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  What Is Tempered Tuning?

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Author Topic:   What Is Tempered Tuning?
Bobby Lee
Sysop

From: Cloverdale, North California, USA

posted 04 November 2004 01:00 PM     profile     
There's still some confusion about this subject, and the terminology related to "tempered tuning". I think I have a pretty good handle on it, so maybe I can shed some light on the subject.

In ancient times, musicians discovered pure harmony. Musical instrument builders eventually realized that there were mathematical relationships between those harmonies. A tube that was 4/3 as long as another tube produced a perfect third harmony, for example.

Musicians developed scales based on those prime-number ratios, and beautiful music was created for thousands of years based on those scales. There was one problem with those scales, though: you couldn't transpose them because each interval had a slightly different size.

The pure harmony system of tuning is called "just intonation", or JI for short. All variations from JI are attempts to solve the problem of transposing. Those systems are said to be "tempered tunings".

By far the most common tempered tuning in use today is the 12-tone "equal temperament", or ET for short. It's so common that most other systems are measured my their variance from ET. The center mark on your electronic tuner (where it says A=440) is the equally tempered mark.

Guitar players tend to use equal temperament. The frets on a guitar are spaced to produce equally tempered notes. Most electronic keyboards also use an equally tempered tuning.

Most steel guitarists don't use a tempered tuning. Instead, we tend to favor just intonation - the pure harmony form of tuning. The reason is simple: we can move the bar to transpose an entire scale and still keep all of the harmonies in tune. A guitar or keyboard can't do that, so they use a tempered tuning instead.

Just intonation looks funny on most electronic tuners. Guitarists are trained to think that the center mark means "in tune", and in fact it does for them. Tuning to equal temperament is the best way for them to get all of their notes in tune. They play "tempered tuning" instruments.

Just intonation requires that we tune some notes flat of the center mark, some on the center mark, and some sharp of the center mark. The average of all of the JI variances is the center mark. That's so that when we transpose by moving the whole scale to a different fret, we don't sound out of tune with the band. They are averaging each note of the scale because they have no choice. We average the root note of the scale (by going to the ET fret marking) and build our pure harmonies up from that.

The "untempered" nature of the pedal steel gives it much of its characteristic "beautiful" sound. A string quartet or an acappela vocal group does the same thing, which accounts for their timeless popularity.

For a long time now, I've heard steel guitarists refer to our pure harmony system as "tempered tuning". That terminology is simply wrong, and makes us look ignorant in the eyes of educated musicians. The pedal steel is usually tuned untempered (just intonation). Guitars and pianos are almost always tempered. Pedal steel almost always is not.

------------------
Bobby Lee - email: quasar@b0b.com - gigs - CDs, Open Hearts
Sierra SD-12 (Ext E9), Williams D-12 Crossover, Sierra S-12 (F Diatonic)
Sierra Laptop 8 (E6add9), Fender Stringmaster (E13, C6, A6)

[This message was edited by Bobby Lee on 04 November 2004 at 01:03 PM.]

Larry Bell
Member

From: Englewood, Florida

posted 04 November 2004 01:27 PM     profile     
Mine is not only tempered . . .
. . . it's TEMPERAMENTAL

I'm not sure I agree that most steel players tune untempered. I think a very large number use Jeff Newman's chart, which adjusts the tonic and, therefore, I would consider it tempered. Many others tune their thirds and sixths a bit sharp of JI to make other intervals less harsh.

I heartily agree with the main point of your post: Many steel players do confuse the term 'tempered tuning' with JI since they see an offset on the tuner. They must realize that most tuners show Equal Temperament, which IS TEMPERED. Granted, the newer Peterson that stores offsets may appear to be an exception, but tuning 'straight up' on a digital tuner will produce a TEMPERED tuning (ET).

