User:BudjarnLambeth/1ed28.7c
| ← 0ed31444/30927 | 1ed31444/30927 | 2ed31444/30927 → |
Arithmetic pitch sequence of 720jot (APS720jot), also known as 1 equal division of 720jot (1ed720jot) or 720-jot equal temperament (720jot-et), is an equal-step scale with steps of 720 jots (~28.7015 cents), or each 720th step of 30103edo.
Although it is not exactly 28.7 cents, it is close enough that it can reasonably be referred to as 1 equal division of 28.7 cents (1ed28.7c). This title is used for ease of navigation and comparison with other arithmetic pitch sequences on the wiki.
Theory
APS720jot divides 2/1 into ~41.8097 equal parts, making it close to 42edo, but with impure octaves and better approximations of harmonics 3/1 and 5/1.
It is very similar to 42ed257/128, which achieves many of the same aims. The difference is that 42ed257/128 has better harmonics 3, 5 and 7, while APS720jot has better harmonics 2, 11 and 13.
APS720jot is a kind of opposite twin to the scale 191zpi. 191zpi makes 42edo into a better 2.3.5.11.13 tuning, while APS720jot makes 42edo into a better 2.3.5.7.17 tuning. They both improve 42edo but in opposite directions.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.5 | -7.7 | -2.3 | -10.8 | +10.4 | +8.2 | +3.0 | +11.3 | -3.7 | -3.2 | -3.8 |
| Relative (%) | +19.0 | -26.7 | -7.9 | -37.5 | +36.2 | +28.6 | +10.4 | +39.5 | -12.9 | -11.1 | -13.4 | |
| Step | 42 | 66 | 97 | 117 | 145 | 155 | 171 | 178 | 189 | 203 | 207 | |
42edo for comparison:
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0 | +12.3 | +13.7 | +2.6 | -8.5 | -12.0 | +9.3 | -11.8 | +0.3 | -1.0 |
| Relative (%) | +0.0 | +43.2 | +47.9 | +9.1 | -29.6 | -41.8 | +32.7 | -41.3 | +1.0 | -3.5 | |
| Steps (reduced) |
42 (0) |
67 (25) |
98 (14) |
118 (34) |
145 (19) |
155 (29) |
172 (4) |
178 (10) |
190 (22) |
204 (36) | |
Scala file
Tuning file for anything that supports Scala. Made with Scale Workshop.
! aps720jot.scl ! Created using Scale Workshop 3.0.1 ! ! https://scaleworkshop.plainsound.org/scale/M7mh0KX7e ! Arithmetic pitch sequence of 720jot 42 ! 28.701432 57.402864 86.104296 114.805728 143.507160 172.208592 200.910024 229.611456 258.312888 287.014320 315.715752 344.417184 373.118616 401.820048 430.521480 459.222912 487.924344 516.625776 545.327208 574.028640 602.730072 631.431504 660.132936 688.834368 717.535800 746.237232 774.938664 803.640096 832.341528 861.042960 889.744392 918.445824 947.147256 975.848688 1004.550120 1033.251552 1061.952984 1090.654416 1119.355848 1148.057280 1176.758712 1205.460144