Lambdoma matrix

Every whole-number ratio, on one grid.

The Lambdoma is a table of ratios. Each column is an overtone number and each row an undertone number, and each cell is column ÷ row. Multiply by a starting frequency and the grid becomes a map of tones you can hear.

Tones play at a fixed low volume. The example uses 1/1 = 256 Hz; set any frequency you like, such as a pitch from your own voice print.

How to read it

  • The top row is the overtone series: 1/1, 2/1, 3/1 … each a whole-number multiple of the starting frequency.
  • The left column is the undertone series: 1/1, 1/2, 1/3 … the starting frequency divided by whole numbers.
  • The green diagonal is where column and row are equal, so every cell is 1/1, the starting frequency itself.
  • Matching ratios line up. 2/1, 4/2, 6/3 and 8/4 are all the same ratio. Tap one and every equal cell is outlined, forming a straight line out from the corner.
  • Within one octave, each ratio is moved up or down by octaves into the range 1 to 2, so you can see which musical interval it is. 3/1 and 3/4, for example, are both a perfect fifth (3/2) once moved.

The MindTimbre layout

Switch Layout to MindTimbre app to see the 16-based version used in the app's Explore tab: row r and column c hold (16 + c) ÷ (16 + r). Its top row climbs in sixteenth steps from 16/16 to 31/16, just short of the octave, and the left column falls the same way.

In MindTimbre

The ratio table in Explore builds this grid from any frequency, including peaks from your voice prints, and you can play any cell. A practitioner version, for building client tone sets from the matrix, is planned for the practitioner portal.

What the matrix is, and isn't

The Lambdoma is arithmetic: ratios of whole numbers and the tones they make. MindTimbre uses it as a map of musical relationships. It doesn't assign any health, emotional or physical meaning to a cell, frequency or ratio.