The monochord is almost nothing: one string stretched over a board, with a single movable bridge that can be slid along its length to shorten the sounding part. From that bare arrangement comes the entire mathematics of pitch, which is why it endures as the ancestor of every frequency Notechord names. Move the bridge and the string begins to reveal its secrets. Halve the sounding length and the pitch jumps exactly an octave, the interval so consonant it can sound like the same note higher up. Stop the string at two-thirds of its length and you hear a perfect fifth.

Stop it at three-quarters and you get a perfect fourth. The pattern is unmistakable, and it is arithmetic: the octave is the ratio 2 to 1, the fifth is 3 to 2, the fourth is 4 to 3, the simplest possible whole-number relationships. What makes this more than a curiosity is that these plain ratios are precisely the intervals the ear hears as consonant, as restful and in agreement. Simple numbers sound good; the connection between mathematics and beauty is sitting right there on a single vibrating string.

The observation is traditionally credited to Pythagoras, and whether or not the legend is exact, it marks the moment number and music were understood as one thing. This is the oldest pitch mathematics we have, the root from which tuning systems and frequency tables grow, and it is the direct ancestor of every note measured on this site. The demonstration ends where the whole catalogue begins: the open, unstopped string, its full length ringing, sounds C3, at 130.813 Hz. From one string and a sliding bridge, the entire ordered world of pitch unfolds.