Flatting the 3rd (or, Just Intonation)

Reece Anderson · Post by **Reece Anderson** » 5 Mar 2004 10:16 am

I agree with Paul and the others he mentioned concerning the JI tuning. If one is skeptical and wants proof, they have but to listen.

Bill Llewellyn · Post by **Bill Llewellyn** » 5 Mar 2004 11:16 am

I have definitely noticed that the PSG playing coming out of Nashville is JI.

David Doggett · Post by **David Doggett** » 5 Mar 2004 11:22 am

I'm happy to find my hack amateur ears agree with those of PF and the other top pros. Tuning ET will not guarantee your steel will sound good with a piano or ET tuned 6-stringers. Fixed pitch instruments tune ET because they have to compromise like that. We don't (at least not to the same extent). Neither do most of the instruments in a symphony orchestra. That ain't no accident.

Cabinet drop can interfere with JI, just not in the same way as with ET.

More advanced electronic keyboards not only do the stretch thing, they give you some other tuning options for alternatives to straight ET.

It's possible on most modern pedal steels to add some compensating (less than half-step) changes to help with some of the major problems, like the A pedal and F lever problem. The straight major chord positions on E9 need the most careful JI tuning. The more dissonant chords (less used on E9) and most of the C6 (or B6) neck chords work better closer to ET.

If you are not using a chord open at the nut, then your tuning will be essentially the same anywhere in the usable range of the neck (that is, in other keys), if you are using the same strings and pedals/knees, because you are using the bar as a movable capo. Depending on your bar pressure, there may be slight differences between your tuning at frets at or near the nut and chords at frets near the middle of the neck. It can help this problem to do the final tweaking of your tuning with the bar at a fret near the center of your typical playing area, say the C or D fret on E9 (you are now fretless and so it may be easier to do this with your ears than a tuner).

I'm still learning, but these are some things I have discovered (many from the kind advice of my betters here on the Forum). [This message was edited by David Doggett on 05 March 2004 at 11:40 AM.]

Jody Cameron · Post by **Jody Cameron** » 5 Mar 2004 12:00 pm

Dave,

I agree about the fixed-pitch instruments, but I sometimes wonder if six-string guitars are truly "fixed-pitch". Theoretically, I suppose they are, but the moment someone puts his fingers on the fretboard, it is often pulled out of tune (sharp) by pressure.
I think this is the reason I've had some troubles in the past being in tune with guitar players. I seem to have more tuning issues with guitar players than with pianos.

David Doggett · Post by **David Doggett** » 5 Mar 2004 12:51 pm

Good point, Jody. Playing in tune on fretted guitars is a whole other complex issue. A guitar is not a truly fixed pitch instrument like a keyboard. As you point out, the frets are fixed, but the string tension changes from fret to fret. Well setup guitars with asymetric nuts and/or bridges customized to string height and gauges help. Some players actually pull strings to pitch sometimes. Also, while many 6-stringers these days start out tuning ET straight up to a tuner, harmonics, etc., I rarely see one who does not hit the root chord of the next song to be played and tweak the tuning by ear (just like in the old days). They are usually tweaking it closer to JI, whether they realize it or not. After doing that for a few songs in different keys, they are in their own tuning world (and your steel, which has not budged a cent may get the blame).

Bob Hoffnar · Post by **Bob Hoffnar** » 5 Mar 2004 1:24 pm

One thing to think of is that if you can't hear the tuning conflicts inherent in fretted instruments and pianos without checking a tuner it is very likely that all the theorizing about tuning will be of no use when it comes to actually playing in tune.

BTW: Bill, all the steel players that I know that get the bulk of major recording work in LA, Texas and NYC us JI also.

John, I don't know what Paul does but when I want to use open strings in a critical recording situation I sometimes need to tweak the notes a bit.

Bob

Buck Dilly · Post by **Buck Dilly** » 5 Mar 2004 4:20 pm

This thread has been very helpful.

Eric West · Post by **Eric West** » 6 Mar 2004 12:05 am

Here's another thing to consider.

I'm not changing my habit of tuning every change and every string to absolute dead on zero. I won't, I wouldn't know where to start.

It was luckily developed in total ignorance.

In fairness to myself, I believe all my "local peers", from Ray Montee, to Larry Behm, DJ, and others will tell you that one of my strong "suits", is playing in tune. ( unless they're all bullshitting me...)

