Equal Temperament VS. Just Intonation?

Jesse Leite · Post by **Jesse Leite** » 24 Jun 2010 6:25 am

I don't want to start any arguments here, but I have a question about sweetened tunings on PSG. Most of the advice I have gotten has been to tune to a sweetened E9 tuning chart. One of my teachers (thanks Burke!) spent over an hour with me helping me create my own custom tuning chart, which has turned out to be quite similar to both Jeff Newman's latest E9 chart, and Jean-Yves Lozach's chart (<--lozach's link here has been loosely translated from French to English using google translator). Since my lesson, I now have a better understanding of how these charts work (although I am still just learning)!

I think the two biggest factors in creating these charts is: 1) incorporating your own cabinet drop, and 2) sweetening the 3rds within each chord because the equal tempered 3rd is quite different from the "pythagorean 3rd"; which is the third you get when you tune by ear using harmonics. In fact the difference between the equal tempered 3rd and the pythagorean 3rd is like 14 cents! The perfect 5th within each chord is also different, but the difference is negligible.

...Now, I won't get any deeper into how this applies to the E9 (that's for another day), but back before equal temperament was invented, music sounded more "in tune" (google pythagorean tuning for more info). The problem with pythagorean tuning is that if you wanted to change the key of your song, you needed to retune your instrument because not all of the semitones were equally spaced apart. Then came equal temperament; which Bach made popular with "The Well Tempered Clavier". Some notes were de-tuned for the purpose of making all semi-tones an equal distance from one another. Although this was a slight sacrifice, now you could play in ANY key on the same piano!

The beauty of our pedal steel guitar is that we can tune using a sweetened tuning (although none of these tuning charts and tuning methods are 100% perfect), yet we can transpose into any key with our bar and the sweetened tuning moves pretty nicely with the bar! However, our guitars and pianos today are all tuned using some form of equal temperament. So as pedal steel guitar players, we have to play in an equal tempered world. My question for you guys is, what tuning method do you use? And if you use a sweetened tuning, of if you tune by ear using harmonics, do you have any trouble playing with the band (playing in an equal tempered world with equal tempered guitars and pianos)? To take it even further, the problematic difference would be our thirds VS their thirds (the pythagorean third VS the equal tempered third... have you guys noticed any problems with these thirds clashing?

Mike Perlowin · Post by **Mike Perlowin** » 24 Jun 2010 10:00 am

When I played with my chamber music trio (which recently disbanded, although we may re-form as some future date.) The other two players insisted I tune equal temperament. I've also been rehearsing with a pianist, and I use the ET steel when I play with him.

ET sounds more in tune with these people and instruments, but when I'm practicing at home, it sounds out of tune to me. So, I have one steel tuned to ET for when I played with them, and another tuned JI for woodshedding.

I took the JI to the L.A. steel jam last February, but I took the ET one to a blues jam a couple of months ago. It didn't seem to make much difference either way.

Bent Romnes · Post by **Bent Romnes** » 24 Jun 2010 10:00 am

Jesse, thanks for getting this out here.
That's right, no arguments, just a re-hash of what method we use and what ends up sounding best to the individual.

For many years I have used the revised Newman chart.
My thinking was If it's good enough for Jeff,It's good enough for me.
I was surprised at the results after we tuned my steel to your iphone ala Burke Carroll. Even my cardboard ears could detect a sweeter tuning.
Bring your chart with you next time you come out, please. I had to mess up the tuning due to installing that new pickup.

Mike Perlowin · Post by **Mike Perlowin** » 24 Jun 2010 10:02 am

BTW I tried tuning to the Peterson presets, and it sounded horribly, painfully, out of tune to me.

Jesse Leite · Post by **Jesse Leite** » 24 Jun 2010 11:31 am

Bent Romnes wrote:For many years I have used the revised Newman chart.
My thinking was If it's good enough for Jeff,It's good enough for me.

Jeff's chart did work well I agree, however knowing what I know now I think Jeff did something funny with the 5ths. The difference between pythagorean 5ths and equal tempered 5ths is approximately 2 cents (eg. if you tune your root E strings to +10 cents, then your pythagorean 5ths B strings would be +12 cents; which is the result you would get when tuning by ear using harmonics). What boggles my mind is that Jeff's 5ths are tuned 2 cents FLATTER than equal tempered 5ths. This makes no sense to me as equal tempered 5ths are already flatter in comparison to a true 5th, so you should be sharpening to get the true fifth, NOT flattening. I hate to say it, but did Jeff make a mistake here? Either way a difference of 2 cents is pretty negligible, but in comparison to a true 5th he is actually a total of 4 cents flat. Jeff's 3rds are right on the mark though, being about 13 cents of difference.[/quote]

Bent Romnes wrote:I was surprised at the results after we tuned my steel to your iphone ala Burke Carroll. Even my cardboard ears could detect a sweeter tuning. Bring your chart with you next time you come out, please. I had to mess up the tuning due to installing that new pickup.

