Tempered Tuning

Mike Harmon · From: Overland, Missouri, USA

I have read a number of posts which refer to "ET" and "JI" tuning. I assume that "ET" is "Equal Temperament", but I haven't a clue as to what "JI" is!

I've seen several different tuning charts, including Newman's, which specify different offsets from Concert A (440) to be used when tuning an E9 steel. My wife got me a Peterson VS-1 tuner for Christmas this year, and I've been using it to tune my steel, but according to the Peterson documentation, the only temperament settings suitable for playing with fretted instruments are the Equal Temperament setting, and Peterson's proprietary "Guitar" setting.

The only downside I've found with the VS-1 so far is that you can't save the offsets for each note; you have to dial them in every time.

Can anyone explain what JI is (as well as any other temperament variations)? I'm a beginner and just know enough music theory to get myself in trouble, so be gentle!

Mike

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Mike Harmon
Fulawka S10 3 & 5
Nashville 400

chas smith · From: Encino, CA, USA

Just Intonation is derived from the relationships (intervals) of the various harmonics in the harmonic series to the fundamental, (which is the note that you played). Essentially, all natural sounds have the same harmonic series, that is, the relationahips are always the same. What changes is, each harmonics relative loudness to the other harmonics when the note is played. Their relative loudness (amplitudes) is what gives that instrument/thing it's individual sound.

The harmonics are numbered sequentially, 1, 2, 3, 4, 5, 6, 7...out to infinity,and mathematically, this also is what their frequency is relative to the fundamental, the first harmonic. So if you are sitting at the piano, and you were to play C below C below middle C, middle C is 261.6hz, the C an octave below that is 130.8hz and the C below that is 65.4hz. Looking above, if the fundamental is C 65.4hz, and the 2nd harmonic is 2/1 (an octave above), it's C 130.8hz. An octave above the 2 would be the 4, 4/2 = 2/1 and that would be middle C, 261.6hz. The 8th and the 16th are also C.

The 3rd harmonic is a G, 196.2hz as is the 6th, 392.4hz, and the 12th and the 24th.

The 5th is an E, 327hz, as is the 10th. The 7th is a Bb, 457.8hz, the 9th is a D, 588.6hz, the 11th is an F#, 719.4hz, the 13th is an A, 850.2hz and the 15th is a B natural, 981hz.

If you're still with me, you may have noticed that the A is 850.2 and not A 880, as it is on the piano. This is because, the harmonic series relates to/is generated by the fundamental and each fundamental has it's own harmonic series. Also, on the piano, the E, above middle C, will be 329.6 and not 327. this is why the 3rds and 6ths are tuned flat from ET to tune out the beats on your guitar.

Perhaps you've seen the fractions (small number ratios) 1/1, 16/15, 9/8, 6/5, 5/4, 4/3, 45/32, 3/2, 8/5, 5/3, 16/9, 15/8, 2/1 used to describe one of the Just scales. As you know, intervals are distances, a 5th is the distance between say a C and G and in the above series, there is a G at the 3rd harmonic and the C below that is the 2nd harmonic. So G/C is 3/2 and that's the "normal" Just 5th. The distance between the 3rd and the 4th is a P4th, C/G, 4/3. The 5th har. is an E and the 4th is a C so this E/C is the 5/4 maj 3rd. The distance between the 6th, G and the 5th E is a minor 3rd, G/E, 6/5.

There is a minor 6th between the 8th and the 5th, C/E, 8/5 and a maj 6th between the 5th, E and the 3rd, G, E/G, 5/3. 16/9 is a b7, 15/8 is a maj7, 16/15 is C/B, a minor 2nd and the just tritone is usually 45/32 although 7/5 and 10/7 are available.

