Tune ANY Tuning via Just Intonation

Rick Aiello · Post by **Rick Aiello** » 15 Feb 2003 1:19 pm

Here is a method that allows you to tune a guitar via Just Intonation ... FOR ANY TUNING ... C6, E9, E13, F#9, D9, C#m, E7 ... etc.

I could make up a seperate tuning chart for each tuning

or you could take a few minutes to figure out what I'm doin' here and make one up yourself ... and use it until you have it memorized ... Harmonic Heaven

--------------------------------------------

Harmonic tuning for Stringed Instruments

The first number indicates the "Chime/Scale note Position". Their positions on the fretboard are as follows:

The 3rd is found just a bit off of the 4th fret (toward the nut) or at the 9th fret ...

The 5th is found at the 7th fret.

The tonic 1st is found at the 5th or 12th fret ... depending on the octave desired.

The second number is the "Initial" reference note. The note that the "chime" is "applied to".

The third number is the "Resultant" note that is produced by this action.

Example:
Tuning the E(3)string to the C(1) string in C6 tunin'.

The 3rd of the 1 is the 3 ..

1) Ring the "chime" at the 4th fret of the tonic C string ... you get a JI "E" (3) note

2) Then ring the chime at the 5th fret of the E string ... you get an E note in the same octave as the JI E produced by chiming the C string

3) Tune the E string until you no longer hear the beats (wah-wah sound ... the closer you get to pitch ... the slower it gets ... when you no longer hear it ... bingo).

Now the overtones produced by your C string will not clash with the fundamental or overtones of the E string.

Here goes

The Thirds
<pre>
The 3rd of the 1 is the 3
The 3rd of the 3b is the 5
The 3rd of the 4 is the 6
The 3rd of the 5 is the 7
The 3rd of the 5# is the 1
The 3rd of the 6 is the 2b
The 3rd of the 7b is the 2
</pre>

The Fifths
<pre>
The 5th of the 1 is the 5
The 5th of the 3b is the 7b
The 5th of the 3 is the 7
The 5th of the 4 is the 1
The 5th of the 5 is the 2
The 5th of the 5# is the 3b
The 5th of the 6 is the 3

</pre>

Now the cool one .... it is useful when the "Initial" reference note is not present in the open tuning.

Thirds & Fifths
<pre>
The 3rd of the 5 is the 5th of the 3 ....... 7
The 3rd of the 5# is the 5th of the 4 ........1
The 3rd of the 7b is the 5th of the 5 ........2 **Extremely handy**
The 3rd of the 1 is the 5th of the 6 ........3
The 3rd of the 3b is the 5th of the 1 ........5

</pre>

It is not always convenient to tune via harmonics ... so here are the JI deviations from ET for using an electronic tuner.

<pre>
Scale Note Deviations from ET(cents)

1 0
2b +12
2 +4
3b +16
3 -14
4 -2
5b -10
5 +2
5# +14
6 -16
7b +18
7 -12
1(8) 0

* These are the 5-Limit JI deviations
</pre>

Now there are a couple of things to be careful of ... the main one involves having a tuning with the 2,5,6 all present ... can't get it beatless ..

Nothin's perfect !!!

------------------
www.horseshoemagnets.com[This message was edited by Rick Aiello on 27 November 2003 at 07:44 AM.]

Andy Volk · Post by **Andy Volk** » 15 Feb 2003 3:17 pm

Thanks Rick!! Very kind of you to post all this - lots to consider. My father-in-law (long associated with the American Association for the Advancment of Science) would be proud.

Rick Aiello · Post by **Rick Aiello** » 15 Feb 2003 3:56 pm

I'm in the middle of checkin' the math ... so check back later ...

I did this about 15 yrs ago ... and I remembered that some of the combinations don't work ...

I'm self correcting

------------------
www.horseshoemagnets.com

Rick Aiello · Post by **Rick Aiello** » 15 Feb 2003 4:52 pm

Ok, think its done now ...

