周波数比一覧
Tone Doublerの技術をマルチプル4以外にも適用できる可能性を考え、周波数比の一覧表を作成しました。
- キーフランクションを変化させずにマルチプルとキーコードの組み合わせのみで表現できる周波数比の全パターン
- マルチプルとデチューン2の組み合わせで表現できる周波数比の全パターン
これらを列挙し、周波数比の低い順にソートしています。
…が、2のべき乗でないマルチプルまで列挙してしまいましたので、見づらいかもしれません…。
| MUL | キー | 平均律の周波数比 | MUL*DT2による近似値 | 次点の近似値 |
|---|---|---|---|---|
| 0 | +0 | 0.5 | MUL:0 DT2:0 (0.5) | |
| 0 | +1 | 0.5297315 | ||
| 0 | +2 | 0.561231 | ||
| 0 | +3 | 0.5946035 | ||
| 0 | +4 | 0.6299605 | ||
| 0 | +5 | 0.66742 | ||
| 0 | +6 | 0.707107 | MUL:0 DT2:1 (0.705) | |
| 0 | +7 | 0.7491535 | ||
| 0 | +8 | 0.7937005 | MUL:0 DT2:2 (0.785) | |
| 0 | +9 | 0.8408965 | MUL:0 DT2:3 (0.865) | |
| 0 | +10 | 0.8908985 | ||
| 0 | +11 | 0.9438745 | ||
| 1 | +0 | 1 | MUL:1 DT2:0 (1) | |
| 1 | +1 | 1.059463 | ||
| 1 | +2 | 1.122462 | ||
| 1 | +3 | 1.189207 | ||
| 1 | +4 | 1.259921 | ||
| 1 | +5 | 1.33484 | ||
| 1 | +6 | 1.414214 | MUL:1 DT2:1 (1.41) | |
| 1 | +7 | 1.498307 | ||
| 1 | +8 | 1.587401 | MUL:1 DT2:2 (1.57) | |
| 1 | +9 | 1.681793 | ||
| 1 | +10 | 1.781797 | MUL:1 DT2:3 (1.73) | |
| 1 | +11 | 1.887749 | ||
| 2 | +0 | 2 | MUL:2 DT2:0 (2) | |
| 2 | +1 | 2.118926 | ||
| 2 | +2 | 2.244924 | ||
| 2 | +3 | 2.378414 | ||
| 2 | +4 | 2.519842 | ||
| 2 | +5 | 2.66968 | ||
| 2 | +6 | 2.828428 | MUL:2 DT2:1 (2.82) | |
| 2 | +7 | 2.996614 | ||
| 3 | +0 | 3 | MUL:3 DT2:0 (3) | |
| 2 | +8 | 3.174802 | MUL:2 DT2:2 (3.14) | |
| 3 | +1 | 3.178389 | ||
| 2 | +9 | 3.363586 | MUL:2 DT2:3 (3.46) | |
| 3 | +2 | 3.367386 | ||
| 2 | +10 | 3.563594 | ||
| 3 | +3 | 3.567621 | ||
| 2 | +11 | 3.775498 | ||
| 3 | +4 | 3.779763 | ||
| 4 | +0 | 4 | MUL:4 DT2:0 (4) | |
| 3 | +5 | 4.00452 | ||
| 4 | +1 | 4.237852 | MUL:3 DT2:1 (4.23) | |
| 3 | +6 | 4.242642 | ||
| 4 | +2 | 4.489848 | ||
| 3 | +7 | 4.494921 | ||
| 4 | +3 | 4.756828 | MUL:3 DT2:2 (4.71) | |
| 3 | +8 | 4.762203 | ||
| 5 | +0 | 5 | MUL:5 DT2:0 (5) | |
| 4 | +4 | 5.039684 | ||
| 3 | +9 | 5.045379 | ||
| 5 | +1 | 5.297315 | MUL:3 DT2:3 (5.19) | |
| 4 | +5 | 5.33936 | ||
| 3 | +10 | 5.345391 | ||
| 5 | +2 | 5.61231 | ||
| 4 | +6 | 5.656856 | MUL:4 DT2:1 (5.64) | |
| 3 | +11 | 5.663247 | ||
| 5 | +3 | 5.946035 | ||
| 4 | +7 | 5.993228 | ||