Now, there are maj 2nds between 13/12, 11/10, 10/9, 9/8 and 8/7 (out to the 16th harmonic, remember, these things keep on going). Each one is different, although not by much, so we normally pick the 9/8, which is perfectly in tune with the 3/2 (notice how 9/8 can be reduced to 3/2). It is not in tune with the 5/3 A, so the "traditional" just scale also includes the 10/9 maj 2nd, that's right two maj 2nds in one scale, notice that 10/9 can be reduced to 5/3, that's how you know they'll be in tune.

A flute sound will be mostly even harmonics, 2, 4 and 8, a clarinet has a more raspy sound and that's because it has a lot of odd harmonics 3, 5, 7, 9...

If you want to tune in just with the Peterson, tune your roots and 5ths straight up. (The tempered 5th is really close to the Just 5th, G above middle C is 391.95 Tempered and 392.4 Just) and then I tune the 3rds and 6ths approx 15 cents flat and after that, everything else is a compromise,(the reason for equal temperment in the first place).

There are a lot of opinions and they are sure to follow...

[This message was edited by chas smith on 15 January 2003 at 07:36 PM.]

Larry Bell · From: Englewood, Florida

as always, excellent dissertation, chas
To cut to the chase, I recommend strongly that you use that nice Peterson tuner to help you learn to tune your guitar by ear to Just Intonation -- that is, tuning the beats out, using harmonics that Carl Dixon and I have both described in recent posts on tuning. Click on SEARCH above -- they were both in the past couple of weeks.

My second recommendation is to experiment with that just tuning to migrate closer to ET or 440 with the thirds and sixths. Find something that works for you and that you can understand. It is difficult to tune ET by ear, but not too difficult to tune JI, then fudge it to avoid some of the pitfalls of JI, like the seriously flat F resulting from the E to F pull on E9. Raising the 3rds and 6ths about 4-8 cents is barely noticeable (they're starting out about 16 cents flat or so) but can help substantially raise the F to something less than a third of a fret off.

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Larry Bell - email: larry@larrybell.org - gigs - Home Page
2000 Fessenden S-12 8x8, 1969 Emmons S-12 6x6, 1971 Dobro

C Dixon · From: Duluth, GA USA

well said Gentlemen. I will add a bit more. JI of course stands for Just Intonation and its definition is in the other two posts. JI in more practical terms refers to tuning any two notes such that there is NO "beat" heard when they are played together.

So what is a "beat"? Good question. It is an entirely different sound than either of the two notes one is picking. It can best be discribed this way.

If you have a note that is ringing say at 440 times a second and you play another note that is ringing at say 440 times a second EXACTLY, these two notes will produce NO beat note (or frequency as it is called).

But say one of these notes is 441 instead of 440, then the ear will hear a third frequency ringing (beating) at 1 cycle per second. This is called the "beat" frequency. It is caused (according to electronic engineers) by the two original notes frequencies) "beating" against each other.

In JI we try to tune so there is NO beats anywhere. Now it gets a bit more complicated than unison notes as in the example above. Here is an example:

1. A 440 (reference)

2. E 660 (JI)

Now if you play an A note and a B note together you would think you would get a beat freguency of 220 HZ. Such is not the case. This is because of the human ear and I won't go into that. Suffice to say, IF the A note was Exactly 440 and the E note was exactly 660, the human ear will hear NO beats.

The same is true of the following:

1. A 440 (reference)

2. C# 550 (JI)

Again, if both notes are exactly as above, the ear will hear NO beat.

So what is the big deal? OK, it is this. IF A is at concert pitch of 440, E is NOT 660 in ET. it is 659.xxxxxxxxxx. And C# in ET is NOT 550 it is 554.xxxxxxxxxx. (I have left the numbers off behind the decimal point for clarity).

So since these two notes are NOT 660 and 550 respectively, the human ear WILL hear a beat frequency that is determined by how far the ET frequency differs from 660 and 550.

Note a very interesting phenomenon.

1. E 660 (JI)

2. E 659.xxxxxxxxx (ET)

They are very close. Less than one cycle (HZ) off.