OK. Here it is:

As I mentioned before in a long forgotten Bill Hankey "Fishtailing Bar" thread, the brain is the most advanced computer there is. WHen the left hand is allowed to work in sync with it, it can and DOES make the corrections necessary to play "in tune". I dunno how it does this, but in my case, it has been a process of a quarter century of hitting that chord three frets up with the Es raised, and the A pedal, and knowing how to make it be "in tune". Right now I couldn't tell you how I do it, or which, if any slants I make. If I thought of it, I couldn't make them. The same holds for ALL of the other combinations I'm used to using a hundred times a night in the last couple thousand gigs.

I know this to be the case, because when I take time to "bone up" on fretted guitar, my intonation suffers measurably. IOW, it "disturbs" the "connection". I have long ago realised that I had to "choose one or the other" to be "serious about".

Now. That said, here is a major part of my "theorum":

I have MANY recordings of BE, BC, BS, PF, JH, and all the "standards" where they are "dead on".

Problem is, they're not.

I'm not saying this lightly, because I know the readership of this forum as well as this thread. More people than I have "too much time on their hands".

I came across this when slowing down Brad Paisley recordings of faster than light Mike J, licks. I also did it with Mr F's and E's recordings.

They sound PERFECTLY in tune on the record, but at 10 % speed they are not. Not all the notes. Only the MAIN notes and phrases.

Anybody catch the later internet email making the rounds where it is pointed out that in reading, only the first and last letter, and the number of letters must be correct? You don't have to sit and decipher them, you just basicaly read it.

Wlel, terhe's a smiliar thnig or rahetr the smae thnig at wrok hree msluiclay.

Only the first and last notes, and the main chord tones, the root and fifth, mainly need to be "perfect". Thirds being slid from or at a "slight minor" aren't even noticed, any more than the third being slightly "sussed". Nor are the fifths when slightly moved toward augmentation. Maybe things like slight flattening of the fifths, or raising of the sixths are more 'offensive'. I dunno. I'd just have to say that the tonic at the very least has to be "dead on".

As reported, MANY a "pro's" guitar has been sat behind after a "perfect set", and found to be "way out".

I don't pretend to be in among "pros", but as someone that tunes dead on to a korg, or other "off the rack" tuner, and plays successfully "in tune", I tend to think my 'theorum' has some merit.

The "Tone Center" has got to be not just in your ear, but between your ears and connected through your heart to your hands.

I might too, add that I do play an occaisonal gig with an ET Electronic Piano, as on the 12-13 of Mar, and I DO notice some things that "sound out".

Also that there ARE guitar players locally that I have played with that couldn't play in tune if their lives depended on it, if they had Leo Fender set their bridges and necks, on their brand new USA Teles, and a couple that play PERFECTLY in tune with old ragged Squiers.

If this doesn't make any sense to you, don't worry about it.

It barely does to me.

It is the only way I can explain a very complicated problem I've been called apon to 'splain to people from time to time.

It's if anything a pointing toward trust in the fantastic machine that God, as referenced my friend Carl, b0b, Mr F, E, BS, MA, myself, and many others refer to as so generously endowing us with: Our minds/bodies.

Man made, and devised "tuners" or "JI tuning charts" are only going to get you as close as God lets you get anyhow.

Some of the BEST players like Richard Edge, Buddy C (the times I saw and heard him at gigs or at my sessions with him) Don West and others tune one or two notes off'n a piano, and do the others "by ear".

Anyhow, thanks for the indulgence. Sometimes the simplest things are the hardest, the easiest, the most complex.

I suppose there's The Muse.....

EJL

[This message was edited by Eric West on 06 March 2004 at 12:19 AM.]

Franklin · Post by **Franklin** » 6 Mar 2004 5:39 am

Eric,
When Don and BC tune by ear, this is called JI.....They chime or just tune the beats out until the guitar pleases their ears. I know alot of pro's and don't know any that use charts to tune to JI, which is what I believe you implied

John....No, is the answer to retuning for various keys when chosing JI. Center of pitch changes after you leave the first fret no matter how you slice it. This is another reason why the 442 thing has come into prominence for a reference to the center of pitch when tuning to pianos and guitars for either method.

