The Perfect Fourth (Pythagorean) 

The Fourth App explores the reciprocal balance of the Pythagorean system: the 4/3 ratio. By dividing the string into four equal parts and isolating three of them (3/4 length), you reveal the Perfect Fourth—the geometric boundary of the ancient Tetrachord. Pluck the virtual string to hear this stable, consonant interval, or move the division point to observe the mathematical transformation. Sticking to our "common language," the results are expressed purely as fractions and powers of 2 and 3, showing how the Fourth (4/3) x (3/2)  = 2 provides the essential structural counterweight to the Fifth. 

Pythagoras proved that what we hear as a "natural leap" is actually a perfect geometric division.

• The Action: Dividing a vibrating string exactly into four.

• The Result: The Octave (The 4:3 ratio). 

• The Truth: Music is simply "Geometry translated into Sound."