28:36:42:49: Difference between revisions

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'''28:36:42:49''' is a septimal [[dominant seventh chord]]. This chord is similar to the harmonic seventh chord [[4:5:6:7]], except the major third is inflected up by [[36/35]] from [[5/4]] to [[9/7]]. This makes it stand out ~~as a dissonance~~ from the rest of the chord. This is in contrast to the [[5-limit]] [[20:25:30:36]] dominant seventh chord, which has the seventh inflected up by 36/35 from [[7/4]] to [[9/5]] compared to 4:5:6:7. This chord occurs on the V of the [[5L 2s|diatonic]] scale in [[superpyth]] temperament.

'''28:36:42:49''' is a septimal [[dominant seventh chord]]. This chord is similar to the harmonic seventh chord [[4:5:6:7]], except the major third is inflected up by [[36/35]] from [[5/4]] to [[9/7]]. This makes it stand out from the rest of the chord, and the [[49/36]] interval between the 9/7 and the [[7/4]] acts as a dissonance. This is in contrast to the [[5-limit]] [[20:25:30:36]] dominant seventh chord, which has the seventh inflected up by 36/35 from [[7/4]] to [[9/5]] compared to 4:5:6:7.

This chord occurs on the V of the [[5L 2s|diatonic]] scale in [[superpyth]] temperament. Note that the [[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 leading 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 ==

* [[14:18:21]] - a subchord of 28:36:42:49

* [[4:6:7]] - another subchord

== References ==

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-{{Infobox chord|ColorName = rz7 or ru-zo7}}
+{{Infobox chord|ColorName = ru zo-7 or r,z7}}
-'''28:36:42:49''' is a septimal [[dominant seventh chord]]. This chord is similar to the harmonic seventh chord [[4:5:6:7]], except the major third is inflected up by [[36/35]] from [[5/4]] to [[9/7]]. This makes it stand out as a dissonance from the rest of the chord. This is in contrast to the [[5-limit]] [[20:25:30:36]] dominant seventh chord, which has the seventh inflected up by 36/35 from [[7/4]] to [[9/5]] compared to 4:5:6:7. This chord occurs on the V of the [[5L 2s|diatonic]] scale in [[superpyth]] temperament.
+'''28:36:42:49''' is a septimal [[dominant seventh chord]]. This chord is similar to the harmonic seventh chord [[4:5:6:7]], except the major third is inflected up by [[36/35]] from [[5/4]] to [[9/7]]. This makes it stand out from the rest of the chord, and the [[49/36]] interval between the 9/7 and the [[7/4]] acts as a dissonance. This is in contrast to the [[5-limit]] [[20:25:30:36]] dominant seventh chord, which has the seventh inflected up by 36/35 from [[7/4]] to [[9/5]] compared to 4:5:6:7.
+This chord occurs on the V of the [[5L 2s|diatonic]] scale in [[superpyth]] temperament. Note that the [[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 leading 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.
+{{chord edo approximation}}
+== See also ==
+* [[14:18:21]] - a subchord of 28:36:42:49
+* [[4:6:7]] - another subchord
+== References ==
+<references/>