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Hello. I have had this question for a long while. Would you please answer in a simple way, as I am sort of new here.

When I ask a tuner to tune my piano, does he tune my piano with equal temperament?
And... does he stretch it?

Then, If most pianos today have an equal temperament, what happens when they are not stretched? When the notes are all mathematically relative no matter the octave(e.g. exactly 440 on one octave and 880 on another being the same note)?

Or does equal temperament means no stretch?

Thank you very much,
Samuel

Temperament has to do with the initial centre octave. If all 12 notes are equally distant from one another, it is called an equal temperament.

Inharmonicity, which all pianos have more or less, dictates the size of the initial octave and other octaves afterwards. That is the reason stretch happens.

Stretch is not something that we do purposely (although we can) . It is something that happens naturally once the piano sounds good with itself.

It changes with every piano.

Hope that helps.

Thank you. So if the piano were not stretched, if I played a do in a low octave and a mi in a high one, they would not harmonize?

Exactly.

Someone who better knows will likely chime in here, but the basic answer is that piano strings do not exhibit a mathematically perfect harmonic series. The mechanical properties of the string are effectively different for each partial/harmonic on a single string. This is referred to as "inharmonicity."

As you probably know when you play an A4 for example, you get the fundamental tone of 440Hz related to the whole length of the string, but also a series of higher harmonics/partials related to the length divided by 2, 3, 4 etc. The combination of these partials is essentially what makes a piano sound like a piano, a trumpet sound like a trumpet etc.

Ideally you would expect the second partial of A4 to sound at 880Hz, but in reality its a little higher. Maybe 881Hz. So now, if you tuned the A5 key to 880Hz it would sound out of tune when played together with A4, as the two tones at 880Hz and 881Hz clash to the ear much more than the 881Hz and 440Hz do. This is basically why the octaves in a piano are stretched.

This link shows the calculated vs. measured partial frequencies for an A4 on a Steinway B.
http://daffy.uah.edu/piano/page4/page8/index.html

You can see that each successively higher partial gets successively sharper relative to the fundamental. So even tuning A5 to 881Hz may not be sufficient, as the 4th partial of the A4 at about 1770Hz instead of the ideal 1760 may still not sound right with the second partial of A5 which will be higher than 1760Hz, but not as much as the fourth partial of A4. This gets further complicated by the fact that the degree of inharmonicity is different for each string because each has a unique length and/or diameter. Tuning a piano to sound right involves a lot of compromises.

So the stretch of the octaves is related to the non-idealities of the strings, rather than whether the piano is equal tempered or not. Generally most pianos are tuned for an equal temperament, though some minor deviations may be made to account for similar inharmonicity issues in the intervals within an octave.

Hopefully got that about right. Still learning

Rob

By the way I love how you say Do and Mi. I'm a big fan of "The Sound of Music"!!

Sincerely,

Jean

A fella once said to me, "You know you are doing something impossible don't you?"

I didn't know where he was headed, but sighed theatrically and said, "Yes I know, but ya gotta' give me points for trying."

'Turns out he was a physics professor who had a good knowledge of inharmosity and stretch who used an ETD to show his students why they couldn't tune a piano with a frequency counter and a strict mathematical scale.

What's musically pleasing will be the correct stretch whether you arrive there by ETD or by aural tuning, and whether you understand the math or not.

That you pick this particular interval makes this sound to me like a trick question.

Not to be pedantic but with a proper understanding of temperament and a proper understanding of stretch the do and mi would harmonise (in the strictest sense of that word also) better.

I'll let someone else explain it fully if they must, but....

When a piano is tuned with no stretch (I have done this for professional electronic organists who like to play the piano from the organ console in their concerts) one of the things that happens is that the tempered major thirds become less tempered and therefore more pure. (more in harmony).

However, solfège predates Julie.

Yes, a high mi will not be as sharp in an unstretched tuning. Being initially wide in ET, then the mi not as sharp, means do-mi not as wide.

