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.  
'''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. The [[49/36]] [[tritone]] represents [[15/11]] in undecimal superpyth, however, 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]], due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents 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]], 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 than 16/15, which is 111.73 cents.

Revision as of 06:38, 27 December 2025

Chord information
Harmonics 28:36:42:49
Subharmonics 1/(63:49:42:36)
Intervals from root 1/19/73/27/4
Cents from root 435¢702¢969¢
Step intervals 9/7, 7/6, 7/6
Step cents 435¢, 267¢, 267¢
Color name rz7 or ru-zo7
Prime limit 7
Genus 3272 (441)
Intervallic odd limit 49
Otonal odd limit 49
Utonal odd limit 63
Consistent edos (d ≥ 2) 5edo*, 22edo*, 27edo*, 31edo*, …

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 3/227/149/421/8 above the tonic, which is octave-equivalent to 27/289/821/16–3/2. 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 than 16/15, which is 111.73 cents.

See also