Slanting in Just Intonation
LETS TUNE UP
For simplicity lets tune our C's straight up (0), E's flat (-14), etc. Personally I tune my C's up (+10) so my A,E and C# are not too flat sounding with ET instruments but for this discussion lets go:
1 E (-14)
2 C (0)
3 A (-16)
4 G (+2)
5 E (-14)
6 C# (-30)
7 C (0)
8 A (-16)
Lets take a run on the 2nd string. The ONLY place where the actual note you're after is goin' to be directly over the fret is at 0,12,24 (a C note of course).
The D note ain't goin' to be found directly over the second fret... it's goin' to be 4 cents SHARP of fret 2.
I hear ya... big deal... well how about that E note... 14 cents FLAT of fret 4.
You need the Bb, how about 18 cents SHARP of fret 10.
Lets look at a similar situation on the First string (E). That baby is ALREADY tuned 14 cents flat of ET initially.
If you want the F note in the Key of C you need to be 12 cents SHARP of Fret One. (This is very important late on) It is +12 because you need to compensate 2X for this note...
Your F note in the Key of C is (-2) and your E string is already (-14). Putting the bar directly over Fret One will give you an F that is (-14). To get it up to the proper pitch of (-2) you must move the bar sharp of Fret One by 12 cents. THIS IS A CRITICAL CONCEPT in this discussion.
Let me take a break to reassure you that I'm not advocating the use of a calculator to find the position of every F note on every string in every Key. Just tryin' to show that to play in JI the frets (which are an ET thing) are just GUIDES and your EAR is goin' to have to control your bar movements.
These 2 note slants CAN be performed perfectly in tune (unlike most 3 note slants). Take this reverse slant move:
E --- 12 ----- 13 ---- E F
C ----------------------- to
G --- 12 ----- 14 --- G A
The E note and the G note are in tune directly over Fret 12.
The F note is actually 12 cents SHARP of Fret 13 and the A note is actually 18 Cents FLAT of Fret 14. (Remember the A note in the Key of C is (-16) and the fourth string was tuned initially (+2) so the bar must be placed (-18) in respect to Fret 14).
This gives you a reverse slant that is NOT NEARLY AS ANGLED as descibed in the tab!!!!!!!!!
Try it...your ear will verify this.
One more interval slant-The famous V7 to I reverse to forward slant:
E ------ 7 ----- 8 ---- B C
C ----------------------- to
A ------ 8 ----- 7 ---- F E
The B note is actually 2 cents SHARP of Fret 7 and the F note is actually 14 cents SHARP of Fret 8.
The resolved C note is actually 14 cents SHARP of Fret 8 and the E note is 2 cents SHARP of Fret 7. In both cases the slant angle is GREATER than described by the tab.
I know...enough already...not quite yet...
3 NOTE SLANTS
Welcome to the world of approximations. You ain't gonna get many of these in perfect tune (if any) no matter what guitar scale or string spacing you have. JB's specs for the JB Frypan were designed to give as much accuracy as possible to all the 3 note slants including those split string ones. (and he should know!!).
Lets look at that Am forward slant from a recent post:
E ------ 5 --- A
C ------ 4 --- E
A ------ 3 --- C
The A note on string one is 2 cents FLAT of Fret 5.
The E note on string two is 14 cents FLAT of Fret 4.
The C note on string three is 16 cents SHARP of Fret 3.
NO WONDER THIS ONE IS A BEAR!!!
I think you have had enough....
I use to torture myself tryin' to hit these slant "AS WRITTEN" and then kickin' myself cause they didn't sound right. When I finally sat down (about 15 yrs ago) and figured all this out I started to let my ears dictate the slant angles instead of the fretboard.
I dug up this stuff and took the time to write it out here thinkin' maybe it would help those of you who are workin' hard to keep "A Dinosaur (Hawaiian Steel) Alive".