Carl,

Have you had a chance to confirm your electronic keyboard tuning question? My Peavey synth is stretched and so are all of my keyboard midi samples in my Pro Tool system.....I also talked to a couple of keyboard wizards after I posted yesterday. They confirmed it as being correct and added that the wurlitzer, Rhodes, and B3's are also stretched tuned. Stretch tuning is ET. Stretching it does not bring it closer to JI. If I understood your implication then you were implying just the opposite. Is that what you meant?

To all, Tune your open G# to A to match the middle A 440 on the piano. Now place the bar perfectly over the twelfth fret on that same string and hit the next A an octave up on the piano.....The conclusion is that the steel is now flat at the twelfth fret to the pianos next A note because the piano is a tempered instrument and the steel is not. We have a fixed bridge which prevents tempering to happen up the neck on each individual string.

When each instrument is played matching octave notes the steel gets farther out of tune as notes progress to the end of the fret board. By testing the tuning between the keyboard and steel this way using only one string the tuning debate doesn't matter.

An adjustible bridge is the only thing that could solve the true tuning problems inherent in steel guitars because of its fixed bridge.....Paul

[This message was edited by Franklin on 06 March 2004 at 05:44 AM.][This message was edited by Franklin on 06 March 2004 at 08:45 AM.]

Eric West · Post by **Eric West** » 6 Mar 2004 6:45 am

Paul. Thanks for answering.

I would imagine they are indeed "tuning out the beats".

This does, as mentioned make some of the intervals "out of tune", and what I was saying was that the differences are seemingly "automatically" adjusted for. Ala the wonder of the brain.

I find myself doing this all the time, and I tune everything to zero. Only in the open positions do I find it awkward in the least.

I REALLY enjoyed your speed picking CDs this last summer, and found myself to be very "in tune" with them regardless of the differences once out of the "open position". Slow or fast.

This further showed me that adjusting "on the fly" is something we automatically do. Probably paying more attention to 'key notes" than others that are "passing".

Time to get up and "plug it in". I've got a bunch of stuff to fool with today, and I'm gonna try a couple tuning things.

Like I said, it's sheer dumbness that's kept me from tuning any other way for 25 years, and has probably just shown me how automatic accurate, in-tune, bar placement is.

Thanks

EJL

HowardR · Post by **HowardR** » 6 Mar 2004 8:05 am

this rank amateur found himself doing a bar slant

Ah, yes, the foundation upon which all was built.....great and informative thread. Thanks to all.

C Dixon · Post by **C Dixon** » 6 Mar 2004 9:17 am

Paul,

I have not had a chance to check it. In the meantime I will go with what you are saying because of my deep respect for you. I will only state that over many years and reading much on the subject of "stretch tuning" on pianos, that it was a due to a mechanical limitation not inherrent in electronic pianos. But again, I stand corrected respectfully, if my understanding is wrong.

carl

Franklin · Post by **Franklin** » 6 Mar 2004 9:44 am

Carl,

I also respect your opinions. I do wish at some point you will not just take my word for it and check it out.....

God bless,

And on another note, I miss your emails....Hope all is well...Paul[This message was edited by Franklin on 06 March 2004 at 09:52 AM.]

Jeff A. Smith · Post by **Jeff A. Smith** » 6 Mar 2004 9:59 am

I believe what Carl may be referring to is what we piano technicians refer to as "inharmonicity."

Overtones are created be the vibrating string breaking up into what are called "ventral segments." The higher the overtone of each string, the smaller the string segments that create the overtone. The smaller the string segments, the more the string's thickness/stiffness sharpens the overtone from what it would be if theoretically accurate.

Inharmonicity, and how it factors into how a piano is tuned, has been discussed here in-depth before.

In a nutshell: Since the overtones of notes in the center section are what primarily determine how well the center section of a piano matches with notes higher or lower on the keyboard, the higher section is tuned sharp and the bass section flat, if you judge this by how the fundamental frequencies of the notes match with an electronic device.

This is not done because of a property inherent in the equal-tempered tuning system itself, but rather because of "inharmonicity," the increasing inability of a physical string to produce overtones that are mathematically accurate, the further up the overtone series one goes on each individual string.

Also, tuners vary in their personal preference of how much "stretching" is needed. Part of this may be due to a tendency noted by some for the human ear to hear higher pitches flat of what they truly are.

On a personal note: Even though I tune pianos and play electric guitar, I do not prefer Equal Temperament on pedal steel guitar; either on E9 or C6. Paul's comments on the subject of how top Nashville pros tune (as expressed sometime ago, in a way very similar to the above) were a major incentive in why I decided to stick with what seems natural to me.

