In Search of the Well Tempered Instrument

"The only time I play on a properly tuned instrument, is when I go to the concert hall for a performance......" (a quote from a well-known pianist).

The purpose of this paper is to focus the attention of pianists and students of the piano on three problems:

1) Since pianos are usually tuned twice a year, practice on a piano which is not in excellent tune harms your listening, by sheer inattention, and takes your listening away from the quality of the sound you are producing.

2) A piano stays in perfect tune only a few weeks, many notes may be acceptable but a few will always be wandering off, sounds which you habitually have to ignore. It would be important to have the piano tuned each month, but cost is prohibitive, as well as making the appointments ahead of time with busy tuners.

3) This paper discusses a laboratory quality instrument, the ACCU-TUNE Model 350, which enables you to tune each string individually to a correct pitch, with several formulae for stretching bass and treble for acoustic truth, without having to learn the complicated "circle of fourths and fifths" which a skilled tuner has mastered. This provides greatest accuracy, you do the work with the tuning "hammer" (wrench) yourself, assuming that you have a firm hand and a feeling for adjustments, and the unit will cost not much more than half a dozen tunings, when mass-produced. The manufacturer is Ward Widener
Widener Engineering
203 Westbrook Drive
Austin TX 78746

4) An Addendum On "Downbearing" in the piano at the end of this article describes the Lowell Downbearing Gauge with specifications for its use.

The Piano and its Tuning

The piano is a unique instrument, with the largest range of pitches of any musical acoustic device. In the early l9 th century the use of the cast-iron frame for stringing was introduced in the US, which stabilized much of the force of the steel strings, as compared to previous pianos which were plagued by the expansion and contraction of wood members under compression. Iron made tuning much more stable, but the case and soundboard have all the propensities of wood to change in response to changes in heating and the seasonal humidities. So it is usual for pianists who are concerned with keeping their instrument in relative tune to have the piano tuned twice a year, first when in spring the air becomes more humid, and again in the fall when the effect of a heating system starts to shrink wood parts.

Piano sound is complex. The instrument itself involves an action with several thousand moving parts, a wood soundboard supported by ribs connecting to a rigid case, and the soundboard itself which under pressure from strings resting on two separate bridges, resounds and transmits the sound to the elastic air medium.

But this is no simple relationship, like that of a vibrating tuning fork touched to your dining room table. The characteristic sound of the "piano" is the result of many interlocking factors relating to the length and thickness of the individual strings, the impedance matching of the soundboard, and the "in-harmonicity" of the piano considered as a whole, since multiple modes are involved across the spectrum of the traditional 88 notes. For an excellent review of the acoustic properties of the piano, from the acoustic physicist's point of view (with references to analytical studies made over the years) take a look at this book:

The Musician's Guide to Acoustics, by Murray Campbell and Clive Greated, Dent and Sons l987 (ISBN 0-460- 04664-6), pp. 241 ff.

I mention this technical study here, because there are so many factors which affect tuning of the instrument, more in fact that a proper tuning can deal with. Some of the factors affecting the final sound are inherent in the strings, case and soundboard, others are related to the human hearing apparatus, and many of the characteristics of piano sound are inexorably tied to the qualities of the individual instrument. Tuning can only do so much, even when resorting to intentional mis-tuning of certain tones to avoid annoying overtones in the harmonic series.

Let me give a brief list of things which should be in order, before tuning is contemplated:

a) The pins must be tight and hold the strings under tension. It seems hardly necessary to mention this, but the wrest plank changes its hold on the pins so slowly over the years, that the gradual loosening may not be immediately apparent.

b) The hammers are the most likely offenders against a good sound overall, they harden over the years, grooves wear in, and filing off the grooves changes the shape, weight and the quality of the sound produced. But hammers can be replaced at a fraction of the cost of the piano.

c) The "let off" or distance from the string at which the hammer is disengaged (you can observe this by pressing a key down slowly and watching for the release under the strings) must be quite near to the string. Wear on action parts may cause early let-off resulting in weak tone. This is always worth checking.

d) After the point of let-off, the key should be able to be depressed a very slight further distances, perhaps only 1/16 inch. This "aftertouch" is really not a matter of touch or delicacy of sound, but insurance that the let-off is complete, and that the action is working correctly. A technician can adjust let-off easily in a hour or less.

e) There are many parts in the complicated grand piano action which wear over the years, if you are a conscientious pianist and practice several hours a day, you may actually wear the action out in a couple of decades or less. If you are a light user the action may outlast you, actions are generally well built and very strong, and the occasional sticking key can be dealt with without much trouble.

