Euler Genus Creator

This tool creates a tone collection (genus)1 based on historical principles laid out by the 18th century mathematician Leonhard Euler.

Step 1: Define the least common multiple (exponens) of the tone collection

   
2n  · 33  · 52  · 70  
   

Step 2: Define the root note of the tone collection

   
 as 2n  · 31  · 51  · 70  
   

Step 3:


Footnotes

1 Tone collections, or genera: Euler 1739, chapters 8-10.


Sources

Euler, Leonhard. Tentamen novae theoriae musicae. St. Petersburg: Typographia Academiae Scientiarum, 1739.
Source | Translation

Euler, Leonhard. "Conjecture sur la raison de quelques dissonances generalement recues dans la musique".
In: Memoires de l'academie des sciences de Berlin, vol. 20, pp. 165-173. Berlin, 1766.
Source | Translation

Euler, Leonhard. "De harmoniae veris principiis per speculum musicum repraesentatis".
In: Novi commentarii academiae scientarium Petropolitanae, vol. 18, pp. 330-353. St. Petersburg, 1774.
Source | Translation


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