Is The Piano An In-Harmonic Instrument
Responding to the question with which we title this article, we will begin by affirming that. In effect, the piano is an inharmonious instrument. This idea may surprise and even scandalize many pianists and piano music lovers. Who, in general, have not studied in depth the causes of this in-harmony. Indeed, the piano is an in-harmonic instrument and this is. Because it has serious problems maintaining its series of harmonics in each note in the way the theory predicts. In this article we will analyze this phenomenon and try to explain briefly the causes that cause it.
A very important detail to clarify is that the piano is inharmonious from the point of view of its tuning; that is to say, the in-harmony present in the piano presents a challenge for its tuning. That can only be resolved through the work of highly trained aural piano tuners. This does not mean that the piano has certain difficulties to integrate harmonically with other instruments. Or that it cannot generate harmonic music considered this harmony from the musical point of view. In fact, when the in-harmony present in the piano is adequately compensated through a professional aural tuning. Which is, in our view, the best way to compensate for the in-harmony. It can be used without problems in a harmonic way.
The fact that the piano is an in-harmonic instrument. This does not necessarily mean that the piano has certain difficulties to integrate harmonically with other instruments. Or that it cannot generate harmonic music considered this harmony from the musical point of view.
In previous articles we have briefly explained what the phenomenon of in-harmony consists of. To understand this phenomenon it is important that we introduce ourselves into the theory of the harmonics of sounds.
When we hear the sound of any musical instrument. Our first sensitive and a-critical experience tells us that what we are hearing is simply a single sound. However, that sound is made up of a series of sounds that have a mathematical relationship to each other, proportional.
These sounds are independent and discreet, that is to say that each one has a defined frequency. But they are all sounding together.
Then, for example, when we listen to the La central of the piano whose fundamental frequency or first harmonic. If tuned according to the pattern tone, vibrates at 440 Hz. or cycles per second. And we analyze that sound with a spectrum analyzer. We obtain that this La is made up of a second harmonic of a frequency of 880 Hz.. A third harmonic of 1320 Hz, a fourth harmonic of 1760 Hz. And so on we find sounds of different frequencies defined and proportional to the 440 Hz. of the central.
This phenomenon occurs with any type of musical instrument including the human voice, and that is what the theory says. That is to say that the relations between harmonics. And the fundamental one are whole proportional relations (880 is exactly the double of 440 and 1320 its triple). Now, in the piano this theory is not exactly fulfilled. This is because their harmonics, also called by partial piano tuners, are slightly deviated from the theory. For example, we can find that the La 4 of the piano although it has its fundamental in 440 Hz. Its second harmonic is not at a frequency of 880 Hz. but vibrates at 882Hz.. The third at 1325 Hz. and the fourth, for example at 1780 Hz.
What Is In-Harmony Or Inharmonious?
We call this phenomenon of deviation of the partial or harmonics in the sound of the piano. In relation to what the theory predicts for them, in-harmony. That is to say that if the theory predicts that these harmonics must be exactly proportional to the fundamental frequency. When making a measurement in the piano we will not find this proportionality but slight deviations from the expected frequencies.
The question that may arise at this point is the following.
Why do these slight deviations in the piano occur with respect to the theory? In order to answer this second question, we must first understand where the harmonics of a piano’s notes come from. What the theory tells us about the behavior of strings that vibrate between two fixed points. Is that such vibration occurs in different ways. Each of these modes of vibration of a string is called vibrational modes. And each of them are the ones that generate the harmonics or partial harmonics.
In other words, a piano string can vibrate in a first way that includes the entire length of the string. (see video representation at 8:50). And by vibrating in this way generates the fundamental frequency or first harmonic. But simultaneously, this same string vibrates in a second way. That takes exactly half the total length of the string, thus generating the second harmonic. At the same time that it vibrates in the two preceding ways. It does so in a third way that pivots to a third of the total length. And in doing so generates the third harmonic; and so on.
All the vibrational modes of the string of a piano (and of any other instrument). Are given in joint form and according to the theory each one of those vibrational modes. Pivots exactly in points that are entire proportions of the total length. We must understand here the term pivotar as the place or node. Where the two parts of the rope that are vibrating flex. However, this explanation represents a theoretical ideal model of the vibration on the string of a piano and not its actual behavior. This is due to the fact that the tension of the piano strings. The fact that they are made of steel and are quite thick means that there is no total and complete flexibility at the pivot point (at the node), but rather a certain rigidity (see graphic in the video at 11:51).
