1ed28.5c
| ← 0ed13167/12952 | 1ed13167/12952 | 2ed13167/12952 → |
Arithmetic pitch sequence of 715jot (APS715jot), also known as 1 equal division of 715jot (1ed715jot) or 715-jot equal temperament (715jot-et), is an equal-step scale with steps of 715 jots (~28.50215 cents), or each 715th step of 30103edo.
Although it is not exactly 28.5 cents, it is close enough that it can reasonably be referred to as 1 equal division of 28.5 cents (1ed28.5c). This title is used for ease of navigation and comparison with other arithmetic pitch sequences on the wiki.
Theory
See also: Table of stretched 42edo tunings
APS715jot divides 2/1 into ~42.1021 equal parts, making it close to 42edo, but with impure octaves and better approximations of harmonics 3/1 and 5/1.
It is a kind of opposite twin to the scale APS720jot, as they improve 42edo’s JI approximation by about the same amount, but in opposite directions (those harmonics which are slightly sharp in one are slightly flat in the other).
APS715jot’s step size is very close to that of 42ed255/128 and 191zpi.
Harmonics
APS720jot has less than 40% relative error on every single prime harmonic from 2 up to 19, making it a suitable full 19-limit tuning.
No other stretched or compressed version of 42edo has that property.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.9 | +7.7 | +6.9 | -5.6 | +10.0 | +5.8 | -2.6 | +4.4 | -12.9 | +13.4 |
| Relative (%) | -10.2 | +27.0 | +24.2 | -19.6 | +35.1 | +20.4 | -9.1 | +15.3 | -45.1 | +46.9 | |
| Steps | 42 | 67 | 98 | 118 | 146 | 156 | 172 | 179 | 190 | 205 | |
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) | |
Notation
APS715jot can use most notation systems designed for 42edo. See 42edo#Notation.
Scala file
Tuning file for anything that supports Scala. Made with Scale Workshop.
! aps715jot.scl ! Created using Scale Workshop 3.0.1 ! ! https://scaleworkshop.plainsound.org/scale/ecmf6OFjI ! Arithmetic pitch sequence of 715jot 42 ! 28.502143 57.004285 85.506428 114.008570 142.510713 171.012856 199.514998 228.017141 256.519283 285.021426 313.523569 342.025711 370.527854 399.029996 427.532139 456.034282 484.536424 513.038567 541.540709 570.042852 598.544995 627.047137 655.549280 684.051422 712.553565 741.055708 769.557850 798.059993 826.562135 855.064278 883.566421 912.068563 940.570706 969.072848 997.574991 1026.077134 1054.579276 1083.081419 1111.583561 1140.085704 1168.587847 1197.089989
Scales
- Eugene/Tritikleismic[9]: 3 8 3 3 8 3 3 8 3
- Eugene/Tritikleismic[15]: 3 3 2 3 3 3 3 2 3 3 3 3 2 3 3
- Lemba[16]: 3 2 3 2 3 3 2 3 3 2 3 2 3 3 2 3
- Qeema/Skateboard[15]: 2 5 2 2 2 5 2 2 2 5 2 2 2 5 2
- Qeema/Skateboard[19]: 2 2 3 2 2 2 2 3 2 2 2 3 2 2 2 2 3 2 2
- Seville/Sevond[14] 1st mode: 1 5 1 5 1 5 1 5 1 5 1 5 1 5
- Seville/Sevond[14] 2nd mode: 5 1 5 1 5 1 5 1 5 1 5 1 5 1
- Seville/Sevond[21]: 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4
- Subsets of MOS scales
(Names used are idiosyncratic.)
- Eugene/Tritikleismic[9]
- Groovy aeolian pentatonic: 11 6 8 3 14
- Otonal mixolydian pentatonic: 14 3 8 11 6
- Pseudo-equipentatonic: 11 6 8 6 11
- Septimal melodic minor pentatonic: 8 3 14 14 3
- Septimal Picardy pentatonic: 8 6 11 3 14
- Undecimal lydian-aeolian pentatonic: 8 14 3 11 6
- Yokai pentatonic: 3 14 8 3 14
Instruments
- Lumatone
- APS715jot can use most types of Lumatone mapping for 42edo