Enjoy

Page Wood · Post by **Page Wood** » 15 Feb 2003 4:52 pm

I'll continue my thought from the previous thread- I think this is worthy discussion...
it seems to me that for another player to throw you off, he's got to be really FLAT- I mean a quarter tone or more off. The steel guitar is a folk instrument- whacky intonation is part of the sound. Besides, all your exact tuning only counts on an open string- as soon as you go for a barred note, you're at the mercy of your ears. I'm not saying there is no place for JI, I just don't see why it would be an issue with steel guitar. Am I wrong here?

Rick Aiello · Post by **Rick Aiello** » 15 Feb 2003 5:12 pm

Page, I'm just tryin' to help out some folks that may not be aware of how to do this.

Besides, all your exact tuning only counts on an open string- as soon as you go for a barred note, you're at the mercy of your ears.

As I stated in the other thread ... setting your open strings to JI is like using the "starting blocks" in track (sprints)...

It gets you in the best position to start your job ... to play beautiful music.

The steel guitar is a folk instrument- whacky intonation is part of the sound.

I think some folks will disagree ... I do.

------------------
www.horseshoemagnets.com [This message was edited by Rick Aiello on 15 February 2003 at 08:31 PM.]

Jesse Pearson · Post by **Jesse Pearson** » 15 Feb 2003 7:12 pm

Page, if your going to continue on from the other thread, maybe it would become clearer to some of us as to what your getting at if you would please explain what you were asked to explain already concerning your statement that "the fiddle and bass player not keeping up are playing flat"? The drummer Elvin Jones talked about color tones, I don't, and I also have played bass for a few years professionally. The sax is a very unstable instrument pitch wise, which is why it is not used in Symphonies. You have to really work it to stay kinda in tune up and down it's range, which is kinda the point I think your trying to make. The sax works great because of this for some types of music and others it doesn't do so well. I think we will understand your point better if you go into your original statements just a little deeper. Thanks...

Page Wood · Post by **Page Wood** » 16 Feb 2003 1:46 am

Ok, if you want to play like Jerry Byrd, that would demand a level of surgical precision involving Just Intonation (and as Rick has informed me, he insists on it!) But I would think for the rest of us mortals playing blues in a bar band, JI would be opening a can of worms in an ET setting- that is, if anyone's ears are sharp enough to catch it! I'm a big fan of "close enough for rock'roll"- a lot of the charm for me is in that tension created by (very slight!) deviations in tuning. When two instruments play the same line in unison, the sound is much fatter if they aren't perfectly matched (much like the effect of a chorus box, or a glee club chorus, for that matter). I find the same to be true with steel guitar slants (split slants!)- the off intonation gives it that special character.But I'm talking about the tight tolerances of intonation- my comment about the "fiddle player not keeping up " meant this: If another player is so far out of tune it's throwing you off, he probably doesn't have an intonation problem- he's flat out FLAT! His tuning being a quarter tone or more off. Now that isn't charming- dock him 5 bucks...

Rick Aiello · Post by **Rick Aiello** » 16 Feb 2003 4:16 am

Surgical precision ...

The first tape I sent to JB, years ago, was 1 song ... I had worked on all my "skills" ... had all my strings tuned "perfect" (ET, straight up) with a Korg tuner ... I was excited and proud.

Less than a week later, I got a letter back ... and he said to the effect "Rick, I listened to a couple of measures ... and had to turn it off ... throw away that &$#@ electronic tuner and learn to tune using Just Intonation".

At that time I had NO IDEA what JI was ... so in my usual fashion .. I started readin', studyin' and practicing ...

These "charts" .... posted above, Tuning in JI ... and here, Playing in JI ... Are the results of that work.

The next year, I sent him another song ... he told me about 1000 things to correct ... and ended the letter with ..."Rick, at least you figured out how to tune your guitar".

Page, as far as blues goes ... do you think Robert Johnson or Muddy Waters tuned ET ???

Put an open ET E tunin' on your steel ... and hit a big ol' A chord with a nice saturated amp .... record it. Do the same now with your E tuning tune via JI ... Ah !!

