Tempered Tuning Armageddon.

chas smith · Post by **chas smith** » 26 May 2004 6:36 pm

But, Chas, they are pegged to ET by their four open strings.

David, ET, equal temperment, and JI, just intonation, are interval relationships. Scales are sequences of interval relationships, typically between octaves.

So, the piano is usually tuned to 12-tone equal temperment, which means that (theoretically) the space between each note is equi-distant and is the distance of the 12th root of 2 (don't get put off by the numbers).

If you wanted an 8-note equal temperment scale, each note would be the 8th root of 2 apart.

Both are equal temperment and both are very different from each other. I think you may be confusing pitch, A-440, with having something to do with temperment, since pianos, equal temperment and A-440 all kind of go together.

Just intonation is based on the relationships of the harmonics in the harmonic series and tends to have very friendly mathematics. You could think of it as tuning the way nature intended.....

Ernie Renn · Post by **Ernie Renn** » 26 May 2004 7:44 pm

After reading all of this technical stuff, it occurs to me that we're probably making too much out of it. It should come down to "does it sound out of tune?"

I remember when a common saying on the bandstand was, "Gimme an E." Now it's, "Where's the tuner?" or "The batteries are dead in the tuner!"

If you sound out of tune, tune up. If you sound in tune don't. Guess it's really pretty simple...

------------------
My best,
Ernie

www.buddyemmons.com

David Doggett · Post by **David Doggett** » 26 May 2004 8:17 pm

Right, Chas, in that quote I was using "ET" as shorthand to mean 12-tone stretched ET with A=440. That brings us to Graham's question about whether pianos are really tuned to that. Maybe somebody who really knows will jump in. My impression was that piano tuners aim for the above, and have beat counting rules that allow them to get there using a few tuning forks. Maybe some tuners deviate from perfect ET for the sake of some of the more common chords and keys. There have been some comments about that in previous threads, but I forget exactly what was said, so I'll shut up on that now. It should be obvious I'm no expert on this stuff. I'm just piecing together a bunch of stuff I'm remembering from past threads on this here.

Earnest brings up the other historical tempered tunings. I've read about them, but haven't heard them (my $300 Casio doesn't seem to include them).

Now I gotta go practice a little for my Friday night gig. We (Gas Money) will be the middle act at the Tritone in a battle-of-the bands staged by Modern Drunkard. The other two are the Sideshow Prophets and Roadhog. I'll be the one sitting down behind that horizontal string thing, with no tattoes (yet), and playing somewhere between JI and ET. We'll be taking no prisoners.

[This message was edited by David Doggett on 26 May 2004 at 09:35 PM.]

Eric West · Post by **Eric West** » 26 May 2004 8:37 pm

I've always had an E, G, B, C, and an A tuning fork handy in my brief case. Haven't missed with my Korg, or now my Pod xt internal.

Dad left a complete set of tuning forks for his piano tuning forty some years ago, and I'll have to look and see how they were marked.

As I think somebody said, it's also who it sounds in tune to..

EJL[This message was edited by Eric West on 26 May 2004 at 10:47 PM.]

chas smith · Post by **chas smith** » 26 May 2004 9:59 pm

After reading all of this technical stuff, it occurs to me that we're probably making too much out of it. It should come down to "does it sound out of tune?"

No argument, I just think it's fascinating. I have a friend, who, in the middle of a technical discussion on something or other, just stopped and said, "I don't want to know how the brakes work, I want to push the pedal and stop the car." Can't argue with that, but I have to know what the brakes are made out of.

Jeff A. Smith · Post by **Jeff A. Smith** » 26 May 2004 10:45 pm

I was always under the impression that pianos were "temper" tuned by professionals with an "ear" so that various chordal combinations would all sound "okay" (whatever that is) to our ear. By this I assume that we're talking some sort of compromise between JI & ET ... but this discussions has seemed to indicate that pianos are ET ... if this is so then why do we have piano tuning professionals?

