Just Intonation
Just Intonation (JI) vs Equal Temperament (ET)
C Scale JI Deviations from ET(cents)
C (1) 0
C# (2b) +12
D (2) +4
Eb (3b) +16
E (3) -14
F (4) -2
Gb (5b) -10
G (5) +2
Ab (5#) +14
A (6) -16
Bb (7b) +18
B (7) -12
C (8) 0
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 1st (root) 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.
The Thirds
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
The Fifths
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
Now the cool one .... it is useful when the "Initial" reference note is not present in the open tuning.
Thirds & Fifths
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
It is not always convenient to tune via harmonics ... so here are the JI deviations from ET for using an electronic tuner.
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
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 ..
Example : E13/9 Tunin' (lo to hi) .... B D E F# G# B C# E .... The F# will clash with the B if it's in tune with the C# and vise versa.
If you are havin' trouble "deciphering my code" ... here is a full explaination
Lets tune C6 using Just Intonation
C6 Tunin' (lo to hi)
C E G A C E
1 3 5 6 1 3
C Maj Scale
C D E F G A B C
1 2 3 4 5 6 7 1
For simplicity sake ... using your tuner ... tune all your strings ET ... Straight up ... just to get the notes "in the ball park"
Now .... tune the C about +8 cents sharp (or just tweak it alittle sharp if you don't have "cents" available on your tuner)
Once this is done ... DON"T fool around with this string ... it is your reference point.....
1) Tune the G string
The 5th of the 1 is the 5 .... this means ... the 5th (scale degree) of an C note (1st in the C scale) is a G note (5th in the C scale).
Chime the C string at the 7th fret (5th of the 1) ... giving you a G note .... same octave as the G that you will produce on the G string ..... The 5th of the 1 is the 5 (5th of C is G)
Chime the G string at the 5th fret ... this produces a G note (5) ...
Now, bring that G string down (flat) ... and bring it back up to match your ringing C string (G note)... Bring it up slowly ... listening ... if you went way down ... you won't hear beats ... to many, too fast .... But as you get closer ... they slow down ... when you FIRST detect they have disappeared ... STOP .. (the most common mistake is to keep goin too far).
Chime them both again ... see if you detect any wah-wah sound ... if not ... your C and G are PERFECTLY in tune
2) Tune the E string (This is the hardest one to do !!!!)
The 3rd of the 1 is the 3 .... this means ... the 3rd (scale degree) of an C note (1st in the C scale) is an E note (3rd in the C scale)
Chime the C string at the 4th fret ... just a hair toward the nut (3rd of the 1) ... this produces a E note (3) .. get it ... The 3rd of the 1 is the 3 (3rd of C is E)
Chime the E string at the 5th fret ... giving you an E note .... same octave as your E that you produced on the C string.
Now, bring your E string down (flat) ... and bring it up to match your ringing C string (E note)... bring it up slowly ... listening ... . when you FIRST detect they have disappeared ... STOP.
Chime them both again ... see if you detect any wah-wah sound ... if not ... your C and E are PERFECTLY in tune
3) Tune the A string
The 5th of the 6 is the 3 .... this means ... the 5th (scale degree) of an A note (6th in the C scale) is an E note (3rd in the C scale).
Chime the E string at the 12th fret ... giving you an E note .... same octave as your E that you will produce on the A string... this is your reference note .
Chime the A string at the 7th fret (5th of the 6) ... this produces a E note (3) .. get it ... The 5th of the 6 is the 3 (5th of the A is the E)
Now, bring your A string down (flat ) ... and then bring it up slowly ... listening ... when you FIRST detect they have disappeared ... STOP.
Chime them both again ... see if you detect any wah-wah sound ... if not ... your A and E are PERFECTLY in tune.
4) Tune your low E
Chime hi E string at 12th fret ...chime low E at 5th fret .... bring it to tune
5) Tune your low C
Chime hi C string at 12th fret ...chime low C at 5th fret .... bring it to tune
Done ...
You may want to go back and re-check ... adjustments on the bass strings screw up the tension across the bridge.
The main reason to use harmonics over just tuning the beats out of open notes ... is that by chiming the strings you produce the SAME NOTE IN THE SAME OCTAVE ... It is much easier to tune unisons ..