28:36:42:49: Difference between revisions
make this clearer |
note 49/36 acts as a dissonance rather than the 9/7 note itself |
||
| Line 1: | Line 1: | ||
{{Infobox chord|ColorName = rz7 or ru-zo7}} | {{Infobox chord|ColorName = rz7 or ru-zo7}} | ||
'''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 | '''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 | 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 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. | 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. | ||
Revision as of 05:50, 29 January 2026
| Chord information |
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 diatonic scale in superpyth temperament. Note that the tritone represents 15/11 in undecimal superpyth, which reduces it to a 15-odd-limit swetismic essentially tempered chord.
On the dominant, this chord is 3/2–27/14–9/4–21/8 above the tonic, which is octave-equivalent to 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 cents, which is much closer to the optimum of around 70 cents[1] than 16/15, which is 111.73 cents.
See also
References
- ↑ Secor, George. "The 17-tone puzzle — and the Neo-medieval Key That Unlocks It" Xenharmonikôn 18, 2006. http://anaphoria.com/Secor17puzzle.pdf