The Pianist's Dilemma

Now I want to talk about the dilemma which confronts every piano student or professional pianist. If you ask your tuner how long his tuning will stay correct, he may tell you till next spring or fall, and in a general sense that is right. But in sheer honestly, he should tell you that a week later there will be changes, and in a month it would not be suitable for a concert or a recording. That is why a concert pianist has it written in his contract for a performance that the piano will be "fresh tuned", which means just a few hours before he plays. That will be a very different piano from the piano he has been practicing on while preparing for the concert, it will sound clearer and cleaner, the harmonies will be the best that Equal Temperament can offer, and the sound will be better to his ears. Hence the remark of a professional pianist that the only piano he play on which is properly tuned is the one at his concert.

There is more of a problem in this, than many of us realize. If you practice long hours daily on a mis-tuned piano, even one slightly off from a fine tuned instrument, you are accustoming your hearing to hearing mis-tuned sounds and intervals as normal. The piano is a difficult instrument to play, it looks easy in one sense since you "play" the notes rather than make them from scratch as with violin or clarinet. But you have a very complicated two-handed score to read, with often six or more notes sounding together, and you must have physical control over the limited parameters of loud/soft, long/short, keys over a three foot graphic display, as well as the use of one or two feet for pedals. Since the piano does not have the control of phrasing which voice of violin have, you must "phrase" passages by devising subtle amplitude and rhythm effects.

In this welter of contrary requirements, one things is easy to forget. Many pianists do not listen attentively to the actual "sound", the way a violinist must, since much of that sound is pre-programmed to a certain extent by the instrument. And if not listening acutely to the sound, one will easily pass over mis-tuning, bad intervals, ringing octaves, a wrong-sounding bass........since there are so many other things which demand prior attention.

To repeat: The pianists faces the dilemma of operating a very complicated instrument with a complex musical program, and often must divert attention to the score and away from the final sound output. In this situation he or she (and she actually hears more acutely) ignores the tuning, and fails to rejoice in the lovely sound of a properly tuned instrument. No violinist faces this problem, in an unfretted instrument or with the human voice the mind makes things sound right even as they are made, intervals automatically true themselves, even beyond the compromises of Equal Temperament. Compared with this necessary attention to detail of sound, the pianist tends to become a rough and crude listener.

Tuning: Costs and Frequency

Most of us have our piano tuned twice a year, roughly when the house heating system goes on, and when it goes off. But when I asked an experienced piano technician and rebuilder, Ole Hansen of Hansen and Son, Shelburne VT 05482, how long a piano stays in perfect tune, he shrugged and suggested "a week...more or less".So the "fresh tuning" which a performer's contract specifies in a necessity, not a whim of the agent's imagination. But not all the notes need attention, generally a few unisons will have started to ring, and with an ACCU-TUNE you can attend to that string without going through the elaborate ritual of the circle of fourths and fifths. The tuner lays the bearings at center octave, and the works from there out, but if all you need is half a dozen notes to be touched up, you can do it with a sensitive and accurate instrument yourself in fifteen minutes or less. It is true, you must have a good hand, a sense of what the adjusting tool does and how to use it. But this lies within the muscular abilities of most of us, there are no special qualities of coordination or effort required.

For the seasonal changes,when spring humidity and fall house-heating change the wood parts of the soundboard/case in relationship to the cast iron harp, it will take more time to go over the whole range of strings. My tuner Ole Hansen always tunes the piano twice successively to ensure it all staying firm and correct, this take more than an hour and he has years of practice. I find with the ACCU-TUNE I can do a complete run of all strings in two hours, the designer of the instrument says he sometimes takes more than three hours to be sure it is all right. The spring/fall session will take more time, whereas the monthly check-up need not take more than an hour --- if the pins are tight and the room is kept fairly equable in humidity.

