th as reference tones in the following tuning instructions.

Actually this discussion and the following suggestions are for those players who have been tuning to pure intervals. When the steps have been followed correctly the guitar will be as perfectly tuned as it could be in the hands of a professional. Nevertheless, when you have finished, your sensitive ear may notice that on each major chord form there is always one tone slightly high. If you start adjusting a particular string on a certain chord form, you only compound the problem because then the next chord form will be completely objectionable. Tune the guitar as instructed below and let it stand. How to help your ear accept equal temperament: It is easier to face a problem if we are prepared in advance and expect it. If you are one of those
persons who is sensitive to pure intervals, here is what you are going to notice on an absolutely perfectly tuned guitar in equal temperament: Play an open E major chord. Listen to G# on the third string and you most likely will want to lower it very slightly. Don’t do it. Ignore it. Enjoy the overall beauty and resonance of chord just as does the pianist.

That troublesome second string: Play an open position A major chord. Listen to the C# on the second string and you may want to lower it slightly. Play a first position C chord and listen to the E on the first string and fourth string at 2. These tones are slightly higher than your ear would like.

Now play an open position G chord. Listen to B on the second string. Yes, it would sound a little better if lowered ever so slightly. Why not try it? Slack off the second string a couple of vibrations and notice what beautiful G chord results. Now play the C chord and with that lowered second string, and you are going to dislike the rough C and E a lot more than before. Take the open B, second string back up to equal temperament so that it will be equally acceptable on all forms. Learn to expect and accept the slight
sharpness of the major third in each chord (and oppositely, the flatness of the minor third in each minor chord). Train your ear to accept tempered intervals and you will be much happier with your guitar.

PROCEDURE:

Tuning the 1st and 6th strings: The E, open 1st string, must be in pure unison with the harmonic of the E, 6th string at the fifth fret. When these two strings have been properly tuned with each other, continue as follows.
Tuning the 4th string: Play a harmonic on the (in tune) 6th string at twelve, and as this harmonic sounds, adjust the 4th string until the tone E on the second fret is in pure unison. Now you have the E, open 1st string,
1st on the 4th string at two, and E, open 6th string tuned pure (permissible because they are octaves).

Tuning the 2nd string: Play a harmonic on the (in tune) 4th string at twelve. As this sounds, adjust the 2nd string until D at the third fret is in pure unison. As you have used two fretted tones for references and as the
frets are positioned for tempered intervals, you now have the open 1st, 2nd ,4th and 6th strings in tempered tuning.

Tuning the 3rd string: As it is easier to adjust a string while listening to a continuous reference tone, you may first try the following: Play a harmonic on the (in tune) 4th string at twelve and as this sounds, adjust
the 3rd string until D at the 7th fret is in pure unison.

Double check: Now make this check to see if you have been accurate or if the instrument plays tune when fretted at seven. Play a harmonic on the (now tuned) G string at twelve, and as this tone sounds, play G on the 1st string at three. The two tones should be in pure unison. If they are not, either you are at fault or the instrument doesn’t fret tune at seven. Go back to the beginning and carefully check each step up to this point. If the tones are still faulty, then readjust the 3rd string until the harmonic at twelve is in unison with the 1st at three. Do not tamper with the 1st and 4th strings because it is the 3rd string you are trying to bring in tune. When
you have the 1st, 6th, 4th, 2nd and 3rd strings in tune, in that order, continue with the remaining 5th string.

Tuning the 5th string: Play the tone A on the (in tune) 3rd string, at the second fret. Listen to this pitch carefully and now adjust the 5th string until the harmonic at twelve is in pure unison. When the foregoing steps are
followed correctly, the strings will be tuned perfectly to equal temperament. No further tuning adjustments are permissible.

*************

I'm still a proponent of 'ET until the hair on the back of your neck stands on end'. Some people can tolerate ET thirds more easily than others. I can't go much closer than -8 or -10 without what Buddy calls the 'pucker factor'.

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Larry Bell - email: larry@larrybell.org - gigs - Home Page
2000 Fessenden S-12 8x8, 1969 Emmons S-12 6x6, 1971 Emmons D-10 9x9, 1971 Dobro

[This message was edited by Jeff Lampert on 21 May 2002 at 07:51 PM.]

Larry/Carl: I believe what you said may have been the case....I guess strobe tuners have settings that allow for "sweetened" tuning, so even though all the tech was doing was flipping the note switch, the tuner was inherently adjusting the Hz he was tuning to. Interesting!

The thing that surprises me is that I did hours of searching on usenet archives on this subject (as it pertains to 6-strings), and it is hardly ever mentioned. Strange...

Interestingly enough, my acoustic sounds great when everything is tuned using A=440Hz. It is all my electrics that do not.

Again, thanks everyone for your input....gotta love this forum!!!

Joe

[This message was edited by Joe Alterio on 22 May 2002 at 07:30 AM.]

You spoke of how good it sounded at the shop but you didn't mention how it sounded at home. If it was worked on, it probably had new strings as well which added to some of the strings slipping south of 440.

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Sierra S12 8+5 A6/D9
Good tunes

The guitar sounded great both at the shop and at home....I did not notice any change in any of the strings' pitch. This, after playing the guitar for a good 15 minutes at the shop and another good 15 minutes at home. Thus, I am extremely sure that how it left the shop is almost exactly how it arrived at home.

Thanks again everyone for all your responses! I think I'm going to have to get some advanced music lessons or something

Try this experiment on your "fixed pitch" fretted instrument. I used a TU-12H digital tuner, with the meter, for a little experiment on my perfectly setup Strat. Strings are not new, about a week old. Normal 6 string guitar tuning.EBGDAE (1-6)

Tuned all open strings to straight up. (ET)
Formed a first position E chord, then hit each note of the chord while watching the meter.
Open E 6th string was still straight up.
5th string B was 4 hz sharp.
4th string E was 1 hz sharp.
3rd string G# was 1hz sharp
2nd string open B was straight up.
1st string open E was straight up.

Played all strings open again, and still straight up.

Played a barred B chord at the 7th fret and all notes were very close to straight up. No more than 2 cents variation.

The harder one presses on a string between frets, the sharper the note. It was easy to sharpen a note 4 hz (16cents). Put your finger gently in the middle, and you get a straight up note.

Ever notice that many great acoustic players have a capo on the second fret? One does not have to push the string down as far to fret a note. Better intonation, easier on the fingers, easier on the ears.

This explains how vibrato works on a fretted instrument. The pressure on the string varies.

So what?

An imperfect scale (ET), plus an imperfect guitar, plus imperfect finger pressure equals imperfect notes.

Fixed pitch instrument? In a perfect world maybe.

An experienced player deals with all this. Fretted strings in a chord are bent slightly to compensate. The neck is pulled or pushed ever so slightly. A big vibrato can cover a lot and sound great.

I am glad it is still an art. The science can explain, but it still takes good hands to please the ears.

Or get enough distortion, delay, reverb, compression, chorus flangers, pitch shifters and play loud as hell.

quote:

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Ever notice that many great acoustic players have a capo on the second fret?

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Might be able to go up in gauge, but string rattle on the frets might be a problem. Depends on fret height, nut height, neck angle, etc.

Jazz players probably would not do this. Jazz chords are mostly closed, and they use the whole neck.

The above link does a great job of explaining intonation, tuning, pitch harmonics, equal temperment,