Some people use an electronic device or a set of forks to set what is called the "temperament octave" in the center of the piano. If you were to take the tuning test to enter the Piano Technician's Guild however, neither of those methods would be accepted.

You would have to learn to tune the entire piano beginning with a single fork. To make a long story short, the temperament octave is tuned so that the beat rates in major third and major sixth intervals increase in speed by about one half beat per second, as one proceeds upwards by half-steps.

Since each piano and set of strings is different, accomplishing this even progression of beat rates in thirds and sixths will not generally match pure, exact equal temperament. However, even the Conn Strobotuner manual for piano tuning (not its basic owner's manual) suggests varying from pure equal temperament when necessary, to achieve this even progression of thirds and sixths; it's more pleasing to the ear.

The intention is still to have the piano equally usable in all twelve keys. So, it isn't really accurate to say that piano tuning involves a compromise between ET and JI, at least in that the general intention still involves 12 equally spaced semi-tones.

However, in another way, aural piano tuning does involve at least one basic principle used when tuning by ear to JI: The final authority and method involves beat rates created by coinciding harmonics between different intervals, or the absence thereof -- not a visual readout of pure ET on an electronic tuner, since the two will not always agree.

Notes are tuned progressively more sharp as one proceeds up from the temperament octave, and flat going down. This is necessary because of "inharmonicity," which refers to the phenomena whereby a string's thickness causes it's harmonics (overtones) to be sharp from what they should theoretically be. When you play different note groups together on a piano, the relationships between overtones and the beat rates created by these relationships are more important than whether the fundamental frequencies of all the notes match theoretical equal temperament.

Some authorities also have mentioned a tendency of the human ear to hear higher frequencies as being flatter than they are, so that may also be a factor in why octave stretching in the treble sounds good, as well as the common desire to have more brilliance in that section.

An acoustic piano that is tuned straight to equal temperament with an electronic device sounds horrible. If that weren't the case, you can be assured that professional piano tuning would have been exposed as a colossal fraud long ago, since it's fairly simple --putting aside the physical techniques involved-- to buy an electronic device and tune every note straight to equal temperament.

Many modern piano tuners use electronic devices as aids, but their end goal still follows the general guideline I've laid out.

Graham Griffith · Post by **Graham Griffith** » 27 May 2004 1:47 am

Jeff,

thanks for answering my question and putting all that in perspective. I actually recall having read this before but had forgotten it.

Graham

PS I'm doing my corporate Hawaiian gig tonight (one song only ... Hawaiian Wedding Song) on the Eharp tuned ET ... I must have rubber ears.

Buddy Emmons · Post by **Buddy Emmons** » 27 May 2004 2:39 am

Oops! I had a thought but I'll save it for the next round.

[This message was edited by Buddy Emmons on 27 May 2004 at 03:46 AM.]

Jeff A. Smith · Post by **Jeff A. Smith** » 27 May 2004 3:24 am

You're welcome, Graham.

I was looking over an article I have by Bill Bremmer on how to pass the PTG tuning exam. Mr. Bremmer is one of the "gurus" in the piano tuning world. In talking about electronic devices and the PTG test, I didn't mention that although one is required to tune the middle section strictly by ear, beginning with a single reference pitch, one is allowed to use a device after that point if they choose. Again, tuners who use a device still have to factor in inharmonicity, so it isn't straight equal temperament.

I think this paragraph from the article by Mr. Bremmer is a good summation of what we've been talking about:

"Different pianos have different amounts of Inharmonicity. This word means that the overtones, harmonics or partials, whichever you choose to call them are exact multiples of the fundemental tone. They are all sharp and the higher the overtone, the sharper (but also the more fainter) it gets. Inharmonicity is the very reason why octaves and all the notes between them must be "stretched" as it is said. The theoretical values for each of the 88 notes of the piano must be altered to accomodate Inharmonicity. Since each piano's Inharmonicity factor is different, the tuning which is perfect for each piano is also unique."

