MT 007.02 / SL 266.01
Ideas in Mathematics: The Grammar of Numbers

1. In class, we have learned that in geometric tuning, every semi-tone is a ratio of the twelfth root of 2, which is approximately 1.059463. Calculate the following intervals in geometric tuning:
   1. c-d
   2. c-e
   3. c-f
   4. c-g
   5. c-a
   6. c-b
2. We have already computed the intervals c-d, c-e, c-f, and c-g in both harmonic and Pythagorean tunings. Convert those intervals to decimals (working to 6 places), and compare your results with the same intervals in geometric tuning. Which intervals are larger in geometric tuning? Which are smaller?