Prodigy chords: Difference between revisions

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A ''prodigy chord'' is an 11 odd limit [[~~Dyadic_chord|~~essentially tempered chord]] in [[~~Marvel_family#Prodigy|~~prodigy ~~temperament~~]]. Since 441/440 is tempered out in prodigy, [[~~werckismic_chords|~~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 1-5~~/~~4-7~~/~~5-16~~/9 ~~tetrad~~ with steps 5/4-9/8-14/11~~-9/8 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 and 1-5/4-7/5-14/9-16/9 with steps 5/4-9/8-10/9-8/7-9/8.~~

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:

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

=Miracle essentially tempered chords=

And a pair of inversely related pentads:

~~[[Gamelismic_clan#~~Miracle|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|~~undecimal marvel chords]]. Then there are the three listed above, and ten essentially miracle chords.

* 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.

== 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.

Three chords may not seem to be many, but consider this: the POTE tuning for prodigy shrinks 540/539 and 243/242 to a third of a cent, and 385/384 to -1/3 cent. Other optimizations are similar. Hence, the miracle essentially tempered chords are already available in prodigy, we just aren't counting them; in effect, we can more or less equate prodigy with miracle. In miracle, we may put the eight different kinds of essentially tempered chords together, for a total of triads: 21, tetrads: 76, pentads: 38, and hexads: 12. There are therefore actually more essentially tempered chords than just ones.

EDOs supporting prodigy/miracle include 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde, 463bcde.

EDOs supporting prodigy/miracle include {{EDOs| 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde, 463bcde }}.

== See also ==

* [[Chords of miracle]]

~~See also~~: [[~~Chords_of_miracle|~~chords ~~of miracle~~]]

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

[[Category:Essentially tempered chords]]

[[Category:Marvel]]

[[Category:Prodigy]]

[[Category:Miracle]]

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-A ''prodigy chord'' is an 11 odd limit [[Dyadic_chord|essentially tempered chord]] in [[Marvel_family#Prodigy|prodigy temperament]]. Since 441/440 is tempered out in prodigy, [[werckismic_chords|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 1-5/4-7/5-16/9 tetrad with steps 5/4-9/8-14/11-9/8 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 and 1-5/4-7/5-14/9-16/9 with steps 5/4-9/8-10/9-8/7-9/8.
+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:
+* 1–5/4–7/5–16/9 with steps 5/4, 9/8, 14/11, 9/8;
-=Miracle essentially tempered chords=
+And a pair of inversely related pentads:
-[[Gamelismic_clan#Miracle|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|undecimal marvel chords]]. Then there are the three listed above, and ten essentially miracle chords.
+* 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.
+== Miracle essentially tempered 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.
 Three chords may not seem to be many, but consider this: the POTE tuning for prodigy shrinks 540/539 and 243/242 to a third of a cent, and 385/384 to -1/3 cent. Other optimizations are similar. Hence, the miracle essentially tempered chords are already available in prodigy, we just aren't counting them; in effect, we can more or less equate prodigy with miracle. In miracle, we may put the eight different kinds of essentially tempered chords together, for a total of triads: 21, tetrads: 76, pentads: 38, and hexads: 12. There are therefore actually more essentially tempered chords than just ones.
-EDOs supporting prodigy/miracle include 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde, 463bcde.
+EDOs supporting prodigy/miracle include {{EDOs| 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde, 463bcde }}.
+== See also ==
+* [[Chords of miracle]]
-See also: [[Chords_of_miracle|chords of miracle]]
+[[Category:11-odd-limit chords]]
+[[Category:Essentially tempered chords]]
+[[Category:Marvel]]
+[[Category:Prodigy]]
+[[Category:Miracle]]