6edt: Difference between revisions

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'''6edt''' is the abbreviation for '''6 Equal Divisions of the Tritave'''.
{{Infobox ET}}
Since 6edt contains one intervals of [[2edt]] and two intervals of [[3edt]], it only introduces 2 new notes. These new notes happen to approximate [[6/5]] and [[5/2]] quite well.
{{ED intro}}
6edt is therefore the smallest edt other than [[5edt]] to accurately approximate [[5-limit]] harmony. 6edt allows for construction of chords such as 2:5:6:15:18:26:31:45:54...
 
== Theory ==
Since 6edt contains one interval of [[2edt]] and two intervals of [[3edt]], it introduces 2 new notes unseen in previous edts. These new notes happen to approximate [[6/5]] and [[5/2]] very well, the former being only 1.351 [[cents]] sharp.
6edt is therefore the smallest edt other than [[5edt]] to accurately approximate [[5-limit]] harmony, as well as some elements from the [[13-limit]] inherited from [[3edt]]. 6edt allows for construction of chords such as 2:5:6:15:18:26:31:45:54...
 
=== Harmonics ===
{{Harmonics in equal|6|3|1|columns=16}}


__TOC__
== Intervals ==
== Intervals ==
{| class="wikitable"
{{Interval table}}
|-
! Degrees
! [[Cent]]s
!hekts
! ApproximateRatios
|-
| colspan="3" | 0
| 1/1
|-
| 1
| 316.993
|216.667
| [[6/5]], [[65/54]]
|-
| 2
| 633.985
|433.333
| [[13/9]]
|-
| 3
| 950.978
|650
| [[19/11]], [[26/15]]
|-
| 4
| 1267.97
|866.667
| [[27/13]]
|-
| 5
| 1584.963
|1093.333
| [[5/2]] ([[5/4]] plus an octave)
|-
| 6
| 1901.955
|1300
| [[3/1]]
|}
 
== 6n-edt Family ==
* [[12edt]]
* [[18edt]]
* [[24edt]]
* [[30edt]]


[[Category:Edt]]
[[Category:Nonoctave]]
[[Category:Nonoctave]]
[[category:Macrotonal]]
[[category:Macrotonal]]


[[Category:todo:add sound examples]]
[[Category:todo:add sound example]]

Latest revision as of 15:31, 31 July 2025

← 5edt 6edt 7edt →
Prime factorization 2 × 3
Step size 316.993 ¢ 
Octave 4\6edt (1267.97 ¢) (→ 2\3edt)
Consistency limit 7
Distinct consistency limit 3
Special properties

6 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 6edt or 6ed3), is a nonoctave tuning system that divides the interval of 3/1 into 6 equal parts of about 317 ¢ each. Each step represents a frequency ratio of 31/6, or the 6th root of 3.

Theory

Since 6edt contains one interval of 2edt and two intervals of 3edt, it introduces 2 new notes unseen in previous edts. These new notes happen to approximate 6/5 and 5/2 very well, the former being only 1.351 cents sharp. 6edt is therefore the smallest edt other than 5edt to accurately approximate 5-limit harmony, as well as some elements from the 13-limit inherited from 3edt. 6edt allows for construction of chords such as 2:5:6:15:18:26:31:45:54...

Harmonics

Approximation of harmonics in 6edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +68 +0 +136 +67 +68 +118 -113 +0 +135 -30 +136 -3 -131 +67 -45 -150
Relative (%) +21.4 +0.0 +42.9 +21.0 +21.4 +37.3 -35.7 +0.0 +42.5 -9.6 +42.9 -0.8 -41.3 +21.0 -14.2 -47.3
Steps
(reduced) 		4
(4) 		6
(0) 		8
(2) 		9
(3) 		10
(4) 		11
(5) 		11
(5) 		12
(0) 		13
(1) 		13
(1) 		14
(2) 		14
(2) 		14
(2) 		15
(3) 		15
(3) 		15
(3)

Intervals

Steps Cents Hekts Approximate ratios
0 0 0 1/1
1 317 216.7 6/5, 7/6, 11/9, 13/11
2 634 433.3 7/5, 10/7, 13/9, 19/13
3 951 650 7/4, 12/7, 19/11
4 1268 866.7 15/7, 19/9, 21/10
5 1585 1083.3 5/2, 18/7
6 1902 1300 3/1
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