9846

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.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

For more information, see Introduction to Harmonics.
    • 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 »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+