But now notice this:

1. C# 550 (JI)

2. C# 554.xxxxxxxxxx (ET)

notice there is almost a 5 cycle (HZ) difference in this case. And that my dear friend is WHY pianists say,

"Your thirds are flat!!!!" When talking to us PSG's whackos

What I am saying is, we can pretty much get away with sharping our 5ths (and 4ths) because they are soooo very close. But the entire piano, organ etc world says them 3rds and 6ths are flat.

But because the PSG gives off such powerful overtones (specific harmonics of the base note/frequency), ET sounds horrible to most SG players. Where the same exact chord on a piano sounds much less offensive (EVEN if the sustain pedal is engaged on the piano). For it is the overtones that permit us to tell that it is a piano or whatever instrument that is playing as oppossed to any other instrument.

This is why, the PSG is its own worst enemy when it comes to trying to tune it. It wants to be tuned JI. It almost demands it for most players. Yet when stuck in a band with keyboards, it clashes and some have had to "sharpen" them 3rds.

Please, NO flames, dang it all. I am NOT the message, I am only the messenger. The message author is GOD. He is the one that made our ears. AND it is our ears where the problem has Always been. It has NOTHING to do with intervals, equal or logrithmic or Eastern versus Western music, or natural versus whatever. Instruments do NOT have a problem with beating with one another. It is the human ear that has the problem.

God love you all,

carl

Dave Birkett · From: Oxnard, CA, USA

I find ET on the steel guitar to be a quite effective paint remover.

Kevin Hatton · From: Buffalo, N.Y.

Bravo guys! Bravo, bravo, bravo. What a great forum we have. Where could a beginner go to get such a detailed expert analysis of tuning. You guys are fantastic to do this. Chas, Larry, and Mr. Dixon, my hat's off to you all. What great players. Mike, this is expert advice that is not available to alot of beginning players.

[This message was edited by Kevin Hatton on 15 January 2003 at 10:35 PM.]

[This message was edited by Kevin Hatton on 15 January 2003 at 10:37 PM.]

Allan Thompson · From: Scotland.

Hi Mike,
There are a lot of different ways to tune a steel guitar, ET, JI, or somewhere in between. What is important is finding the tuning method that is best for you to play in tune. Jeff Newman and others use JI, Buddy Emmons, Weldon Myrick and others use ET, Jeff, Buddy and Weldon sound in tune to me.

John Kavanagh · From: Kentville, Nova Scotia, Canada * R.I.P.

Carl's right, though you might just as well look at it the other way and say that the human ear is right and it's the instruments that have the problem. And of course we don't tune our thirds flat, pianos tune them sharp, but that's also another issue.

This topic can (and will) generate a lot of conversation, but one thing that doesn't get mentioned enough is that there are a lot of ways to "temper" just intonation that aren't as radical or as out-of-tune as equal temperament. People who tune organs and harpsichords deal with this all the time. The issue is different, and easier, on steel guitar, because you don't have have 12 immutable pitches, just the relationships between the open strings, and the pedalled changes. You can put the bar where it wants to be.

[This message was edited by John Kavanagh on 16 January 2003 at 08:34 AM.]

David Doggett · Posted 16 Jan 2003 9:46 am

I always like to point out that symphony orchestras solved this problem long ago by getting rid of any instrument that requires ET. Essentially all symphonic music and opera uses JI. They only put up with ET on the rare occassions when they roll a piano out on stage for a piano concerto.

If you play with keyboards, you may have to compromise and use ET or close to it. Regular 6-string guitars may require less compromise to play with. Six-stringers will tune their Es to a tuner (A440 or ET), and may tune all their strings that way. But before they start a song, many will hit the root chord, and then touch up their tuning so it sounds good - they are then moving closer to JI.

Also, a little vibrato covers up lots of these JI/ET problems, especially on the long notes where it really matters. And because you play your steel by ear to match the bass and other prominent instruments (or vocals), the JI/ET problem is less noticable when playing than when comparing single open strings for tuning purposes.

