44ed5/2
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Prime factorization
22 × 11
Step size
36.0526¢
Octave
33\44ed5/2 (1189.74¢) (→3\4ed5/2)
Twelfth
53\44ed5/2 (1910.79¢)
Consistency limit
2
Distinct consistency limit
2
| ← 43ed5/2 | 44ed5/2 | 45ed5/2 → |
44 equal divisions of 5/2 (abbreviated 44ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 44 equal parts of about 36.1 ¢ each. Each step represents a frequency ratio of (5/2)1/44, or the 44th root of 5/2.
Notation
A possible notation system takes a 7-note 11-tone system and adds eighth-tone accidentals. The 11 basic tones would be: A A#/Bb B C C#/Db D D#/Eb E F F#/Gb G A. A major chord on A would be spelled A C- D-.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 36.053 | |
| 2 | 72.105 | 25/24, 26/25 |
| 3 | 108.158 | |
| 4 | 144.21 | 12/11, 13/12 |
| 5 | 180.263 | |
| 6 | 216.316 | 17/15, 25/22 |
| 7 | 252.368 | 15/13, 22/19 |
| 8 | 288.421 | 13/11 |
| 9 | 324.473 | |
| 10 | 360.526 | 21/17 |
| 11 | 396.578 | 29/23 |
| 12 | 432.631 | |
| 13 | 468.684 | 17/13, 25/19 |
| 14 | 504.736 | |
| 15 | 540.789 | 15/11, 26/19 |
| 16 | 576.841 | 7/5 |
| 17 | 612.894 | 10/7 |
| 18 | 648.947 | |
| 19 | 684.999 | |
| 20 | 721.052 | |
| 21 | 757.104 | 17/11 |
| 22 | 793.157 | 19/12, 30/19 |
| 23 | 829.209 | 21/13, 29/18 |
| 24 | 865.262 | |
| 25 | 901.315 | |
| 26 | 937.367 | 12/7, 31/18 |
| 27 | 973.42 | 7/4 |
| 28 | 1009.472 | 25/14 |
| 29 | 1045.525 | 11/6, 31/17 |
| 30 | 1081.578 | |
| 31 | 1117.63 | 19/10, 21/11 |
| 32 | 1153.683 | |
| 33 | 1189.735 | |
| 34 | 1225.788 | |
| 35 | 1261.84 | 31/15 |
| 36 | 1297.893 | |
| 37 | 1333.946 | 13/6 |
| 38 | 1369.998 | 11/5 |
| 39 | 1406.051 | |
| 40 | 1442.103 | 30/13 |
| 41 | 1478.156 | |
| 42 | 1514.209 | 12/5 |
| 43 | 1550.261 | |
| 44 | 1586.314 | 5/2 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -10.3 | +8.8 | +15.5 | -10.3 | -1.4 | -15.9 | +5.3 | +17.7 | +15.5 | -5.3 | -11.7 |
| Relative (%) | -28.5 | +24.5 | +43.1 | -28.5 | -4.0 | -44.2 | +14.6 | +49.0 | +43.1 | -14.6 | -32.4 | |
| Steps (reduced) |
33 (33) |
53 (9) |
67 (23) |
77 (33) |
86 (42) |
93 (5) |
100 (12) |
106 (18) |
111 (23) |
115 (27) |
119 (31) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -6.1 | +9.9 | -1.4 | -5.0 | -1.8 | +7.4 | -14.1 | +5.3 | -7.1 | -15.5 | +15.7 |
| Relative (%) | -16.8 | +27.3 | -4.0 | -13.9 | -5.0 | +20.5 | -39.1 | +14.6 | -19.7 | -43.1 | +43.5 | |
| Steps (reduced) |
123 (35) |
127 (39) |
130 (42) |
133 (1) |
136 (4) |
139 (7) |
141 (9) |
144 (12) |
146 (14) |
148 (16) |
151 (19) | |
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