Okay, I'm done.

C Dixon · Post by **C Dixon** » 27 May 2004 7:17 am

Reference piano tuning. The above is correct. But I am afraid it has, and continues to leave, the wrong perception in many.

Yes, the piano IS tuned ET in the octave around middle C. It is also tuned pretty much ET within any given octave. But the difference is, a given octave is NOT tuned to the same pitch as another one. This due to the so-called and almost universally accepted "stretch-tuning" technique peculiar to the piano and possibly Harp.

It was found early on that IF all octaves on a piano were tuned pure ET, that the upper octaves "sounded" progressively flatter referencing the middle C octave and the lower octaves sounded progressively sharper to the middle C octave.

After much trial and error long ago, it was determined that this was due to (as the posters have said) the inharmonicity of "ringing" strings of different lengths and diameters.

To counteract this, and cause a piano to be perceived (sound) as though it was tuned to ET on all octaves, they progressively sharpened ever so slightly each octave above the middle C octave and progressively flattened ever so slightly each octave below the middle C octave.

The end result is a piano that sounds like it was tuned from one end to the other straight ET; even though the highest octave has notes tuned almost 30 cents sharp!

This should not be confused with JI in any shape, form or manner. Or "it's tuned to a compromise between JI and ET". When a highly skilled piano tuner stretch tunes a piano according to the most accepted standards, that piano will sound almost dead on ET over every one of its 88 keys.

Now there have been attempts to alter the above and shift certain notes to suit a given player in a given key. This has been done by more than one great piano tuner to satisfy (usually) an eccentric pianist.

But IF you called the best most highly skilled piano tuner to tune your piano and you did not request otherwise, he would almost assuredly stretch it according to the aforementioned method.

In fact, one of the finest electronic strobe tuners has a piano stretch method programmed into it. And it is accurate to .001 cents average and NO less than .01 cents absolute. It is the Precision Strobe Tuner-3.

It is my understanding that many former skilled "fork" tuners are now using it (where they had disdain for other all other electronic "gimmicks") to tune pianos. What makes this tuner soooo great is it has filters sooo accurate that even the bottom most notes on a piano causes NO shimmy in the display. A feat next to impossible on almost every other tuner made.

The most interesting thing of all (to me) when it comes to a piano being tuned "ET" (strecthed) by a skilled piano tuner, is how beautiful it sounds to MY ears. Yet, IF that skilled tuner was to tune my steel and all its changes using that same method, it sounds horrible.

Of course as has been said many times on this forum, there is no mystery of why this happens. We are blessed with one of the world's most beautiful instruments but we are cursed at the same time.

Every musical instrument produces (overtones) that are distinctly different from every other musical instrument. It is this fact that tells us what instrument is playing. Our ears subconsciously pick up on these subtle and almost inaudible ovetones and we know istantly what instrument it is.

But for some reason the overtones on a steel guitar clash (for most players) when it is tuned exactly as a piano or ET. If you doubt this, tune just your E G# B to be in total unison to the E G# B keys on a finely tuned piano. And listen to each.

For most players the piano is quite tolerable and to some it sounds beautiful. Yet to most steel players it sounds terrible on the steel guitar.

Only in Heaven will an imperfect world be a thing of the past. Something to think about. Remember Our precious creator is NOT bound by logic he gave man to live by on earth! Praise his holy name.

carl

Alan Pagliere · Post by **Alan Pagliere** » 27 May 2004 7:46 am

I'm with Eric West on this ET thing:

<BLOCKQUOTE>quote:<HR>
When somebody in a band wants an E note, I play what's perfectly centered in my Korg. I don't ask them if they are using it as a Third, Sixth, or Fifth. Similarly with a B, D, G, or any other note.
<HR></BLOCKQUOTE>

If I only ever played in E, and only ever played songs that had but one chord in them, I think I could tune this thing perfectly. But darn it, even in E, I find I'm often moving to A and B ....