I will. I am developing a calculator similar to the one on Lozach's website. I did a few tests and the results he gets are almost identical to what Burke showed me, except the starting point is too flat (it seems the starting point he uses on the open E's just matches the cabinet drop value you enter). By the time you play the flat sounding A+LKL chord, you have to do some hefty bar compensation. Burke taught me to start with the E's at +8 or +10 cents, this way the flatter sounding chord triads (like that A+LKL) can be played closer to the fret. This is probably why Jeff Newman started his E's at +10 cents; which I wholeheartedly agree with. Anyway, next time I come out Bent, we'll use my spreadsheet calculator and I'll make a tuning chart for "red" ...then you can try it for a few weeks and let me know what you think.

Mike Perlowin wrote:ET sounds more in tune with these people and instruments, but when I'm practicing at home, it sounds out of tune to me. So, I have one steel tuned to ET for when I played with them, and another tuned JI for woodshedding.

That's interesting thanks Mike! Maybe I could half the 3rd's difference to get a 50/50 result (closer to equal tempered, but sweeter than true 3rds). I'll have to experiment.

admin · Post by **b0b** » 24 Jun 2010 11:44 am

I selected "made my own custom chart", but actually I don't make a physical chart. My tempering numbers are real easy to remember. I'm not too picky about tuning anymore. Just get it in the ballpark. Most of my numbers are -5, 0 or +5 cents.

Jesse Leite · Post by **Jesse Leite** » 24 Jun 2010 12:43 pm

b0b wrote:I'm not too picky about tuning anymore. Just get it in the ballpark. Most of my numbers are -5, 0 or +5 cents.

That's the thing eh Bob, how much can our ears really detect as musicians? Or how much can the crowd detect? I'm not sure I'd notice a difference of a few cents if something was slightly out. In theory I want to get my tuning chart as accurate as possible, but in practice having some fluctuation shouldn't be an issue.

Thanks for the replies! It's interesting to see these poll results!

Earnest Bovine · Post by **Earnest Bovine** » 24 Jun 2010 1:15 pm

Jesse Leite wrote: What boggles my mind is that Jeff's 5ths are tuned 2 cents FLATTER than equal tempered 5ths. This makes no sense to me as equal tempered 5ths are already flatter in comparison to a true 5th, so you should be sharpening to get the true fifth, NOT flattening.

Yes; just 5ths are 702 cents. There are useful tunings that use 698 cents as the fifth; for example the meantone that I like. That's still much closer to just than the 3rds that we hear every day, so it doesn't sound bad.

But actually Jeff's 5ths are mostly not 698 cents. They are all over the place. Some are much wider, and some are much narrower. If you tune this way, modst of your fifths would be ugly and musically useless (in my opinion only!)

Earnest Bovine · Post by **Earnest Bovine** » 24 Jun 2010 1:25 pm

Here is the Jeff Newman E9 temperament from the link you posted:

And here are the same numbers, reformatted for easy inspection:[tab]E9
G 441.5 + 6 cents
D 439 - 4 cents (string 2)
D 441.5 + 6 cents (string 9)
A 441 + 4 cents
E 442.5 +10 cents
B 442 + 8 cents
F# 441.5 + 6 cents
C# 438.5 - 6 cents
G# 439 - 4 cents
D# 440.5 + 2 cents (strings 4 and 8 )
D# 439 - 4 cents (string 2)
A# 442.5 +10 cents
E# 435.5 -22 cents
[/tab]

