28:36:42:49: Difference between revisions
better word |
No edit summary |
||
| Line 5: | Line 5: | ||
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. | 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 == | == See also == | ||
Latest revision as of 04:33, 26 May 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 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 | 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
- ↑ Secor, George. "The 17-tone puzzle — and the Neo-medieval Key That Unlocks It" Xenharmonikôn 18, 2006. http://anaphoria.com/Secor17puzzle.pdf