Indiana University

Piano Technology

Piano Shop Resources

Pythagorean Tuning

  1. Tune A4 to fork. The number 4 indicates notes in the octave above middle C4.
  2. Tune A3 to A4. The number 3 indicates notes in the octave below middle C4.
  3. Tune E4 to A3 and make a perfect 5th.
  4. Tune B3 to E4 and make a perfect 4th.
  5. Tune F#3 to B3 and make a perfect 4th.
  6. Tune C#4 to F#3 and make a perfect 5th.
  7. Tune G#3 to C#4 and make a perfect 4th.
  8. Tune D4 to A3 and make a perfect 4th.
  9. Tune G3 to D4 and make a perfect 5th.
  10. Tune C4 to G3 and make a perfect 4th.
  11. Tune F3 to C4 and make a perfect 5th.
  12. Tune Bb3 to F3 and make a perfect 4th.
  13. Tune Eb4 to Bb3 and make a perfect 4th.

The results look like this with the wolf between G# and Eb.

C - G - D - A - E - B - F# - C# - G# ** Eb - Bb - F - C

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The wolf can be placed anywhere and this will also move the nice sounding schismatic 3rds.

For example if the wolf is between D and Bbb.

C - G - D ** Bbb - Fb - Cb - Gb - Db - Ab - Eb - Bb - F - C

The nice sounding schismatic triads are then C-Fb-G,F-Bbb-C,and G-Cb-D.