Wizard/Chords - Revision history

Lériendil: Lériendil moved page Chords of wizard to Wizard/Chords

2025-06-22T21:53:06Z

Lériendil moved page Chords of wizard to Wizard/Chords

← Older revision	Revision as of 21:53, 22 June 2025
(No difference)

FloraC: Fix linking. Categories

2025-01-26T09:50:01Z

Fix linking. Categories

← Older revision		Revision as of 09:50, 26 January 2025
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	Below are listed the [[11-odd-limit]] [[dyadic ~~chords~~]] of [[11-limit]] [[wizard]] temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by [[540/539]] are [[swetismic chords\|swetismic]], by [[385/384]] [[keenanismic chords\|keenanismic]], and by [[225/224]] [[marvel chords\|marvel]]. Those requiring tempering by any two of 540/539, 385/384 or 225/224 are labeled [[undecimal marvel chords\|unimarvel]].		Below are listed the [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[wizard]] temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by [[540/539]] are [[swetismic chords\|swetismic]], by [[385/384]] [[keenanismic chords\|keenanismic]], and by [[225/224]] [[marvel chords\|marvel]]. Those requiring tempering by any two of 540/539, 385/384 or 225/224 are labeled [[undecimal marvel chords\|unimarvel]].

	The normal mapping for wizard is wiz = {{mapping\| 2 1 5 2 8 \| 0 6 -1 10 -3 }}. From this we may derive a val '''v''' = wiz[1] + 100 wiz[2] = {{val\| 2 601 -95 1002 -292 }}. Since '''v''' is approximately 100 times the generator chain val, {{val\| 0 6 -1 10 -3 }}, it will sort elements of the 11-odd-limit tonality diamond in the same order, but it uniquely encodes each interval. Since it is a val of wizard, we may take a chord, find the smallest element under the mapping, and use it to translate the whole chord starting at zero. The val '''v''' is what might be called a quasi higher rank val; it has a [[comma basis]] of 225/224, 385/384, 4000/3993, 1001255211106304, which are the commas of wizard plus a complex interval which can play no role in ordinary circumstances, so that '''v''' can be used in place of the mapping for wizard.		The normal mapping for wizard is wiz = {{mapping\| 2 1 5 2 8 \| 0 6 -1 10 -3 }}. From this we may derive a val '''v''' = wiz[1] + 100 wiz[2] = {{val\| 2 601 -95 1002 -292 }}. Since '''v''' is approximately 100 times the generator chain val, {{val\| 0 6 -1 10 -3 }}, it will sort elements of the 11-odd-limit tonality diamond in the same order, but it uniquely encodes each interval. Since it is a val of wizard, we may take a chord, find the smallest element under the mapping, and use it to translate the whole chord starting at zero. The val '''v''' is what might be called a quasi higher rank val; it has a [[comma basis]] of 225/224, 385/384, 4000/3993, 1001255211106304, which are the commas of wizard plus a complex interval which can play no role in ordinary circumstances, so that '''v''' can be used in place of the mapping for wizard.
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	[[Category:Lists of chords]]		[[Category:Lists of chords]]
	[[Category:Dyadic chords]]		[[Category:Dyadic chords]]
	~~[[Category:11-limit]]~~
	[[Category:Wizard]]		[[Category:Wizard]]
			[[Category:Triads]]
			[[Category:Tetrads]]
			[[Category:Pentads]]

FloraC: Cleanup

2025-01-26T09:49:07Z

Cleanup

Show changes

BudjarnLambeth: Categorised this uncategorised page

2023-04-25T11:10:32Z

Categorised this uncategorised page

← Older revision		Revision as of 11:10, 25 April 2023
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	\| \| 30		\| \| 30
	\|}		\|}
			[[Category:Lists of chords]]
			[[Category:Dyadic chords]]
			[[Category:11-limit]]
			[[Category:Wizard]]

Cmloegcmluin: unhyphenate "comma basis"

2021-11-12T20:23:40Z

unhyphenate "comma basis"

← Older revision		Revision as of 20:23, 12 November 2021
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	Below are listed the [[Dyadic_chord\|dyadic chords]] of 11-limit [[Marvel_temperaments#Wizard\|wizard temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 385/384 keenanismic, and by 225/224 marvel. Those requiring tempering by any two of 540/539, 385/384 or 225/224 are labeled unimarvel.		Below are listed the [[Dyadic_chord\|dyadic chords]] of 11-limit [[Marvel_temperaments#Wizard\|wizard temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 385/384 keenanismic, and by 225/224 marvel. Those requiring tempering by any two of 540/539, 385/384 or 225/224 are labeled unimarvel.