Here are Jeff's fifths:[tab]ET fifth = 700 cents
JI fifth = 702 cents
width of Jeff Newman 5th interval (7 semitones):
(first one, G to D, is actually complement of 4th)
G to D 690 cents (strings 1 and 2, complemented)
D to A 708 cents (strings 3 and 2)
D to A 698 cents (strings 9 and 6)
A to E 702 cents
E to B 698 cents
B to F# 698 cents
F# to C# 688 cents (yikes!)
C# to G# 702 cents
G# to D# 700 cents (D# on string 2)
G# to D# 706 cents (D# on string 4 or 8 )
D# to A# 714 cents (D# on string 2)
D# to A# 708 cents (D# on string 4 or 8 )
A# to E# 668 cents (double yikes!!)
[/tab]

and here are Jeff's major thirds:
[tab]ET major third = 400 cents
JI major third = 386 cents
width of Jeff Newman major third interval (4 semitones):
G to B 402 cents (strings 1 and 5, complemented)
D to F# 410 cents (strings 1 and 2)
D to F# 400 cents (strings 7 and 9)
A to C# 390 cents
E to G# 386 cents
B to D# 394 cents (D# on string 4 or 8 )
B to D# 388 cents (D# on string 2)
F# to A# 404 cents
C# to E# 384 cents
[/tab]

(I'm sure there are mistakes in here so please proofread these for me.)

Earnest Bovine · Post by **Earnest Bovine** » 24 Jun 2010 1:31 pm

In Jeff Newman's E9 tuning chart, I'm sure that A#=442.5 is a misprint.

Marc Jenkins · Post by **Marc Jenkins** » 24 Jun 2010 2:23 pm

Like Earnest, I'm using a meantone tuning, and am very happy with it.

John Steele · Post by **John Steele** » 24 Jun 2010 4:04 pm

"I just tune everything to a perfect +/- 0 cents on my equal tempered tuner."

When you include the word "just" in that statement, it makes it sound like doing so is some sort of resignation to apathy, or an easy way out or something, rather than a carefully thought-out decision dictated by logic and reflecting the musical world which surrounds us.

Also, a request for clarification: I know what Just Intonation is, and Equal Temperament, and Meantone, and Well Temperament - but I don't understand what's meant by a "sweetened" tunng. Is it none of the above ? Does Mr. Newman's chart reflect a sweetened tuning ?

- John

Jesse Leite · Post by **Jesse Leite** » 24 Jun 2010 4:15 pm

Thanks for the info! So I did some research... it seems meantone temperaments are more in the middle between just intonation (pythagorean) and equal temperament (12-TET). It looks like the 5ths are narrowed EQUALLY (as they are in equal temperament), but they are not narrowed AS FAR as far they would be with the standard 12-TET equal temperament. The thirds would end up closer to just intonation, but they wouldn't be quite pure pythagorean thirds. Does this sound right? If so, then rather than the thirds being a difference of 13-14 cents (when compared to equal tempered thirds)... meantone thirds would be less of a difference; ie. 10 cents or something, depending on the meantone temperament used.

I know I am worrying too much about this

After all, I have a tuning chart that works GREAT for me already. I really just want to understand the logic behind Jeff Newman's chart, and why it's so popular. I don't understand why he stacked his fifths the way he did, and why they are so scattered? I am wondering he tuned a PSG by ear, then took readings and compiled it into a chart? That would explain the inconsistencies I think.

John Steele wrote:Also, a request for clarification: I know what Just Intonation is, and Equal Temperament, and Meantone, and Well Temperament - but I don't understand what's meant by a "sweetened" tunng. Is it none of the above ? Does Mr. Newman's chart reflect a sweetened tuning ?

Nowadays when you buy an electronic tuner (not including feature packed tuners like Petersons), they all seem to be calibrated with 12-TET equal temperament, right? The biggest problem with equal temperament and well temperament is how the thirds turn out to be so different from the pure thirds that we know in our "just intonation" or "pythagorean" tunings. Technically, equal temperament is equally out of tune in any key. So to answer your question, I *think* a sweetened tuning is anything other than equal temperament. Any temperament that brings us closer to just intonation (pythagorean tuning) will naturally sound sweeter to our ears ...but maybe not in comparison with the "out-of-tune" band. The real question is, how much do we compromise?

Eric West · Post by **Eric West** » 24 Jun 2010 5:40 pm

I stumbled on a good answer to a lot of this "tuning business" recently though it got me quite a bit of flak..

Pick YOUR OWN CHOICE of "professional" steel rides. Medium speed at least..

Preferably with either a piano or guitar in the same track.

Slow them WAY down with your best SOnar, Cuebase, Cool Edit or ProTools.

Notice what is out of tune.

Notice that ten cents is nothing compared to the dissonance you hear.

Also, I can't read too much of this stuff mainly cause I'm just in and out here tonight.

Jeff's Tuning Chart came directly from Lloyd Green's setup one afternoon with his permission.

Ever wonder why Lloyd sounded more in tune than Jeff? (To put it mildly..)

Like I said. Do a "slowdown" test from the most professional cuts you can find.