Once you start really listening to the sound, you cannot go back. Most of us have had to play the piano just as it stands, ignoring ringing sounds until they cross the threshold of tolerance, or until the tuner comes on his schedule. If you become sensitive to off-beating sounds, the way a tuner is, that is if you hear amplitude pressure-rhythms in the notes, aside from the actual musical "pitches", then you will want your piano perfect each time you sit down to practice or to play for your own pleasure. Raising the level of acoustic attention and pleasure should be the aim of any musical endeavor.

Methods of Traditional Tuning

Let's assume that these things are in relatively good working order, now we can proceed to discuss the matter of Tuning. On the subject of Tuning, I again refer to The Musician's Guide to Acoustics, Campbell and Greated, p. 252 ff. which gives a good overview of the two aspects of basic tuning technique:

First is the traditional "laying the bearings" or setting a central octave in proper pitch using the time-honored methods which involve attending to the "beats" or pulsations of amplitude (loudness) which accompany two sounds which are being tuned to the piano's Equal Temperament system. This system has faults, but it allows you to play in all keys equally (C and G, p 178 ff.)

Piano technicians who do tuning listen to these beats, not to the pitches the way musicians do, and base their tuning on their sense of the proper beat/ratios for each note being tuned. This is a complicated process which involves actual beat/ratios like. 89 and 10.37, which the tuner perceives through experience, since he can not actually count beats to two decimals accuracy. In fact he checks the sounds continually by sounding thirds and their inverse, the sixths, which tell the ear quickly if something is far wrong. But these thirds/sixths relationships become faster and faster as you go up the scales, so here again is a perceptual rather than a factual, mathematical relationship.

Second is the matter of stretching the bass sounds downwards and the treble sounds upwards, a matter which is dependent partly on human acoustic perception, but even more on complex properties inherent in the structure of the piano. Suffice it to say that the strings must be "stretched" correctly for a given piano, or you will hear errors as soon as you play. The tuner knows this by ear and experience, you normally trust his judgment, and the good sounding result marks a first-class tuner and his work.

A Scientific Tuning Instrument

When I say A Scientific Instrument, you may think of something complicated and hard to use. In the case of the ACCU-TUNE there are no complications other than pushing a button for registering the note you are working with. A series of lights rises or descends showing sharpness or flatness, you adjust the pins until the lights stand still. But the instrument "hears" the sounds in a different mode from what you hear. A magnetic pickup is placed directly above each string, while the adjacent strings are damped with the rubber tuner's wedge. The instrument does not read sound, which is a complicated set of relationships between string, bridge, soundboard, and the room. It reads the vibrating motion of the string, and tunes the string to a given, correct frequency, stretching high and low notes mathematically on a precise set of curves.

This system has the exact frequencies to four decimal places encoded in its memory chip, it compares the reading from each string with the numbers in memory, and signals with the light sequence as you approach the theoretically correct number. That's all there is to it.

This permits you to make all the string adjustments in relation to an exact mathematical model of great accuracy, you can tune one string, or the whole piano one note at a time in this uncomplicated manner. There are no learning curves like those which a tuner has had to deal with, no practice tuning a hundred pianos until you are skilled enough to qualify. It is true, the tuner can do the job in an hour if he is fast, he can do it very well if he is skilled. But not every tuner does the same work, some are better and some less good, whereas if you tune with the ACCU-TUNE and the lights flash in the right order, the work is done right. It will be slower than the tuner's job, but you gain by being able to do checkups when needed, and in a few years you have recovered the cost of the instrument. I consider this saving of cost the least significant factor, far more important is having your piano always in tune, and learning to really listen to sounds with refocused attention and enjoyment.

A Tuning Instrument?

This detailed discussion leads me to this point: Does this sound interesting to you as a system for tuning your piano, do you think you could do it yourself and would you want to? Instruments professional tuners use cost over $1400, but I have found an excellent instrument which is soon to be available in a new version, which I think answers the needs of "self-tuner".

