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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]]. | 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]] | 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>Erlich, Paul. "Tuning, Tonality and 22-Tone Temperament." Xenharmonicon 17, 1998. [http://sethares.engr.wisc.edu/paperspdf/Erlich-22.pdf http://sethares.engr.wisc.edu/paperspdf/Erlich-22.pdf]</ref> than 16/15, which is 111.73 cents. | ||
== See also == | == See also == | ||
* [[14:18:21]] - a subchord of 28:36:42:49 | * [[14:18:21]] - a subchord of 28:36:42:49 | ||
* [[4:6:7]] - another subchord | * [[4:6:7]] - another subchord | ||
== References == | |||
<references/> | |||
Revision as of 06:42, 27 December 2025
| 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 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 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 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, 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 cents, which is much closer to the optimum of around 70 cents[1] than 16/15, which is 111.73 cents.
See also
References
- ↑ Erlich, Paul. "Tuning, Tonality and 22-Tone Temperament." Xenharmonicon 17, 1998. http://sethares.engr.wisc.edu/paperspdf/Erlich-22.pdf