5edt: Difference between revisions
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5edt has steps too large to be used melodically, though it has some notable harmonic properties shared by other 5''n''-edts (such as [[10edt]], [[15edt]], etc.). It has a surprisingly accurate [[5/4]] major third (only 5.92{{cent}} flat), five of them making a tritave. (This phenomenon cannot be seen in single-digit [[edo]]s, and it is not until [[19edo]] that an approximation of 5/4 to within 10{{c}} can be seen.) 5edt 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 marvel comma [[225/224]]. | 5edt has steps too large to be used melodically, though it has some notable harmonic properties shared by other 5''n''-edts (such as [[10edt]], [[15edt]], etc.). It has a surprisingly accurate [[5/4]] major third (only 5.92{{cent}} flat), five of them making a tritave. (This phenomenon cannot be seen in single-digit [[edo]]s, and it is not until [[19edo]] that an approximation of 5/4 to within 10{{c}} can be seen.) 5edt 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 marvel comma [[225/224]]. | ||
5edt is the | 5edt is the first edt to encompass elements of [[5-limit]] harmony. The available chords are 4:5:12 and 5:12:15; being inversions of each other, they essentially act as "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. Also available is the chord 9:14:27, which can express the single [[7-limit]] consonance found in 5edt. | ||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|5|3|1|columns=15}} | {{Harmonics in equal|5|3|1|columns=15}} | ||
== | == Intervals == | ||
{| class="wikitable right-all left-4" | {| class="wikitable right-all left-4" | ||
|- | |- | ||
! | ! # | ||
! Cents | ! Cents | ||
! Hekts | ! Hekts | ||
! Approximate | ! Approximate ratios | ||
|- | |- | ||
| 0 | | 0 | ||
| | | 0 | ||
| 0 | | 0 | ||
| [[1/1]] | | [[1/1]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 380 | | 380 | ||
| 260 | | 260 | ||
| [[5/4]] | | [[5/4]] | ||
|- | |- | ||
| 2 | | 2 | ||
| | | 761 | ||
| 520 | | 520 | ||
| [[14/9]] | | [[14/9]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 1141 | | 1141 | ||
| 780 | | 780 | ||
| [[27/14]] | | [[27/14]] | ||
|- | |- | ||
| 4 | | 4 | ||
| | | 1522 | ||
| 1040 | | 1040 | ||
| [[12/5]] | | [[12/5]] | ||
|- | |- | ||
| 5 | | 5 | ||
| | | 1902 | ||
| 1300 | | 1300 | ||
| [[3/1]] | | [[3/1]] | ||
|} | |} | ||
[[Category:Todo:add sound example]] | [[Category:Todo:add sound example]] | ||