Acoustics by design
In the courtyard of the Abdullah-khan Madrasah, built between 1588 and 1590, the ornate tilework is more than decoration. The complex geometric patterns covering the walls are a sophisticated form of acoustic engineering. This design minimizes echoes, a feature important for the building's function as a school. A teacher's voice could carry clearly across the open space without being garbled by reverberation, a common problem in large, hard-surfaced enclosures.
The scientific principle at work is destructive wave interference. Sound travels in waves with peaks and troughs. The complex, multi-layered tile patterns create numerous reflective surfaces at different depths. Sound waves bouncing off these surfaces travel slightly different distances before reaching a listener's ear. The geometry is tuned so that the path differences cause the reflected sound waves to be out of phase with each other—the peak of one wave aligns with the trough of another. This alignment causes the waves to cancel each other out, drastically reducing echo. This effect is targeted specifically at the primary frequencies of human speech, roughly 300 to 3400 Hertz.
The mathematics of the tiles
The builders of the Abdullah-khan Madrasah were masters of mathematics, and the walls show their theorem. The decoration uses majolica and mosaics of glazed bricks to form complex Islamic geometric patterns, or girih. These patterns are not random; they are tessellations built from a set of specific polygonal shapes, often based on 8-pointed or 10-pointed stars. The construction of these repeating, non-periodic designs requires a deep understanding of geometry.
This mathematical knowledge is important for the acoustic properties of the courtyard. Creating a surface that can selectively cancel specific sound frequencies requires precise control over the reflection paths of sound waves. The architects used their advanced understanding of tiling and geometry to create, in effect, a massive acoustic diffuser. Some of these girih patterns exhibit properties of quasicrystals, a form of matter whose structure was not formally described by Western science until the 1970s. This architectural feature demonstrates a seamless mix of art, mathematics, and physics, applying advanced scientific principles centuries before they were formally codified.