Space and time – the monochord in the lambdoma
One string, one movable bridge. On the monochord you can hear that pitch and string length are inversely related, like frequency and wavelength.
The monochord is the basic instrument of Pythagorean music theory: a single string over a sound box, with a movable bridge. If the bridge divides the string in the middle, each half sounds an octave higher than the whole string. At two thirds you hear the fifth, at three quarters the fourth.
The buttons set the bridge at the classical divisions and play first the whole string, then the shortened part. The slider allows any position.
Length and frequency
On the monochord a physical law can be heard directly: halve the length and the frequency doubles. String length and pitch are inversely proportional, just like the wavelength and frequency of any vibration.
In the lambdoma this corresponds to the two axes. One counts multiples (overtones, higher frequencies), the other parts (undertones, longer strings). Each cell connects both.
This relationship is more than acoustics. Wavelength is a quantity of space, frequency a quantity of time. If music in the lambdoma necessarily runs into this law, then it can also prompt reflections on the relation between space and time. And there are good reasons to complete these reflections into a fourness: the tetractys of energy, space, time and matter (see All is number – all is frequency).
Anyone who wants to go deeper will find extensive literature on the monochord, the lambdoma, harmonics and cymatics, the study of visible patterns of vibration.
Kayser’s drawing
Hans Kayser recorded the relation between lambdoma and monochord in a drawing of his own. The equal-tone lines of the lambdoma, the lines on which all cells have the same tone, match exactly the points at which the string is divided. What appears in the lambdoma as a table is, on the monochord, a sequence of bridge positions.