Grok Just Intonation vs. Equal Temperament on a PSG?

[Georg]

Hey folks.
Thought that before I started new threads about "JI" capable steel-pedaling mechanics, that I should ask this simple question:
"Do you really understand the difference between Just Intonation and Equal temperament tunings?"

Easier to discuss mechanical details surrounding true Just Intonation tuning on a pedal steel guitar when all involved at least understand what the goal is, me thinks.

There's of course only one true Equal Temperament tuning and many possible variants of Just Intonation tunings, but I'm simply aiming at moving what's know as a "sweet tuning", a JI variant that is close enough to Equal Temperament to sound right alongside a piano, around with the PSG mechanics so all technically possible pedal combinations sounds "sweet" everywhere on the neck, without having to slant the bar or avoid certain strings.

For a truly JI tuned PSG it should be enough to offset the straight bar relative to those fret-markers, and pick any strings you like and make the chord sound good. So my method involves introducing mechanics for multiple, tunable, pitches not only on open strings, but also for raised and lowered strings, so they always match.

So before I start boring everyone with threads about such "unnecessary" stuff: do you find it interesting enough to bother..?

[Allan]

This not 'opening a can of worms' - this is a whole barrel of the wiggling buggers.
When I was younger I was 'blessed' with perfect pitch - thankfully that has faded as I have aged. Back then I could listen once to a new release by a band and name the key, the guitar used, the amplifier used, all the techno stuff. I used to re-tune my guitar (6 string or bass, not PSG) between songs depending on the key we were going to play in. I never knew back then why I had to do this but I do mean that I HAD to do it. I had never heard of 'JI' and 'ET' but I knew there was something going on.
If you want to start threads on this subject I will be very interested in how you would deal with this matter in a mechanical way. I assume that you are looking at the mechanics of doing it? From a mathematical standpoint it may be possible to work out the variants that would allow for a working tuning that would allow for a limited number of keys to be accommodated but to do this for all keys seems complex in the extreme. I have not even touched on the problems of cabinet drop and such things here as I know, from other threads, that you are dealing with that as a stand alone issue.
I assume that you are looking at this from a purely personal stand point as there seems to be little real agreement about what compromises constitute the 'sweet tuning' anyhow. The most interesting writings on this, for me, seem to be from Joe Wright. I can't recall where I saw his stuff on the subject but I do remember that I saw a lot of sense in it at the time.

So, I, for one, would be interested in what you come up with on this subject. I do have to add, however, that I would most likely read the threads with interest but am unlikely to have anything to add.

Good stuff, Allan.....

[Georg]

Well, Allan, I still have my 40 year old 6 string Les Paul copy tuned to: E-A-D-G-C-F, with the G string slightly shortened at the nut. With minimal finger-gymnastics (pressure variation) it was no problem getting perfect JI chords all over the place (neck) on that guitar. Was fun playing it too

You're correct in that I don't give a hoot in body-drop detuning and such. The best, and in my opinion the ONLY cure for such detuning, is to build, or buy, a PSG that doesn't have audible body-drop.


For my PSGs I will use this more than 400 year old "Universal JI tuning" as guide...

Code: Select all

C   C#	 D-   D   Eb-   Eb  E   F   F#-   F#    G   G#    A   Bb-  Bb  B    C
1/1 25/24 10/9 9/8 32/27 6/5 5/4 4/3 25/18 45/32 3/2 25/16 5/3 16/9 9/5 15/8 2/1

...since it reduces the multiple-pitch problem to 16 pitches/octave to cover nearly all keys. I'm pragmatic, and know that "perfect" is an unreachable goal - something to strive for but not to go nuts about, but "near perfect" is better than what we have now, IMO. Besides, for a quite normal 3P+5L JI tuned PSG many of the conflicts are solved in line with that 16 pitch tuning already, so it's a good starting point. Just half a dozen or so conflicts left.

You can find the "Universal JI tuning" on the bottom of this first section of Just Intonation Explained, and there's an mp3 file there too. Might be interesting also for those who don't understand what all the fuss is about, or don't care.

When I start a real thread, I will focus on the chords and pedal/lever combinations that cause most problems for most "JI tuners" first. So interested "sweet" or "JI" tuning players can start mapping those unusable chords-pedal/lever combinations on their PSGs now. Will probably be slow going and take time to sort out what isn't JI related, but I'm in no hurry.

Mechanically only the complexity involved in cross-compensating pedal/lever pulls beyond the usual split and JI-compensators pose problems. Guess a few PSG builders may be interested in "how" problems can be solved, even if not all see a need.

[Eldon]

Lead on Georg, I'm waiting to be educated!!

[Georg]

First mechanical gismo in place in the Pedal Steel section

[Don McGregor]

My head hurts already, but lead on. I need to understand this.

[Georg]

Don, I can't be sure about what in the "JI vs. ET" tuning of PSGs that makes your head hurt, so will you kindly enlighten me so I can find the right cure for that headache..?

My head hurts a bit when I go into the matter too, but I'm used to that after decades of being troubled by sour chords and trying to find working solutions.


To expand:
The "12 fixed-pitch tone/octave" difference, and problem, for JI vs. ET, is easiest to grok by reading part 3. Why Is This Different from Our Normal Tuning?, from the article/site I referenced to earlier.
Intervals for 12 tone/octave "JI", "sweet" or "harmonic" tuning - different names for the purest sounding chords, clearly don't add up in 100 cents intervals like "ET" tuning does, and if we don't retune a "JI" tuned instrument correctly as/when we change key, chances are the resulting chords sound awful.

On a PSG the bar allows us to change key by changing fret, which works, and sounds, fine until we want to play chords in different keys without moving the bar to the frets that correspond directly with each of the keys we want to play in. Try as hard as we can, on a "JI" tuned PSG some pedal/lever combinations only introduce the right intervals and produce good-sounding chords for specific keys on specific frets. On other frets in other keys, those pedal/lever combinations produce chords too sour to be usable, and some pedal/lever combinations can't really be used at all in any key.
The reason is of course that on a "JI" tuned PSG the pedals/levers are tuned "JI" too, and without some form of retuning of the pedals based on which pedal/lever combination that's used, those useless pedal/lever combinations will stay useless.

So, to repeat what I have said before: I start by mapping up "useless pedal/lever combinations" - only have to play a "JI" tuned PSG some to find them, and then try to design the mechanics to retune some of pedals slightly on-the-fly, so more, or ideally all pedal/lever combinations produce good-sounding "JI" chords automatically.

I hope the above reduced the headache some...