This manufacturer of a fine and accurate instrument for tuning, with a variety of proven "stretch" factors, sells his instrument at a very reasonable cost, and if interested I suggest you reach him directly. I have been using his tuner for several years with great satisfaction, I find that if I listen to my piano attentively, it needs to be tuned about once a month, and the difference between playing on a well tuned piano after an hour's work on it, is striking. Mr Widener is friendly and articulate and can explain the details of his instrument explicitly. If you write to him for his brochure, a phone call will be better understood after reading it, naturally.

I should mention that the ACCU-TUNE Model 350 sells direct from the manufacturer at under half the cost of the tuner which most professional piano tuners use, which puts it within the range of the pianist or teacher who wants to do his own tuning. For further information contact:

Ward Widener
203 Westbrook Drive
Austen TX 78746
Ph: 512 327 1555

The Lowell Downbearing Gauge

The term "Downbearing" refers to the downward pressure of the strings on the bridge of the piano, it loads the soundboard with a proper pressure for the piano's best lively response to the energy of the hammered strings. If there is no downbearing the sound will be weak and flat. Each piano has an optimum downbearing which is partly built into the design of the instrument, and in small degree adjusted by bolts on the iron frame for final tuning by a skilled technician. The tuner-technician will check downbearing with a small metal gage which he applies over the centerline of the bridge to touch the sounding part of the string over the centerline and the string on the hitch-pin side. The amount of clearance which he measures in audible click or feel, determines the correct amount of downbearing. Downbearing and Hammers are probably the two most important final factors in a piano's excellence of sound and both will determine "tone" greatly.

The little metal gauge which every tuner uses is adequate but does not give a completely accurate measure of the exact downbearing. In 1986 the "Lowell Downbearing Gauge" Pat. 4798005 (no longer available) was introduced and a number of these were purchased by piano technicians, but no original instructions seem to have survived and an Internet search gives no information for their use. It seems the Lowell manufacturer ceased production and is no longer able to give specifications for use. Having the use of one of these excellent gages on loan from Ole Hansen ( Hansen and Son, Shelburne VT 05482, Ph.985,8451), I decided to work up a set of specs. for his and my use, which I will run through here for the piano public's information.

About the gauge: It operates with a screw adjusted sensitive bubble level, which fits atop an adjustable-width pair of feet which can be set to any convenient width for use first on the sounding and then on the hitch pin side of the string over the bridge center. Comparing the readings of these two positions will give you the ANGLE of the downbearing very exactly. This is quite different from the metal "click" method and gives precise readings which are useful for a summer as against winter check of the downbearing, which changes with seasonal atmosphere. (There is also a magnetic foot used for the heavy bass strings, working through the copper windings onto the steel wire inside. This can be used on the plain strings also for convenience, but the two "feet" are more accurate with their precise contact on the string.)

My first problem was to decide exactly what the marks on the gauge bubble mean. Since there were no instructions, I laid out a precise gauge of metal with a straight section and another machined off from it at a two degree angle. Holding this in a stable vise, I set the gauge to one of these planes with the bubble centered in one of the larger markings (one with four sub-divisions) and then reset the gauge and adjusted it on the 2 degree plane. The bubble moved over two major markings (or eight small ones), so I could state that a major division ( | . . . | ) was one degree. Checked and rechecked this seems a clear finding. And each of the small divisions would hence be a quarter of a degree. (I found by careful testing that with a foot width setting of 3/4 in., a feeler gage of .010 on one side will give a bubble shift of one degree, while a one inch foot setting ---beyond range of the gage ---- would require a shim of .013 for a one degree bubble movement. For reference, with this gage a one degree discrimination means a one-side eleventation of .013 which is a little less than 1/64th of an inch as .0156.)

Next I tried the gauge with gracious permission at the Johnson Piano showroom at White River VT, on a number of new pianos, and found that the Steinways all had a one degree downbearing angle from the center range where the overstrung strings stopped, up through the treble. Other pianos bore this figure out as a general standard for downbearing in the summer months with a Relative Humidity of 60-70. I then set the downbearing on the 1928 Steinway L which Old Hansen had rebuilt for me, to one degree in early fall RH 75; and checking it in midwinter with a RH of an ideal 40 for pianos, I found the downbearing quarter of a degree reduced, exactly as I had expected.

