35/29: Difference between revisions
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'''35/29''', the '''doublewide minor third''', is a minor third in [[29-limit]] [[just intonation]]. It is sharp of [[32/27]], the Pythagorean minor third, by [[945/928]], and sharp of [[6/5]], the classical minor third, by [[175/174]]. It is flat by [[29/24]], another 29-limit minor third, by [[841/840]] ({{S|29}}), a comma 2.06{{C}} in size. | |||
== Approximation == | |||
{{Interval edo approximation|35/29}} | |||
== Temperaments == | |||
The 35/29 interval gives an excellent generator for the [[doublewide]] temperament with a half octave. It lies between [[59edo|16\59]] ([[118edo|32\118]]) and [[11edo|3\11]] ([[22edo|6\22]]), which may also serve as generators for doublewide. | |||
[[Category:Third]] | [[Category:Third]] | ||
[[Category:Minor third]] | [[Category:Minor third]] | ||
Latest revision as of 12:03, 4 February 2026
| Interval information |
[sound info]
35/29, the doublewide minor third, is a minor third in 29-limit just intonation. It is sharp of 32/27, the Pythagorean minor third, by 945/928, and sharp of 6/5, the classical minor third, by 175/174. It is flat by 29/24, another 29-limit minor third, by 841/840 (S29), a comma 2.06 ¢ in size.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 4 | 1\4 | 300.00 | -25.56 | -8.52 |
| 11 | 3\11 | 327.27 | +1.71 | +1.57 |
| 15 | 4\15 | 320.00 | -5.56 | -6.95 |
| 22 | 6\22 | 327.27 | +1.71 | +3.14 |
| 26 | 7\26 | 323.08 | -2.49 | -5.39 |
| 33 | 9\33 | 327.27 | +1.71 | +4.70 |
| 37 | 10\37 | 324.32 | -1.24 | -3.82 |
| 44 | 12\44 | 327.27 | +1.71 | +6.27 |
| 48 | 13\48 | 325.00 | -0.56 | -2.25 |
| 55 | 15\55 | 327.27 | +1.71 | +7.84 |
| 59 | 16\59 | 325.42 | -0.14 | -0.68 |
| 63 | 17\63 | 323.81 | -1.75 | -9.20 |
| 66 | 18\66 | 327.27 | +1.71 | +9.41 |
| 70 | 19\70 | 325.71 | +0.15 | +0.89 |
| 74 | 20\74 | 324.32 | -1.24 | -7.63 |
Temperaments
The 35/29 interval gives an excellent generator for the doublewide temperament with a half octave. It lies between 16\59 (32\118) and 3\11 (6\22), which may also serve as generators for doublewide.