[pianotech] Cents to beats on the fly

[Mark Schecter]

Having learned tuning aurally, then taken up ETD years ago, it took a while to adapt my language and thinking to the paradigm of cents instead of beats. I finally discovered a useful rule that helps me convert cents to beats and vice versa in my head. There are several logical steps, but once you get The Rule and start using it, it becomes second nature, at least it did for me. Numbers are rounded for clarity of concept. Bottom line is in Step 7. 

Starting with the obvious:

1 All half steps (in ET) equal 100 cents. 
2 A4 is 440 Hz. 
3 G#4 is 415 Hz. (rounded)
4 A half step at A4 is 25 Hz./beats 
5 100 cents at A4 is 25 Hz. 
6 1 cent at (A4) is .25 Hz./beats (at fundamental) 
 a 1 cent (at A4) is .5 beats at A5 (second partial=2x)
 b 1 cent (at A4) is 1 beat at A6 (fourth partial=4x) 
7 The Rule: In ET, 1 cent equals 1 Hz./beat at A6 (and only A6), true whether A6 is the fundamental or a partial of some other note. 

There are other implications, but I'll leave it there for now. 

~Mark Schecter