------------------
Larry Bell - email: larry@larrybell.org - gigs - Home Page
2003 Fessenden S/D-12 8x8, 1969 Emmons S-12 6x6, 1971 Dobro, Standel and Peavey Amps

chas smith
Member

From: Encino, CA, USA

posted 04 November 2004 02:31 PM     profile     
quote:
A tube that was 4/3 as long as another tube produced a perfect third harmony, for example.
Slight correction, 5/4 is the just 3rd, 4/3 is the p4 and it would be the air column that is in tune, not the tube itself, which has more complicated math. I would also add to, " you couldn't transpose them because each interval had a slightly different size." that equal temperment means that each interval, in the octave, is the same size. In a 12 tone et scale, there are 12 equally spaced intervals, in a 7 tone et scale, there are 7 equally spaced intervals.

This stuff fascinates me.

Jon Light
Member

From: Brooklyn, NY

posted 04 November 2004 02:47 PM     profile     
This is not my favorite subject. I can't say that it interests me much except for the little bit of it that I need to understand in order to make informed choices regarding tuning my instrument. So let me repeat the one point here that was my biggest source of confusion, just for the benefit of others who may be as simple-minded or misinformed as me.

----I used to think that "tuning straight up" meant tuning in an unaltered, therefore untempered, JI manner. It took numerous blows to the head to make me understand that all standard electronic tuners are equal temperment and "straight up" means tuning so that the needle is centered on an ET dial. So "straight up" means ET.

I think much confusion comes from misunderstanding the terminology--in this case nobody's fault but my own--and I guess that is the reason for the original post. It sure can help the discourse to have everyone on the same page.

David Doggett
Member

From: Philadelphia, Pennsylvania, USA

posted 04 November 2004 02:50 PM     profile     
Excellent explanation, b0b. Larry is simply pointing out that pure JI and "equal" temper (ET) are at opposite extremes of the possibilities. I think he is right that many steelers do something in between, which is what Newman's tuning chart is. They are simply inventing their own tempered tuning, but it is not pure ET. Also, many regular guitar players do not have a clear understanding of tempering. They will tune each open string straight up. Then they will hit a chord and tweak the tuning a little so that chord sounds right. They have moved closer to JI for that chord, but other chords will be off. If that chord is the tonic for the key they will play in, then the basic chords of that key will sound pretty good. Also, other keys that use bar chords might be okay. But if they move to another key using open strings, things will be way off, and they will tweak it a little. Keys with a lot of overlap in chords might ge okay, such as changing from the key of C to the key of G, or key of E to key of A. But going from C to E, or E to G, will require some retuning. Many guitar players will hit their tonic chord for the next song and retune a little. After doing that for half a set, they may have wandered far from either JI or ET. But don't try to tell them that.

[This message was edited by David Doggett on 04 November 2004 at 02:51 PM.]

mickd
Member

From: london,england

posted 04 November 2004 02:56 PM     profile     
trying to understand these JI threads always leaves me "bad tempered" - probably means I'm not in tune
Bobby Lee
Sysop

From: Cloverdale, North California, USA

posted 04 November 2004 03:06 PM     profile     
Chas is right about the ratio. Chas is an instrument builder, so he knows these things much better than I do.

Larry, changing the root frequency has no effect on the tuning system. JI is JI whether your E's are at zero or +5 cents - it's just a higher JI.

But you are correct that most players don't in fact tune 100% untempered. We tend to tweak a note or two that doesn't fit (like the F# on E9th), and cabinet drop has its inevitable effect. But our ideal is the untempered tuning. It's what most of us hear in our heads, and what we strive for.

My main reason for this post is to dispel the myth that anyone who tunes to various offsets on an electronic tuner or to their ears is using a "tempered tuning". In most cases, we're trying to get the pure harmonies. No beats between notes. That's what "untempered" means. Tempered tunings have beats in the harmonies.
Tom Olson
Member

From: Spokane, WA

posted 04 November 2004 03:30 PM     profile     
Excellent explanations from all. If I could add something, which I believe is correct, but might not be:

It's my understanding (some or all of the following might be wrong) that one of the reasons tempered tuning came about has its roots in how the first musical instruments were developed.

Some of the first musical instruments were stringed instruments -- for example, maybe similar to a harp. Since there was no musical scale, the strings were simply tuned to each other so that they sounded good when played together.

For example, the second string was tuned to be a 5th of the first string, the third string was tuned to be a 5th of the second string, etc. etc. -- so, eventually, they ended up with a harp that was basically tuned to the circle of 5ths.

