Tuning and temperament (10 mins, ~9 MB)

In Pythagorean tuning the 5ths are true i.e. in the frequency ratio 3/2. In 1/4 Comma Mean Tone the major 3rds are true i.e. in the frequency ratio 5/4. Both tunings give rise to the wolf which restricts the number of playable keys to 6 major and 3 minor. In Equal Temperament all keys are playable but neither the 3rds or 5ths are true. In circular temperaments the total reduction in all 5ths round the circle is one comma; all keys are playable but some usually sound better in tune than others.