User:BudjarnLambeth/Sandbox2
Title1
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.1 | -8.5 | -8.2 | +4.1 | -12.6 | +19.5 | -12.3 | -16.9 | +0.0 | +34.3 | -16.7 |
| Relative (%) | -4.1 | -8.5 | -8.2 | +4.1 | -12.6 | +19.6 | -12.4 | -17.0 | +0.0 | +34.4 | -16.7 | |
| Steps (reduced) |
12 (12) |
19 (19) |
24 (24) |
28 (28) |
31 (31) |
34 (34) |
36 (36) |
38 (38) |
40 (0) |
42 (2) |
43 (3) | |
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.4 | +3.4 | +6.7 | +21.5 | +6.7 | +40.7 | +10.1 | +6.7 | +24.9 | -39.9 | +10.1 |
| Relative (%) | +3.3 | +3.3 | +6.7 | +21.4 | +6.7 | +40.6 | +10.0 | +6.7 | +24.8 | -39.8 | +10.0 | |
| Steps (reduced) |
12 (5) |
19 (5) |
24 (3) |
28 (0) |
31 (3) |
34 (6) |
36 (1) |
38 (3) |
40 (5) |
41 (6) |
43 (1) | |
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.2 | +0.0 | +2.5 | +16.6 | +1.2 | +34.7 | +3.7 | +0.0 | +17.8 | -47.1 | +2.5 |
| Relative (%) | +1.2 | +0.0 | +2.5 | +16.6 | +1.2 | +34.6 | +3.7 | +0.0 | +17.8 | -47.1 | +2.5 | |
| Steps (reduced) |
12 (12) |
19 (0) |
24 (5) |
28 (9) |
31 (12) |
34 (15) |
36 (17) |
38 (0) |
40 (2) |
41 (3) |
43 (5) | |
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.8 | -0.8 | +1.5 | +15.5 | +0.0 | +33.3 | +2.3 | -1.5 | +16.2 | -48.7 | +0.8 |
| Relative (%) | +0.8 | -0.8 | +1.5 | +15.4 | +0.0 | +33.3 | +2.3 | -1.5 | +16.2 | -48.7 | +0.8 | |
| Steps (reduced) |
12 (12) |
19 (19) |
24 (24) |
28 (28) |
31 (0) |
34 (3) |
36 (5) |
38 (7) |
40 (9) |
41 (10) |
43 (12) | |
Title2
Octave stretch or compression
What follows is a comparison of stretched- and compressed-octave 41edo tunings.
- Step size: 29.277 ¢, octave size: NNN ¢
Stretching the octave of EDONAME by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. Its 11-limit WE tuning and 11-limit TE tuning both do this. So does 184zpi, whose octave is identical to WE within 0.02 ¢.
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.4 | +1.0 | +0.7 | -5.0 | +1.4 | -2.0 | +1.1 | +2.1 | -4.6 | +6.0 | +1.8 |
| Relative (%) | +1.2 | +3.6 | +2.4 | -17.1 | +4.8 | -6.7 | +3.7 | +7.2 | -15.9 | +20.5 | +6.0 | |
| Step | 41 | 65 | 82 | 95 | 106 | 115 | 123 | 130 | 136 | 142 | 147 | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +9.6 | -1.6 | -3.9 | +1.4 | +13.6 | +2.5 | -3.3 | -4.3 | -0.9 | +6.4 | -12.0 | +2.1 |
| Relative (%) | +32.7 | -5.5 | -13.5 | +4.9 | +46.4 | +8.4 | -11.3 | -14.6 | -3.1 | +21.8 | -41.1 | +7.2 | |
| Step | 152 | 156 | 160 | 164 | 168 | 171 | 174 | 177 | 180 | 183 | 185 | 188 | |
- 41edo
- Step size: 29.268 ¢, octave size: 1200.0 ¢
Pure-octaves 41edo approximates all harmonics up to 16 within NNN ¢. The octaves of its compressed tuning 147ed12 differ by only 0.1 ¢ from pure. The octaves of its 13-limit WE and TE tuning differ by less than 0.1 ¢ from pure.
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0 | +0.5 | +0.0 | -5.8 | +0.5 | -3.0 | +0.0 | +1.0 | -5.8 | +4.8 | +0.5 |
| Relative (%) | +0.0 | +1.7 | +0.0 | -19.9 | +1.7 | -10.2 | +0.0 | +3.3 | -19.9 | +16.3 | +1.7 | |
| Steps (reduced) |
41 (0) |
65 (24) |
82 (0) |
95 (13) |
106 (24) |
115 (33) |
123 (0) |
130 (7) |
136 (13) |
142 (19) |
147 (24) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +8.3 | -3.0 | -5.3 | +0.0 | +12.1 | +1.0 | -4.8 | -5.8 | -2.5 | +4.8 | -13.6 | +0.5 |
| Relative (%) | +28.2 | -10.2 | -18.3 | +0.0 | +41.4 | +3.3 | -16.5 | -19.9 | -8.5 | +16.3 | -46.6 | +1.7 | |
| Steps (reduced) |
152 (29) |
156 (33) |
160 (37) |
164 (0) |
168 (4) |
171 (7) |
174 (10) |
177 (13) |
180 (16) |
183 (19) |
185 (21) |
188 (24) | |
- 147ed12 — step size: 29.265 ¢, octave size: 1199.87 ¢
- 106ed6 — step size: 29.264 ¢, octave size: 1199.69 ¢
- 65edt — step size: 29.261 ¢, octave size: 1199.81 ¢
Compressing the octave of 41edo by around 0.2 ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tunings 147ed12, 106ed6 and 65edt do this.
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.2 | +0.2 | -0.4 | -6.3 | +0.0 | -3.5 | -0.6 | +0.4 | -6.4 | +4.1 | -0.2 |
| Relative (%) | -0.6 | +0.6 | -1.3 | -21.4 | +0.0 | -12.0 | -1.9 | +1.3 | -22.0 | +14.1 | -0.6 | |
| Steps (reduced) |
41 (41) |
65 (65) |
82 (82) |
95 (95) |
106 (0) |
115 (9) |
123 (17) |
130 (24) |
136 (30) |
142 (36) |
147 (41) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.6 | -3.7 | -6.1 | -0.7 | +11.4 | +0.2 | -5.6 | -6.6 | -3.3 | +3.9 | -14.5 | -0.4 |
| Relative (%) | +25.8 | -12.6 | -20.8 | -2.6 | +38.8 | +0.6 | -19.2 | -22.7 | -11.3 | +13.5 | -49.5 | -1.3 | |
| Steps (reduced) |
152 (46) |
156 (50) |
160 (54) |
164 (58) |
168 (62) |
171 (65) |
174 (68) |
177 (71) |
180 (74) |
183 (77) |
185 (79) |
188 (82) | |