Prodigy chords: Difference between revisions

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A '''prodigy chord''' is an [[11-odd-limit]] [[essentially tempered chord]] in [[prodigy]] temperament. Since [[441/440]] is tempered out in prodigy, [[werckismic chords]] are also prodigy chords, and since [[225/224]] is tempered out, the [[9-odd-limit]] [[marvel chords]] are prodigy chords. Aside from these, there are three more prodigy chords:

A '''prodigy chord''' is an [[11-odd-limit]] [[essentially tempered chord]] in [[prodigy]] temperament. Since [[441/440]] is tempered out in prodigy, [[werckismic chords]] are also prodigy chords, and since [[225/224]] is tempered out, the [[9-odd-limit]] [[marvel chords]] are prodigy chords. Aside from these, there are three more prodigy chords, with a palindromic tetrad:

* ~~a 1-5~~/~~4-7~~/~~5-16~~/9 ~~tetrad~~ with steps 5/4-9/8-14/11-9/8;

* 1–5/4–7/5–16/9 with steps 5/4, 9/8, 14/11, 9/8;

~~and~~ a pair of inversely related pentads:

And a pair of inversely related pentads:

* ~~1-5~~/~~4-7~~/~~5-8~~/~~5-16~~/9 with steps 5/4-9/8-8/7-10/9-9/8;

* 1–5/4–7/5–8/5–16/9 with steps 5/4, 9/8, 8/7, 10/9, 9/8, and its inverse

* ~~1-5~~/~~4-7~~/~~5-14~~/~~9-16~~/9 with steps 5/4-9/8-10/9-8/7-9/8.

* 1–5/4–7/5–14/9–16/9 with steps 5/4, 9/8, 10/9, 8/7, 9/8.

== Miracle essentially tempered chords ==

11-limit [[miracle]] temperament tempers out an astonishing five commas which allow essential tempering: [[540/539]], 441/440, [[385/384]], [[243/242]] and 225/224, and hence has all of the essentially tempered chords of each of them. Further chords come from [[Breed family #Jove, aka Wonder|jove]] and [[undecimal marvel chords]]. Then there are the three listed above, and ten essentially miracle chords.

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* [[Chords of miracle]]

[[Category:11-odd-limit]]

[[Category:11-odd-limit chords]]

~~[[Category:Chords~~]]

[[Category:Essentially tempered chords]]

~~[[Category:Dyadic]]~~

[[Category:Marvel]]

[[Category:Prodigy]]

[[Category:Miracle]]

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-A '''prodigy chord''' is an [[11-odd-limit]] [[essentially tempered chord]] in [[prodigy]] temperament. Since [[441/440]] is tempered out in prodigy, [[werckismic chords]] are also prodigy chords, and since [[225/224]] is tempered out, the [[9-odd-limit]] [[marvel chords]] are prodigy chords. Aside from these, there are three more prodigy chords:
+A '''prodigy chord''' is an [[11-odd-limit]] [[essentially tempered chord]] in [[prodigy]] temperament. Since [[441/440]] is tempered out in prodigy, [[werckismic chords]] are also prodigy chords, and since [[225/224]] is tempered out, the [[9-odd-limit]] [[marvel chords]] are prodigy chords. Aside from these, there are three more prodigy chords, with a palindromic tetrad:
-* a 1-5/4-7/5-16/9 tetrad with steps 5/4-9/8-14/11-9/8;
+* 1–5/4–7/5–16/9 with steps 5/4, 9/8, 14/11, 9/8;
-and a pair of inversely related pentads:
+And a pair of inversely related pentads:
-* 1-5/4-7/5-8/5-16/9 with steps 5/4-9/8-8/7-10/9-9/8;
+* 1–5/4–7/5–8/5–16/9 with steps 5/4, 9/8, 8/7, 10/9, 9/8, and its inverse
-* 1-5/4-7/5-14/9-16/9 with steps 5/4-9/8-10/9-8/7-9/8.
+* 1–5/4–7/5–14/9–16/9 with steps 5/4, 9/8, 10/9, 8/7, 9/8.
 == Miracle essentially tempered chords ==
-{{main| Miracle chords }}
+{{Main| Miracle chords }}
 -limit [[miracle]] temperament tempers out an astonishing five commas which allow essential tempering: [[540/539]], 441/440, [[385/384]], [[243/242]] and 225/224, and hence has all of the essentially tempered chords of each of them. Further chords come from [[Breed family #Jove, aka Wonder|jove]] and [[undecimal marvel chords]]. Then there are the three listed above, and ten essentially miracle chords.
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 * [[Chords of miracle]]
-[[Category:11-odd-limit]]
+[[Category:11-odd-limit chords]]
-[[Category:Chords]]
 [[Category:Essentially tempered chords]]
-[[Category:Dyadic]]
 [[Category:Marvel]]
 [[Category:Prodigy]]
 [[Category:Miracle]]