It is also true that the piano is a horribly out of tune instrument, even when tuned well. Well, why do we continue to accept it? IMHO, humans' ability to adapt. Not only have we gotten used to the sound of an out-of-tune M3, M6, etc, but, we perceive and expect it as the desireable and identifiable tone quality of the piano. We don't just allow it to go on, we love it, search for it, revel in it.

I sometimes imagine just how the piano story would have unfolded if, years ago, people said "no way" to the demands that composers and piano tuners placed on our ears, by tuning farther and farther away from just, and closer to equal.

There is a shimmer in the treble harmony of a finely tuned ET that quickly becomes harsh if overstretched.
Equally the pleasant slow undulations of the tenor and lower regions can sound drunken and comic if allowed to get too fast from over stretching.
This is where finer and finer tuning pays off. Inexperienced tuners introduce too much artificial stretch in both directions with no consideration for the finer musical effect on those with more musical listening skills. We, as tuners, are collaborators with the musical community, not dictators.

Ask any professional flute player with a major symphony orchestra. They will tell you that they have to play sharper with piano accompanent (those that ever play with piano accompaniment) than they do with the orchestra. The Piano is already sharp enough.

There is a sharper, faster, louder syndrome that sets in with any musical pursuit that, if not reigned in early, becomes an excercise in tail chasing. We get used to hearing things that way. There was an article in the musical times many years ago dealing with this under the heading: a plea for sanity.

Many tuners are a big fish in a small pond and it is easy to have very musical people accept our dictates. We live, if not careful, in a strange sort of vacuum. We are constantly told we must have exceptional hearing. It is part of the mystique that has grown up around us. We get awful fond of displaying our knowledge of the mechanics of ET and inharmonicity. How often do we sit down with an intelligent top flight musician and have an equal discussion?

No consummate professional really believes in their own legend

If you have the chance to get hands on a higher class digital piano, for instacne in a music store, ask somebody to help you to demonstrate you the stretch effect, and right away also some different temperaments. The sales agent should be able to show you how to switch these settings in seconds by pressing a few buttons. Then you can listen to it yourself, which will help to get a better idea about it. It´s quite impressive to compare effects like this!

RXD writes:
>>There is a shimmer in the treble harmony of a finely tuned ET that quickly becomes harsh if overstretched.
Equally the pleasant slow undulations of the tenor and lower regions can sound drunken and comic if allowed to get too fast from over stretching.
This is where finer and finer tuning pays off. Inexperienced tuners introduce too much artificial stretch in both directions with no consideration for the finer musical effect on those with more musical listening skills. We, as tuners, are collaborators with the musical community, not dictators. <<

This isn't very definitive. I am asked to greatly reduce the stretch in recording studios, and expand it for concerti. Non of the bass players understood why a "proper" tuning sounded so flat in lower regions, but they and the producers certainly understood the clarity when I took the stretch out of the bass. I suggest that we tuners are not collaborators so much as enablers.

>>Ask any professional flute player with a major symphony orchestra. They will tell you that they have to play sharper with piano accompanent (those that ever play with piano accompaniment) than they do with the orchestra. The Piano is already sharp enough. <<

It isn't just the flutes, it is virtually all musicians. As a member of the Blair Quartet said, "Everything changes as soon as the piano begins to play". This is a function of ET, in which all the thirds are wide, and musicians hear them as "sharp". I maintain almost all of the pianos in a mild well-temperament, and this greatly reduces the other musicians' sense of the piano being "sharp". The string players feel their intonation is much more easily secured when there is a tonal center to the tuning.

>>There is a sharper, faster, louder syndrome that sets in with any musical pursuit that, if not reigned in early, becomes an excercise in tail chasing. We get used to hearing things that way. There was an article in the musical times many years ago dealing with this under the heading: a plea for sanity. <<

I think this is a result of not only ET, but of excessively brilliant pianos. When there is little tonal change with volume, the player has to resort to excessive loudness to make melodic lines stand out. Ears quickly become fatigued, and then there is nothing to be done but play louder.

