10176

# Lambdoma Matrix

This lambdoma matrix is based upon string length; with its inverse frequency ratio matrix they comprise the primary tools for Harmonics—the study of ratio and proportion. All ratios to the right of the 1/1 diagonal are less than 1. Even times even ratios and their reciprocals are shown in color. If you imagine a string length placed in the 1/16 column and extended one row above that column, then drawing a line through the 1/2 ratio vector will cut the string in half. Notice that drawing a line through the 1/2 ratio vector does not end at 1/1, but rather above 1/1 at the 0/0 origin. Also, drawing a line to the left of the diagonal through any ratio vector starting at the 0/0 origin extends the string length by the ratio vector amount. Please note that a division or extension of string length only works in an equally spaced grid. Try it on graph paper. The string length lambdoma matrix is constructed with rows of the overtone series and columns of the undertone series. The slider adjusts the index of the lambdoma matrix from 16 to 1.

### PERMANENT CITATION

Contributed by: Drew Lesso
 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.