Piano tuning vs emsemble sounds
2002-09-12 by Carol Beigel
This post will try to explain why the tuning on your piano may not perfectly match the tone-generated ensemble sounds. However, if the piano is properly tuned, the differences should be barely noticeable. Piano tuning theory differs from reality because piano wire has actual stiffness. Harmony is a system of compromises, and many musical schemes have been used over time, i.e. Meantone, Well-Temperament and Equal Temperament just to name a few. The great mystery discovered by Pythagoras over 1500 years ago was that you can\ufffdt tune strings by the numbers. If you take a string and pluck it, you get a Fundamental tone. If you pinch it in half you get a tone that is one octave higher; pluck that segment in half and you get another octave higher, etc. Do that 8 times and the value of the frequency for that highest tone equals \ufffdx\ufffd. Now take the same string and this time pinch it in thirds (instead of halves). Do that 12 times and you get the Circle of Fifths, which are the 12 tones that make up the octave. However, the great mystery is that when you get to \ufffdx\ufffd it is now 33% higher! This significant deviation was known throughout musical history as the \ufffdwolf\ufffd and threw any tuning of stringed instruments into a tizzy until about 1918. Where to start was a big problem. No matter what key you picked to start the tuning, only half the tones were musically useable. Keyboard instruments were finally laid out in the key of C and are still that way today. All the tuning compromises were done on the black keys, or the \ufffdhalf tones\ufffd. There was a huge difference between the color and mood of each key signature, and you could only play music written for the way your piano was tuned. As time went by, musicians wanted more out of their music. Everytime the \ufffdwolf\ufffd could be reduced, more keys became musically available for composition. Bach wrote his 26 Inventions because there were only 26 ways he could play with the harmony. During his lifetime, a new tuning system appeared called Well Temperament, so he wrote music for it called the Well-tempered Clavichord. Mozart had more tones to work with, and Beethoven had even more harmony at his disposal because tuning systems had found a way to further reduce this \ufffdwolf\ufffd. However, no tuning system was \ufffdall purpose\ufffd until the early 20th century with the use of Equal Temperament. By this time calculus had been invented, and a system for making each tone on the keyboard equidistant was in place. Today, this tonal distance is 1/12th the square root of 2. However, now that we use a one-size-fits-all temperament, our music has lost the color that individual key signatures once gave it. No matter what key signature the music is written in, they all sound the same today in Equal Temperament so we only hear our music in black-and-white. Because piano wire has stiffness, the numbers will never match the theoretical values. For instance, the A above middle C is set to a standard pitch of 440 hertz. In theory, the A an octave below it would be tuned to 220 hertz. A very clean stringing scale might have this lower A tuned to 222 hertz before the octave is \ufffdbeatless\ufffd. A tuner would then need to spread out this 2 hertz difference over the 12 tones in the octave. There can be as much as a 15 hertz difference among different piano brands and models. A graph of a well-tuned piano that is pleasing to the ears does not look like a perfect horizontal line. The line would be at an angle, with the bass tones starting about 30 cents flat and the high treble tones gradually increasing to 30 cents sharp. Each piano will have its own anomalies. Tone generators are pretty much bound by the mathematical values assigned by MIDI. It probably makes a difference if the \ufffdsampling\ufffd was done on a Steinway or a Yamaha piano for the bass and high treble notes. Yamaha pianos have a very clean tone with very little stretch in the octaves; Steinways have a large amount of stretch with a very verve sound. However, XG tone generators were sampled on Yamaha pianos! A piano tuner sets the pitch of the piano \ufffd the standard international pitch being A=440 hertz. If your piano sits in a humid room, and measures out at A=442 in the middle of the summer, it might be prudent to leave the pitch alone knowing that it will probably drop to A440 as soon as the heating season starts. Often in the middle of the winter, pianos can be 25 cents flat. This is why piano technicians recommend climate control for the piano. Tuning forks can change their pitch if they are dropped or get bumped by the other tools in the tool kit. They also change their pitch with the temperature. The dial tone on the telephone is close to A440. You can always use the M tune feature on the Disklavier to help compensate for the pitch fluctuations of the piano. Using a computer to tune a piano lets you see what you are hearing. You can instantly see what is going on with the piano pitch; calculate the perfect tuning for that particular instrument and can show the piano owner how the pitch is affected by the humidity or lack of it. But the most wonderful thing a good tuning program will do is calculate the historic temperaments we almost lost so we can hear the music the way the composers heard it! Piano tuning is still an art \ufffd even when using a computer. There is a large window of what is considered \ufffdcorrect\ufffd. Not only does all this theory come into play when tuning, but also the physical adjusting of the tuning pins and the rendering of the strings. No two tuners work alike, so you may have to try a few before you find one that makes your piano sound the way you want. Carol Beigel crbrpt@... _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com