User:CompactStar/Ed11/4: Difference between revisions
Rework the trivial statements into something more informative; improve linking and style |
mNo edit summary |
||
| (3 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{Editable user page}} | |||
The '''equal division of 11/4''' ('''ed11/4''') is a [[tuning]] obtained by dividing the [[11/4|undecimal semi-augmented eleventh (11/4)]] in a certain number of [[equal]] steps. | The '''equal division of 11/4''' ('''ed11/4''') is a [[tuning]] obtained by dividing the [[11/4|undecimal semi-augmented eleventh (11/4)]] in a certain number of [[equal]] steps. | ||
== Properties == | == Properties == | ||
Division of 11/4 into equal parts does not necessarily imply directly using this interval as an [[equivalence | Division of 11/4 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed11/4 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy. | ||
The structural utility of 11/4 is apparent by being central to much [[11-limit]] harmony, as well as being a fairly trivial point to split the difference between the [[octave]] and the [[tritave]]. | |||
[[Category: | One approach to ed11/4 tunings is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in [[meantone]] a stack of four [[3/2]]'s is equated with [[5/1]], here a stack of four [[20/11]]'s is equated with [[16/11]], tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5-, 7-, 12-, and 17-note [[mos scale]]s, coincidentally similar to [[Pythagorean tuning]]. | ||
[[Category:Ed11/4| ]] <!-- main article --> | |||
[[Category:Edonoi]] | |||
[[Category:Lists of scales]] | |||
Latest revision as of 12:04, 18 May 2025
|
This user page is editable by any wiki editor.
As a general rule, most users expect their user space to be edited only by themselves, except for minor edits (e.g. maintenance), undoing obviously harmful edits such as vandalism or disruptive editing, and user talk pages. However, by including this message box, the author of this user page has indicated that this page is open to contributions from other users (e.g. content-related edits). |
The equal division of 11/4 (ed11/4) is a tuning obtained by dividing the undecimal semi-augmented eleventh (11/4) in a certain number of equal steps.
Properties
Division of 11/4 into equal parts does not necessarily imply directly using this interval as an equivalence. Many, though not all, ed11/4 scales have a perceptually important false octave, with various degrees of accuracy.
The structural utility of 11/4 is apparent by being central to much 11-limit harmony, as well as being a fairly trivial point to split the difference between the octave and the tritave.
One approach to ed11/4 tunings is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone a stack of four 3/2's is equated with 5/1, here a stack of four 20/11's is equated with 16/11, tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5-, 7-, 12-, and 17-note mos scales, coincidentally similar to Pythagorean tuning.