![]() Or, if you instead pressed your finger at a third-in from the end, the string would vibrate as a stationary wave shown at the bottom, with two stationary nodes forming. If you now press with a finger at the centre of the string, you will get the second vibration form, with a stationary node forming at the centre. Let’s say a string vibrates as shown in the top vibration form. By touching lightly onto a tight vibrating string with a finger, one can force the string to vibrate in a standing wave pattern which will have a stationary node at the position of the finger. The mathematics of music began after Pythagoras drew some conclusions after experimenting with vibrating strings of different lengths. (Even more precisely, the vibrating string vibrates the air around it then, that air propagates a compression wave the wave vibrates your eardrum this sensation is processed in the brain as a perception of sound.) The sound you hear is the vibrations of that string. Remember that a piano key is connected to a hammer which hits a tight string. Actually, what must be tuned is the corresponding string inside the piano. In this article I will abuse terminology by saying that a piano key is tuned. The Pythagorean tuning is still in use today. ![]() Attempts to find the right frequencies goes all the way back to Pythagoras, an ancient greek philosopher from the 6th century BCE. ![]() However, not only it is hard to memorize the proper pitch, it is hard to determine theoretically what the frequencies should be. (Two of these schemes I discuss at length in the remainder of this article.) Here is a demonstration of what tuning skill is required of a violin player, in which a violin player is asked to switch between three different tuning schemes. Musicians are expected to hear and memorize the way the musical notes and intervals should sound. Thus, tuning a musical instrument is not only a theoretical exercise for the instrument maker. Even on a violin, it is not enough to tune the strings: there are no frets like on a guitar and a player must remember where to depress a string. On a clarinet or a saxophone the player can alter the pitch by pressing or relaxing a reed. Wind instruments with no holes, such as trombones, require the player to remember how much to elongate an air pipe of the instrument so as to produce the desired air vibration. Wind instruments, such as flutes, have holes in carefully calculated locations to produce sound at desirable frequencies. Please refer to the piano keyboard diagram above, for the names and location of piano keys.Īlthough I am using a piano as the case study, this applies to all musical instruments. The vibration frequencies to which the strings should be tuned, is the subject of this article. I used a piano as a case study, noting that there are metal strings inside the piano that vibrate at different rates. ![]() In the preceding article The Physical Nature of Musical Sound I have talked about how air vibration affects a human eardrum and causes the perception of sound pitch. One-sentence summary: In this article I will explain the math for the Just intonation and Pythagorean tunings for the diatonic major scale (all the white keys on the piano). ![]()
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