Altered pentad: Difference between revisions

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: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-11-11 01:42:02 UTC</tt>.<br>

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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The altered pentad is an essentially tempered five-note chord, which can also be considered a pentatonic scale, representing 16:18:21:25:28 while tempering out the septimal kleisma (225:224). As such, 28:25 becomes the same as a whole tone and so there are four step sizes instead of five. The altered pentad has a number of the more esoteric 7-limit intervals (including the diminished fourth, 32:25, and the septimal narrow fourth, 21:16) that don't show up in ordinary pentads.

In septimal meantone systems, such as [[31edo]], the altered pentad becomes potentially important. In 31edo, the altered pentads have step sizes 87565 or 78565 (in contrast to the ordinary pentads, which are 87655 or 78556). As such, each altered pentad can be derived from a regular pentad by moving just one note by a diesis. One drawback of meantone[12] (the so-called superdiatonic scale) has only two each of the ordinary (5:6:7:8:9) otonal and utonal pentads, just as it has only two of each 7-limit tetrad.

But if the altered pentad is included as an allowable consonance in meantone[12], this means we now have six consonant chords, just like we have six triads in the diatonic scale. And two modes of meantone[12] become especially interesting. The mode sLsLsLLsLsLL has otonal pentads on the tonic and dominant, and an altered pentad on the subdominant (which, however, is a septimal narrow fourth above the tonic rather than a perfect fourth). Meanwhile the mode LLsLsLLsLsLs has utonal pentads on the tonic and subdominant, and an altered pentad on the (septimal wide fifth) dominant.

These modes can be considered analogous to the major and minor diatonic modes, as both allow a version of the familiar I-IV-V chord progression (the only differences being that either the fourth or fifth is replaced by a septimal narrow/wide version, and the pentad on that note is altered). Furthermore, these modes are melodically as different as possible (enhancing contrast between them), since the tonic in each case is on one end of the chain of fifths.

One might want to consider using the altered pentad with timbres that contain subharmonics as well as harmonics, since these may allow ratios involving composite numbers like 21 and 25 to be more easily perceived (21 being, for instance, the distance between the third subharmonic and the seventh harmonic).</pre></div>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Altered pentad&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The altered pentad is an essentially tempered five-note chord, which can also be considered a pentatonic scale, representing 16:18:21:25:28 while tempering out the septimal kleisma (225:224). As such, 28:25 becomes the same as a whole tone and so there are four step sizes instead of five. The altered pentad has a number of the more esoteric 7-limit intervals (including the diminished fourth, 32:25, and the septimal narrow fourth, 21:16) that don't show up in ordinary pentads.&lt;br /&gt;

In septimal meantone systems, such as &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;, the altered pentad becomes potentially important. In 31edo, the altered pentads have step sizes 87565 or 78565 (in contrast to the ordinary pentads, which are 87655 or 78556). As such, each altered pentad can be derived from a regular pentad by moving just one note by a diesis. One drawback of meantone[12] (the so-called superdiatonic scale) has only two each of the ordinary (5:6:7:8:9) otonal and utonal pentads, just as it has only two of each 7-limit tetrad.&lt;br /&gt;

But if the altered pentad is included as an allowable consonance in meantone[12], this means we now have six consonant chords, just like we have six triads in the diatonic scale. And two modes of meantone[12] become especially interesting. The mode sLsLsLLsLsLL has otonal pentads on the tonic and dominant, and an altered pentad on the subdominant (which, however, is a septimal narrow fourth above the tonic rather than a perfect fourth). Meanwhile the mode LLsLsLLsLsLs has utonal pentads on the tonic and subdominant, and an altered pentad on the (septimal wide fifth) dominant.&lt;br /&gt;