How To Tune a Piano:
A Summary of Chapters 6 and 7 from "Piano Servicing, Tuning, and Rebuilding" by Arthur Reblitz
Part I of V
All good mommies have to take breaks from kissing their babies to do other things, like get manicures, continue promising careers, or learn something about piano tuning. Because I don't have nails or a career, I decided to start opening my tuning book during Drakeson's afternoon naps. After 2 pages of "Tuning Theory and Terminology," I was smitten. I'm probably not the only mommy without nails or a career, so for the rest of us out there, this is for you.
When something vibrates, it causes the surrounding air vibrate, and our eardrums process these vibrations as sound. When the vibrations are irregular, we hear noise. When the vibrations are regular and within the range of human hearing, we hear a musical tone. The vibration speed, called frequency, is measured in cycles per second called hertz or hz. The higher the hz, the higher the pitch. When all other factors are equal, wires that are shorter, thinner, or under more tension produce higher pitches. Also, stiffness is measured by ratio of shortness and thickness. Stiffer wires are also higher.
When a wire vibrates, it simultaneously divides itself into 2 vibrating halves, 3 thirds, 4 fourths, and so on. It's difficult to imagine, so here's a picture. A vibrating wire does all these things at once.
The imaginary pitch on the left of the picture is called the fundamental or the first partial. While we are listening to this imaginary fundamental, we can also more softly hear the second pitch in the diagram, called the second partial or first overtone. The frequency of either half is twice that of the fundamental. For the third partial or second overtone, the sound is softer than the second partial, and the frequency of each third is three times as fast. Etc. A harmonic is a frequency that is an exact multiple of the fundamental. Theoretically this is every partial, but in reality, wire stiffness causes partials to be inexact, and the difference between the two is called inharmonicity.
Aside: The first diagram creates a unison with the fundamental frequency. Because the next diagram has twice the frequency, the pitch sounds one octave higher. The third sounds a fifth and an octave above, the fourth two octaves above, and the fifth a major third and two octaves above.
If two wires that are tuned to the same pitch are struck at the same time, the resulting sound is louder due to constructive interference. If they are not synchronized, however, they will produce a softer tone due to destructive interference. Let's assume one wire is tuned at x hz, and a second wire is tuned at x+4 hz. The second string will vibrate 4 more times than the first in one second, and the vibrations of both strings will be synchronized 4 times. Those times, which are louder than the rest of the second, create periodic shifts in volume called beats. Beats occurring more than 15 times a second are difficult to hear, and the sound is instead interpreted as two distinct pitches. Partials and fundamentals can each cause beats if the frequencies are close. The goal of tuning a piano is to create the fewest beats when any combination of pitches is played.
Reblitz goes on to teach note names and define intervals, but all my friends know that part. If you don't and you would like to, just give me a call. What we didn't know, however, is that tuners like unisons, M2nds, m3rds, M3rds, P4ths, P5ths, M6ths, 8ves, M10ths, P12ths, P15ths, and M17ths. Adjacent or successive intervals are the same interval starting a half step apart (C-E, C#-F). Contiguous intervals are the same interval with one overlapping pitch (C-E, E-G#). When there are three or more contiguous intervals, they are called stacked (C-E, E-G#, G#-C). This brings me to the final point of our first lesson. Tuners call all the black notes sharps and don't believe in flats. They also do things like call diminished fourths major thirds. They keep us in tune, though, so let's forgive them. See you in Part II.
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