6edt: Difference between revisions

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=6 Equal Divisions of the Tritave=
{{Infobox ET}}
{{ED intro}}


{| class="wikitable"
== 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.
| | Degrees
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...
| | Cents
| | ApproximateRatios
|-
| | 0
| | 0
| | 1/1
|-
| | 1
| | 316.993
| | [[6/5|6/5]], 65/54
|-
| | 2
| | 633.985
| | [[13/9|13/9]]
|-
| | 3
| | 950.978
| | 19/11, 26/15
|-
| | 4
| | 1267.970
| | 27/13
|-
| | 5
| | 1584.963
| | 5/2 ([[5/4|5/4]] plus an octave)
|-
| | 6
| | 1901.955
| | 3/1
|}


Since 6edt contains 1 intervals of [[2edt|2edt]] and 2 intervals of [[3edt|3edt]], it only introduces 2 new notes. These new notes happen to approximate 6/5 and 5/2 quite well.
=== Harmonics ===
{{Harmonics in equal|6|3|1|columns=16}}


6edt is therefore smallest edt other than [[5edt|5edt]] to accurately approximate 5-limit harmony. 6edt allows for construction of chords chords such as 2:5:6:15:18:26:31:45:54...
== Intervals ==
{{Interval table}}


==6n-edt Family:==
[[Category:Nonoctave]]
[[12edt|12edt]]
[[category:Macrotonal]]


[[18edt|18edt]]
[[Category:todo:add sound example]]
 
[[24edt|24edt]]
 
[[30edt|30edt]]      [[Category:edonoi]]
[[Category:edt]]
[[Category:equal]]
[[Category:todo:add_sound_examples]]
[[category:macrotonal]]

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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