	The normal mapping for wizard is wiz = [<2 1 5 2 8\|, <0 6 -1 10 -3\|]. From this we may derive a val v = wiz[1] + 100 wiz[2] = <2 601 -95 1002 -292\|. Since v is approximately 100 times the generator chain val, <0 6 -1 10 -3\|, it will sort elements of the 11-limit tonality diamond in the same order, but it uniquely encodes each interval. Since it is a val of wizard, we may take a chord, find the smallest element under the mapping, and use it to translate the whole chord starting at zero. The val v is what might be called a quasi higher rank val; it has a [[comma-basis]] of 225/224, 385/384, 4000/3993, 1001255211106304, which are the commas of wizard plus a complex interval which can play no role in ordinary circumstances, so that v can be used in place of the mapping for wizard.		The normal mapping for wizard is wiz = [<2 1 5 2 8\|, <0 6 -1 10 -3\|]. From this we may derive a val v = wiz[1] + 100 wiz[2] = <2 601 -95 1002 -292\|. Since v is approximately 100 times the generator chain val, <0 6 -1 10 -3\|, it will sort elements of the 11-limit tonality diamond in the same order, but it uniquely encodes each interval. Since it is a val of wizard, we may take a chord, find the smallest element under the mapping, and use it to translate the whole chord starting at zero. The val v is what might be called a quasi higher rank val; it has a [[comma basis]] of 225/224, 385/384, 4000/3993, 1001255211106304, which are the commas of wizard plus a complex interval which can play no role in ordinary circumstances, so that v can be used in place of the mapping for wizard.

	Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.		Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.

Cmloegcmluin: fix typo, add link, and hyphen

2021-11-08T22:50:53Z

fix typo, add link, and hyphen

← Older revision		Revision as of 22:50, 8 November 2021
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	Below are listed the [[Dyadic_chord\|dyadic chords]] of 11-limit [[Marvel_temperaments#Wizard\|wizard temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 385/384 keenanismic, and by 225/224 marvel. Those requiring tempering by any two of 540/539, 385/384 or 225/224 are labeled unimarvel.		Below are listed the [[Dyadic_chord\|dyadic chords]] of 11-limit [[Marvel_temperaments#Wizard\|wizard temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 385/384 keenanismic, and by 225/224 marvel. Those requiring tempering by any two of 540/539, 385/384 or 225/224 are labeled unimarvel.

	The normal mapping for wizard is wiz = [<2 1 5 2 8\|, <0 6 -1 10 -3\|]. From this we may derive a val v = wiz[1] + 100 wiz[2] = <2 601 -95 1002 -292\|. Since v is approximately 100 times the generator chain val, <0 6 -1 10 -3\|, it will sort elements of the 11-limit tonality diamond in the same order, but it uniquely encodes each interval. Since it is a val of wizard, we may take a chord, find the smallest element under the mapping, and use it to translate the whole chord starting at zero. The val v is what might be called a quasi higher rank val; it has a comma ~~comma~~ basis 225/224, 385/384, 4000/3993, 1001255211106304, which are the commas of wizard plus a complex interval which can play no role in ordinary circumstances, so that v can be used in place of the mapping for wizard.		The normal mapping for wizard is wiz = [<2 1 5 2 8\|, <0 6 -1 10 -3\|]. From this we may derive a val v = wiz[1] + 100 wiz[2] = <2 601 -95 1002 -292\|. Since v is approximately 100 times the generator chain val, <0 6 -1 10 -3\|, it will sort elements of the 11-limit tonality diamond in the same order, but it uniquely encodes each interval. Since it is a val of wizard, we may take a chord, find the smallest element under the mapping, and use it to translate the whole chord starting at zero. The val v is what might be called a quasi higher rank val; it has a [[comma-basis]] of 225/224, 385/384, 4000/3993, 1001255211106304, which are the commas of wizard plus a complex interval which can play no role in ordinary circumstances, so that v can be used in place of the mapping for wizard.

	Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.		Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>genewardsmith: Imported revision 288420974 - Original comment:

2011-12-24T21:25:08Z

**Imported revision 288420974 - Original comment: **

← Older revision		Revision as of 21:25, 24 December 2011
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	<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:genewardsmith\|genewardsmith]] and made on <tt>2011-12-24 18:15:59 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-12-24 21:25:08 UTC</tt>.<br>
	: The original revision id was <tt>~~288415602~~</tt>.<br>		: The original revision id was <tt>288420974</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>
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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">Below are listed the [[Dyadic chord\|dyadic chords]] of 11-limit [[Marvel temperaments#Wizard\|wizard temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 385/384 keenanismic, and by 225/224 marvel. Those requiring tempering by any two of 540/539, 385/384 or 225/224 are labeled unimarvel.		<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">Below are listed the [[Dyadic chord\|dyadic chords]] of 11-limit [[Marvel temperaments#Wizard\|wizard temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 385/384 keenanismic, and by 225/224 marvel. Those requiring tempering by any two of 540/539, 385/384 or 225/224 are labeled unimarvel.

