Altered pentad - Revision history

FloraC: Improve intro. Update to contemporary terminology

2024-10-09T10:32:58Z

Improve intro. Update to contemporary terminology

← Older revision		Revision as of 10:32, 9 October 2024
Line 1:		Line 1:
	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).		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:Pentads]]
	~~[[Category:Essentially tempered chords]]~~
	[[Category:5-tone scales]]		[[Category:5-tone scales]]
			[[Category:Marvel]]

BudjarnLambeth: Added to category “5 tone scales”

2024-01-03T07:31:41Z

Added to category “5 tone scales”

← Older revision		Revision as of 07:31, 3 January 2024
Line 12:		Line 12:
	[[Category:Pentads]]		[[Category:Pentads]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
			[[Category:5-tone scales]]

BudjarnLambeth: Added to category “essentially tempered chords”

2024-01-03T07:31:11Z

Added to category “essentially tempered chords”

← Older revision		Revision as of 07:31, 3 January 2024
Line 11:		Line 11:
	[[Category:meantone]]		[[Category:meantone]]
	[[Category:Pentads]]		[[Category:Pentads]]
			[[Category:Essentially tempered chords]]

BudjarnLambeth: Added to category “pentads”

2024-01-03T07:30:47Z

Added to category “pentads”

← Older revision		Revision as of 07:30, 3 January 2024
Line 10:		Line 10:
	[[Category:31edo]]		[[Category:31edo]]
	[[Category:meantone]]		[[Category:meantone]]
			[[Category:Pentads]]

BudjarnLambeth: Added in-text links

2024-01-03T07:29:47Z

Added in-text links

← Older revision		Revision as of 07:29, 3 January 2024
Line 1:		Line 1:
	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.		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.

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
Line 1:		Line 1:
	~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~		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.
	~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~
	~~: This revision was by author [[User:MasonGreen1\|MasonGreen1]] and made on <tt>2016-11-11 01:43:43 UTC</tt>.<br>~~
	~~: The original revision id was <tt>599161572</tt>.<br>~~
	~~: The revision comment was: <tt></tt><br>~~
	~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>~~
	~~<h4>Original Wikitext content:</h4>~~
	<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, 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.

	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) 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.		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.
Line 14:		Line 7:
	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).~~</pre></div>~~		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).
	~~<h4>Original HTML content~~:~~</h4>~~		[[Category:31edo]]
	<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"><html><head><title>Altered pentad</title></head><body>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.<br />		[[Category:meantone]]
	~~<br />~~
	In septimal meantone systems, such as <a class="wiki_link" href="/31edo">31edo</a>, 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.<br />~~
	~~<br />~~
	~~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.<br />
	~~<br />~~
	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.<br />
	~~<br />~~
	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).</body></html></pre></div>

Wikispaces>MasonGreen1: Imported revision 599161572 - Original comment:

2016-11-11T01:43:43Z

**Imported revision 599161572 - Original comment: **

Wikispaces>MasonGreen1: Imported revision 599161560 - Original comment:

2016-11-11T01:43:00Z

**Imported revision 599161560 - Original comment: **

Wikispaces>MasonGreen1: Imported revision 599161544 - Original comment:

2016-11-11T01:42:24Z

**Imported revision 599161544 - Original comment: **

Wikispaces>MasonGreen1: Imported revision 599161538 - Original comment:

2016-11-11T01:42:02Z

**Imported revision 599161538 - Original comment: **

New page

<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-11-11 01:42:02 UTC</tt>.<br>
: The original revision id was <tt>599161538</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<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>
<h4>Original HTML content:</h4>
<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"><html><head><title>Altered pentad</title></head><body>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.<br />
<br />
In septimal meantone systems, such as <a class="wiki_link" href="/31edo">31edo</a>, 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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
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).</body></html></pre></div>

← Older revision		Revision as of 01:43, 11 November 2016
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:MasonGreen1\|MasonGreen1]] and made on <tt>2016-11-11 01:43:00 UTC</tt>.<br>		: This revision was by author [[User:MasonGreen1\|MasonGreen1]] and made on <tt>2016-11-11 01:43:43 UTC</tt>.<br>
	: The original revision id was <tt>~~599161560~~</tt>.<br>		: The original revision id was <tt>599161572</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 8:		Line 8:
	<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, 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.		<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, 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.

	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.		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) 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.
Line 18:		Line 18:
	<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"><html><head><title>Altered pentad</title></head><body>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.<br />		<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"><html><head><title>Altered pentad</title></head><body>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.<br />
	<br />		<br />
	In septimal meantone systems, such as <a class="wiki_link" href="/31edo">31edo</a>, 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.<br />		In septimal meantone systems, such as <a class="wiki_link" href="/31edo">31edo</a>, 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.<br />
	<br />		<br />
	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.<br />		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.<br />

← Older revision		Revision as of 01:42, 11 November 2016
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:MasonGreen1\|MasonGreen1]] and made on <tt>2016-11-11 01:42:02 UTC</tt>.<br>		: This revision was by author [[User:MasonGreen1\|MasonGreen1]] and made on <tt>2016-11-11 01:42:24 UTC</tt>.<br>
	: The original revision id was <tt>~~599161538~~</tt>.<br>		: The original revision id was <tt>599161544</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
	<h4>Original Wikitext content:</h4>		<h4>Original Wikitext content:</h4>
	<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.		<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, named by Mason Green, 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.		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.
Line 16:		Line 16:
	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>		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>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<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"><html><head><title>Altered pentad</title></head><body>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.<br />		<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"><html><head><title>Altered pentad</title></head><body>The altered pentad, named by Mason Green, 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.<br />
	<br />		<br />
	In septimal meantone systems, such as <a class="wiki_link" href="/31edo">31edo</a>, 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.<br />		In septimal meantone systems, such as <a class="wiki_link" href="/31edo">31edo</a>, 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.<br />