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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.
Contributed by: Drew Lesso (April 2008)
After work by: Albert von Thimus, Hans Kayser, and Ernest G. McClain
Open content licensed under CC BY-NC-SA
For more information, see Introduction to Harmonics.
Wolfram Demonstrations Project
Published: April 26 2008