Xenllium: Created page with "{{Infobox ET}} '''13 equal divisions of the perfect fourth''' ('''13ed4/3''') is the tuning system that divides the fourth into 13 steps of 38.3112 cents each. It can be thought of as a 4/3.5/3.7/6 subgroup analogue to 9edf or Carlos Alpha. It very closely approximates the intervals of 8/7 (at 6 steps) and 7/6 (at 7 steps), along with 5/4 (at 10 steps); these approximations are related to the slender temperament, te..."

2025-11-16T03:58:39Z

Created page with "{{Infobox ET}} '''13 equal divisions of the perfect fourth''' ('''13ed4/3''') is the tuning system that divides the fourth into 13 steps of 38.3112 cents each. It can be thought of as a 4/3.5/3.7/6 subgroup analogue to 9edf or Carlos Alpha. It very closely approximates the intervals of 8/7 (at 6 steps) and 7/6 (at 7 steps), along with 5/4 (at 10 steps); these approximations are related to the slender temperament, te..."

New page

{{Infobox ET}}
'''13 equal divisions of the perfect fourth''' ('''13ed4/3''') is the [[tuning system]] that divides the fourth into 13 steps of 38.3112 [[cent]]s each. It can be thought of as a 4/3.5/3.7/6 [[subgroup]] analogue to [[9edf]] or [[Carlos Alpha]]. It very closely approximates the intervals of [[8/7]] (at 6 steps) and [[7/6]] (at 7 steps), along with [[5/4]] (at 10 steps); these approximations are related to the [[Marvel temperaments|slender temperament]], tempering out [[225/224]] and [[589824/588245]] in the 7-limit. This tuning is close to every three steps of [[94edo]] or to [[88ed7]].

== Intervals ==
These are the intervals up to a perfect fourth up.
{| class="wikitable mw-collapsible"
|+ Intervals of 13ed4/3
|-
! Degrees
! Cents
! Approximation by <br>2.3.5.7.11.23 subgroup
|-
|1
|38.31
|[[46/45]], [[45/44]]
|-
|2
|76.62
|[[24/23]], [[23/22]], [[22/21]]
|-
|3
|114.93
|[[16/15]], [[15/14]]
|-
|4
|153.24
|[[12/11]]
|-
|5
|191.56
|
|-
|6
|229.87
|[[8/7]]
|-
|7
|268.18
|[[7/6]]
|-
|8
|306.49
|
|-
|9
|344.80
|[[11/9]]
|-
|10
|383.11
|[[5/4]]
|-
|11
|421.42
|[[23/18]]
|-
|12
|459.73
|[[30/23]]
|-
|'''13'''
|'''498.04'''
|'''[[4/3]]'''
|}

== Harmonics ==
{{Harmonics in equal|13|4|3}}
{{Harmonics in equal|13|4|3|start=12|collapsed=1}}

== See also ==
* [[Equal-step tuning]]

13ed4/3 - Revision history