Xenharmonic Wiki

5edt: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>FREEZE
No edit summary
+subsets and supersets
 
(15 intermediate revisions by 8 users not shown)
Line 1: Line 1:
=5 Equal Divisions of the Tritave=
{{Infobox ET}}
{{ED intro}}


{| class="wikitable"
== Theory ==
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 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 in equal|5|3|1|columns=15}}
 
=== Subsets and supersets ===
5edt is the 3rd [[prime equal division|prime edt]], after [[3edt]] and before [[7edt]].
 
== Intervals ==
{| class="wikitable right-all left-4"
|-
|-
| | Degrees
! #
| | Cents
! Cents
| | Approximate Ratios
! Hekts
! Approximate ratios
|-
|-
| | 0
| 0
| | 0
| 0
| | [[1/1|1/1]]
| 0
| [[1/1]]
|-
|-
| | 1
| 1
| | 380.391
| 380
| | [[5/4|5/4]]
| 260
| [[5/4]]
|-
|-
| | 2
| 2
| | 760.782
| 761
| | [[14/9|14/9]]
| 520
| [[14/9]]
|-
|-
| | 3
| 3
| | 1141.173
| 1141
| | [[27/14|27/14]]
| 780
| [[27/14]]
|-
|-
| | 4
| 4
| | 1521.564
| 1522
| | 12/5 ([[6/5|6/5]] plus an octave)
| 1040
| [[12/5]]
|-
|-
| | 5
| 5
| | 1901.955
| 1902
| | 3/1
| 1300
| [[3/1]]
|}
|}


<span style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse; line-height: normal;">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.</span>
[[Category:Todo:add sound example]]
 
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:==
[[10edt|10edt]]
 
[[15edt|15edt]]
 
[[20edt|20edt]]
 
[[25edt|25edt]]
 
[[30edt|30edt]]
 
...
[[Category:edonoi]]
[[Category:edt]]
[[Category:equal]]
[[Category:todo:add_sound_examples]]
Retrieved from "https://en.xen.wiki/w/5edt"