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=The 7-limit 4et tablet=

Suppose m0, m1, m2 and m3 are four monzos denoting four notes of a 7-limit tetrad, either otonal or utonal, with distinct pitch classes, so that all four chord elements are represented. The product of the four notes is represented by the monzo m = m0+m1+m2+m3, and the pitch class for m, which ignores the first coefficient m[1] defining octaves, is represented by the other three, m[2], m[3] and m[4]. This pitch class is uniquely associated to the tetrad, and can be used to name it. If the tetrad is otonal with the root being |* e3 e5 e7&gt;, where the asterisk can be any integer value, then m = |* 4e3+1 4e5+1 4e7+1&gt;. on the other hand, if it is utonal, with the fifth of the chord |* e3 e5 e7&gt; then m = |* 4e3-1 4e5-1 4e7-1&gt;. If we denote the 3-tuple  [(m[3]+m[4]-2)/2 (m[2]+m[4]-2)/2 (m[2]+m[3]-2)/2] by [a b c], then if the tetrad is otonal, [a b c] = [e5+e7 e3+e7 e3+e5], whereas if it is utonal [a b c] = [e5+e7-1 e3+e7-1 e3+e5-1]. From this it follows that [a b c] is a triple of integers, and that a+b+c is even if the tetrad is otonal, and odd if the tetrad is utonal. Hence every triple of integers refers uniquely to a 7-limit tetrad; this is the [[The Seven Limit Symmetrical Lattices|cubic lattice of 7-limit tetrads]].  

=The 7-limit 5et tablet=

&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="The 7-limit 4et tablet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;The 7-limit 4et tablet&lt;/h1&gt;

Suppose m0, m1, m2 and m3 are four monzos denoting four notes of a 7-limit tetrad, either otonal or utonal, with distinct pitch classes, so that all four chord elements are represented. The product of the four notes is represented by the monzo m = m0+m1+m2+m3, and the pitch class for m, which ignores the first coefficient m[1] defining octaves, is represented by the other three, m[2], m[3] and m[4]. This pitch class is uniquely associated to the tetrad, and can be used to name it. If the tetrad is otonal with the root being |* e3 e5 e7&amp;gt;, where the asterisk can be any integer value, then m = |* 4e3+1 4e5+1 4e7+1&amp;gt;. on the other hand, if it is utonal, with the fifth of the chord |* e3 e5 e7&amp;gt; then m = |* 4e3-1 4e5-1 4e7-1&amp;gt;. If we denote the 3-tuple  [(m[3]+m[4]-2)/2 (m[2]+m[4]-2)/2 (m[2]+m[3]-2)/2] by [a b c], then if the tetrad is otonal, [a b c] = [e5+e7 e3+e7 e3+e5], whereas if it is utonal [a b c] = [e5+e7-1 e3+e7-1 e3+e5-1]. From this it follows that [a b c] is a triple of integers, and that a+b+c is even if the tetrad is otonal, and odd if the tetrad is utonal. Hence every triple of integers refers uniquely to a 7-limit tetrad; this is the &lt;a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices"&gt;cubic lattice of 7-limit tetrads&lt;/a&gt;. &lt;br /&gt;

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&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="The 7-limit 5et tablet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;The 7-limit 5et tablet&lt;/h1&gt;