12-tone solution to the Rational Walls puzzle

7-tone | 5-tone

The lengths of the segments shown here correspond to a 12-tone equal-tempered scale spanning two octaves, for a total of 25 lengths. Choose wall lengths to build adjoining rectangles. The most recently selected wall is colored red. Any segment that falls within about 1% of a simple integer ratio from the previous one will be colored with the color corresponding to that ratio. Clicking a rectangle plays the interval associated with it. Clicking the name of an interval in the legend plays the justly tuned interval, starting from the lowest tone available. The "Play Chord" button plays all selected tones together.

Each rectangle is tiled with squares to show an integer ratio it approximates. A consonant, pleasant sounding interval approximates a simple integer ratio, so it corresponds to a rectangle that can be tiled well with a small number of tiles (such as 3 x 2). A dissonant, unpleasant sounding interval will not fit a small integer ratio, so it either requires a large number of tiles (such as 10 x 9), or it will have gaps at the edges of the tiling pattern.

Note: Flash must be enabled for sounds.