Then if you want some entertainment and they do actually expound apon their particular tuning, read how they are super concerned about 2 or three cents one way or the other.

It's truly in the playing, and like my buddy Clete said, how you've trained your ears over the years.

Gotta run.

Even in the skewed slanted language of the "progressive" pollster, I'm still reading more people in the "ET" slot.

EJL

Jesse Leite · Post by **Jesse Leite** » 24 Jun 2010 6:02 pm

Eric West wrote:Then if you want some entertainment and they do actually expound apon their particular tuning, read how they are super concerned about 2 or three cents one way or the other....It's truly in the playing, and like my buddy Clete said, how you've trained your ears over the years.

I have to agree with you. I don't think my ears would scowl at a note being a few cents out, let alone even notice the difference. Like I mentioned earlier, I have a tuning chart that already works GREAT for me! I am just trying understand how all these temperaments and charts work because I am currently developing a tuning chart calculator (similar to Lozach's), but I want it to be a bit more flexible. I want the user to be able to choose a chart that is equal tempered, or choose a chart that is slightly "sweetened", or choose a chart that will give them the same result you would get from tuning by ear with harmonics (which i think gets you as close as you can get to "just intonation" on a PSG) ...all the while taking the cabinet drop of their own guitar into account. Why can't we just live in a perfect world?

Just kidding!

Marc Jenkins · Post by **Marc Jenkins** » 24 Jun 2010 6:43 pm

Jesse, see a thread I started about 2 years back on meantone: http://bb.steelguitarforum.com/viewtopi ... t=meantone

Eric West · Post by **Eric West** » 24 Jun 2010 7:37 pm

Well don't get me wrong.

I think the problem starts when somebody says that they are happy tuning to a tuner that is "ET" (Standard stretch).

Then people seem to pile in and say that they must do it because they are ignorant, or their ears are somehow less refined.

Then the people that prefer beating chords say the same thing about the beatless...

Then somebody famous inevitably piles in and declares how everybody must hear things, or tune.

Then somebody more famous gets in the fray and says that it's not that complicated.

Then a few more steps...

Then the fight is on..

I guess to me, I have come to understand that in the light of the "test" I posted, there's a whole lot more crap coming from the "side" that says that they make these micro=adjustments, and sound perfectly in tune.

They don't.

I also didn't mean to disparage Jeff Newmann's playing "in tune". It is just to me appearant that he and Lloyd came out with differing intonations using presumably the same tuning system.

Gotta run and pave til daylight.

Gratefully.

EJL

David Griffin · Post by **David Griffin** » 24 Jun 2010 7:59 pm

Eric: At the risk of starting another war of words w/ you(which I assure you,I'm not),you are the ONLY person I've ever heard of that listens to music SLOWED DOWN!:whoa:

Jesse Leite · Post by **Jesse Leite** » 24 Jun 2010 8:18 pm

Marc Jenkins wrote:Jesse, see a thread I started about 2 years back on meantone: http://bb.steelguitarforum.com/viewtopi ... t=meantone

Thanks Marc, I am reading through this thread and it is super-interesting... However, it also makes my head hurt. I've been reading about meantone but I am still confused. Is there still a wolf fifth in meantone? How does meantone fit in with just intonation and equal temperament? Now I am second guessing myself in thinking that just intonation is the same as pythagorean tuning... is it the same? If I tune my steel by ear using harmonics, what temperament will I be getting closest to?

Eric West wrote:Then the fight is on.

Key words, "then the fight is on"... you said it! I've hesitated about starting this thread, but I've been itching to learn more so I caved in. I know in the end, every player is different, and every instrument is different. There is no perfect way to tune a PSG I guess. It makes me wonder how much of this all matters anyway. With my 6 string guitars I am more than happy tuning to my cheap little ET tuners. The problem with pedal steel is that a beginner cannot just pick up a cheap tuner and tune everything ET in any order they want like they can with a 6 string guitar. Because of things like cabinet drop and other physics related issues (which are mostly over my head), I think pedal steel guitarists need to have SOME sort of method to their madness. I am very surprised by how so many people have voted for "I just tune everything to a perfect +/- 0 cents on my equal tempered tuner" on my poll. How do you guys tune everything to +/- 0 cents and still account for cabinet drop?

Like I mentioned, I am very happy with the current chart I am using now (thanks again Burke), but WHY am I happy with it? What makes it tick scientifically? Roots, thirds, fifths, wolves, tempers ...I need an Advil. Goodnight.

