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.

    Tuning and Temperaments     Early Music Institute     School of Music     IU Bloomington    

    I welcome any comments or suggestions, email me at psloffer@indiana.edu

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