As I stated in the other thread ... Get your steel in tune with itself first and foremost ...

Let the tension you like and enjoy be built between you and your bands ET tuned instruments ... Not between your guitar's strings ....

Kinda like havin' your cake and eatin' it to ... you get the JI sound that is heard on all your hero's steel guitar records and you get the "chorus effect" tension by playin' with ET backup ....

Just my opinions of course

This JI vs ET war ... it never ends

------------------
www.horseshoemagnets.com [This message was edited by Rick Aiello on 16 February 2003 at 07:18 AM.]

Jesse Pearson · Post by **Jesse Pearson** » 16 Feb 2003 7:47 am

You guys are some of the hippest, deepest thinking musicians I have yet run a cross. The famous guys I've been lucky enough to personally meet, have never gone in to the cool insights (Rick) I keep getting from you steel players. Its no wonder a steel player set up all the mikes and levels on the amps for Stevie Ray Vaughns first two albums. Page thanks for going a little deeper.

Bob Stone · Post by **Bob Stone** » 16 Feb 2003 9:49 am

Thanks for the great post Rick. I'm gonna try some JT. Your anecdote about Jerry Byrd telling you to tune your guitar contains a strong lesson.

Thanks again.

Page Wood · Post by **Page Wood** » 16 Feb 2003 10:53 am

Robert Johnson tuned JI?? I didn't know that!
Jesse, I'm no expert on this subject- I just have my opinions. I was really hoping those who are would chime in- maybe more on this in the archives...(or too much!)

Rick Aiello · Post by **Rick Aiello** » 16 Feb 2003 11:12 am

Thats what Legba told me when I was at the crossroads with my Ricky Frypan

Seriuosly, it is a pretty safe assumption that any of these greats from the past (and present) who used open tunings and "tune by ear" are using JI ... they just might not know the term.

Alot of steelers don't use the harmonic method to tune JI ... they just tune the strings till the "beats" are gone ... its still JI....

But by using harmonics ... the fundamental (which can be overpowering ) is eliminated and the crisper/clearer overtones (partials) are easier to hear and manipulate ... For me anyway.

------------------
www.horseshoemagnets.com [This message was edited by Rick Aiello on 16 February 2003 at 11:39 AM.]

Bobby Lee · Post by **Bobby Lee** » 16 Feb 2003 1:23 pm

Page Wood wrote:

But I would think for the rest of us mortals playing blues in a bar band, JI would be opening a can of worms in an ET setting

The 3rds and flatted 7ths in blues are about as far from ET as any modern music gets. Guitarists are always bending strings, bassists play fretless, and vocalists sing what feels right. Blues in ET just sounds wrong, IMHO. That's why you can't get decent sounding blues from Band-In-A-Box or from a sequencer. The real blue notes are in the spaces between the equally tempered notes.

Trust your ears.

------------------
<img align=right src="http://b0b.com/b0b.gif" width="64" height="64">Bobby Lee - email: quasar@b0b.com - gigs - CDs
Sierra Session 12 (E9), Williams 400X (Emaj9, D6), Sierra Olympic 12 (C6add9), Sierra Laptop 8 (D13), Fender Stringmaster (E13, A6), Roland Handsonic[This message was edited by Bobby Lee on 16 February 2003 at 01:27 PM.]

Page Wood · Post by **Page Wood** » 16 Feb 2003 6:46 pm

wow... are you saying that the origin of blue notes themselves may have been the result of early bluesmen trying to deal with JI without really knowing what it was? That's a remarkable thought...

Jesse Pearson · Post by **Jesse Pearson** » 16 Feb 2003 7:51 pm

Bobby, I just can't reconcile that hypothesis. Not concerning band in the box, I have never used that, but blues bands haven't used fretles bass since Leo Fender showed up for the most part. In guitar bends, a good practice is bending up to the same intervals , that the keyboards and bass and rhythm guitar are using. This is where I think alot of us are having a hard time with this stuff. I concede that I wasn't tuning the steel up right, but I have never heard any pro blues players teach what your saying. Rick said the harp is tuned to JI and I need to test this out on my own harps. The chorus effect that Page talked about makes sense and would explain the harp working so well. I mean, it would mean I have been wrong most of my life and also most of the players I have played with. Man, this is some heavy stuff, back to the drawing board I guess.

