Lambdoma Matrix harmonically consonant keyboard

Barbara Hero's matrix of wholenumber ratios organises the harmonic series into a unique keyboard. This online version aims to reproduce her innovative work and make it accessible to anyone. Best enjoyed on larger screens.

Sound

Note data

Last frequency
Number of notes

Appearance

Historical Context

Arranging notes and designing instruments using ratios originated in multiple regions over two millennia ago. There is evidence of them being used in ancient Mesopotamia, Egypt and later Greece. Though there's only a small number of surviving diagrams, the idea of a matrix (or table) arranged in a diamond was eventually realised as a musical instrument in the 1970s by Barbera Hero.

Hero's keyboard was designed to facilitate the study of pure harmonics or Just intonation but also to provide therapeutic sound experiences. This is the next iteration of that legacy - an online musical instrument accessible to anyone

Musical ratios

The Lambdoma matrix is a set of carefully arranged whole number ratios. Each ratio represents a musical frequency when given a fundamental. For example, with a fundamental of 440Hz (A in Western music) the ratio 3:2 equates to 440 * 3/2 = 660Hz (or E). This allows us to hear the a form of the harmonic series. Moreover, its design means that notes are organised in ways that allow us to create consonant melodies.

Playing Guide

The base note can be set to any frequency, but between 128Hz and 480Hz is recommended as this limits the range of overtones and undertones to be in the audible range while playing in quadrant 1 (1:1 through 8:8)

The colour schemes provide some visual meaning but not dictate how its played. Graduated is used to illustrate how the notes ascend in pitch (left to right). To see and hear all the notes from Barbera Hero's resonant harmonic scale, ensure the keyboard grid size is 16 x 16 or higher. Mirrored shows chromatic overtones and their undertone counterpart. Octaves colours all notes that are the same regardless of octave. Overtones and undertones are hopefully self-explanatory

Given the size of the keyboard it's best enjoyed on larger screens, in particular touch screens but the instrument is also compatible with MIDI devices

Note that, if the same note is selected as is aleady playing (1/1 and 2/2 for example), only one will play.