Vibrational Modes Of Piano Strings
In an ideal rope with no stiffness problems, the rope would pivot in the node perfectly along its entire length. This type of rope the pivot reaches exactly the nodal point. In a real piano, where the rigidity of the string does not allow that pivot to be ideal as the theory predicts, the string when pivoting at the nodal point does so with a certain rigidity so that it does not do it exactly at the nodal point but because of its rigidity the pivot is shifted to one side and to the other (see drawing in the video at 13:28).
In this way, when the pivot is displaced we find that the part of the rope that is vibrating is shorter than the total length that goes from the node to the fixed part of the rope. Since the length that effectively vibrates is shorter, what is generated is that the harmonic frequency generated by that shorter string is slightly higher in Hz. or Cps. than it would be if the vibration occurred exactly at the nodal point. It is precisely this superior change in frequency that generates slightly deviated harmonics, as we mentioned earlier.
In conclusion, the exact cause of in-harmony or inharmonious on the piano is that, at the nodal points at which the piano string has to pivot, the pivot it makes is not exactly flexible nor is it carried out over its entire length as the ideal string theory says it should be. Inside real pianos where the strings have certain characteristics that lead them to have rigidity in the pivot points, these points are displaced in such a way that the segment of string that will effectively vibrate will be shorter and will therefore generate a harmonic slightly deviated from the theoretical frequency it should have.
This harmonic thus obtained will therefore be in-harmonic, i.e. it will be outside the theoretical measure expected for it, and this occurs in all the harmonics of the piano. In other words: all the harmonics of the piano are deviated from the frequency expected for them and we call this in-harmony. Once we have understood what disharmony is and what its cause is, we will try to answer the question of what effect such disharmony has on pianos.
We know that tuning a piano consists of making certain parts of certain intervals coincide in order to make them sound in a certain way. Now, if the partials that we have to match to achieve the tuning of the intervals are slightly deviated then the measurement of the intervals must likewise be slightly modified to compensate for that deviation. In short, the consequence or effect generated by in-harmony in pianos is the slight modification or detuning of the measurement of the intervals.
Compensation For In-Harmony In Tuning
Now, this slight compensation made over the intervals to circumvent the problem of in-harmony cannot be made by anyone other than a highly trained aural tuner in this matter. In other words, it can be done by any other tuner but the quality of the tuning will be considerably lower than the one done, for example the graduates of the Escuela de Tecnología Pianística de Buenos Aires, because they are specifically trained to perform aural compensations of excellent quality.
A fundamental clarification, which we have not made so far in this article, is that when we refer to tuners we always add the quality of aural. We do this to differentiate those tuners who have such a musical ear training that they tune pianos not by electronic instruments or computers but by their own ear. In solving the problem of in-harmony in pianos, which, as we have already said, consists in compensating for the deviations of the harmonics, it is vital for the quality of the tuning that it is performed by an aural tuner.
This is because only the well-trained human ear has the ability to harmonically and effectively compensate for the great in-harmonic variation that a piano possesses and that is caused: on the one hand, because harmonics deviate within the same note in very different ways depending on what type of harmonic is involved, and on the other hand, because they vary from note to note; and to further complicate the issue, they also vary from piano to piano.
The Value Of The Aural Tuning Of Pianos
With the foregoing we want to express that what electronic instruments or computers do, which those tuners not aurally trained use to compensate for the inharmonious deviation we have been talking about, is nothing more than emulating what an aural tuner does. While it is true that in some cases the result achieved by them is very close to that achieved by an aural tuner, it is never achieved in terms of quality, simply because they work with curves that are not perfectly adapted to each note and each piano in particular. That’s why we insist so strongly that aural tuning is and will be the cornerstone of professional piano tuning.
As a conclusion, it remains for us to express that if, as musicians, pianists, teachers or music lovers of the piano, we want to give back to this instrument the splendor that it has as king of instruments, we must carry out a profound revaluation of the aural tuning of pianos, of the work of the aural tuner of the piano. And to put in brackets or as a secondary tool not entirely ideal the tuning of people who use electronic instruments because they do not reach the excellence in tuning of which the piano is capable.
At the Escuela de Tecnología Pianística de Buenos Aires they understand the importance of aural piano tuning and teach our students to tune without the assistance of electronic instruments. So if you want to learn how to tune your own piano or dedicate yourself professionally to this profitable activity, our teaching of the aural method of tuning will give you the possibility of obtaining, from each piano you come across, a tuning of the highest quality.