	The normal mapping for wizard is wiz = [<2 1 5 2 8\|, <0 6 -1 10 -3\|]. From this we may derive a val v = wiz[1] + 100 wiz[2] = <2 601 -95 1002 -292\|. Since v is approximately 100 times the generator chain val, <0 6 -1 10 -3\|, it will sort elements of the 11-limit tonality diamond in the same order, but it uniquely encodes each interval. Since it is a val of wizard, we may take a chord, find the smallest element under the mapping, and use it to translate the whole chord starting at zero. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.		The normal mapping for wizard is wiz = [<2 1 5 2 8\|, <0 6 -1 10 -3\|]. From this we may derive a val v = wiz[1] + 100 wiz[2] = <2 601 -95 1002 -292\|. Since v is approximately 100 times the generator chain val, <0 6 -1 10 -3\|, it will sort elements of the 11-limit tonality diamond in the same order, but it uniquely encodes each interval. Since it is a val of wizard, we may take a chord, find the smallest element under the mapping, and use it to translate the whole chord starting at zero. The val v is what might be called a quasi higher rank val; it has a comma comma basis 225/224, 385/384, 4000/3993, 1001255211106304, which are the commas of wizard plus a complex interval which can play no role in ordinary circumstances, so that v can be used in place of the mapping for wizard.

			Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.

	Wizard has MOS of size 6, 10, 16, 22, 28, 50 and 72. It may be seen that even ten notes supplies enough chords to be interesting, and that by the time we reach 22 we might feel we are pretty well supplied.		Wizard has MOS of size 6, 10, 16, 22, 28, 50 and 72. It may be seen that even ten notes supplies enough chords to be interesting, and that by the time we reach 22 we might feel we are pretty well supplied.
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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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Chords of wizard</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Marvel%20temperaments#Wizard">wizard temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 385/384 keenanismic, and by 225/224 marvel. Those requiring tempering by any two of 540/539, 385/384 or 225/224 are labeled unimarvel.<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>Chords of wizard</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Marvel%20temperaments#Wizard">wizard temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 385/384 keenanismic, and by 225/224 marvel. Those requiring tempering by any two of 540/539, 385/384 or 225/224 are labeled unimarvel.<br />
	<br />		<br />
	The normal mapping for wizard is wiz = [&lt;2 1 5 2 8\|, &lt;0 6 -1 10 -3\|]. From this we may derive a val v = wiz[1] + 100 wiz[2] = &lt;2 601 -95 1002 -292\|. Since v is approximately 100 times the generator chain val, &lt;0 6 -1 10 -3\|, it will sort elements of the 11-limit tonality diamond in the same order, but it uniquely encodes each interval. Since it is a val of wizard, we may take a chord, find the smallest element under the mapping, and use it to translate the whole chord starting at zero. Under &quot;Chord&quot; is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.<br />		The normal mapping for wizard is wiz = [&lt;2 1 5 2 8\|, &lt;0 6 -1 10 -3\|]. From this we may derive a val v = wiz[1] + 100 wiz[2] = &lt;2 601 -95 1002 -292\|. Since v is approximately 100 times the generator chain val, &lt;0 6 -1 10 -3\|, it will sort elements of the 11-limit tonality diamond in the same order, but it uniquely encodes each interval. Since it is a val of wizard, we may take a chord, find the smallest element under the mapping, and use it to translate the whole chord starting at zero. The val v is what might be called a quasi higher rank val; it has a comma comma basis 225/224, 385/384, 4000/3993, 1001255211106304, which are the commas of wizard plus a complex interval which can play no role in ordinary circumstances, so that v can be used in place of the mapping for wizard.<br />
			<br />
			Under &quot;Chord&quot; is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.<br />
	<br />		<br />
	Wizard has MOS of size 6, 10, 16, 22, 28, 50 and 72. It may be seen that even ten notes supplies enough chords to be interesting, and that by the time we reach 22 we might feel we are pretty well supplied.<br />		Wizard has MOS of size 6, 10, 16, 22, 28, 50 and 72. It may be seen that even ten notes supplies enough chords to be interesting, and that by the time we reach 22 we might feel we are pretty well supplied.<br />

Wikispaces>genewardsmith: Imported revision 288415602 - Original comment:

2011-12-24T18:15:59Z

**Imported revision 288415602 - Original comment: **

Show changes

Wizard/Chords - Revision history

Lériendil: Lériendil moved page Chords of wizard to Wizard/Chords

FloraC: Fix linking. Categories

FloraC: Cleanup

BudjarnLambeth: Categorised this uncategorised page

Cmloegcmluin: unhyphenate "comma basis"

Cmloegcmluin: fix typo, add link, and hyphen

Wikispaces>FREEZE at 00:00, 17 July 2018

Wikispaces>genewardsmith: **Imported revision 288420974 - Original comment: **

Wikispaces>genewardsmith: **Imported revision 288415602 - Original comment: **

Wikispaces>genewardsmith: Imported revision 288420974 - Original comment:

Wikispaces>genewardsmith: Imported revision 288415602 - Original comment: