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Defects of Equal Divisions of the Octave Relative to Just Intonation

Data from Tuning List Digest Number 811, Messages 3 & 4. That was back when the Tuning List was on the Mills College server. Currently the discussion takes place on the Alternate Tunings Mailing List at Yahoo Groups, and has over 1000 members. That's where you should go right now if you have no idea what the following means, but would like to.

    Date: Mon, 18 Sep 2000 02:45:35 -0400
   From: "Paul H. Erlich" 
Subject: Defects of ETs

Using diadic harmonic entropy, odd-limit 223, s=0.06%, we get the following
defects relative to JI with entropy values between cents obtained by 
linear interpolation between 1200-tET values, where at the n-limit we're 
evaluating the complete n-limit otonal chord 1:3:...:n, or equivalently, 
the utonal chord 1/n:...:1/3:1.

Whenever certain colors aren't visible at the top of a given column, that ET is not consistent within those odd limits.

bar chart

Well, it ain't exactly the mandala that Paul's Harmonic Entropy color maps are, but it does kind of bring the data to life, I think.

Generated from Microsoft Excel 2000, data entry and formatting by David J. Finnamore September 20, 2000.

WARNING: Not responsible for damage to instruments or ears from willful use of defective temperaments!  Playing in tunings with greater cumulative error than that of 12t-ET may void your warranty and/or result in personal injury.

Just kidding - come on, lighten up!

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