28:36:42:49

Revision as of 05:50, 29 January 2026 by Overthink (talk | contribs) (note 49/36 acts as a dissonance rather than the 9/7 note itself)

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.

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*, …

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 3/227/149/421/8 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 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

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