Marc Jenkins · Post by **Marc Jenkins** » 24 Jun 2010 9:01 pm

Jesse Leite wrote:
Marc Jenkins wrote:Jesse, see a thread I started about 2 years back on meantone: http://bb.steelguitarforum.com/viewtopi ... t=meantone
Thanks Marc, I am reading through this thread and it is super-interesting... However, it also makes my head hurt. I've been reading about meantone but I am still confused. Is there still a wolf fifth in meantone? How does meantone fit in with just intonation and equal temperament? Now I am second guessing myself in thinking that just intonation is the same as pythagorean tuning... is it the same? If I tune my steel by ear using harmonics, what temperament will I be getting closest to?
I need an Advil. Goodnight.

Well, it's not too late yet on the west coast...

Jesse, meantone is not a single tuning. I'd suggest starting here: http://en.wikipedia.org/wiki/Meantone_temperament and 'How Equal Temperament Ruined Harmony (and Why You Should Care)' by Ross W. Duffin. He really gets into it.

JI and Pythagorean seem the same to me, but I might be wrong. If you tune the beats out with harmonics, that's JI. Sixth comma meantone, which I use, is right between JI and ET. Also, equal temperament actually IS a meantone tuning, specifically 12th-comma. The reason I was drawn to meantone is that since not all of the intervals are there to tune in the open position, you can have sweeter intervals than ET, but not have nasty discrepancies (how well do the F# on the C pedal and the 1st string open F# tune together, for example?). I was worried, when developing my tuning, that I;d have to deal with the wolf. Since you don't have to deal with every note, you can just make the wolf a note you'll never play in that position.

Email me if you'd like more, or if this ends up an ugly thread. I love this stuff!

admin · Post by **b0b** » 24 Jun 2010 10:17 pm

I tune my 8-string D6th to meantone except for the A&B pedals, which I tune by ear to be beatless for country ballads. But the question was about E9th.

Eric West · Post by **Eric West** » 25 Jun 2010 11:43 am

Eric: At the risk of starting another war of words w/ you(which I assure you,I'm not),you are the ONLY person I've ever heard of that listens to music SLOWED DOWN! -DG-

Well I'll pretend that you aren't spoiling for some kind of whatever you call it. It always was the standard way to cop things off 33rpm records when turntables had 16rpm functions. Those Earl Scruggs records and other stuff would yield a half speed, lower octave version of the song.

If what you say is true about yourself, I'm at least glad you're getting out a little more in your later life.

EJL

Brian McGaughey · Post by **Brian McGaughey** » 25 Jun 2010 8:12 pm

I voted for using my own chart but I tune more toward straight up ET with increased vibrato when a piano or organ is in the mix.

Bob Hoffnar · Post by **Bob Hoffnar** » 25 Jun 2010 11:01 pm

I really just want to understand the logic behind Jeff Newman's chart, and why it's so popular. I don't understand why he stacked his fifths the way he did, and why they are so scattered?

From my experience the reason the 5ths are tuned that way has to do with the practical application of the music that most people play on the E9 tuning. Its a common usage issue. Jeff's approach was to get people to stop screwing around and start playing. As with all of Jeff's contributions to the playing and learning the instrument it works.

I am wondering he tuned a PSG by ear, then took readings and compiled it into a chart? That would explain the inconsistencies I think.

That is correct sir. He actually checked with all the best studio level players he could find, which was most of them, to verify the consistency of his numbers and usefulness of his chart.

CrowBear Schmitt · Post by **CrowBear Schmitt** » 26 Jun 2010 12:46 am

when Jean Yves Lozach came up w: his lil' program, i firmly believe he did us a favor
yes, i did vote for him
i used it to find cabinet drop on my steel & referencing his tuning variations

First, tuning by harmonics is what any steeler should know ; no one should be without it
How was life before tuners ?

since i have a peterson tuner (stroborack), i got my Es to 440 w: pedals A&B engaged - then i let them off & used the Es i have there as my reference
yes, it's gonna be a bit flat on the tuner but yer ears won't necessarily hear it)
then i went along tuning my fifths,seconds, thirds, fourths, & so on by harmonics & setting them in the peterson

since there are at least three chords ( E, B, F#)as reference on the E9 tuning, getting the Ebs & F# are going to demand certain compromises

Those who just choose the sweetened tunings on a peterson, Buddy or Jeff's charts rather than go through the rigamarole of harmonic tuning will be close enough & thus stand before the promised land

The Steel Guitar Forum

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Equal Temperament VS. Just Intonation?