User:CompactStar/Ed11/5: Difference between revisions

The '''equal division of 11/5''' ('''ed11/5''') is a [[tuning]] obtained by dividing the [[11/5|neutral ninth (11/5)]] into a certain number of [[equal]] steps.  

Division of 11/5 into equal parts does not necessarily imply directly using this interval as an [[equivalence]], or not. The question of equivalence has not even been posed yet. The utility of 11/5 as a base though is apparent by it being, beside the true high ninth of a just dominant 11th chord, the best option for "no-twos-or-threes" harmony after the extremely wide [[5/1|harmonic 5]], and the awkwardly narrow [[7/5|small septimal tritone]]. It is also a relatively strong consonance. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.

The simplest chord without 2's or 3's that sounds consonant and stable is 11:13:17, so it can be viewed as the fundamental sonority of no-twos-or-threes music. A neutral ninth-reduced stack of four 121/85's fall short of [[17/13]] by the small comma 2093663/2088025. Tempering out this comma together with the additional comma 54925/54043 results in [[catfish]] temperament, which can be viewed as an analog to [[meantone]]. It possesses [[mos scale]]s of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.

 

== Ed11/5-edo correspondence ==

! Ed11/5

! Edo

| [[8ed11/5]]

| [[7edo]]

| [[9ed11/5]]

| [[8edo]]

| [[16ed11/5]]

| [[14edo]]

| [[18ed11/5]]

| [[16edo]]

| [[24ed11/5]]

| [[21edo]]

| [[25ed11/5]]

| [[22edo]]

| [[27ed11/5]]

| [[24edo]]

| [[33ed11/5]]

| [[29edo]]

| [[50ed11/5]]

| [[44edo]]

 

== Individual pages for ed11/5's ==

 

[[Category:Ed11/5| ]] <!-- main article -->