Thanks for taking the time to offer your thoughts, Paul.

David Doggett · Post by **David Doggett** » 6 Mar 2004 10:54 am

Eric, I think ear-hand coodination, slight bar slants, and vibrato do help either JI or ET tuning to sound acceptable. For example, on two string harmony playing, experienced players seem to get really good at hearing both strings and making the bar play both in tune regardless of the inversion or where you are on the neck. Nevertheless, no matter how acceptable you think your ET tuning may sound, I venture to bet that if you recorded it and sent it to the same studio ears that rejected PFs ET tuned tracks, you'd get some of them sent back for retuning the same way he did.

I have noticed that when playing with a big group ET is not as harsh sounding as when I play alone. But even in a group, my part sounds better JI when it's a prominent upfront part.

Jim Cohen related an interesting experience in a previous post on this topic. He was recording something with a piano, and he tuned ET to match it. But everyone agreed that it sounded better when the steel was tuned JI, although no one knew why. My guess is that our ears and brains can handle slight mismatches between instruments, but we want to hear each instrument well in tune with itself. Jim's ear-hand coordination probably minimized the mismatch with the piano; but always having the ET thirds sound sharp within the steel chords apparently didn't sound as good as having the steel tuned JI within itself.

We can use tuners, theory and charts as guides, as well as beat tuning, harmonics, etc., but in the end we have to listen to the music and the whole mix and do whatever it takes to make that sound best, and that may not be the same thing for everyone.

David Doggett · Post by **David Doggett** » 6 Mar 2004 11:40 am

To follow up a little on that last point about each instrument being in tune with itself, a JI tuned piano could not play in tune with itself, even if it stayed exclusively in one key. With a perfect JI tuned scale, the II chord, and others, such as the VI chord, would be drastically out of tune with themselves. The ear wants to here the JI third in tune within each chord, not necessarily in tune with the rest of the JI scale. In other words, in the key of C, a D major chord would want to be in tune with the D JI scale (at least in terms of the 3rd), not the C JI scale. Because of this problem, and the key change problem, pianos just will always sound better tuned ET.

The steel guitar does not have this problem, because if your chord is in JI tune with itself at the C fret, the bar acts as a capo that keeps it in JI tune with itself at the D fret. So we do not need ET for this problem the way a piano does. For the same reason, changing keys is not a problem for us, especially if the open nut postition is not involved.

We can get in trouble when we change grips, so that a string that was tuned to a JI 3rd, is not the 3rd for the new grip. In some of the main positions, we can take care of that by the way we tune the pedal and knee stops. Compensators can also help, as well as bar slanting. At some point, particularly on the C6 neck, you just can't fix eveything for all the different grips and using all the different strings as the root. For that reason a lot of people tune the C6 neck ET or close to it. Fortunately, with the more dissonant chords typically played on the C6 neck, ET sounds better than on the E9 neck, which uses more straight major chords.

So it's not simply a matter of either JI or ET, but what works where. Our instrument's flexibility in being able to use a mixture of JI and ET and bar-adjusted pitch is one of the things that gives it such a thrilling sound in the hands of masters. And in the hands of an inexperienced klutz like me, it can be more painful than chewing tinfoil.

Eric West · Post by **Eric West** » 6 Mar 2004 1:01 pm

DD. Here's where "Technique" comes in. Thanks for making me think about it.

A nice strong "octave" played to "set the scene" is played, and then "fill notes" or "color chords" are played in the space where the "scene is set". If a seventh doesn't sound right, back off, or turn it into a "unison" til it does. Good strong "root/fifths" do the same thing.

Mind ye, this happens in spans of less than a second. Only those that think quickly survive at all.

Like tempo, often it's a "battle of wills", and more than that, I cannot explain.

You can lose at any time. It's an option taken my too many in the name of "being right". You can noodle along looking for "agreement" or you can set it.

Espressing it in terms of charts, programmed specialised tunings, is way beyond me and my quarter century of succesfully playing in tune while in mostly 'hack bands".

I guess as close as I can come with my limited credentials is to say that like tempo, it MUST come from within. You HAVE to be CERTAIN. It can NOT happen soley with the "ear", though it cannot happen without it. It's like having a firm handshake without "squeezing".