However, when they tuned the 13th string as a 5th of the 12th string, they found out that the 13th string was close to some octave of the 12th string, but not quite. Consequently, when the 1st string and the 13th string were played together (and certain other strings) a horrible sound was produced.

So, they figured out that if they "tweeked" each string a bit so that the 12th and 13th strings were perfect octaves, then they could have an instrument that was much more versatile, although it could not play perfect 5ths.

The above may be an over simplification, but I believe that I have the basic concept down. Maybe this has already been explained above -- if so, just ignore what I said.

Also, it seems to me that certain instruments are perfectly suited to being tuned to JI. For example, a string ensemble that consists only of instruments in the violin family can be tuned JI and can sound absolutely beautiful. The reason is that no more than two strings can be played at the same time on the instrument AND because only adjacent strings can be played at the same time AND because adjacent strings are tuned as 5ths.

Again, I might be wrong.

Harold Dye
Member

From: Cullman, Alabama, USA

posted 04 November 2004 05:19 PM     profile     
HUH??

I played the other nite and someone said the piano sounded out of tune....they said even the steel player noiced it..

Dan Tyack
Member

From: Seattle, WA USA

posted 04 November 2004 10:13 PM     profile     
Thanks for the clear explanation, Bob.

Harold: all pianos are out of tune, that's the nature of ET.

John Daugherty
Member

From: Rolla, Missouri, USA

posted 05 November 2004 08:38 AM     profile     
I never understood how anyone could make a "tempered" chart like the one Jeff provided. I think the amount of offset is dependent on the cabinet drop of each instrument.
I could never be in tune by using that chart. Also, how can you use open strings and play with a keyboard if you don't tune straight up? Should we play steel guitar rag in Eb and not use Leons arrangement? I am bonded to MY guitar and tune that baby the way she wants to be tuned..........JD
Joe Henry
Member

From: Ebersberg, Germany

posted 05 November 2004 10:41 AM     profile     
sorry, wrong post

[This message was edited by Joe Henry on 05 November 2004 at 11:00 AM.]

David Doggett
Member

From: Philadelphia, Pennsylvania, USA

posted 05 November 2004 11:14 AM     profile     
Our situation is made worse by the way steel guitar sustains notes so well. Pianos and acoustic guitars are fading from the moment the note is hit, and those clashing ET overtones fade faster than the fundamental. But we sustain all those overtones. That makes JI sound all the more sweet, and ET sound worse than it does on piano or regular guitar.
Bobby Lee
Sysop

From: Cloverdale, North California, USA

posted 05 November 2004 12:35 PM     profile     
quote:
I never understood how anyone could make a "tempered" chart like the one Jeff provided.
My point is that Jeff's chart is not a "tempered tuning". As long as steel players continue to call the beatless tuning "tempered", we look like fools among educated musicians.

Pianos are always tempered. Guitars are always tempered. Steel guitars, violins and other fretless instruments are usually untempered because they have no need for temperament.

As for playing with the piano, I played in a trio - piano, bass and steel - for four years. The piano had more tuning problems than I did, but for about 3 months after each piano tuning everything sounded fine. And yes, I did use open strings.

------------------
Bobby Lee - email: quasar@b0b.com - gigs - CDs, Open Hearts
Sierra SD-12 (Ext E9), Williams D-12 Crossover, Sierra S-12 (F Diatonic)
Sierra Laptop 8 (E6add9), Fender Stringmaster (E13, C6, A6)

Lee Baucum
Member

From: McAllen, Texas (Extreme South) - The Final Frontier

posted 05 November 2004 03:02 PM     profile     
I tune as close to "straight up" as my ears can stand. That works best with the two guitar players I play with.

I call it Tampered Tuning.

------------------
"Once the game is over, the king and the pawn go back into the same box."

Lee, from South Texas
Down On The Rio Grande


Gerald Menke
Member

From: Brooklyn, NY, USA

posted 11 November 2004 12:54 PM     profile     
Bobby, thank you for laying out the big points of this topic so clearly. I have observed this JI/ET debate since joining the forum, and feel it is time for me to weigh in; I respectfully disagree with you. But before I get into that, I think it might be worthwhile to go into a little more detail as to just why musicians and composers began using the tempered system versus just intonation or "pure tuning" as it is sometimes called.