| 6 | +0 | 6 | MUL:6 DT2:0 (6) | |
| 5 | +4 | 6.299605 | MUL:4 DT2:2 (6.28) | |
| 4 | +8 | 6.349604 | ||
| 6 | +1 | 6.356778 | ||
| 5 | +5 | 6.6742 | ||
| 4 | +9 | 6.727172 | ||
| 6 | +2 | 6.734772 | MUL:4 DT2:3 (6.92) | |
| 7 | +0 | 7 | MUL:7 DT2:0 (7) | |
| 5 | +6 | 7.07107 | MUL:5 DT2:1 (7.05) | |
| 4 | +10 | 7.127188 | ||
| 6 | +3 | 7.135242 | ||
| 7 | +1 | 7.416241 | ||
| 5 | +7 | 7.491535 | ||
| 4 | +11 | 7.550996 | ||
| 6 | +4 | 7.559526 | ||
| 7 | +2 | 7.857234 | MUL:5 DT2:2 (7.85) | |
| 5 | +8 | 7.937005 | ||
| 8 | +0 | 8 | MUL:8 DT2:0 (8) | |
| 6 | +5 | 8.00904 | ||
| 7 | +3 | 8.324449 | ||
| 5 | +9 | 8.408965 | ||
| 8 | +1 | 8.475704 | MUL:6 DT2:1 (8.46) | |
| 6 | +6 | 8.485284 | MUL:5 DT2:3 (8.65) | |
| 7 | +4 | 8.819447 | ||
| 5 | +10 | 8.908985 | ||
| 8 | +2 | 8.979696 | ||
| 6 | +7 | 8.989842 | ||
| 9 | +0 | 9 | MUL:9 DT2:0 (9) | |
| 7 | +5 | 9.34388 | ||
| 5 | +11 | 9.438745 | MUL:6 DT2:2 (9.42) | |
| 8 | +3 | 9.513656 | ||
| 6 | +8 | 9.524406 | ||
| 9 | +1 | 9.535167 | ||
| 7 | +6 | 9.899498 | MUL:7 DT2:1 (9.87) | |
| 10 | +0 | 10 | MUL:10DT2:0 (10) | |
| 8 | +4 | 10.079368 | ||
| 6 | +9 | 10.090758 | ||
| 9 | +2 | 10.102158 | ||
| 7 | +7 | 10.488149 | MUL:6 DT2:3 (10.38) | |
| 10 | +1 | 10.59463 | ||
| 8 | +5 | 10.67872 | ||
| 6 | +10 | 10.690782 | ||
| 9 | +3 | 10.702863 | MUL:7 DT2:2 (10.99) | |
| 11 | +0 | 11 | MUL:11 DT2:0 (11) | |
| 7 | +8 | 11.111807 | ||
| 10 | +2 | 11.22462 | ||
| 8 | +6 | 11.313712 | MUL:8 DT2:1 (11.28) | |
| 6 | +11 | 11.326494 | ||
| 9 | +4 | 11.339289 | ||
| 11 | +1 | 11.654093 | ||
| 7 | +9 | 11.772551 | ||
| 10 | +3 | 11.89207 | ||
| 8 | +7 | 11.986456 | ||
| 12 | +0 | 12 | MUL:12 DT2:0 (12) | |
| 9 | +5 | 12.01356 | MUL:7 DT2:3 (12.11) | |
| 11 | +2 | 12.347082 | ||
| 7 | +10 | 12.472579 | ||
| 10 | +4 | 12.59921 | MUL:8 DT2:2 (12.56) | |
| 8 | +8 | 12.699208 | MUL:9 DT2:1 (12.69) | |
| 12 | +1 | 12.713556 | ||
| 9 | +6 | 12.727926 | ||
| 13 | +0 | 13 | MUL:13 DT2:0 (13) | |
| 11 | +3 | 13.081277 | ||
| 7 | +11 | 13.214243 | ||
| 10 | +5 | 13.3484 | ||
| 8 | +9 | 13.454344 | ||
| 12 | +2 | 13.469544 | ||
| 9 | +7 | 13.484763 | ||
| 13 | +1 | 13.773019 | ||