That darn E has to serve so many functions: root, flat third in the vi, fifth in the IV, flat-seventh in the II, etc., not to mention dozens of other functions in chords in those other 11 keys.... I'm a purist when it comes to many things, but on this one, I'm shootin' the difference.

Earnest Bovine · Post by **Earnest Bovine** » 27 May 2004 8:01 am

for Jeff Smith:
What are the actual numbers for inharmonicity on various pianos?

Pete Burak · Post by **Pete Burak** » 27 May 2004 9:06 am

Seriously now...

Wether you use a tuner, by ear, JI or ET...

Do you guys tune your open E's with the A+B pedals up, or A+B pedals down?

I'm hoping Buddy and Paul will "chime" in (pun intended!).

Brad Sarno · Post by **Brad Sarno** » 27 May 2004 9:19 am

For a very informative chart that describes the relationship between ET and Harmonically Resonant (JI), check here:
http://www.bazantar.com/grid.html

This grid is layed out in the key of D but the deviations from ET are pretty clear and will apply to any key. You can see that the (favorite) real naturally occuring major third falls about 14 cents flat of the ET third. It's these intervals based on ratios that are the "God Given" musical intervals. Bach did us a huge service and disservice at the same time by developing ET. In my opinion it's these natural harmonic intervals that best grab our heartstrings in music. Not that I haven't been moved by piano or other ET music, but the steel and other potentially "in tune" instruments seem to have the most emotive power when the intervals, especially the major third are true and not ET. Without that real major third, it seems that steel players will try to compensate with vibrato, but that true intervalic relationship of the 1st, 3rd and 5th isn't there. It's like a lens that never really gets into focus. When all three of these notes are right with the 3rd at 14 cents flat and the 5th at zero ET or more accurately 2 cents sharp of zero ET, then the whole chord or any pairs of notes in the chord will have a huge array of overtones all locked in harmony and sync. There's great power and magic in music when this grid of overtones locks in like this. Since the ET 5th is so close to true, it's really the ET major 3rd that's the problematic note in that case. 13.69 cents too sharp to be exact. Equal Temperament is the great world of musical comprimise. Steel guitar seems to have this ability to ride the fence on the issue. One reason I love it so much.

IMVHO

Brad Sarno

C Dixon · Post by **C Dixon** » 27 May 2004 9:20 am

Pete,

I tune them with A and B up, but I am going to start tuning them down after hearing the rationale behind it. I now believe it may be a very good idea. We will see.

I too have a question? For those who tune the beats out (JI), HOW do you tune the E's on your C6 neck?

carl[This message was edited by C Dixon on 27 May 2004 at 10:25 AM.]

Tony Orth · Post by **Tony Orth** » 27 May 2004 9:33 am

Carl, (or anyone)

I've looked at, and tried several tuning charts. Do most of these charts take cabinet drop into consideration in the JI tunings?

If so, now that I have a Legrande III, with no drop, how would that affect the chart.

Admittedly, I'm not a math wizard.

Tony

Brad Sarno · Post by **Brad Sarno** » 27 May 2004 10:13 am

Carl said regarding equal temperament of a E, G# and B (E major chord):

"For most players the piano is quite tolerable and to some it sounds beautiful. Yet to most steel players it sounds terrible on the steel guitar."

Carl, I've thought about that alot. I'm not sure, but I believe it has everything to do with the the harmonic makeup of the extended overtones. The steel is much more rich in overtones and they seem to extend higher than piano and many other instruments. Another way to look at it is with the example of distorted electric guitar since distortion greatly expands and enhances the range of strong overtones for the sake of analysis. The guitar power chord being made of a 1, a 5 and an octave 1 on top, sounds really cool with all the distortion overtones. Rock and Roll. As soon as you add the third to the chord, it goes to hell in a wash of mud and warble and ugly beats. Since the ET 5th is within 2 cents of being JI, the power chord sounds in tune and the thick array of overtones are in tune as well. If you do the same thing on an acoustic guitar or clean electric or piano, you can get away with the ET 3rd in there.