In fact, I don't even like to tune my strings open. After tuning my Es open to A440 ET, I tune everything else by ear at the C or D fret (on E9) so my normal bar pressure is accounted for. Now if I go back and play the strings open, they are not quite in tune, but I hardly ever use open strings on pedal steel, especially not on something with long notes where the fine tuning would matter.

Ron Randall · From: Dallas, Texas, USA

Mike Harmon,

I use the VS-1 tuner and I tune my all my non- pedal necks to Just Intonation. I use G, G6, C6,B6. I know a few tricks with that Peterson VS1.
No, it will not memorize your offsets from ET. I wish it would but...

Yes, yes, yes, I know how to tune by ear, tune out the beats on and on. Darn hard though when I can't hear while everyone else is making racket. The VS-1 is very fast and dead accurate. I know 2 ways to skin this cat.

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Fender Stringmaster T-8
Fender Custom D-8
8 string Benoit
Peavey Amps

C Dixon · From: Duluth, GA USA

I have a comment and a question about symphony orchestra instruments.

First the comment:

Certain instruments such as the violin have almost unlimited ability to "JI tune" (while playing), to what ever medium they want. This of course includes Violas, Chelos and bass vials. Instruments like the piano, do not have this flexibility. I do not believe the harp does either, but not sure. Nor does an organ.

Now my question:

Do instruments like the flute, clarinet, oboe and bassoon along with horns like the French horn have enough "player bend" to shift a fixed C# frequency (as designed), from 554.365262 to 550?

"Inquiring minds want to know."

Anyone?

carl

Earnest Bovine · From: Los Angeles CA USA

Jim Smith · From: Midlothian, TX, USA

I played trombone from second grade through high school and even made first chair in the Allstate Band.

As I got into the advanced stuff, one thing I was taught was the difference in the pitch of notes depending on the key. For example a C# is a different note from Db and I played them with the slide in slightly different positions.

I didn't really understand the reasoning then, but I have to think that other players were and still are taught the same thing. There are ways to tweak the pitch of notes on all wind and string instruments that I know of.

Earnest Bovine · From: Los Angeles CA USA

Kenny Dail · From: Kinston, N.C. R.I.P.

I got a headache...where is the aspirin? I think I played better before I learned so much?????

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kd...and the beat goes on...

[This message was edited by Kenny Dail on 16 January 2003 at 01:11 PM.]

C Dixon · From: Duluth, GA USA

Earnest,

THANK YOU THANK YOU THANK YOU.

In my 60 YRS trying to learn and play music, I have NEVER heard it said better. I simply have to rest my case on every word you typed.

Also, I appreciate the facts about certain players (on specific instruments) being able to shift a note with their mouth. I had often wondered about that, never dreaming they were capable of shifting the base frequency that much. That is interesting to know.

Thanks again, and may the good Lord richly bless you always,

carl

David Doggett · Posted 16 Jan 2003 5:10 pm

I beg to differ with Earnest. It is true that harps, pianos, chimes and other percussion instruments are tuned or built to ET. However these are all only occassional contributors in symphonic music and opera.

All of the strings, which are of course the main instruments, are tuned to the A440 (not all their strings, only their A string) of the first violinist (the Concert Master) at the beginning of the performance. The other open strings are all fifths, which from the thread above you will recall are negligibly close to ET. All fingered notes are then played by ear, which will bring them close to ET only if a tempered instrument such as a piano is a dominant part of the sound at the moment.

All of the horns (woodwind or brass, I play sax) have their valves, finger holes, etc. tuned ET, of course (or possibly some near compromise, as Earnest explains - and that's all news to me, not being a brass player). But as mentioned above, all these musicians (at the professional level) will also play with their lips to what sounds right to their ear, usually meaning JI.

Of course, in a fast run, there is not time to adjust to the ear, so then things may be closer to ET. However, as the trombone player above mentioned, advanced string and horn players may anticipate adjustments to JI (or possibly ET if they are playing with a piano) even when things are going fast.