An instrument that is tuned using just intonation in the key of C, for example will not be able to circulate through the other keys without nightmarish dissonance in those keys. The I, IV and V chords will sound terrific, absolutely beatless. But try and play a ii major, or in a remote key on a piano (or guitar for that matter) tuned using just intonation -- E major for example -- and your hair will stand on end. The beats between the 4ths and 5ths will be horrendous. But stay in the key of C, and you will be in a beatless paradise of “in tune-ness”. Some just intonation devotees find it hard to enjoy ET music because due to the tuning compromises, it is full of intervals that are not in tune.

Any time you stray from just intonation, which virtually no one in the realm of popular music uses, you are compromising. Equal temperament is the big compromise, sacrificing beatless intervals to allow for modal mixing. That after all, was the point of J.S. Bach's "Well Tempered Clavier", to show that ET allows the player to circulate through all of the keys.

I do agree with you in that we steel players, along with those who play just about any fretless instrument can play more "in tune" than any of the “fixed” note generating instruments such as the piano or guitar. But that is a factor of our not having fixed notes in the same way that pianos and fretted instruments do; we adjust just by moving the bar microtonal amounts, constantly “re-tuning”. The steel itself is not really tuned in a manner that we can really call “just intonation”. I have all but given up playing six string guitar, as it is just about impossible to get one really "in tune", i.e. all chords to sound “beatless”.

To hear music using just intonation, check out some music by Harry Partch, LaMonte Young or Terry Riley. Some of Partch’s music features octaves divided into 43 units! Those of us who use tuners to get our “e’s” and tune by ear from there and those who use tuning charts are playing using tempered tunings, not just intonation. Otherwise we couldn’t play “Lovesick Blues” (or any other song with modulations) without sending the audience running for the exits.

Bobby Lee
Sysop

From: Cloverdale, North California, USA

posted 11 November 2004 05:50 PM     profile     
My main point in this topic is the terminology. There are a lot of steel players who think that if you don't tune "straight up" on the tuner, you are using a "tempered tuning". That's wrong.

Any tuning that has beats in some of the harmonies is tempered. That includes tuning "straight up". If your harmonies have no beats all all, you are tuning "untempered", a.k.a. Just Intonation.

I'm not intending to argue about which method sounds better. I use different tuning methods on different guitars, even on different necks of the same guitar! I like untempered and I like meantone, and I don't get bent out of shape on equal temperament either.

But my biggest point, the reason I started this topic, is that steel players continue to call their beatless tunings "tempered". It makes us look like a pretty ignorant bunch of yahoos. Beatless is not tempered. Tempered tunings have beats. That's what tempered means.

------------------
Bobby Lee - email: quasar@b0b.com - gigs - CDs, Open Hearts
Sierra SD-12 (Ext E9), Williams D-12 Crossover, Sierra S-12 (F Diatonic)
Sierra Laptop 8 (E6add9), Fender Stringmaster (E13, C6, A6)

Bobby Lee
Sysop

From: Cloverdale, North California, USA

posted 11 November 2004 05:52 PM     profile     
By the way, Bach didn't use equal temperament. That's not what "The Well Tempered Clavier" is about. You have been misinformed, as I once was.
Tom Olson
Member

From: Spokane, WA

posted 11 November 2004 05:55 PM     profile     
I know this is a bit off-topic, but wouldn't it be fair to say that the problem with JI starts when you have an instrument on which all of the notes are non-variable in pitch (like a piano) OR when you try to play more than three notes at the same time on the same instrument. Maybe not -- just thought I'd blurt that out.
chas smith
Member

From: Encino, CA, USA

posted 11 November 2004 07:04 PM     profile     
I tune my E9 neck to a sort of "hybrid", that being a combination of Just and Tempered. For instance, most of the 3rds are Just and the 7th string, F# has the same number of beats with the B as it does with the C#.

The C6 has the 3rds and 6ths in Just, as well as the 5, 6 and 7 pedals, everything else is tuned to be tolerable.

