26ed5: Difference between revisions

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* 5.6.7/4.11/3.13/4.17/11.19/8.23/11.29/7.31/7 subgroup

==== ''N''th-~~prime~~ subgroups ====

==== ''N''th-basis subgroups ====

These are some [[Half-prime subgroup|''n''th-~~prime~~ subgroups]] which 26ed5 approximates well:

These are some [[Half-prime subgroup|''n''th-basis subgroups]]{{idiosyncratic}} which 26ed5 approximates well:

{| class="wikitable"

|+ ~~Loose~~ ''n''th-~~prime~~ subgroups ~~(non-prime numerators allowed)~~

|+ ''N''th-basis subgroups

!Family

!Most distinctive related families

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{| class="wikitable"

|+ ~~Strict~~ ''n''th-prime subgroups ~~(only prime numerators allowed)~~

|+ ''N''th-prime subgroups

!Family

!Most distinctive related families

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Note that 5/1 = 10/2 = 55/11, & 6/1 = 12/2 = 66/11.

Note that any subset of any of these subgroup elements is still a valid ''n''th-~~prime~~ subgroup. So one can remove as many basis elements as desired to simplify the subgroup down, if they so wish.

Note that any subset of any of these subgroup elements is still a valid ''n''th-basis subgroup. So one can remove as many basis elements as desired to simplify the subgroup down, if they so wish.

Of all subgroup interpretations of 26ed5, be they integer or fractional, the ''~~loose~~ 60th-~~prime~~ subgroup interpretation'' might be the most useful, as it includes more simple, small-numeral [[consonance]]s than any other interpretation. It includes a 6/5, 7/4, 9/4, 13/4, 11/3 and of course 5/1.

Of all subgroup interpretations of 26ed5, be they integer or fractional, the ''60th-basis subgroup interpretation'' might be the most useful, as it includes more simple, small-numeral [[consonance]]s than any other interpretation. It includes a 6/5, 7/4, 9/4, 13/4, 11/3 and of course 5/1.

== Intervals ==

{| class="wikitable mw-collapsible"

|+

Intervals of 26ed5 ~~(loose subgroups used)~~

Intervals of 26ed5

! rowspan="2" |Step

! rowspan="2" |Cents

! colspan="8" |Just intonation approximation

|-

!60th-~~prime~~

!60th-basis

!68th-~~prime~~

!68th-basis

!88th-~~prime~~

!88th-basis

!90th-~~prime~~

!90th-basis

!112th-~~prime~~

!112th-basis

!130th-~~prime~~

!130th-basis

!Integer (5.6.12.22.32... as above)

!Integer (simplified)

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! colspan="7" |Just intonation approximation

|-