riccardoM wrote:If you have fun that way, suit yourself.
The future will be pianos that self-tune via sensors on every note.
Ps if technology that gives food to me also offers food to you
Oh, so then??? What is this tone? How dare you? You better check yourself!! My sentence about technology was not referring to the fact that I believe I am the master of the world or otherwise better than any other person regarding technology; it was to say that I am certainly not the type who disdains it, but when I see that it doesn't work, it doesn't work and I say so openly! So try to stay calm and respect the opinions of those who think differently from you!! You are free to think whatever you want and even strenuously defend your points of view, but without being offensive!
Returning to the topic at hand...
Call all the tuners you want and ask them: www.aiarp.it since you don't trust those who have already replied to you here; you can find many others on that site. If I say that reasoning is wrong, it is because I have excellent reasons to support this thesis, and you can refute it and assert your idea in any way, but without being offensive! Who knows you?? Who gave you this confidence?
To tune my piano, I call my trusted tuner, but since I respect your opinion, I renew my invitation to carry out your idea on your own piano if you are convinced it works; why should I care??
Sergio wrote:I would like to add: inharmonicity within an octave does not have such a linear progression as to be able to precisely "train" an advanced tuner, for that matter. The electronic device can deduce (but not exactly) the octave spacing.
What do you think, Simone?
Great point...
Starting from the definition of inharmonicity, which is the degree of deviation of real harmonics from the ideal harmonics of the harmonic series, it can be inferred that the less elastic (stiff), thicker, and shorter a string is, the greater the inharmonicity will be, and therefore the more the real partials will deviate from the ideal harmonics.
The strings are made of harmonic steel and their thickness is the result of several passes through a machine that decreases their cross-section at each pass.
The plate/scale is appropriately calculated using the following relationship:
delivered from which, by performing simple substitutions, we obtain:
Here, the behavior of string elongation is not taken into account, nor the fact that bass strings are copper-wound, the non-homogeneity of the cross-section especially in the bass where the winding is not homogeneous, torsional vibrations, longitudinal vibrations, the decay transient, and rotational vibrations; one thus ends up complicating that simple relationship so much that using a computer for calculating a complete scale becomes practically necessary.
All these variables together with other theoretical ones determine inharmonicity. By theoretical, I mean just the fact that the real string does not have a cross-section in the order of [missing values] and a length of [missing values].
Thus, we can say that every string possesses its own inharmonicity which is different from any other on the piano. Tension, but in particular tuning, causes the string subjected to pulling to thin out. As it thins, the variables mentioned above are modified: torsional vibrations, rotational vibrations, etc., etc.; therefore, the inharmonicity also changes, as does the tension required to bring it to frequency according to the formulas reported above. These variables are then not linear for all strings, because each string has its own length and cross-section, so each responds differently to the change in tension. Piano manufacturers still try to compensate for these problems with different non-linear string sections and lengths. Returning to tuning, we particularly notice that if the cross-section (d) of the string becomes smaller, since f is inversely proportional to d, the frequency increases; therefore, to re-establish the initial frequency, the tension, which is instead directly proportional to the frequency, must be lower. In essence, with the thinning of the string, the same frequency is obtained by applying a lower tension load (fewer kg). This operation is limited by the breaking point, i.e., that limit identified by the intersection of the graphs of thinning vs. time and tension vs. time. The meeting point of the two graphs represents the breaking point. To be extreme, it is much easier to break an acute string because it has higher tension and is thinner.
I will now show you the graph representing the measurement made on the real correction and that made by a software which calculates a curve called Railsback by its inventor (curve of"}
Average inharmonicity).
The jagged red line represents the actual correction made based on the inharmonicity of each individual note, which turns out to be VERY DIFFERENT from the Railsback average value curve.
Now I will show you the correction curve of a software—the name of which I will not mention for obvious reasons—for piano tuning, and I want to specify that all electronic tuners are based on this principle; therefore, I have taken a random one, since they do not allow the calculation of the inharmonicity of every note, but instead perform an average based on octave-by-octave inharmonicity calculations, almost completely neglecting the calculation for high notes as they contain fewer partials.
As you can see, the graph looks more like Railsback, precisely because it performs an average estimate of inharmonicity.
I will tell you: the results are not even bad and the division of the central octave is good, but there is a reason why the division of the center is good, which is the same reason why tuning starts from the center even by ear. In the center, inharmonicity is very low (you can see it from the graphs, particularly from the first one, which is clearer with the keyboard at the bottom, where in the center the inharmonicity correction is close to zero); consequently, it is very simple for both the tuner and the electronic instrument to establish the correct ratios. This is why tuning starts with A 440Hz, because statistically it is the string with the least inharmonicity. The problem arises when going down or up. Going up, the sounds become progressively increasing, and at the bottom, decreasing. The tuner restores the correct harmonic ratios by ear based on the beats that are generated between the fundamental of one note and the partials of the second (which partial depends on the harmonic ratio we have chosen), and does not worry in the slightest about what the inharmonicity of the string being tuned is, because the ear takes into account harmonic ratios, not inharmonicity; therefore, once the correct number of beats is established, that tuning already takes inharmonicity into account—this is why it is said that in terms of tuning, the human ear is very, very rigorous. The software, on the contrary, must always adhere to mathematical rules, so it takes the theoretical frequency for that note, corrects it by reporting the value intercepted on the inharmonicity graph for that note, and indicates whether the note is flat or sharp. However, you can see in the first graph that this approach is not always valid, because every string has a different inharmonicity coefficient.
This is why, all things considered, these software programs do not produce poor results, but they have nothing to do with tuning by ear.
Now, returning to the initial topic, having cleared up these matters. Recording a frequency and using an electronic tuner to reproduce that same frequency is something that does not work, because we have said that with every tuning, physical variables that determine inharmonicity are modified, and thus the inharmonicity itself is modified. This means that by reproducing the same frequencies as previous tunings, the harmonic ratios will certainly not be respected. It will certainly be a decent tuning, setting aside all the complications arising from the correct use of the tuning hammer, stabilization of the pins, etc., etc., but it will not be EXACT like one done by ear.
