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Yes, good point. Also, the partials of a note will decay differently. Not all partials sustain equally.

If you pluck the strings with a plectrum up a scale will it sound as "accurate" as the notes played with the keys ? Or just pluck the low and high notes from a scale .Will those plucked notes match the sounds made with the hammers? Would the plucked notes lose too many frequencies to be of practical use ?

Thread necromancy?

Newer members forget to check post dates when they either scan posts from the old days or find a post as part of search. It's an honest and harmless transgression. The only real problem is how many of these posters are gone or inactive. Some forums lock threads after a certain period of inactivity.

Kurt

when you strike a note, you hear not only the fundamental, but the harmonics also, they are all mixed in the same note, and these harmonics unfortunately are not so pure... So the harmonics present in a note might interfere with the fundamental note. Some concerts pianos are tuned with "stretch", and some are tuned without strech. Both methods will never be perfect, but we like both tuning methods anyway. Some passages will sound better doing octaves, and some passages will sound worse when playing scales, and viceversa. There is no perfection in tuning. Do you give more importance to the harmonics or to the fundamental present in the same note? It's up to you, whichever method you choose, it will never sound perfect.

To summarize:

Equal temperament is where the ratio of each note to the next of a central octave equals the twelfth root of two or 1.059463 . Twelve of these spacings then gives a ratio of two, an octave.

If strings were truly one dimensional, that is they had zero diameter, stretching octaves would not be necessary. Real strings have a diameter. This means that the effective length of a vibrating string depends on the harmonic, overtone, partial or whatever one wishes to call it. This effect is less for longer strings, which is why it is easier to get a good tuning with a larger piano, or at least with longer strings.

In effect one tunes a lower pitched string so its partials harmonize with notes further up the keyboard, or down in the case of the top end.

This is the physicists explanation. Esthetics, preferences and taste start from this foundation.

Great thread - Marty in Minnesota and VGrantano have since passed. It is heart warming to see posts by them both today.

Couldn't agree more. I still miss Marty every time I come to this forum.

Me too. Hard to believe it's been four years.

post: Don Mannino-
See what you started? Ask 5 tuners their opinions about tuning, and you will always get 10 opinions!

Pique and I have talked a bit about this subject, and my impression is that she feels that the tuning which speaks to her is one with relatively little stretch, especially in the middle of the piano and into the treble.

I teach a class at PTG conventions called "The Sound of Your Tuning" in which I tune 2 matched pianos with widely different octave stretch, then listen to the results. This can be done by ear, or by machine - I use Reyburn Cybertuner along with my ears to do this. In the class I tune one piano to the narrowest octave style that is what I consider to be musically acceptable. The other piano is tuned with the octaves set as wide as possible, maybe a bit beyond good taste, but still musically workable. The affect of these two tunings is rather dramatic on the tone of the piano.

For those not familiar with the technical aspects of piano strings: Pianos by nature require that octaves _not_ be tuned to mathematically correct frequencies. A3 should be 220hz, and A4 should be 440hz, but the 2nd partial of A3 is actually a little higher than 440. All harmonics of piano strings naturally are sharper than the mathematically calculated pitch would be. When the tuner sets the octaves, the tuner naturally listens to these harmonics, which are sharp, so this ends up creating what one might call "stretch" in the octaves.

The tuner then has a choice as to which partial to tune to! The higher the partial one listens to, the wider the octave will become. This is why I can tune 2 pianos so differently right next to each other, and both sound musical, but different!

When tuning the middle octaves very wide, this affects the sound of the temperament. The 12 notes within the octave are still equally spaced, so you still have an equal temperament, but relatively speaking their separation is wider, so the natural 'beats' that one hears change in speed. This is perhaps the most important factor which causes a wide octave stretch tuning style to sound different from a narrow one.

The width of the treble and bass octaves also impact the tone of the piano.

Pique attended one of my tuning seminars in Seattle some years ago, and we discussed this idea afterwards, as I think she was still in the midst of learning about her tuning mystery at that time. (I think I got left out of the book because I wasn't quite colorful enough - that's OK!) In our discussion she seemed to prefer the sample tuning I did with a very narrow stretch, although I think that tuning was _too_ narrow for her tastes - and mine!

