StepLadder

StepLadder calculates and plays metronome beat rates corresponding to the harmonic beats generated by specific intervals that result from a tempered piano tuning (such as equal temperament).

For example, if we played a minor 3rd starting on F3, then the closest overtone harmonics of F3 and and G3# would be

F3 --> 6 x 174.61 Hz = 1047.68 Hz
G3# --> 5 x 207.65 Hz = 1038.26 Hz

When played simultaneously, these overtones will interfere with each other, creating a beat rate that is equal to the difference of their frequencies:

1047.68 - 1038.26 = 9.42 Hz

If we multiply this by 60 beats per minute, and divide by four, we can get the following beat rate:

(9.42 ÷ 4) * 5 x 60 = 141 bpm

141 bpm is almost exactly 4 times slower than the 9.42 Hz beat rate generated by the interference of the two closest harmonics (there will be a negligible difference due to rounding). With some practice, it is possible to train oneself to

1. Hear the beats generated by the harmonics
2. Time them against the metronome

The ability to do this will allow a piano tuner to accomplish a measurable and superior accuracy.

StepLadder acts like a kind of tape measure, performing the calculations above for various intervals with the click of a button and allowing a tuner to quickly measure the accuracy of a tempered tuning.