Altered pentad: Difference between revisions

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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.

The '''altered pentad''', named by [[Mason Green]], is a [[25-odd-limit]] [[plurichord]] that can also be considered a pentatonic scale. It is defined as a chord that represents 16:18:21:25:28 (1–9/8–21/16–14/9–7/4) while [[tempering out]] the [[225/224|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 septimal supermajor third, [[9/7]]; and the septimal narrow fourth, [[21/16]]) that do not 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]].

== Utility in septimal meantone ==

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 [[m-chromatic]] 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.

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.

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).

[[Category:~~31edo~~]]

[[Category:~~meantone~~]]

[[Category:25-odd-limit chords]]

[[Category:Plurichords]]

[[Category:Pentads]]

[[Category:5-tone scales]]

[[Category:Marvel]]

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-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.
+The '''altered pentad''', named by [[Mason Green]], is a [[25-odd-limit]] [[plurichord]] that can also be considered a pentatonic scale. It is defined as a chord that represents 16:18:21:25:28 (1–9/8–21/16–14/9–7/4) while [[tempering out]] the [[225/224|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 septimal supermajor third, [[9/7]]; and the septimal narrow fourth, [[21/16]]) that do not 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]].
+== Utility in septimal meantone ==
+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 [[m-chromatic]] 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.
+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.
+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).
-[[Category:31edo]]
-[[Category:meantone]]
+[[Category:25-odd-limit chords]]
+[[Category:Plurichords]]
 [[Category:Pentads]]
+[[Category:5-tone scales]]
+[[Category:Marvel]]