In short, go out and play it like you own it, and do so until someone convinces you otherwise. ET electronic piani are the most convincing to me.

That's as much of my secret as I'm going to give away, but it's the whole thing.

Second only to the secret of having as much time out in front of yourself as you can where you know what is going to happen.

Now that's a real secret..

EJL. [This message was edited by Eric West on 06 March 2004 at 01:11 PM.]

Dan Hatfield · Post by **Dan Hatfield** » 9 Mar 2004 12:36 pm

I may be all wet in my logic but I have always thought that the technique of tuning the piano "sharp" as you go higher in pitch and "flat" as you go lower in pitch was due to the fact that the instrument will stay reasonably in tune for a longer period of time when you do it that way. I know it to be a fact that an acoustic piano begins going out of tune as soon as the tuner walks out the door; if you wanted your baby grand to always be in tune, you would have to tune it once a week; very few people can afford $75 a week to keep their piano in tune, so they usually try to have it done maybe once a year. The higher the pitch the smaller and shorter the string, and the higher the tension on that string. Each string is being pounded by a felt-tipped hammer, so the pitch is going to start going down on each string as soon as the tuner walks out the door. The thing is, the higher pitched strings are going to drop faster -- hence they need to be tuned sharper to begin with so that theoretically everything will tend to even out over time.

Now this was explained to me around 40 years ago by a professional tuner, but he may have been out to lunch; it sure makes sense to me, however. If I am wrong about this I am sure someone will tell me.

There are probably other reasons for tuning this way as have been stated above, but maybe this is partially responsible for the practice.

Dan

Jeff Hogsten · Post by **Jeff Hogsten** » 9 Mar 2004 4:25 pm

I think how good a persons ear is has someting to do with it. I may read someone thinks they are in good tune but could a person with a better ear hear the same thing a think it was out. I dont know if this is true or a rumor but Ive heard that Emmons cant stand to listen to the black album because he now thinks it is out of tune. I went to college with a keyboard player who is now a well know session player that had such a good ear that when he was driving and listening to the radio he would have to speed up or down at times to get the whinning,or whatever term you use to describe the noise a tire makes on the road,in tune with the song. I wonder if he may hear something Ive recorded that sounds fine to me and think it was out of tune. Just a thought, actually I woudnt want to hear that good, it could drive you crazy

Jeff

Jeff A. Smith · Post by **Jeff A. Smith** » 9 Mar 2004 4:36 pm

Dan, that's more of an agreeable byproduct. (I'm assuming you've read my previous post.)

Why would professional concert artists, who have every piano they play stretch-tuned right before they perform, insist on this? It isn't because a tuning that is done properly will drop that quickly, I can tell you that. From the standpoint of the artist, they may not know technically what is going on, but the bottom line from their perspective is that pianos that aren't stretch-tuned just don't sound very good.

The fact is, even if you just tune the octaves beatless on a piano, and then check them with an electronic tuner, you will already find the phenomena of "inharmonicity" has produced a treble section that is sharp, with the opposite in the bass section.

If you're interested in the subject, find any basic book on piano tuning (public library?) and see what it says about "inharmonicity," and why pianos are always stretch-tuned. I went to school for a year to learn how to tune and repair pianos, I've read many books on the subject, and I've never heard the reason you suggest given as a primary one.

Frankly Dan, this is from the most basic level of technical knowledge that any qualified tuner has. The tuner you had, if he in fact told you everything he knew on the subject, may have tuned adequately, but he couldn't have had a very deep knowledge of what he was doing.

I know it to be a fact that an acoustic piano begins going out of tune as soon as the tuner walks out the door

If the pinblock on your piano is in good condition, and you are hearing significant and audible variations "as soon as the tuner walks out the door," you need to find another tuner, Dan. Part of what separates a good tuner from a bad one is competency in the physical technques of setting the string and setting the pin. That's not something that someone learns overnight, but it is absolutely crucial in producing a tuning that will last a reasonable period of time.

What I've said is easily verifiable in any reasonably good book on the subject, or on the internet. You don't have to take my word for it. [This message was edited by Jeff A. Smith on 09 March 2004 at 05:52 PM.]

Jeff A. Smith · Post by **Jeff A. Smith** » 9 Mar 2004 5:03 pm

One last personal comment on what this thread was originally about, and not with any presumption of being a steel player whose opinion means anything:

I have experimented around with the compromise method that some advocate, where the relevant notes in question are tuned between JI and ET. I find that to be a very agreeable compromise, and would happily switch to it in a situation where my own limited abilities as a steel player (and an ear that hears an awful lot of ET) seemed to dictate it.

