Have you ever heard a triplet while playing a doublet on a violin?
If there is a violin or two friends with wind instruments nearby, try to raise your instruments loudly and play very accurate double notes - say #F and A over middle DO. Play very carefully, loud enough and try to hear a little lower than what you are playing, look for D an octave lower. Assuming you did what you wanted, you should hear a sound that adds fullness to double note you're playing - that's third note.
According to records in violin books, Tartini discovered this strange physical phenomenon as early as 1714 and described his observations in detail in book "Trattato di Musica", published in 1754. Therefore, this phenomenon is also called Tartini tone. In later music history, Mozart's father (Leopold Mozart), Bai Yao (Pierre Baio) and so on all have ink on these phenomena. Generally speaking, their understanding is quite correct: this is a physical phenomenon that occurs due to difference in frequencies of two sounds. Since then, let this natural phenomenon help players practice and judge serve. As mentioned above, when pitch is correct, frequency difference simply brings out exact third tone, if not, it means that pitch is inaccurate and inconsistent. However, over time, Ivan Galamian and Carl Flesch abandoned use of this phenomenon for practicing intonation. The exact cause has yet to be verified, and at present I assume that it is related to advent of law of averages. In equal law, this phenomenon, which is characteristic of pure law, is disadvantageous.
In traditional violin science, this phenomenon is believed to occur in inner ear. However, having had opportunity to come into contact with world of sounds, I realized that some of physical phenomena of sound waves mentioned by them are closely related to music. The phenomena coincide with each other. Thanks to convenience of Internet in recent years, many intertwined professional issues can be found without going to the library for books, and you can find related documents. my foundation took shape after asking for advice.
In simple terms, third tone is difference between two sound frequencies, that is, subtraction (internal difference) (differential tone), for example, sound A = 440 Hz sounds together with sound C = 528 Hz, will give a pitch of 528 - 440 = 88, F= 88 Hz. In this case, it is a major triad, pitch of which is separated from each other by more than two octaves. At same time, what is not mentioned in traditional theory of third tone is that there will be a physical phenomenon of a summing tone between two tones. The resulting harmonics (overtones) are masked, so they can be ignored, but in sounding physics must be known. These two phenomena are collectively referred to as "combined tones". This is what I was looking for: this is not just a phenomenon heard by ears, but a physical phenomenon that exists objectively.
The above example is ideal value (pure number) used for calculation. There is no pure wave pattern in nature. Any sound produced has many overtones, and intermodulation between two sounds plus overtones. Intermodulation will produce larger and more complex sound waves. This combination of different sounds creates differences in timbres of individual instruments and even performers. This phenomenon is not only a necessary condition for richness of sound with correct reproduction of pitch, but also shows that harmony is indeed supported by physical background. It is possible that many of harmonies that we "covertly hear" are exactly those "invisible" bass lines that composers have used this characteristic to create (this is often case with Bach's unaccompanied violins). A properly tuned organ can even take advantage of characteristics of building and add third tone characteristics to extend sound range not present in original pipe size (resulting tone) (no or no fundamental). .missing foundation) (college entrance exams were tested).
To understand this a little deeper, closer two sounds, lower third note will be (eg: 440 - 396 = 44, lower value). The farther apart two sounds, higher third will be (for example: 440 - 330 = 110 more). When two tones are very close to each other but not same, two tones interfere with each other, resulting in beat frequency (or beat frequency) phenomenon, which is mainly used in piano tuning. Since piano does not have a pure temperament, it can be clearly understood through beat frequency phenomenon whether adjusted temperament is suitable. A difference of 1 Hz per second means one beat per second, a difference of 2 Hz means one beat per second, and so on. As I understand it, piano tuning is fourth fast and fifth slow. In this part, piano tuner is much more experienced than me, and other musical instruments do not have this phenomenon.
This chart shows spacing relationship that can be applied to other tones if it matches corresponding spacing.
The phenomenon of combined sounds was hardly mentioned in home music club, but in physics, it seems to be an area that high school students will dabble in. This strange phenomenon is due to fact that most of those involved in music lack mathematics, and most of those involved in science lack artistic and literary literacy. Maybe it's because of my interest in science since childhood (before my second year of high school, I aspired to be a scientist. I got high marks in physics, chemistry, and science at joint high school admissions). , and my sanitary education was only on verge of passing, not to mention history and geography!). When it comes to topic, you naturally want to know. But profession no longer exists, and I hope that specialists more clearly versed in physics will point out my delusions, or at least simply explain physics of sound of musicians so that more musicians can understand these natural phenomena are indeed our blessing.