28:36:42:49: Difference between revisions

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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.  
'''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. 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 [[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 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/>

Latest revision as of 04:33, 26 May 2026

Chord information
Harmonics 28:36:42:49
Subharmonics 1/(63:49:42:36)
Intervals from root 1/1–9/7–3/2–7/4
Cents from root 0¢–435¢–702¢–969¢
Step intervals 9/7, 7/6, 7/6
Step cents 435¢, 267¢, 267¢
Color name ru zo-7 or r,z7
Prime limit 7
Genus 32⋅72 (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 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 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 cents, which is much closer to the optimum of around 70 cents[1] than 16/15, which is 111.73 cents.


Edo approximations for 28:36:42:49 ▶
intervals: 9/7, 3/2, 7/4 · ≤ 60edo, RMS rel. error ≤ 15%
  Edo Steps Cents (¢) Absolute errors (¢) RMS (¢) RMS (%)
▶ 9 0  3  5  7 0.00 400.00 666.67 933.33 0.00 -35.08 -35.29 -35.49 15.28 11.46
▶ 14 0  5  8 11 0.00 428.57 685.71 942.86 0.00  -6.51 -16.24 -25.97 9.84 11.48
▶ 22 0  8 13 18 0.00 436.36 709.09 981.82 0.00  +1.28  +7.14 +12.99 5.17 9.47
▶ 27 0 10 16 22 0.00 444.44 711.11 977.78 0.00  +9.36  +9.16  +8.95 3.97 8.93
▶ 31 0 11 18 25 0.00 425.81 696.77 967.74 0.00  -9.28  -5.18  -1.08 3.66 9.47
▶ 32 0 12 19 26 0.00 450.00 712.50 975.00 0.00 +14.92 +10.54  +6.17 5.51 14.70
▶ 36 0 13 21 29 0.00 433.33 700.00 966.67 0.00  -1.75  -1.96  -2.16 0.86 2.58
▶ 41 0 15 24 33 0.00 439.02 702.44 965.85 0.00  +3.94  +0.48  -2.97 2.45 8.38
▶ 45 0 16 26 36 0.00 426.67 693.33 960.00 0.00  -8.42  -8.62  -8.83 3.74 14.01
▶ 50 0 18 29 40 0.00 432.00 696.00 960.00 0.00  -3.08  -5.96  -8.83 3.28 13.67
▶ 58 0 21 34 47 0.00 434.48 703.45 972.41 0.00  -0.60  +1.49  +3.59 1.62 7.81

See also

References

  1. ↑ Secor, George. "The 17-tone puzzle — and the Neo-medieval Key That Unlocks It" Xenharmonikôn 18, 2006. http://anaphoria.com/Secor17puzzle.pdf
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