Why Do Pianos Have A “Tempered” Scale?

 As mentioned in our posts about early Western music’s evolution, originally there was no harmonic music, as in, two or three notes sang together, or melodies played over accompanying full block chords. Monks chanted Latin hymns, one note at a time, up and down the scale, with nary a third or a triad.

Singing a pleasant string of single notes was as natural as breathing, and probably dated back to pre-history. But when humans started singing or playing instruments in harmony, things got a little more complicated. In order to understand why, we need to take a look at the "mathematics" of the musical scale. Enter our old buddy, Pythagoras.

History teaches us that up until the great Greek philosopher, mathematician and scientist, Pythagoras of Samos, conceived and wrote down his mathematical formula for musical note frequencies, no one had any idea of the mathematical relationships of notes on a scale. But Pythagoras noticed that a note exactly one octave above another note was created by trimming a sounding device, either human vocal chords or a string, to exactly half it’s current length.

This set him off developing the mathematical relationships of the entire musical scale. He was the first to declare a scale made up of 12 equally-spaced semi-tones, pre-defining the 12 tones we now see on a piano, going from any note to the note exactly one octave higher (like C3 to C4.)

As harmonic and chordal music evolved, including the singing & playing of pieces many various keys, an interesting mathematical rule presented itself. If you wanted to sing or play instruments in any potential key, and have all the 3rds, 4ths, 5ths, 6ths, etc. sound in proper relationship to each other, mathematically you needed 26 "semi-tones" to each octave. The G# in a major E chord (E-G#-B) needed to be a totally different note than the Ab in an Ab major chord (Ab-C-Eb).

This was no problem for singers and other instruments, like the violin or wind instruments, that only played one or two notes at a time. Whenever switching through various songs in various keys, the singers or players compensated by slightly shifting their voice or finger-position or wind pressure to hit the proper frequency for that key. A violin player in an orchestra unwittingly move their finger position just slightly to make a G# or an Ab, respectively.

But then some silly dudes started inventing keyboard instruments that could play whole chords and melody with two hands. Based on Pythagoras’ 12-tone scale, they invented the modern-shaped octave, with twelve white-and-black keys. Trouble is, music was evolving and concerts were now featuring pieces in several different keys, instead of playing every song in the key of C or G (which got boooooring!) but as we discovered, if you were going to play in multiple keys, you needed up to 26 notes to hit every note at it’s pure frequency. And that was just too many keys to an octave. You would have t build a piano twice as wide, or with just 3 octaves instead of 7, to hold all those keys, and no one, not even the biggest-handed pianist, would be able to stretch to play an octave.

So, instead a compromise was reached. The keyboard would remain just 12 notes to an octave, but the piano strings would be tuned just slightly off of "pure" pitch for any interval except the octave, to compensate for moving around through many keys in a concert. That compromise was called "tempering" the musical scale, and over the centuries, many different temperaments were tried, falling in and out of favor. By the modern era, the compromise called the "equal temperament" was settled on, and became the temperament of choice for all modern orchestras and players. Thus, our 20th and 21st Century ears have gotten used to the "equal temperament", and that’s the amount of space between the notes that sounds "right" to our brains.

For more check out these related posts

• Why, and How Often, Must You Tune A Piano