But mostly, as Ernest correctly points out, they are not thinking about ET or JI with each note, they are simply always playing what sounds best to their ear as best they can. Because our ears (and brains?) are biologically setup to respond favorably to JI, that is what ear players and vocalists will mostly gravitate to, in the absence of a tempered instrument being a dominant part of the mix.

Earnest, I'd love to hear you play some of your classical stuff on pedal steel. Do you have any CDs? I just worked out an adaptation for steel of the theme from the middle Adagio movement of Mozart's Clarinet Concerto in A. But I'm not at your level.

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Student of the Steel, and cheap instrument connoisseur: customized 1970 Sho-Bud Maverick, Fessy S12U, Emmons S12 E9 P/P, Nashville 400, Fender Squire, Peavey Transtube Supreme into JBL 15", 1968 Gibson J50, '60s Kay arch-top, 7-string Raybro, customized Korean Regal square-neck, roundneck Dobro 90C, 1938 Conn Chu Berry tenor sax, '50s Berg mouthpiece, Hamilton upright piano. You make it, I'll play it (more or less)

Dave Birkett · From: Oxnard, CA, USA

As a former tenor sax player, I had to continually vary my embouchure in order to make a simple major scale sound right. In tuning the instrument to the 1st-chair clarinetist, who got her note from a Conn Strobe, I would use a certain and almost arbitrary fixed tension of the mouth muscles and then adjust the mouthpiece or even the neck if the temperature was cold. If another player were to use my horn, he or she would have had to make further adjusments because his or her embouchure would have been diffent. I've heard jazz players who could vary the pitch with their embouchure a huge amount. We all had a target pitch in our minds, but whether this pitch was JI or ET, I don't know as this subject wasn't a part of the curriculum. I suspect, however, it was JI, as the only ET instrument in the band that I can recall was a glockenspiel, the influence of which on the band as a whole was minimal. As Chas pointed out, the tonic note being played certain instrument would suggest the target pitches to the other players.

chas smith · From: Encino, CA, USA

Well, to add some more complication about orchestra players, when there are accidentals in the score, that note will be played differently depending on the direction of the 'line'. By that I mean, if we are in the key of C and there is a scale run up with an F# in it, that F# will be played sharper, if the scale run is down, it will be played flatter.

Part of what makes an orchestra sound so vibrant is that they are out of tune with each other. Although I have heard some orchestras that were a little too vibrant.

Thirty years ago I was working with the Buchla 200 "Electric Music Box" patchpoint synthesizer. One of the biggest problems with synthesizers is/was that all of the sound came from oscillators and all of the waveform harmonics (except for the sine tones, which have no harmonics (harmonics are actually sine tones)) were electrically generated and as such were perfectly in tune with the fundamental, and chords, if we were using chords, could be perfectly in tune also (when they weren't drifting). The sum of all this "intuneness" tended to be very "lifeless" and even when it was making very complex sounds (my favorite was feedback loops inside of feedback loops affecting other feedback loops), while interesting, were still "lifeless" compared to natural sounds. I used to compare it to the difference between the chaos and indeterminancy of nature vs the sterility of a planned community. If you live in a planned community and are offended by that statement, I apologize to you.

All if the instruments in the Gamelon orchestras, in Indonesia, are tuned specific to that orchestra. You wouldn't bring an instrument from another orchestra and sit in. And they are tuned so that one side is slightly out of tune with the other side so that it makes a "shimmer" in the air when they are playing.

So while I can appreciate the quest for in tune perfection, it may not be necessary.

[This message was edited by chas smith on 16 January 2003 at 09:55 PM.]

Dave Birkett · From: Oxnard, CA, USA

Is the crux of this issue the difficulty of playing our quite-capable-of-being-well-tuned steels with almost-impossible-to-tune six-string guitars?