Remember, these octave widths are all relative things - one cannot set fixed frequencies for the octaves and call it correct, wide, or narrow. The harmonics of the strings are sharp by different amounts in different pianos. So if one used a machine to tune at fixed frequencies that gave wide sounding octaves in a Kawai RX-2, then used the same numbers to tune the same notes in a Steinway O, the octaves in the Steinway might sound neutral, or even narrow. So these stretch amounts are tailored to each individual piano. Tuners talk about tuning "Clean 4:2 octaves" and this is a way of expressing the octave stretch independent of which piano it is. Precise 4:2 octaves in 2 different pianos will have different resulting frequencies, but the musical sound will be similar. Good tuning machines listen to the harmonics of the strings, and allow the tuner to set the octaves to particular harmonics like this. Or, of course, it can always be done by ear. Besides just the tuners musical sense and experience, there are specific interval tests which tuners can use to verify what they are hearing.

The affect on tone varies some according to the individual piano, but here are some generalizations about tuning tone:

- Extra Wide octaves in the center of the piano cause the temperament area to sound brighter, more aggressive, less focused perhaps, and more "tense." This is because the 3rds and 6ths are made to beat faster when the octaves are wide. The 5ths are more pure than a normal stretch would give, but these are not as audible during complex music than the business of the 3rds and 6ths. There are very fine tuners at work today who regularly tune center octaves so that they are very, very wide, and the 5ths are almost pure! So the old Pythagorean comma gets put into the octave, instead of compromising all of the 5ths between! This is how the wide tuning in my seminar is done - I try to get the 5ths pure.

- Narrow octaves in the center of the piano tend to make the temperament area sound more sweet and pure in tone, even though the 5ths will tend to beat faster than they might in a "normal" tuning.

- The relative width of the octaves in the high treble also impacts the tone. Concert tunings are often stretched higher in the top octaves, as this can add brilliance and intensity to the tone up there.

- A more narrow octave in the treble area helps the piano to sing more, and 'bite' less, as the lower partials within the octaves set up sympathetic ringing that builds sustain. Some of the attack of the tone is quickly transferred to an octave above or below, reducing intensity and adding sustain.

- Low bass tone will sound a little deeper and fatter if the octaves are tuned so that one of the lower partials beats slowly but audibly. Usually this is the 6th partial of the lower note, and when one plays a solid octave down at the bottom one hears a deep, slow GROWL sort of sound. Widened octaves here also slow down the naturally occurring beats in higher partials of the octaves - it is common for the 12th or 14th partial of the low note to be beating very fast with the 6th or 7th partial of the upper note. Widening the octave stretch down here slows these down - but if not done tastefully the low growl will get too ugly and loud. The shorter the piano, the greater the disparity between all of these harmonics, making it harder to choose a "correct" octave in the low bass. Ask tuners why they dislike tuning spinets . . .

So there is no one "correct" way to tune any octave. The inexperienced tuner can easily get lost trying to over-think all of this, so it's a little dangerous to try to ask your tuner to do something in precise terms. Asking your tuner to add a little extra stretch to the octaves so that you can hear the tone, or making them slightly less stretched than what the tuner normally would do, is not an unreasonable request to make.

For me, choosing the best octave for the piano, the room, and the pianist are part of the fun of being a piano technician. When I hit it right, I am happy with the sound, and the pianist thinks I'm a wonder worker! It is true that pianists tend to hire the piano tuner who naturally tunes the piano they way they like it - and that's why every city should have multiple quality tuners!

I remember returning to my home town after a few years of working for piano companies. I tuned a bunch of pianos for a dealer event, and one of my old customers was there. I played some Brahms I think, and some of the teachers played, and my old customer got kind of teary-eyed, and said "You tuned these pianos, didn't you!" I said yes, and she said "I really miss the sound of your tunings." This is what inspired me to teach the seminar I mentioned - to encourage piano tuners to play with these concepts, and to tune pianos in a style that creates the kind of sound they and their clients are looking for.

