Pythagorean Intervals

The Tone App demonstrates the birth of the perfect Tone: the 9/8 ratio. In the Pythagorean system, the Tone is not merely a random distance, but the precise mathematical difference between a Perfect Fifth (3/2) and a Perfect Fourth (4/3). By dividing the string into nine parts and isolating eight of them (8/9 length), you produce the 9/8 interval, the fundamental building block of all scales. Pluck the virtual string to hear its clear, resonant character starting from a frequency of D 146.66 Hz. You can click the string to move the red markers or use the side controls for fine-tuning; the app will highlight exactly when you hit a pure Pythagorean interval. All results are expressed strictly in terms of fractions and powers of 2 and 3, revealing the mathematical "genetic code"  behind the sound. 

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 2:1 ratio). 

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