To accommodate the piano keyboard, the Western world created 12 intervals as a mathematical compromise.
It turns out that in the world of music, there are as many tones and octaves as you want.
“During the 17th and 18th centuries there was a lot of argument about tuning and people were coming up with different ways to do it. In the 17th century there were even people arguing for more than 12 pitches to the octave and some people including George Frederick Handel had a keyboard with split keys on it, so he actually had 14 pitches to the octave.”
Kyle Gann is a composer and author. His book, "The Arithmetic of Listening: Tuning Theory and History for the Impractical Musician," discusses how 12 tones won the west, and how that might be changing once again. Gann said breaking the standard of 12 intervals creates new tones and harmonies.
He said it’s much easier to explain pure tuning than the system we currently use.
“It was all about getting the most consonant chords purely in tune," Gann said. "If you get those perfectly in tune, then each chord will work in some keys but not in others."
Gann said that he keeps his personal pianos tuned to an 1800s scheme which he feels gives a more pure and colorful range of sounds than the 12-interval standard called equal temperament. He explained that theorists quit arguing about tuning by the 18th century— as the piano began its reign as Europe’s most popular instrument. The sound and consequently the intervals, were decided by piano tuners; strings were easy to retune, pianos not so much. He said a piano is very difficult to re-tune, compared to a harpsichord, which can be retuned fairly quickly.
Gann said that when playing the music of composers not boxed in by equal temperament on a piano tuned to the period equivalent, the music is not unrecognizable to the listener but feels different to play.
“I love to play the slow movement of Beethoven’s 'Appassionata Sonata' because it’s in the key of D-flat and D-flat is a really strange key in that (modern) tuning; it’s got a real buzz to it. That’s a slow movement, very languid but you play it in its correct tuning and it has a kind of energy to it that keeps it going when if I take it down a half step to the key of C I want to play it faster because it no longer has the energy to sustain the chords.”
Gann explained that the problems of a 12-interval keyboard are readily apparent when trying to match tone with a barbershop quartet.
“I did a keyboard transcription of a barbershop quartet song,” Gann said. “I had to have about thirty pitches to the octave to get them all in. So, you can, if you have enough pitches on your keyboard, play perfectly in tune with a barbershop quartet but you can’t do it with just twelve.”
Gann said computer programs now allow composers to come up with any tone they want and said that these are creeping into pop music.
“There’s a song I’d recommend by They Might Be Giants called 'Dog' which is in 31-tone equal temperament. It’s really brilliant the way they do it and the breaks between verses are done by a harmonica and I hope it was a microtonal harmonica but I’m told they just did electronic pitch bins on it.”
"The Arithmetic of Listening" is just out from the University of Illinois Press.
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