Dan Tyack · From: Olympia, WA USA

When I play classical music (it's rare, believe me) I usually stick to one note at a time and let my ear be the judge.

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www.tyack.com

skip cons · From: Lago Vista TX

Excellent treatsie.
I use a tuner called the PST-2.
A strobe tuner you can load up two complete JI scales into. I have both my E9 and C6th (Newman) JI scales in the machine, including al lthe pedals and knees - Takes all of 2 minutes to go through the whole mess.
ss

John Kavanagh · From: Kentville, Nova Scotia, Canada * R.I.P.

Another problem is this idea that we get from looking at keyboard instruments and tuning machines that there are a fixed number of pitches. What really makes music isn't so much the pitch of one note as the RELATIONSHIP between the notes. (I think this is one of those obvious but really important things) So a major third above C is a particular INTERVAL, and where the e is depends on where the c is.

I think a good player of any orchestral instrument tries to be "in tune" in the context of what he or she hears, as David said. "In tune" dosen't mean playing your C# here and your Db there, it means listening to the other players - especially the leader of your own section - and making sure that any note you're playing is in true relationship to the notes other people are playing, whether it's a unison, a fifth, a third, or whatever.

If you recorded and analysed every pitch played by a good professional orchestra playing music they knew well in a room with good acoustics, I'm convinced the tuning would be better than it would be if they all played precisely in equal temperament.

"Just Intonation" is not really a scale, since even in a seven note diatonic scale the relationships don't all work out - the d you get by going up four thirds isn't the same one you'd get going up two fifths, for instance, and we all know you can't tune a six-string guitar by fourths and have the third come out sweet. I think people call a strict Pythogorean scale "Just Intonation" when it might make more sense to use that term to mean an approach to intonation in which the goal is to make every chord and interval accurate and "in tune" in the natural, mathematical sense our ears recognise. If they're good ears.

John Kavanagh · From: Kentville, Nova Scotia, Canada * R.I.P.

Two small points

This is further to what Chas Smith said earlier - a lot of players sharp thirds or leading tones if they're hearing in a linear fashion - a melody often sounds more expressive if the ascending semitones are sharp. Violinists do this especially - sometimes they'll make a third that's even sharper than ET. (That's guys with good ears and bad judgement - a lot of fiddlers just play sharp 'cause they're out-of-tune)

That may be why they'll say C# is higher than Db. If you're in the key of, say, Eb, a C# would usually be a chromatic lower neighbour to D, and you might want to really squeeeze up to that next note, but Db would be a fifth below Ab, and you'd want to hear that in tune, so it would be lower. I've heard string teachers talk about this.

Also, and my references may be out-of-date, but I think that harps are usually tuned so that the enharmonics aren't exactly the same, to get the thirds better.
The Eb's on the e strings would be tuned to a major third from the g strings, and the D#'s on the d strings would be tuned to a major third from the b strings. That would mean that you'd sometimes get unisons beating slowly, to avoid thirds that beat fast. The little disks that stop the strings are slightly adjustable, I think, so you might be able to put it in strict ET if you wanted, and perhaps they do now.

Boy, this one never ends. But it's important, and interesting. I enjoy talking and thinking about how music is put together (it makes my wife's eyes glaze over in seconds, and she's a musician), but I'm also pretty sure it doesn't help me play any better.

[This message was edited by John Kavanagh on 17 January 2003 at 08:27 AM.]

John Kavanagh · From: Kentville, Nova Scotia, Canada * R.I.P.

oops, one more.

"ET may not be perfect, but it's better than what you usually get."

I missed this wise comment by Earl first time around, and I think that in practise it's often the best attitude to take. I recently refretted my viol in ET to match the harpsichordist I usually play with, and if I'm consistently in tune to him, I'm doing better than my own average anyway.

Is there any reward or penalty for three posts in a row? I'll shut up now.

[This message was edited by John Kavanagh on 17 January 2003 at 08:15 AM.]

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