28:36:42:49: Difference between revisions

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This chord occurs on the V of the [[5L 2s|diatonic]] scale in [[superpyth]] temperament. Note that the [[49/36]] [[tritone]] represents [[15/11]] in undecimal superpyth, which reduces it to a [[15-odd-limit]] [[swetismic chords|swetismic]] [[essentially tempered chord]].

On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence|octave-equivalent]] to [[28/27|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by inflecting the 27/28 up by [[28/27]], and the 21/16 down by [[21/20]]. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>Secor, George. "The 17-tone puzzle — and the Neo-medieval Key That Unlocks It" Xenharmonikôn 18, 2006. http://anaphoria.com/Secor17puzzle.pdf</ref> than 16/15, which is 111.73 cents.

On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence|octave-equivalent]] to [[28/27|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by inflecting the 27/28 up by [[28/27]] to [[1/1]], and the 21/16 down by [[21/20]] to 5/4. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>Secor, George. "The 17-tone puzzle — and the Neo-medieval Key That Unlocks It" Xenharmonikôn 18, 2006. http://anaphoria.com/Secor17puzzle.pdf</ref> than 16/15, which is 111.73 cents.

== See also ==

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 This chord occurs on the V of the [[5L 2s|diatonic]] scale in [[superpyth]] temperament. Note that the [[49/36]] [[tritone]] represents [[15/11]] in undecimal superpyth, which reduces it to a [[15-odd-limit]] [[swetismic chords|swetismic]] [[essentially tempered chord]].
-On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence|octave-equivalent]] to [[28/27|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by inflecting the 27/28 up by [[28/27]], and the 21/16 down by [[21/20]]. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>Secor, George. "The 17-tone puzzle — and the Neo-medieval Key That Unlocks It" Xenharmonikôn 18, 2006. http://anaphoria.com/Secor17puzzle.pdf</ref> than 16/15, which is 111.73 cents.
+On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence|octave-equivalent]] to [[28/27|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by inflecting the 27/28 up by [[28/27]] to [[1/1]], and the 21/16 down by [[21/20]] to 5/4. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>Secor, George. "The 17-tone puzzle — and the Neo-medieval Key That Unlocks It" Xenharmonikôn 18, 2006. http://anaphoria.com/Secor17puzzle.pdf</ref> than 16/15, which is 111.73 cents.
 == See also ==