With steel, being very overtone-rich like a distorted guitar, that ET 3rd creates a whole array of overtones and beats that clash with the 1-5 interval. It's in the overtones. The same probably goes for piano with its fundamental and first few overtones being so predominant, the extended overtones are less significant and the clashing is quieter. To my ear, the steel just doesn't sound nearly as pretty with a ET G# when playing the basic forms.

IMVVHO

Brad Sarno

Bobby Lee · Post by **Bobby Lee** » 27 May 2004 10:24 am

Carl,
I've been tuning my C's 5 cents above ET and my E's 5 cents below ET on my C6th. This is the same as the relationship between my E's and G#'s on the E9th.

FWIW, I don't think that any of this is all that critical. Intervals sound in tune to me if they're anywhere between JI and ET. If the average ET offset of the notes of a chord is anywhere close to zero, it sounds in tune with ET instruments. To me, anyway.

I know the math, but I don't lose sleep over it. Pitch isn't just about being in tune - it's also about expression. Miles Davis played some wonderful notes against Gil Evans' piano. I'm not going to throw out "Sketches of Spain" just because Miles wasn't ET or JI or whatever.

------------------
<img align=right src="http://b0b.com/Hotb0b.gif" width="96 height="96">Bobby Lee - email: quasar@b0b.com - gigs - CDs, Open Hearts
Sierra Session 12 (E9), Williams 400X (Emaj9, D6), Sierra Olympic 12 (C6add9),
Sierra Laptop 8 (E6add9), Fender Stringmaster (E13, A6),
Roland Handsonic, Line 6 Variax

David Doggett · Post by **David Doggett** » 27 May 2004 10:28 am

Pete, check out this recent discussion of tuning with pedals up or down, and cabinet drop.
http://steelguitarforum.com/Forum5/HTML/007386.html

Cabinet drop will screw up either JI or ET, but mostly only when playing open strings at the nut.

Jim Peters · Post by **Jim Peters** » 27 May 2004 1:09 pm

Brad ,again,well thought out as always. When I was at your house, you tuned my GFI your way, and it sounded great. I took the guitar later that week to another friend, who strummed across the strings, made a couple adjustments by ear, sounded great! I'm using any old guitar tuner I have, tune the open strings straight up, tune the pedals straight up, guess what- sounds great! I agree with some others, you have to play with some others, if the bass player says give me an E, I can't ask if he wants ET or JI, he gets 440 tuned pitches. You sure are a deep thinker, and we all appreciate it! Thanks , JimP

David Doggett · Post by **David Doggett** » 27 May 2004 1:59 pm

Jim, I've never had a bassist or guitarist ask me for a G#, which is the only open string I have not very close to ET A=440. Because I tune my Es to the tuner without my pedals down, they are always dead on, but my pedaled As are about 438, because of cabinet drop. As you can see, typical cabinet drop can be almost as far from ET A=440 as the typical adjusted JI many of us use. Still, even the A is as close as most gittar players get with the cheapo blinking-light meters they mostly use. Fortunately, we're not trying out for Juliard, we're just rockin' for a bunch of rowdy drunks.

C Dixon · Post by **C Dixon** » 27 May 2004 2:04 pm

<BLOCKQUOTE>quote:<HR>"I've looked at, and tried several tuning charts. Do most of these charts take cabinet drop into consideration in the JI tunings?

If so, now that I have a Legrande III, with no drop, how would that affect the chart."<HR></BLOCKQUOTE>

Tony,

I do not believe most charts take into account cabinet drop. However, Jeff Newman's chart may be due to some degree because of cabinet drop. If you have his chart, he tunes the E's (E9th) and the C's (C6) to 442.5.

