DonSmith wrote:Would it be possible for you to tune a Steinway using Pianoteq, then upload the fxp file in the files section?
Hello Don,
Please pardon my rather long dissertations on various aspects of real-, sampled- and modeled pianos. If "brevity is the soul of wit" (Goethe), then I suffer from not being very witty. However, I truly think this information -- albeit wordy -- might clarify some terms used in this thread.
I am tinkering with exactly this thought of tuning a Steinway in Pianoteq. As stated in an earlier posting to this thread, a Steinway D is marketed as a 9' (nominally 270cm) long piano, but few people know that the Model D's actual "speaking" string length is only 201cm (2.01) when measured from the agraffes to the hitch pins.
While I do not currently own the PRO version of Pianoteq, which would allow note-by-note tuning, I have played around with maximizing the "octave" harmonics by setting all of the Spectrum Profile sliders to their minimum (-15dB) positions, then setting Slider #1 at about 0dB and #2 and #4 sliders to their +15db maximum values. I have also temporarily set Sympathetic Resonance quite high, while the opposite is done to the Duplex Scaling, Quadratic, unison width values, which are set to their minimum settings. Of course, this is all done in Equal temperament.
An aside -- Inharmonicity:
While such extreme settings would not work with real world performances, the intention is to most clearly isolate the audible effects of inharmonicity in the virtually modeled strings. The implication, of course, is that one may set the degree of stretched tuning required to null out the effects of inharmonicity in a piano's various octaves.
For those who are not exactly familiar with the term 'inharmonicity', we are talking about the non-integer mathematical multiples of overtones' octave frequencies as compared to the fundamental frequency. (In contrast, a theoretically "perfectly" flexible string would be free to vibrate all the way out to its very ends -- the resulting harmonic frequencies of such a perfect string would be exactly 2X, 3X, 4X ... 8X the fundamental frequency.) Inharmonicity occurs because movements at the very ends of all strings ARE CONSTRAINED by the agraffes and the hitch pins -- the effect shows up mostly when the strings are short and/or the strings are considered to be "thick" in comparison to their speaking lengths. When the ends of these comparatively thick strings are unduly "constricted" from vibrating as perfect strings, their upper harmonics tend to resonate at higher frequencies than their fundamental (full string length) frequencies would imply.
Second aside: Stretch tuning is a compensation for Inharmonicity that plagues all pianos. In effect, one "stretches" (tunes slightly sharp the fundamental frequencies of notes in the keyboard's upper octaves, ... and tunes slightly flat the fundamental frequencies of notes in the piano's lower octaves) to make sure that simultaneously played octave notes do not warble against each other. This occurrence does plague even the longest commercially available concert grands, but it does so to a somewhat lesser extent than everyday pianos. Apparently this is why Pianoteq allows one to select a 10 meter (nearly 33') string length to minimize the prospect of inharmonicity.
The act of stretch tuning is to make sharper the upper octaves' notes to sound in unison with the raised harmonics of strings in the middle of the piano's keyboard. In a similar manner, with shorter grand pianos and upright models, the upper harmonics of these supposedly longest strings of the piano ... also vibrate a frequencies higher than the fundamental tones.
Since we shouldn't be raising the pitches of the middle range of the piano keyboard to compensate for relative short low-note strings' raised upper harmonic frequencies due to inharmonicity, we must LOWER (or flatten) the fundamental frequencies of shorter pianos' lowest notes, such that their inharmonic overtones MATCH the fundamental tones of the pianos' mid range notes.
Back to the original discussion:
Then by playing various notes in octaves, say C3 with C4 and or C5, and then listen for the amount of "warbling" of the original note's octave harmonics with the fundamental frequencies of the two notes sounding at octaves. Next, I use the Octave Stretching slider to "null out" the warbling sound patterns. Unfortunately, for regular Pianoteq (not the PRO edition), the various Octave Stretching slider positions seem to act globally upon the entire keyboard. For any given setting (usually around about 1.15 seems to work well), I can null out some of the notes, but not all octaves of all of the tones.
When I tune a real piano by ear, I first "lay the bearing", meaning that I carefully tune the middle 1-1/2 to 2 chromatic octaves according to the rules of equal temperament. This is achieved by blocking the two outside strings of notes in the middle section, and then tune the higher octaves in such a manner that their higher fundamental frequencies do not "warble" against the corresponding octave harmonics of the center octaves' strings.
In effect, what I accomplish is a form of stretch tuning. Once assured the piano is basically going to be in tune, I remove the felt covering of the original octaves' notes, and then tune all of the unison string pitches of all of the notes.
In essence, when tuning this way, sorry to say, I do NOT tune to a specific degree of stretching, other than to null out the warbling sensations due to the strings' inharmonicities. Therefore, I am not in a position to say that perhaps a low C should be tuned 10 cents flat, or the highest C should be tuned perhaps 30 cents sharper than the nominal middle C frequency.
I hope this sheds some light on how this is done with a real Steinway or other fine grand piano.
There are many, many other considerations to be set with Pianoteq: For Example: The so-called strike point affects the major additional harmonic that accompanies a given struck note. Sometimes, the second major harmonic is the octave (desired in my opinion), but sometimes the next most prominent harmonic sounds at a high fifth or even an even higher third (the so-called odd harmonics #3 and #5, respectively).
On top of this, the damper position, in the Action section, governs whether the second most important harmonic present when the damper comes down ... is an octave (2nd or 4th harmonic), or a high fifth (3rd harmonic) or a very high third (5th harmonic). Ideally, in the piano's lower octaves, the strike position and the damper positions should each yield a consistent set of next most prominent harmonics.
If this is not done, then some of the notes will ring with a prominent octave harmonic, but some adjacent notes may sound prominent high fifth overtones or even higher thirds in the harmonic series. This happens on many pianos of lesser quality, including Steinways smaller than nominally 7' (models smaller than Model B or D).
I hope this serves to help clarify the piano tuner/technicians tasks to accomplish when tuning over some 200 strings per piano.
Cheers,
Joe
Last edited by jcfelice88keys (23-12-2009 06:10)
