Culture · 6 pages · 12 min
Why pure intervals and piano intervals disagree
Pure intervals use simple ratios, and a piano's fixed twelve steps cannot keep them all.
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From the opening
A pure interval is two pitches in a simple frequency ratio, such as an octave at two to one, a fifth at three to two, a fourth at four to three, or a major third at five to four. A piano in twelve-tone equal temperament matches the octave and misses the others, because its pitches are locked to equal ratio steps that do not land on all of those fractions. The opening covers octave two to one, fifth three to two, twelve fifths miss seven octaves, and piano thirds run wide of five to four.
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Inside
- Octave two to one, fifth three to two
- Twelve fifths miss seven octaves
- Piano thirds run wide of five to four
- Voices can retune and pianos cannot
- Where the idea stops applying
- A distinction worth keeping
Sources
- Just intonation ratios and the Pythagorean comma
- Equal-tempered fifths and thirds on the modern piano