Indiana University

Piano Technology

Piano Shop Resources

Kellner 1/5 Comma Well-Temperament 

Go to Dr. Herbert Anton Kellner web page

  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 F3 to A3 making a wide 3rd with 4 beats per second.
  4. Tune C4 to F3 making a perfect 5th.
  5. Tune D4 to A3 making a wide 1/5c 4th beating around 2 beats per second.
  6. Tune G3 to C4 and D4. Make a wide G3C4 1/5c 4th and a narrow G3D4 1/5c 5th. 1/5 Comma 5ths beat a little less than 2 beats per second.
  7. Tune E4 making a narrow 1/5c A3E4 5th. The C4E4 3rd should beat 2 beats per second.
  8. Tune B3 making a perfect B3E4 4th. The G3B3 3rd should beat around 4 beats per second.
  9. Tune C3 to C4 making a good octave with a perfect C3F3 4th and a narrow C3G3 5th.
  10. Tune D3 to D4 making a good octave with a wide D3G3 4th and a narrow D3A3 5th.
  11. Tune E3 to E4 making a good octave with a wide E3A3 4th and a perfect E3B3 5th.
  12. Tune F#3 making a wide 1/5c F#3B3 4th. The D3F#3 3rd beats 3 beats per second.
  13. Tune C#4 making a perfect F#3C#4 5th.
  14. Tune Bb3 making a perfect F3Bb3 4th.
  15. Tune Eb4 making a perfect Bb3Eb4 4th.
  16. Tune G#3/Ab3 making a perfect G#3C#4 4th and a perfect Ab3Eb3 5th.
  17. Tune F4,F#4,G4,G#4 etc. checking 4ths,5ths and octaves.
  18. Tune Eb3,C#3,B2,Bb2 etc. checking 3rds, 4ths, 5ths and octaves
  19. The results look like this with five 1/5 comma tempered 5ths. 1/5th comma 5ths are narrow by around 1� to 2 beats per second. 1/5 comma 4ths are wide by around 2+ beats per second.

F - C 1/5 G 1/5 D 1/5 A 1/5 E - B 1/5 F# - C# - G# - Eb - Bb - F

Cents and Frequency table for Kellner 1/5 Comma Well-Temperament