User:MisterShafXen/45ed4: Difference between revisions
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Prime factorization
32 × 5
Step size
53.3333 ¢
Octave
23\45ed4 (1226.67 ¢)
Twelfth
36\45ed4 (1920 ¢) (→ 4\5ed4)
Consistency limit
1
Distinct consistency limit
1
Created page with "{{Infobox ET}} {{ED intro}} == Intervals == {{Interval table|45ed4}}" Tags: Visual edit Mobile edit Mobile web edit |
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Latest revision as of 14:44, 1 August 2025
| ← 43ed4 | 45ed4 | 47ed4 → |
45 equal divisions of the 4th harmonic (abbreviated 45ed4) is a nonoctave tuning system that divides the interval of 4/1 into 45 equal parts of about 53.3 ¢ each. Each step represents a frequency ratio of 41/45, or the 45th root of 4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 53.3 | |
| 2 | 106.7 | |
| 3 | 160 | 11/10, 23/21 |
| 4 | 213.3 | 17/15, 26/23 |
| 5 | 266.7 | |
| 6 | 320 | |
| 7 | 373.3 | 26/21, 31/25 |
| 8 | 426.7 | |
| 9 | 480 | |
| 10 | 533.3 | 15/11, 19/14 |
| 11 | 586.7 | 7/5 |
| 12 | 640 | |
| 13 | 693.3 | |
| 14 | 746.7 | |
| 15 | 800 | |
| 16 | 853.3 | 23/14 |
| 17 | 906.7 | |
| 18 | 960 | |
| 19 | 1013.3 | |
| 20 | 1066.7 | 13/7 |
| 21 | 1120 | 21/11 |
| 22 | 1173.3 | |
| 23 | 1226.7 | |
| 24 | 1280 | 21/10, 23/11 |
| 25 | 1333.3 | |
| 26 | 1386.7 | 20/9, 29/13 |
| 27 | 1440 | 23/10 |
| 28 | 1493.3 | 26/11 |
| 29 | 1546.7 | 22/9 |
| 30 | 1600 | |
| 31 | 1653.3 | 13/5 |
| 32 | 1706.7 | |
| 33 | 1760 | |
| 34 | 1813.3 | |
| 35 | 1866.7 | |
| 36 | 1920 | |
| 37 | 1973.3 | |
| 38 | 2026.7 | |
| 39 | 2080 | 10/3 |
| 40 | 2133.3 | |
| 41 | 2186.7 | |
| 42 | 2240 | |
| 43 | 2293.3 | |
| 44 | 2346.7 | |
| 45 | 2400 |