Equal Temperament: What It Costs and What It Buys
Twelve equal semitones solve the problem pure intervals create. The cost is small in fifths, large in thirds, and paid by every fixed-pitch instrument.
Topic
Tuning & Temperament
Just intonation, meantone, well temperament and equal temperament — and the cents that separate them.
Every fixed-pitch instrument makes a compromise, and the compromise has a name. These articles explain just intonation and beating, the comma problems that make tempering necessary, and what equal temperament costs; then what meantone and the well temperaments did instead, and why the difference is audible.
Just Intonation, Beating and Why Intervals Sound in Tune
Pure intervals come from small whole-number ratios, and beating is what stops them sounding pure. What just intonation gives, and what it cannot fix.
Meantone and Well Temperament: Why Keys Used to Sound Different
Quarter-comma meantone, the wolf fifth and the well temperaments in between: what keyboard tuning did to each key before equal temperament settled the argument.
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