MusicianCV · TRPythagorean comma
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Tuning and pitch systems
Pythagorean comma · 531441:524288 → 12 × 701.955 ¢ − 7 × 1200 ¢ ≈ 23.46 ¢
Fix a reference frequency before comparing tunings. An octave doubles frequency. Convert a frequency ratio to cents with 1200 × log₂(ratio).
Example
Read the ratio alongside the worked calculation. · 531441:524288 / 12 × 701.955 ¢ − 7 × 1200 ¢ ≈ 23.46 ¢
Read the ratio alongside the worked calculation.531441:524288 12 × 701.955 ¢ − 7 × 1200 ¢ ≈ 23.46 ¢
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How does a frequency difference differ from a ratio?
Answer
Moving the same interval to another pitch preserves the ratio. The difference in hertz can change.Related topics
Reference tuning versus transpositionReferences
Frequency and Pitch of Sound
Subject-expert review pending.