Xenharmonic Wiki

16ed5/2: Difference between revisions

← Older edit
VisualWikitext
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,160 edits
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Fredg999 category edits (talk | contribs)
autopatrolled, Bots, emailconfirmed
4,330 edits
m Removing from Category:Ed5/2 using Cat-a-lot
 
(7 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
'''16ED5/2''' is the equal division of the [[5/2]] interval into 16 parts of 99.1446 [[cent]]s each. This is the scale which occurs as the dominant reformed Mixolydian mode tuned as an equal division of a just interval.
'''16ED5/2''' is the equal division of the [[5/2]] interval into 16 parts of 99.1446 [[cent]]s each. 16 equal divisions of the just major tenth is not a "real" xenharmonic tuning; it is a slightly compressed version of the normal [[12edo|12-tone scale]].  
 
== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable"
Line 102: Line 101:
|}
|}


Coincidentally, 133 steps of the pyrite EDX of this size exceed 11 octaves by only 2.978¢.
== Harmonics ==
{{Harmonics in equal
| steps = 16
| num = 5
| denom = 2
}}
{{Harmonics in equal
| steps = 16
| num = 5
| denom = 2
| start = 12
| collapsed = 1
}}


== Regular temperaments ==
== Regular temperaments ==
Line 112: Line 123:


Another temperament related to 16ed5/2 is ''[[quintapole]]'' (12&85). It is practically identical to the [[18/17s equal temperament #Related temperament|Galilei tuning]], which is generated by the ratios 2/1 and 18/17.
Another temperament related to 16ed5/2 is ''[[quintapole]]'' (12&85). It is practically identical to the [[18/17s equal temperament #Related temperament|Galilei tuning]], which is generated by the ratios 2/1 and 18/17.
== Scale tree ==
Ed5/2 scales can be approximated in [[EDO]]s by subdividing their approximations of 5/2.
{| class="wikitable"
|+
! colspan="4" |Major tenth
! Period
!Notes
|-
|9\7
|
|
|
|96.429
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|-
|
|31\24
|
|
|96.875
|
|-
|22\17
|
|
|
|97.059
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|-
|
|35\27
|
|
|97.{{Overline|2}}
|
|-
| 13\10
|
|
|
|97.5
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|-
|17\13
|
|
|
|98.077
|
|-
|21\16
|
|
|
|98.4375
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|-
|
|25\19
|
|
|98.684
|
|-
|
|
|29\22
|
|98.8{{Overline|63}}
|
|-
|
|
|
|33\25
|99
|
|-
|4\3
|
|
|
|100
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|-
|
| 19\14
|
|
|101.786
|
|-
|15\11
|
|
|
|102.{{Overline|27}}
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|-
|
|26\19
|
|
|102.632
|
|-
|11\8
|
|
|
|103.125
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|-
|
|18\13
|
|
|103.846
|
|-
|
|
|25\18
|
|104.1{{Overline|6}}
|
|}


== See also ==
== See also ==
* [[16edX|16EDX]]
* [[12edo|12EDO]] - relative EDO
* [[12edo|12EDO]] - relative EDO
* [[28ed5|28ED5]] - relative ED5
* [[28ed5|28ED5]] - relative ED5
Line 122: Line 261:
* [[18/17 equal-step tuning|AS18/17]] - relative [[AS|ambitonal sequence]]
* [[18/17 equal-step tuning|AS18/17]] - relative [[AS|ambitonal sequence]]


[[Category:Ed5/2]]
[[Category:Nonoctave]]
[[Category:Nonoctave]]
Retrieved from "https://en.xen.wiki/w/16ed5/2"