MusicianCV · TRTwelve-tone equal temperament
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Tuning and pitch systems
Twelve-tone equal temperament divides the octave into twelve equal frequency ratios. Each step multiplies frequency by the twelfth root of two. The ratios are equal; the differences in hertz are not, so a semitone spans more hertz in a higher register.
This system supports convenient keyboard transposition, but it is not a universal account of musical pitch. Makam performance and historical tunings need their own context. Always identify the pitch system before applying a keyboard-based interval calculation.
Example
One octave is 12 semitones with ratio 2; two octaves are 24 semitones with ratio 4.
Twelve-tone equal temperament1 → 2^(1/12) → 2^(2/12)
Try it
What frequency ratio spans three octaves?
Answer
8:1: each octave multiplies frequency by two.Related topics
Reading small pitch differences in cents · Understanding makam beyond a scaleReferences
Frequency and Pitch of Sound
Subject-expert review pending.