Wizard/Chords: Difference between revisions

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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.

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[[Category:Lists of chords]]

[[Category:Dyadic chords]]

~~[[Category:11-limit]]~~

[[Category:Wizard]]

[[Category:Triads]]

[[Category:Tetrads]]

[[Category:Pentads]]

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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.
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 [[Category:Lists of chords]]
 [[Category:Dyadic chords]]
-[[Category:11-limit]]
 [[Category:Wizard]]
+[[Category:Triads]]
+[[Category:Tetrads]]
+[[Category:Pentads]]