The next thing to face was this: How does the downbearing get adjusted to this precise tolerance? On the center struts of the cast iron frame there are two large brass nuts which lock around a tapered pin which fits the tuning hammer head. These are fine-tuning adjustments for the last tuning of the piano's downbearing after everything else has been put in order, but these adjustments are not to be trifled with in ignorance. They stress the cast frame of the piano in such a manner as to pull the frame down over the bridge, thus increasing the string angle and pressure on the bridge and thus down onto the soundboard support ribs. When a piano is set up the downbearing should be almost correct from the original design itself, and the adjustments are meant as only a final tuning to be handled with care. Over stress could crack the cast iron which is a brittle material, so only someone who understand piano design and construction should be making these final adjustments.

On the other hand, if one has use of the Lowell gauge, and determines that the angle of strings over the bridge is flat, giving a flat and weak sound to the instrument, a carefully done fine adjustment would seem to be in order. But the question would be: How much adjustment, and how does one decide how far to go? Here again, we need data. I found that on the Steinway the brass adjusting nuts have a thread of 16 to the inch, which means one clockwise turn of the nut will move the frame down .0625 or 1/16th inch. Since the nut is hexagonic, each flat will give a down motion of about .010 or ten thousandths of an inch. Using motion in this small range should not run any risk to the frame of the piano. The tapered center bolt goes down into the wood frame below, it is first turned down clockwise to clear, then the brass nut can be turned down from prior (or a neutral no pressure) position to give a proper downbearing. Best start from a position where your gauge shows too little angle, then go down flat by flat until you get a proper one degree angle.

Season is important since the soundboard moves greatly with the RH. I found my piano which was clearly lacking in tone brightness, had a zero degree across all the reachable strings, so I started increasing downbearing on the center nuts first while checking with the less moveable treble nut as I went along. I found that a total motion of five flats of the nut, meaning about .052 or 52 thousandths of an inch, have me a one degree figure at a RH of 70 in early fall. (Checking in winter at RH40 I found its was about a quarter degree less.)

RESULT? The piano at long last came into its full tone and power. The brightness of the sound was immediately noticeable, there was also increased "punch" on loud notes, and I realized how important properly adjusted downbearing is for realizing a good piano's full potential. The Lowell gauge with its readable figures is much more accurate than the traditional technician's click-gauge, but an experienced piano technician who had done hundreds of pianos will get to the same place via judgment and experience. The Lowell gage however will check fine seasonable changes better, since it has recordable figure to write down and compare.

ADDENDUM: When recording piano there are always problems, the piano is a very difficult instrument to record properly since there are abundant upper harmonics which modern microphones had a good ear for. I find that for a recording setup Ole Hansen puts a strip of masking tape over the strings on the first inch out of the agraffes in order to mask unwanted harmonics. I had some annoying buzz in the middle octaves, tried tape and then strung a thin strip of quarter inch wide felt across the whole range, pushing down firmly in the two spaces of each unison. The harmonics disappeared instantly, and there was only a few percent loss in terminal ringing of a struck string.

In fact the piano sound became so clear, that I began to notice a recorded knocking sound, something like an acorn falling on the floor. I traced this back to the jacks not coming out ofth way easily, which caused a slight key pressure just enough to cause the pressed key itself to drop suddenly onto its felt ring. This key-to-board sound is enough to make an audible clunk, which I found I could get rid of by first squeezing with long pliers the felt rings of the white key row (at least, back row inaccessible) to fluff the up a bit; then I applied a micro-amount of high-graphite grease to the jacks to enable them to slip out effortlessly. The sound was gone, and to my surprise I found the touch much lighter with the improved jack action, and when playing a gentle piano the knock was gone.

For this last adjustment I got much value from the Swedish Royal Society's Five Lectures with sound downloads, and would like to recommend this site for anyone interested in learning more about the acoustics of the pianoforte.

William Harris
Prof. Em. Middlebury College