I do remember a thread (although I won't go to the trouble of finding it) where Buddy Emmons described what he does with his thirds on E9, and I think it ended up being essentially the same thing. It wasn't straight ET.[This message was edited by Jeff A. Smith on 09 March 2004 at 05:07 PM.]

Donny Hinson · Post by **Donny Hinson** » 9 Mar 2004 6:34 pm

I've had a lot of people tune my baby grand. Once, a tuner tuned everything with a strobe, and it sound three times worse than when he started. Most use a fork or a meter for one note, and then try to balance the whole keyboard. One young man (who does the best job of all) has his own system, and I quote his method...

"I tune middle "C" with a fork, then I tune all the other "C" notes in unison, and then I just tune all the other notes so all chords are acceptable".

Not scientific, but it works.

In the argument of how to tune a steel, my opinion is that there's literally no "right way". Every method is wrong. This does not, however, preclude you from sounding good with either method. Once the bar hits the strings...all bets are off. From there on in, it's the player's job to make it sound good. Some master players can do this with either JI or ET, and the rest of us pick the one that suits us best.

Personally, I don't care how you tune it, as long as you can play it in tune. That's what's important!

Dan Hatfield · Post by **Dan Hatfield** » 10 Mar 2004 8:59 am

Jeff, I will accept your explanation of the "inharmonicity" phenomenon. I don't know anything about it but have always been facinated by the procedures involved in piano tuning. The only thing I would disagree with is your reference to "Why would professional concert artists, who have every piano they play stretch-tuned right before they perform, insist on this?" as support for your argument only. I think it also supports my argument that pianos do not stay in tune very long. If a concert artist does a concert six nights in a row he will have the piano tuned six times. Why would he demand this if the instrument stays in perfect tune?

So I am sure you are correct about the reasons for "stretch" tuning and I will pursue finding more info on the subject. Thanks for your input. Dan

Rick Aiello · Post by **Rick Aiello** » 10 Mar 2004 10:26 am

Here is a nice paper on Inharmonicity...

------------------

www.horseshoemagnets.com

Jeff A. Smith · Post by **Jeff A. Smith** » 10 Mar 2004 10:47 am

If a concert artist does a concert six nights in a row he will have the piano tuned six times. Why would he demand this if the instrument stays in perfect tune?

A reasonable question.

You are correct that if the same piano is used on six consecutive nights, it will not be in perfect tune after even one full performance.

However, the assumption I believe you are making, that the piano in this particular situation would obey a rule that the further up the keyboard you go, the more you will encounter a general tendency of flatness sufficient to justify stretch-tuning, is incorrect.

You will indeed, after a single performance, tend to find more isolated notes in the upper half of the piano that are out of tune, but these will for the most part just be single strings within the three-string unisons of that section.

Further, when you get up into the very top of the treble, it would be common for there not to be any change at all.

It's even common for me to return to a good grand piano I tuned a year before or longer, and not have to significantly alter the top octave.

Something you have to factor into the equation, when you are considering how a tuning fluctuates over time, is that the major cause of tuning instability (let's say during a one-year period) will be humidity changes. The part of the piano that is most drastically affected by these annual changes is the center section, because that is where the soundboard (which supports the strings, and will absorb and lose humidity) rises and falls with these changes the most dramatically. The high treble, within a yearly period, is much less affected by humidity changes than the center section or most of the bass.

My experience has been that the tendency for the entire treble to flatten (and not just isolated unisons or notes) more than the rest of the piano, in a general sense, requires a period of time longer than the yearly cycle.

So, while the tendency you mention does unquestionably exist, one has to be careful about generalizing too much according to that one factor. The most clear-cut and common example of it would be a situation in which a good piano, all other things being equal, isn't tuned for a at least several years. One would then expect to see that the piano was progressively flat, in a comprehensive sense, as one progresses upward into the treble.

Although some grand pianos do have certain problems in parts of the upper half that adversely affect their ability to hold a tuning, it is usually possible (and necessary) for the tuner to deliver several very firm blows to everything he tunes in the upper half, without the tuning being noticeably affected. [This message was edited by Jeff A. Smith on 10 March 2004 at 11:07 AM.]