Maximal evenness: Difference between revisions
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: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2014-08-22 18:04 | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2014-08-22 18:05:04 UTC</tt>.<br> | ||
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Maximally even sets tend to be familiar and musically relevant scale collections. Examples: | Maximally even sets tend to be familiar and musically relevant scale collections. Examples: | ||
* The maximally even heptatonic set of [[19edo]] is, like the one in 12edo, a diatonic scale. | * The maximally even heptatonic set of [[19edo]] is, like the one in 12edo, a diatonic scale. | ||
* The maximally even heptatonic sets of [[17edo]] and [[24edo]], in contrary, are Maqamic[7]. | * The maximally even heptatonic sets of [[17edo]] and [[24edo]], in contrary, are Maqamic[7]. | ||
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Maximally even sets tend to be familiar and musically relevant scale collections. Examples:<br /> | Maximally even sets tend to be familiar and musically relevant scale collections. Examples:<br /> | ||
<ul><li>The maximally even heptatonic set of <a class="wiki_link" href="/19edo">19edo</a> is, like the one in 12edo, a diatonic scale.</li><li>The maximally even heptatonic sets of <a class="wiki_link" href="/17edo">17edo</a> and <a class="wiki_link" href="/24edo">24edo</a>, in contrary, are Maqamic[7].</li><li>The maximally even heptatonic set of <a class="wiki_link" href="/22edo">22edo</a> is Porcupine[7] (the superpythagorean diatonic scale in 22edo is not maximally even), the maximally even octatonic set of 22edo is the octatonic scale of Hedgehog, the maximally even nonatonic set of 22edo is Orwell[9], while the maximally even decatonic set of 22edo is the symmetric decatonic scale of Pajara.</li><li>The maximally even 13-element set in 24edo is Ivan Wyschnegradsky's diatonicized chromatic scale.</li></ul><br /> | <ul><li>The maximally even heptatonic set of <a class="wiki_link" href="/19edo">19edo</a> is, like the one in 12edo, a diatonic scale.</li><li>The maximally even heptatonic sets of <a class="wiki_link" href="/17edo">17edo</a> and <a class="wiki_link" href="/24edo">24edo</a>, in contrary, are Maqamic[7].</li><li>The maximally even heptatonic set of <a class="wiki_link" href="/22edo">22edo</a> is Porcupine[7] (the superpythagorean diatonic scale in 22edo is not maximally even), the maximally even octatonic set of 22edo is the octatonic scale of Hedgehog, the maximally even nonatonic set of 22edo is Orwell[9], while the maximally even decatonic set of 22edo is the symmetric decatonic scale of Pajara.</li><li>The maximally even 13-element set in 24edo is Ivan Wyschnegradsky's diatonicized chromatic scale.</li></ul><br /> | ||
Note that &quot;maximally even&quot; is equivalent to &quot;quasi-equal-interval-symmetrical&quot; in <a class="wiki_link" href="/Joel%20Mandelbaum">Joel Mandelbaum</a>'s 1961 thesis <a class="wiki_link_ext" href="http://www.anaphoria.com/mandelbaum.html" rel="nofollow">Multiple Divisions of the Octave and the Tonal Resources of 19-Tone Temperament</a>. Previous versions of this article have conflated &quot;quasi-equal&quot; with &quot;quasi-equal-interval symmetrical&quot;. In fact, &quot;quasi-equal&quot; scales, according to Mandelbaum, meet the first criterion listed above, but not necessarily the second.</body></html></pre></div> | Note that &quot;maximally even&quot; is equivalent to &quot;quasi-equal-interval-symmetrical&quot; in <a class="wiki_link" href="/Joel%20Mandelbaum">Joel Mandelbaum</a>'s 1961 thesis <a class="wiki_link_ext" href="http://www.anaphoria.com/mandelbaum.html" rel="nofollow">Multiple Divisions of the Octave and the Tonal Resources of 19-Tone Temperament</a>. Previous versions of this article have conflated &quot;quasi-equal&quot; with &quot;quasi-equal-interval symmetrical&quot;. In fact, &quot;quasi-equal&quot; scales, according to Mandelbaum, meet the first criterion listed above, but not necessarily the second.</body></html></pre></div> | ||