User:Contribution/327ed7
| ← 326ed7 | 327ed7 | 328ed7 → |
327 equal divisions of the 7th harmonic (abbreviated 327ed7) is a nonoctave tuning system that divides the interval of 7/1 into 327 equal parts of about 10.3 ¢ each. Each step represents a frequency ratio of 71/327, or the 327th root of 7.
Theory
327ed7 is related to 695zpi no-2 no-3 no-5 analogue.
695zpi sets a height record on the Riemann zeta function with primes 2, 3 and 5 removed.
There is no better peak until the 2485zpi no-2 no-3 no-5 analogue, related to 934ed7.
5.50170634367309287643484991017769754899729226704541986574311048539416
327.005976583980785662359711182151706915324382836632556050595015540
5.6157930141135163017766685402444293609627477857549470376596348292657
933.950702612953471546210854419427367873650944163629066387540013694
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.94 | +3.96 | +0.42 | -4.71 | -0.99 | +0.00 | -4.53 | -2.39 | +0.65 | +0.48 | +4.37 | -0.27 | -4.94 | -0.76 | +0.83 |
| Relative (%) | -48.0 | +38.4 | +4.0 | -45.8 | -9.6 | +0.0 | -43.9 | -23.2 | +6.3 | +4.6 | +42.4 | -2.6 | -48.0 | -7.4 | +8.1 | |
| Steps | 116 | 185 | 233 | 270 | 301 | 327 | 349 | 369 | 387 | 403 | 418 | 431 | 443 | 455 | 466 | |
| Harmonic | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.10 | +2.97 | +2.09 | -4.30 | +3.96 | -4.47 | +1.00 | -0.57 | +0.87 | +5.09 | +1.56 | +0.42 | +1.48 | +4.60 | -0.65 | -4.11 |
| Relative (%) | -10.7 | +28.8 | +20.2 | -41.7 | +38.4 | -43.3 | +9.7 | -5.5 | +8.5 | +49.4 | +15.2 | +4.0 | +14.4 | +44.7 | -6.4 | -39.9 | |
| Steps | 476 | 486 | 495 | 503 | 512 | 519 | 527 | 534 | 541 | 548 | 554 | 560 | 566 | 572 | 577 | 582 | |
| Harmonic | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.43 | +4.26 | -4.71 | -1.97 | +2.10 | -2.86 | +3.68 | +1.06 | -0.48 | -0.99 | -0.51 | +0.89 | +3.20 | -3.95 | +0.03 | +4.79 |
| Relative (%) | +43.0 | +41.4 | -45.8 | -19.2 | +20.4 | -27.7 | +35.8 | +10.3 | -4.6 | -9.6 | -5.0 | +8.7 | +31.0 | -38.3 | +0.3 | +46.5 | |
| Steps | 588 | 593 | 597 | 602 | 607 | 611 | 616 | 620 | 624 | 628 | 632 | 636 | 640 | 643 | 647 | 651 | |
| Harmonic | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -4.07 | +2.86 | +0.15 | -1.92 | -3.38 | -4.24 | -4.53 | -4.26 | -3.46 | -2.15 | -0.34 | +1.95 | +4.71 | -2.39 | +1.25 |
| Relative (%) | +0.0 | -39.5 | +27.7 | +1.4 | -18.7 | -32.8 | -41.1 | -43.9 | -41.4 | -33.6 | -20.9 | -3.3 | +18.9 | +45.7 | -23.2 | +12.1 | |
| Steps | 654 | 657 | 661 | 664 | 667 | 670 | 673 | 676 | 679 | 682 | 685 | 688 | 691 | 694 | 696 | 699 | |
In 327ed7, the following harmonics are pretty good (less than 1.1 cent error): 1, 4, 6, 7, 10, 11, 13, 15, 16, 17, 23, 24, 25, 28, 31, 40, 41, 42, 43, 44, 47, 49, 52, 60, 66, 68, 70, 73, 77, 91, 96, 105, 112, 114, 119, 121, 124, 127, 130, 134, 138, 143, 150, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 187, 188, 195, 196, 202, 208, 213, 217, 233, 240, 243
Riemann zeta
327ed7 has an exceptionally strong no-2 no-3 no-5 zeta peak.