[This message was edited by Jesse Pearson on 16 February 2003 at 07:57 PM.]

Bobby Lee · Post by **Bobby Lee** » 16 Feb 2003 8:41 pm

I don't think that most blues players even think about such things. The harp is obviously JI to start with, and harp players bend the notes from there. The idea of nailing a note to the 12th root of 2 is alien to the very basis of blues: emotional expression.

Whether the bass is fretless or fretted, he's only playing one note at a time. There's no interval to calculate, and tone-wise he's in his own own space. The root and 5th of a chord in ET vs. JI is only a 2 cent difference. Those are the bass notes that people are building the chords above. What's the difference if the bass player's thirds are JI or ET? Who notices?

Piano... Ever notice how a good blues piano player treats the thirds and sevenths? With the major third, it's often next to a flatted third grace note. With the dominent 7th, it's often next to a major sixth grace note. That's because the singer, sax player, harmonica player or slide guitarist who's doing the real melody is playing JI notes in the spaces between those intervals. By fudging one note with the chromatic note adjacent to it, the pianist approximates the real blues tones. That technique is a staple of the blues piano sound.

The Hammond organ, another staple in blues, uses a dopler effect from a Leslie to obscure the actual pitch. No one can tell if the beats are coming or going.

Calling a guitar an equally tempered instrument is a real stretch. Many guitarists tune a handful of chords by ear, and that's that. In blues, open E and open G tunings are plentiful. Those are JI tunings - they sound awful any other way. Even if a guitarist says he tunes ET, he bends strings to pitch using his ear, which will give him JI every time. I've yet to meet a human who could nail ET pitches by ear, while performing.

The 20th century taught us to accept thirds that were up to 15 cents sharp, but it didn't teach us to reject harmonies that obeyed the laws of physics. Equal temperment is a very convenient suspension of disbelief in the ear of the listener. It allows us to develop more advanced musical systems that include free modulation on fixed-pitch instruments. But it doesn't make just intonation sound bad. If you adhere to the physical laws of harmony, and build your chords on the same root that everyone else is using, you can't sound out of tune.

If it sounds in tune, it IS in tune.

------------------
<img align=right src="http://b0b.com/b0b.gif" width="64" height="64">Bobby Lee - email: quasar@b0b.com - gigs - CDs
Sierra Session 12 (E9), Williams 400X (Emaj9, D6), Sierra Olympic 12 (C6add9), Sierra Laptop 8 (D13), Fender Stringmaster (E13, A6), Roland Handsonic

Rick Aiello · Post by **Rick Aiello** » 16 Feb 2003 8:53 pm

I've done about as much damage to this subject as I can ...

Jesse, you can get ET Harmonicas ... but most are JI ... check this site out .. it gives a side-by-side audio comparison of JI vs ET harmonicas ...

http://www.patmissin.com/tunings/tunings.html

------------------
www.horseshoemagnets.com[This message was edited by Rick Aiello on 16 February 2003 at 08:59 PM.]

Jesse Pearson · Post by **Jesse Pearson** » 16 Feb 2003 9:21 pm

Bob, when I tune up a guitar to open G or open D, using my boss turner which is EI, I'm dead on to Johnny Winter, Blind Willie Johnson, Robert Johnson ect. Same thing goes with a regular guitar doing Stevie Ray or Eric Clapton ect. When I tune up with the EI tuner, no one has ever complained about my tuning as long as the intonation on the instrument is right. This is what I don't get. I don't know what to make out of this stuff cause I know you guys know what your talking about. I gotta start recording and testing all this stuff and take it from there, but thats why I'm here anyways, trying ta get it together. Thanks for your help...