However, I have a non-pedal 12-string that is tuned:
G
E
D
C
A
G
E
D
C
A
G
C
and it sounds the best tuned in equal temperment.

b0b
Sysop

From: Cloverdale, California, USA

posted 11 November 2004 07:25 PM     profile     
Chas, you should try meantone on that lap steel. It's real similar to my 12 string C6th neck. Meantone solves the "D" problem nicely.

Tom, 4 note chords aren't necessarily a problem in JI. Consider the C6th lap steel. Augmented and dim7 chords get pretty tricky, though.
Gerald Menke
Member

From: Brooklyn, NY, USA

posted 12 November 2004 07:05 AM     profile     
Dear Bobby,

You are absolutely correct, Bach did not use equal temperament, I appreciate your correcting me! He did, however, write the 48 pieces -- a prelude and fugue in each of the 12 minor and major keys -- on a well-tempered instrument -- one whose tuning had been tweaked to allow for playing in all of the keys, C major being the most "in tune" incidentally. It was, to be sure, tuned in a way that is more similar to the equal temperament system than just intonation, which has its roots in the tuning system developed by Pythagoras, which you mentioned.

At the end of the day, I don't know if knowing or caring about this stuff will make me play any better, I doubt Buddy Charlton cared when he was playing for Ernest Tubb all those years. He probably just tuned by ear to Leon and let her rip.

chas smith
Member

From: Encino, CA, USA

posted 12 November 2004 10:21 AM     profile     
b0b, you're tuning C->G->D->A->E ? It didn't occur to me at the time. When I was a teenager, I tuned my mother's piano to meantone, she wasn't very happy about it.
Bobby Lee
Sysop

From: Cloverdale, North California, USA

posted 12 November 2004 11:16 AM     profile     
Chas, I center my meantone temperament on D, with a 2.5 cent stretch of the 4ths. The result is:
C +5
G +2.5
D 0
A -2.5
E -5
It's smoother than equal temperament. Works pretty well.
David Doggett
Member

From: Philadelphia, Pennsylvania, USA

posted 12 November 2004 12:10 PM     profile     
Gerald, to the extent I understand your disagreement with b0b, I think b0b is right, and you are misunderstanding some things. The formal and informal terminology is very confusing on this issue.

First of all, singers, fretless strings and horns in pop or any other kind of music tend to match JI to the extent that they can. After all they are playing to their ears, not a tempered tuner. However, they may on sustained notes match a piano or fretted bass that is laying out a strong tempered note.

Second, if you take your E from a tuner and then tune everything else to it by ear, tuning out beats, that is JI. The fact that you have taken your tuning from E or some other note rather than A (440) doesn't change that. Your instrument is tuned JI to itself, regardless of what the root is. Now, if you have compromised some places and allowed some beats and split the difference, those strings or pedal/lever stops are tempered in some way, not necessarily equal tempered. So what most of us do is a mixture of JI and some tempering. If it is mostly JI, b0b seems to be objecting to calling that a tempered tuning, and I see his point. It's mostly JI, with maybe a tempered tweak in a few places.

With some compensators for things like the F lever it is possible to tune a pedal steel almost completely JI up to a point. Contrary to what you said, the steel guitar can have movable JI chords, so key modulations are no problem with us. The problem is when you get too many pedals and knees and strings to get every permutation JI even with compensators, whether in the same key or modulations. Another problems is when playing with keyboards and other ET instruments. But plenty of top players tune JI by ear and handle both of the above problems very well.

[This message was edited by David Doggett on 12 November 2004 at 12:11 PM.]

Ben Slaughter
Member

From: Madera, California

posted 12 November 2004 02:12 PM     profile     
These definitions helped my understanding. From Websters:

tem·per : to dilute, qualify, or soften by the addition or influence of something else

tem·per·a·ment: the process of slightly modifying the musical intervals of the pure scale to produce a set of 12 equally spaced tones to the octave which enables a keyboard instrument to play in all keys

Bobby Lee
Sysop

From: Cloverdale, North California, USA

posted 12 November 2004 02:14 PM     profile     
Well put, David. The actual JI ratios that most players use are described on this page. If you don't understand what it means, don't worry about it. It won't make one iota of difference in your playing. It's just a reference for people who have read Harry Partch's "Genesis".

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