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'''5edt''' (5 Equal Divisions of the Tritave) subdivides the interval of the [[tritave]], frequency ratio 3:1, into 5 equal-sized parts, each 380.391 [[Cent]]s in size. | |||
== Steps == | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Degrees | |||
! Cents | |||
! Approximate Ratios | |||
|- | |- | ||
| 0 | |||
| 0 | |||
| [[1/1|1/1]] | |||
|- | |- | ||
| 1 | |||
| 380.391 | |||
| [[5/4|5/4]] | |||
|- | |- | ||
| 2 | |||
| 760.782 | |||
| [[14/9|14/9]] | |||
|- | |- | ||
| 3 | |||
| 1141.173 | |||
| [[27/14|27/14]] | |||
|- | |- | ||
| 4 | |||
| 1521.564 | |||
| 12/5 ([[6/5|6/5]] plus an octave) | |||
|- | |- | ||
| 5 | |||
| 1901.955 | |||
| 3/1 | |||
|} | |} | ||
5edt isn't very useful melodically, though it has many notable harmonic properties shared by other 5n-edts (EDTs with 5 as a prime factor). It has a surprisingly accurate major third, five of them making a tritave. It therefore tempers out 3125/3072, the magic comma. Two of these major thirds give a septimal minor sixth, meaning that it also tempers out the 7-limit comma 225/224. | |||
5edt is the lowest equal division of the tritave to encompass 5-limit harmony. The available chords are 4:5:12 and 5:12:15; essentially major and minor chords. This is similar to [[6edt|6edt]], which contains the same chords but with the major thirds transposed an octave higher, and vice versa. | 5edt is the lowest equal division of the tritave to encompass 5-limit harmony. The available chords are 4:5:12 and 5:12:15; essentially major and minor chords. This is similar to [[6edt|6edt]], which contains the same chords but with the major thirds transposed an octave higher, and vice versa. | ||
==Other 5n-edts:== | ==Other 5n-edts:== | ||
[[10edt|10edt]] | * [[10edt|10edt]] | ||
* [[15edt|15edt]] | |||
[[15edt|15edt]] | * [[20edt|20edt]] | ||
* [[25edt|25edt]] | |||
[[20edt|20edt]] | * [[30edt|30edt]] | ||
[[25edt|25edt]] | |||
[[30edt|30edt]] | |||
... | ... | ||
Revision as of 11:46, 30 September 2018
5edt (5 Equal Divisions of the Tritave) subdivides the interval of the tritave, frequency ratio 3:1, into 5 equal-sized parts, each 380.391 Cents in size.
Steps
| Degrees | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 380.391 | 5/4 |
| 2 | 760.782 | 14/9 |
| 3 | 1141.173 | 27/14 |
| 4 | 1521.564 | 12/5 (6/5 plus an octave) |
| 5 | 1901.955 | 3/1 |
5edt isn't very useful melodically, though it has many notable harmonic properties shared by other 5n-edts (EDTs with 5 as a prime factor). It has a surprisingly accurate major third, five of them making a tritave. It therefore tempers out 3125/3072, the magic comma. Two of these major thirds give a septimal minor sixth, meaning that it also tempers out the 7-limit comma 225/224.
5edt is the lowest equal division of the tritave to encompass 5-limit harmony. The available chords are 4:5:12 and 5:12:15; essentially major and minor chords. This is similar to 6edt, which contains the same chords but with the major thirds transposed an octave higher, and vice versa.
Other 5n-edts:
...