<<Many tuners are a big fish in a small pond and it is easy to have very musical people accept our dictates. We live, if not careful, in a strange sort of vacuum. We are constantly told we must have exceptional hearing. It is part of the mystique that has grown up around us. We get awful fond of displaying our knowledge of the mechanics of ET and inharmonicity. How often do we sit down with an intelligent top flight musician and have an equal discussion? <<

Not sure what is meant by "equal" discussion, but I am surrounded by professional musicians that will discuss tuning intelligently. I have no dictates, but if I did, I think I would be told where to go in a hurry. I have options that I offer, in terms of stretch and temperament, and that is what I do, offer them. Tune first, talk later is the most certain route to expanding pianists' horizons. Many of them are totally unaware of how limiting ET really is until they have learned to recognize the palette a circulating temperament offers, and the response is 90% of them leave ET whenever they can.

Regards,

This is one of the most absurd statements I have ever read at PW.

Professional, and skilled amateur instrumentalists and vocalists, do not perform in ET. Having to adjust to a fixed pitch instrument, such as a piano, lessens tuning integrity which is natural to the ear. It has nothing to do with ET "stretch" or a piano being "sharp."

One must understand the emergence of polyphony in the development of the western tradition. This background training is often missed or neglected in learning the craft of piano tuning and in its contempory execution.

Don't be silly, Marty.

Do you really want me to tear apart what you just imagined.... Again!!!!

Ed. Thank you for taking the time to analyse what I wrote. I was particularly struck by your colleagues phrase that everything changes when a piano is thrown into the mix. I have no problems with your additional information, just a couple of things best discussed over a drink.

There must have been something in the water in the late 1960's. I was delving into the old temperaments when there wasn't a lot out there. Did I devour Jorgensen when he brought his book out. I offered a prize for a composition in his 5 and12. Only two professors entered anything so we all went out for dinner. That was the inaugural meeting of a poker school which was later joined by a fourth... A new composition professor.

I was involved with a piano quintet recording- tune and attend. An established string quartet with piano thrown into the mix!!! I did finish up putting together a temperament that suited what was going on coupled with my previous knowledge There was a longish cello solo and his last D never matched the piano when the ensemble came back in. My findings were pretty much the same as yours.

I be ame a lot more interested in piano technology when I was working as a professional musician and often had exposed things with piano. much from the subject of this thread and also the compromised tenor of smaller pianos. There's a lot to involve an intensely curious young musician.

Anyway, I'm listening to a hundred year old challen concert grand. As I walked up to the church, all I could hear was the piano but as I entered, only then did I hear the 60 strong orchestra. Sounds like I won't have much to do before tha concert. The piano was rebuilt about 10 years ago. It was covered and being used as a bench in an art room when I found it.

There is nothing silly about it. My opinion is based on a lifetime of performing experience as a flutist and pianist.

Tear apart to you heart's content. My rebuttals will be direct and cogent.

Sorry, Marty, your opening rudeness was totally uncalled for, it was a bit early in the day for the usual excuse for such an outburst. The way you voiced your objection seemed a bit too pretentious for reasoning bred of genuine practical experience, at least not the professionals I know. It showed but a fuzzy understanding of the matter.

Give me some cogent reasoning to start with but think about it for a day or two to remove the emotional content.

You sometimes say things that I really find genuinely funny and sometimes they are just plain silly.
Please curb your rudeness You are probably the only one left on this forum who betrays their upbringing in this way. People will begin to think your mother never taught you anything!!

I, of course, am never unintentionally rude.

Mr. or Ms. d,

There was nothing rude about my observation of the statement you had made. There is a big difference between being rude and being honest and direct.

Thank you everyone.