Hi Rick, I'll give it a listen. You haven't done any damage, just the opposite in fact. [This message was edited by Jesse Pearson on 16 February 2003 at 09:27 PM.]

Page Wood · Post by **Page Wood** » 16 Feb 2003 10:19 pm

Nice one Rick- I can't believe you just pulled that site out of a hat...
I listened to both (all three?) samples- and I say my ear buys all of them- they all sound CORRECT (or in tune). But what's really cool is each has a different INFLECTION- or color - like when your voice goes up at the end of a sentence to form a question.I think Bob is right that you buy ET because your used to it, but you also buy JI because it's correct.

Jeff Au Hoy · Post by **Jeff Au Hoy** » 17 Feb 2003 1:09 am

Rick Aiello · Post by **Rick Aiello** » 17 Feb 2003 4:04 am

Yep

Jesse Pearson · Post by **Jesse Pearson** » 17 Feb 2003 8:00 am

If Jeff is tuned to the guitars E, is the guitarist using a standard tuner, tuning fork or the piano to tune up to. They are all EI right? That would mean Jeff's E is not at (-14) from an EI pitched E right? That would throw all of his other strings off from JI.

I can't believe that somebody didn't hip Johnny W. to this, if they had we guitarist who play bottle neck would know about it by now. I have been record copying for along time, I have good relative pitch but have seen much better. When I play bass on blues, I walk it alot like the guy with Albert Collins. Isn't it true that players with perfect picth are at odds alot of times with other instruments being alittle out, to the point it drives em nuts?

What Bob said about everyone tuning to the same root makes alot of sense. Your point of reference at the starting gate must be everything. Who's gonna notice, JB did, he must have perfect pitch? Rick, what about Jeff's high E string?

Rick Aiello · Post by **Rick Aiello** » 17 Feb 2003 9:01 am

Jesse, as I said in the original post (last year) .... it is pretty standard amoung JI steel guitarist using ... say C6 ... to tune the C string about 5-10 cents sharp of its ET value initially ... and go from their.

That way their E and A are not too far from the E & A of the rhythm guitar.

I understand JB does as Jeff does ... tunes his E to standard pitch (ET) ... therefore their C is 14 cents sharp to ET ... their G is 16 cents sharp to ET... and the A is 2 cents flat to ET.

Personally, I seem to be more successful playin' with ET instruments ... if I use my tuner to put my C at around +8 cents sharp of ET ... which makes all my open strings (+/-) 5-10 cents to the rhythm guitars notes ... A nice compromise.

It's the "distance" between notes that makes it JI ... not the "reference note".

As I have been sayin ... as long as your steel is in tune with itself ... no matter where your "reference note" is originally tuned .... you have a head start on playin' in tune.

Sorry to "Rock your world" (or would that be "Blues your world"

) with this ... but I would be very suprised to learn that J. Winter, Ry Cooder, D. Allman, etc. ... uses/used an electronic tuner to tune each string on their slide guitars or tuned each one of their open strings to a piano ...

------------------
www.horseshoemagnets.com[This message was edited by Rick Aiello on 17 February 2003 at 09:44 AM.]

Bobby Lee · Post by **Bobby Lee** » 17 Feb 2003 10:16 am

I think that the differences in timbre of the various instruments is much more apparent to the listener than the slight variations in temperment. I recorded a song once that had bass and nylon string guitar (both tuned ET) with a pedal steel tuned to meantone temperment. Everything sounded nicely tuned.

You hear each timbre in its own sonic space. The ear is quick to resolve minor variations in pitch, even when multiple instruments are playing the same note.

I often tune the root note of my steel a bit sharp, so that the differences average out better against the electronic keyboard. I think that's common practice these days.

------------------
<img align=right src="http://b0b.com/b0b.gif" width="64" height="64">Bobby Lee - email: quasar@b0b.com - gigs - CDs
Sierra Session 12 (E9), Williams 400X (Emaj9, D6), Sierra Olympic 12 (C6add9), Sierra Laptop 8 (D13), Fender Stringmaster (E13, A6), Roland Handsonic