And while this might be due to cabinet drop, I now believe (whether Jeff realized it or not) that most of this sharping of the E's was due to his thirds being flat of other instruments. So by sharping the entire tuning, it brings those thirds more in tune with other instruments such as the piano and regular guitar. Thus clashes are less whether they be thirds, roots or fifths.

As to the LeGrande III, there probably would be NO need to change your tuning method using tuning charts. The really deciding factor is whether you wish to tune ET or JI or somewhere in between. I believe this is more of a governing factor than whether one has cabinet drop (or not) more or less.

I know of no PSG which has cabinet drop anywhere near the distance JI is from ET, when it comes to our thirds.

carl

Jeff A. Smith · Post by **Jeff A. Smith** » 27 May 2004 2:06 pm

<BLOCKQUOTE>quote:<HR> for Jeff Smith:
What are the actual numbers for inharmonicity on various pianos?<HR></BLOCKQUOTE> Earnest, there may indeed be a large reference work on that subject, but I'm not aware of it. If you Google around a little, you may find a few selected makes. I didn't find anything in a quick search to pass on.

Some devices have certain pianos programmed into them, like those by Yamaha that have some of their pianos in them. However, since brand new pianos of the same make and model will still have significant variances in inharmonicity, any preset that isn't for that specific individual instrument will be at best a close approximation. See the graph here:

http://www.kenfoster.com/PianoTuning/SuperTuning.html

Six different brand new pianos of the same make and model were measured for the amount of inharmonicity in the temperament notes (F below middle C to the F above) using just the fourth partial. These variations would cause some significant challenges in tuning using a "one size fits all" approach.

The devices a lot of pro tuners use these days have the ability to calibrate inharmonicity for each individual piano, rather than having to rely on a preset program:

http://www.veritune.com/veritune.asp?id=29

<BLOCKQUOTE>quote:<HR> Automatically calculated tunings

Each product adapts its tuning to fit each individual piano. Although the specific methods vary greatly, they all include taking measurements of the piano's inharmonicity in order to determine a set of target frequencies that will produce a desirable tuning. <HR></BLOCKQUOTE> And, furher down: <BLOCKQUOTE>quote:<HR>Measurement step required before tuning

In order to calculate a tuning, both the Accu-Tuner and the CyberTuner require that an extra measurement step be performed before tuning can begin. During this measurement step, the inharmonicity is read in order to calculate the tuning. On the Accu-Tuner, this is a manual step in which for three different notes the string is first tuned to a targeted pitch, and then using the buttons the Accu-Tuner is set to the note an octave above, adjusted to stop the lights, and then the stretch numbers are stored. On the CyberTuner, the software guides you through a sequence of playing each of five (or six) notes three times each during which the notes are recorded and then analyzed for inharmonicity. The Verituner has the option of performing all of these measurements simultaneously while tuning the piano thus bypassing any pre-measurement steps. <HR></BLOCKQUOTE> But, there are still those who say the best job is not done by a machine:

http://www.amarilli.co.uk/piano/tngmeter.asp

Jeff

[This message was edited by Jeff A. Smith on 27 May 2004 at 03:10 PM.]

Earnest Bovine · Post by **Earnest Bovine** » 27 May 2004 2:29 pm

Yes, Jeff, I had read about those electronic tuners that let you calibrate the tuner according to the inharmonicity of each piano, but I didn't find any typical real world numbers on those sites. That's why I asked you!

Jeff A. Smith · Post by **Jeff A. Smith** » 27 May 2004 4:30 pm

Earnest, you should become a member of the technician's forum here:

http://www.pianoworld.com/ubb/ubb/ultimatebb.php

There are people, who know a fraction of what you know about pianos, who get on there and ask technical questions to some very experienced techs, including Bill Bremmer whom I mentioned earlier.

My guess is that these guys could help you if anyone could.

You would probably have a lot to teach them also.