Wow, sorry for such a long post!

Don Mannino, MPA
Kawai America

Don, This is the clearest and despite it's length most concise explanation of stretch I've read. Two more variables to the ideal amount of stretch are the composer (often what period) and even what key the work is written in. It so happens that my "ideal" stretch was likewise evaluated with Brahms Intermezzo op-8 no.1 in the key of A. It has delicate harmonics with subtle dissonances that came out very sweet with very little stretch. At higher amounts of stretch they were harsh. On the other hand Beethoven sonatas especially the first movement of the Pathetique (E flat) sounds a little too tame at this stretch so I have to push it more, which I'm willing to put up with. I believe this tuning could only be accomplished aurally, and I am very happy with it.

Indeed what an excellent post of Don Mannino. Never read such a clear summary of the impact of stretch on tuning. Would have shortened Pique’s interesting book considerably 😀.

It's all about constrained minimum entropy.

Partials are going to beat. Intervals will sound busy. Different composers chose different ways of dealing with these issues.

Mozart often writes a final chord with the octaves as whole notes but the third and fifth as quarters or halves to get rid of the vibrating crap.

Chopin ends some pieces with a single of Bb1 and D7, or F#1 and A#4, reducing the fast beating to a nice gentle vocal vibrato.

To complicate things even further I think the obsession with 440hz doesn't help our tuners (and our strings...). If we all went back to a baroque pitch A=415hz, piano strings and soundboards would be under less stress, and have a longer life.

Given the excellent new posts on this, perhaps some more thread necromancy would be a good idea?

And sound like crap. You can't change the tension that much without destroying the tone unless you completely rescale the stringing. I know this for a fact. Ask anyone else who has played a piano 200 cents low and then brought it (carefully) back to pitch.

Pianos were and are designed for a specific reference frequency.

I would suggest that, if you prefer 415Hz, you simply transpose every piece down a half step. That way, you get the reduction of strain on the singers without the loss of tonal quality in the instrument, OR, you could play the harpsichord (as I do) at 415Hz instead. Much more important is the evil of ET. God gave us Just, Meantone, Werkmeister, Vallotti and Young for a reason, and I say that as an Atheist.

sound like crap?? it's a myth, try to run a blind test, let's improvise something unknown, first on a piano at 415, then on the same piano at 440. Which is which? we would fail miserably the test.

Sorry, but you must be living on a different planet. The impedance of the string/bridge/soundboard interface is essential to the sustain and therefore to the attack of the sound as well. I have modern a clavichord scaled for 440Hz which I tuned down to 392Hz for French baroque work. The clavichord was practically silent with no sustain. If I were to rescale it, it would regain its brightness and sustain.

Anyway, If you want to tune your piano 200 cents low, go ahead. It has no effect on me.

My experience with my antique square piano would tend to support this. When I bought the piano it was tuned to A=392 and sounded fabulous. My tuner tried taking it up to A=415 and this destroyed both the richness of the bass, and the beauty of the treble. I have left it at A=392. I am not saying that this experience is necessarily relevant to what would happen if you change the pitch in a modern instrument, but to me it seems likely.

Further to this aspect of the discussion, can I ask Prout whether you think that if I were to retune my Bluthner from A=440 to A=435, there would be any significant change in the tone? I ask because the "TIEFE STIMMUNG" inscription seems to imply that the piano is designed for A=435. Perhaps there might be an improvement in the tone? Or is the difference too small?

Don't you think it would be fairer to run a blind test? If you are used to listen to your piano at 440 and you suddenly change it at 415, to compensate the change, you will also need to get used to it, give your piano and your ears a few days of adaptation to the new tuning, and you will begin to like it as much as before. Try it. If a pianist plays the Moonlight sonata at 415 you would spot it because you are used to hear it all your life at 440. But if you ask the pianist to play some chords, scales etc, you wouldn't tell if the same piano was tuned at 415 or 440.