| 11 | +4 | 13.859131 | MUL:8 DT2:3 (13.84) | |
| 14 | +0 | 14 | MUL:14 DT2:0 (14) | |
| 10 | +6 | 14.14214 | MUL:9 DT2:2 (14.13) | MUL:10 DT2:1 (14.1) |
| 8 | +10 | 14.254376 | ||
| 12 | +3 | 14.270484 | ||
| 9 | +8 | 14.286609 | ||
| 13 | +2 | 14.592006 | ||
| 11 | +5 | 14.68324 | ||
| 14 | +1 | 14.832482 | ||
| 10 | +7 | 14.98307 | ||
| 15 | +0 | 15 | MUL:15 DT2:0 (15) | |
| 8 | +11 | 15.101992 | ||
| 12 | +4 | 15.119052 | ||
| 9 | +9 | 15.136137 | ||
| 13 | +3 | 15.459691 | MUL:11 DT2:1 (15.51) | |
| 11 | +6 | 15.556354 | MUL:9 DT2:3 (15.57) | |
| 14 | +2 | 15.714468 | MUL:10 DT2:2 (15.7) | |
| 10 | +8 | 15.87401 | ||
| 15 | +1 | 15.891945 | ||
| 12 | +5 | 16.01808 | ||
| 9 | +10 | 16.036173 | ||
| 13 | +4 | 16.378973 | ||
| 11 | +7 | 16.481377 | ||
| 14 | +3 | 16.648898 | ||
| 10 | +9 | 16.81793 | ||
| 15 | +2 | 16.83693 | ||
| 12 | +6 | 16.970568 | MUL:12 DT2:1 (16.92) | |
| 9 | +11 | 16.989741 | ||
| 13 | +5 | 17.35292 | MUL:10 DT2:3 (17.3) | MUL:11 DT2:2 (17.27) |
| 11 | +8 | 17.461411 | ||
| 14 | +4 | 17.638894 | ||
| 10 | +10 | 17.81797 | ||
| 15 | +3 | 17.838105 | ||
| 12 | +7 | 17.979684 | ||
| 13 | +6 | 18.384782 | MUL:13 DT2:1 (18.33) | |
| 11 | +9 | 18.499723 | ||
| 14 | +5 | 18.68776 | ||
| 10 | +11 | 18.87749 | MUL:12 DT2:2 (18.84) | |
| 15 | +4 | 18.898815 | ||
| 12 | +8 | 19.048812 | MUL:11 DT2:3 (19.03) | |
| 13 | +7 | 19.477991 | ||
| 11 | +10 | 19.599767 | ||
| 14 | +6 | 19.798996 | MUL:14 DT2:1 (19.74) | |
| 15 | +5 | 20.0226 | ||
| 12 | +9 | 20.181516 | ||
| 13 | +8 | 20.636213 | MUL:13 DT2:2 (20.41) | |
| 11 | +11 | 20.765239 | MUL:12 DT2:3 (20.76) | |
| 14 | +7 | 20.976298 | ||
| 15 | +6 | 21.21321 | MUL:15 DT2:1 (21.15) | |
| 12 | +10 | 21.381564 | ||
| 13 | +9 | 21.863309 | MUL:14 DT2:2 (21.98) | |
| 14 | +8 | 22.223614 | ||
| 15 | +7 | 22.474605 | MUL:13 DT2:3 (22.49) | |
| 12 | +11 | 22.652988 | ||
| 13 | +10 | 23.163361 | ||
| 14 | +9 | 23.545102 | MUL:15 DT2:2 (23.55) | |
| 15 | +8 | 23.811015 | ||
| 13 | +11 | 24.540737 | MUL:14 DT2:3 (24.22) | |
| 14 | +10 | 24.945158 | ||
| 15 | +9 | 25.226895 | ||
| 14 | +11 | 26.428486 | MUL:15 DT2:3 (25.95) | |
| 15 | +10 | 26.726955 | ||
| 15 | +11 | 28.316235 |