Altered pentad: Difference between revisions

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The altered pentad, named by Mason Green, is an essentially tempered five-note chord that can also be considered a pentatonic scale. It is defined as a chord that represents 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.

The altered pentad, named by Mason Green, is an [[Essentially tempered chord|essentially tempered]] five-note chord that can also be considered a pentatonic scale. It is defined as a chord that represents 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|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) is that it 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.

In septimal [[meantone]] systems, such as [[31edo|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) is that it 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.

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-The altered pentad, named by Mason Green, is an essentially tempered five-note chord that can also be considered a pentatonic scale. It is defined as a chord that represents 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.
+The altered pentad, named by Mason Green, is an [[Essentially tempered chord|essentially tempered]] five-note chord that can also be considered a pentatonic scale. It is defined as a chord that represents 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|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) is that it 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.
+In septimal [[meantone]] systems, such as [[31edo|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) is that it 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.