Xenllium: Created page with "{{Infobox ET}} '''15 equal divisions of the perfect fourth''' ('''15ed4/3''') is the tuning system that divides the fourth into 15 steps of 33.203 cents each. It can be thought of as a 4/3.8/7.32/13.32/17.19/16 subgroup analogue to 11edf or Carlos Beta. It very closely approximates the intervals of 8/7 (at 7 steps) and 7/6 (at 8 steps), along with 18/17 (at 3 steps), 19/16 (at 9 steps) and 17/13 (at 14 steps); these approximations..."

2025-11-16T05:03:50Z

Created page with "{{Infobox ET}} '''15 equal divisions of the perfect fourth''' ('''15ed4/3''') is the tuning system that divides the fourth into 15 steps of 33.203 cents each. It can be thought of as a 4/3.8/7.32/13.32/17.19/16 subgroup analogue to 11edf or Carlos Beta. It very closely approximates the intervals of 8/7 (at 7 steps) and 7/6 (at 8 steps), along with 18/17 (at 3 steps), 19/16 (at 9 steps) and 17/13 (at 14 steps); these approximations..."

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{{Infobox ET}}
'''15 equal divisions of the perfect fourth''' ('''15ed4/3''') is the [[tuning system]] that divides the fourth into 15 steps of 33.203 [[cent]]s each. It can be thought of as a 4/3.8/7.32/13.32/17.19/16 [[subgroup]] analogue to [[11edf]] or [[Carlos Beta]]. It very closely approximates the intervals of [[8/7]] (at 7 steps) and [[7/6]] (at 8 steps), along with [[18/17]] (at 3 steps), [[19/16]] (at 9 steps) and [[17/13]] (at 14 steps); these approximations are related to the temperament which tempers out [[343/342]], [[833/832]], [[1729/1728]] and [[4624/4617]] in the 2.3.7.13.17.19 subgroup (36 & 181), along with [[4914/4913]], [[8281/8262]] and 4747561509943/4696546738176 ({{monzo| -31 -7 0 15 }}, laquintrizo comma). This tuning is close to every seven steps of [[253edo]] or every other step of [[19ed6/5]].

== Intervals ==
These are the intervals up to a perfect fourth up.
{| class="wikitable mw-collapsible"
|+ Intervals of 15ed4/3
|-
! Degrees
! Cents
! Approximation by <br>2.3.7.11/5.13.17.19.23 subgroup
|-
|1
|33.20
|[[52/51]]
|-
|2
|66.41
|[[27/26]]
|-
|3
|99.61
|[[18/17]]
|-
|4
|132.81
|
|-
|5
|166.01
|[[11/10]]
|-
|6
|199.22
|
|-
|7
|232.42
|[[8/7]]
|-
|8
|265.62
|[[7/6]]
|-
|9
|298.83
|[[19/16]]
|-
|10
|332.03
|[[23/19]]
|-
|11
|365.23
|[[21/17]]
|-
|12
|398.44
|[[34/27]]
|-
|13
|431.64
|
|-
|14
|464.84
|[[17/13]]
|-
|'''15'''
|'''498.04'''
|'''[[4/3]]'''
|}

== Harmonics ==
{{Harmonics in equal|15|4|3}}
{{Harmonics in equal|15|4|3|start=12|collapsed=1}}

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

15ed4/3 - Revision history