5edt: Difference between revisions
reworked |
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| Line 7: | Line 7: | ||
! Degrees | ! Degrees | ||
! Cents | ! Cents | ||
!hekts | |||
! Approximate Ratios | ! Approximate Ratios | ||
|- | |- | ||
| 0 | | 0 | ||
| 0 | | colspan="2" | 0 | ||
| [[1/1]] | | [[1/1]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 380.391 | | 380.391 | ||
|260 | |||
| [[5/4]] | | [[5/4]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 760.782 | | 760.782 | ||
|520 | |||
| [[14/9]] | | [[14/9]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 1141.173 | | 1141.173 | ||
|780 | |||
| [[27/14]] | | [[27/14]] | ||
|- | |- | ||
| 4 | | 4 | ||
| 1521.564 | | 1521.564 | ||
|1040 | |||
| [[12/5]] ([[6/5|6/5]] plus an octave) | | [[12/5]] ([[6/5|6/5]] plus an octave) | ||
|- | |- | ||
| 5 | | 5 | ||
| 1901.955 | | 1901.955 | ||
|1300 | |||
| [[3/1]] | | [[3/1]] | ||
|} | |} | ||
Revision as of 16:56, 10 April 2019
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 | hekts | Approximate Ratios |
|---|---|---|---|
| 0 | 0 | 1/1 | |
| 1 | 380.391 | 260 | 5/4 |
| 2 | 760.782 | 520 | 14/9 |
| 3 | 1141.173 | 780 | 27/14 |
| 4 | 1521.564 | 1040 | 12/5 (6/5 plus an octave) |
| 5 | 1901.955 | 1300 | 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.