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m Trying to tame the huge complex subgroups and make them more sensible: a very long way to go yet, but it’s a atart
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One can also use any subset of that subgroup for example:
One can also use any subset of that subgroup for example:
* Only the 11-limit numbers: '''5.6.12.22.32.44.49.56.63'''
* Only numbers below 40: '''5.6.12.22.32.34'''
* Only numbers below 40: '''5.6.12.22.32.34'''
* Only numbers below 50: '''5.6.12.22.32.34.44.46.49'''
* Only 5 and the composite numbers: '''5.6.12.22.32.34.44.46.49.53.56.63'''
* Only 6 and the primes: '''5.6.41.59.67'''
* Only 6 and the primes: '''5.6.41.59.67'''


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Fractional subgroups are another approach to taming 26ed5. One can use any of the JI ratios approximated by its individual intervals as [[basis element]]s for a subgroup.
Fractional subgroups are another approach to taming 26ed5. One can use any of the JI ratios approximated by its individual intervals as [[basis element]]s for a subgroup.


There are dozens of possible combinations, here is a small sampling of possible ones:
There are dozens of possible combinations, for example the '''5.6.7/4.11/3.13/4''' subgroup, the '''5.6.7/4.9/4.9/7.11/3.13/4.13/7.13/9''' subgroup, etc.
* 5.6.7/4.11/3.13/4 subgroup
* 5.6.7/4.9/4.9/7.11/3.13/4.13/7.13/9 subgroup
* 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-prime subgroups ====
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!Most distinctive related families
!Most distinctive related families
!Subgroup basis elements
!Subgroup basis elements
!Optional extra elements (sprinkle in any 1 or 2 of these)
|-
|-
!16th-prime
!16th-prime
|8th-, quarter- & half-prime
|8th-, quarter- & half-prime
|7/4.13/4.17/16.19/8
|7/4.13/4.17/16.19/8
|
|-
|-
!18th-prime
!18th-prime
|9th- & 6th-prime
|9th- & 6th-prime
|11/3.13/9.19/9.23/18.31/9
|11/3.13/9.19/9.23/18.31/9
|
|-
|-
!30th-prime
!30th-prime
|15th- & 10th-prime
|15th- & 10th-prime
|11/3.17/15.23/15.41/30.47/10
|11/3.17/15.23/15
|41/30.47/10
|-
|-
!60th-prime
!60th-prime
|15th-, 10th- & quarter-prime
|15th-, 10th- & quarter-prime
|7/4.11/3.13/4.17/15.23/15.29/20.41/30.43/15.47/10.61/20
|7/4.11/3.13/4.17/15
|23/15.29/20.41/30.43/15.47/10.61/20
|-
|-
!68th-prime
!68th-prime
|17th- & quarter-prime
|17th- & quarter-prime
|7/4.13/4.41/34.43/17.67/34
|7/4.13/4.41/34.43/17
|67/34
|-
|-
!88th-prime
!88th-prime
|11th- & 8th-prime
|11th- & 8th-prime
|7/4.13/4.17/11.19/8.23/11.47/44.53/44.67/22
|7/4.13/4.17/11.19/8.23/11
|47/44.53/44.67/22
|-
|-
!90th-prime
!90th-prime
|15th-, 10th-, 9th- & 6th-prime
|15th-, 10th-, 9th- & 6th-prime
|11/3.13/9.17/15.19/9.23/15.23/18.31/9.41/30.43/15.47/19.49/30
|11/3.13/9.17/15.19/9
|23/15.23/18.31/9.41/30.43/15.47/19.49/30
|-
|-
!140th-basis
!140th-basis
|14th-, 10th- & quarter-basis
|14th-, 10th- & quarter-basis
|7/4.13/4.23/14.29/7.29/20.31/7.61/20
|7/4.13/4.23/14.29/7.31/7
|29/20.61/20
|}
|}


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


{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
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!Most distinctive related families
!Most distinctive related families
!Subgroup basis elements
!Subgroup basis elements
!Optional extra elements (sprinkle in any 1 or 2 of these)
|-
|-
!11th-basis
!11th-basis
|
|
|14/11.15/11.16/11.17/11.18/11.23/11.28/11.55/11.66/11
|14/11.15/11.16/11.55/11.66/11
|17/11.18/11.28/11.23/11
|-
|-
!14th-basis
!14th-basis
|7th- & half-basis
|7th- & half-basis
|9/7.10/2.12/2.20/7.23/14.24/7.29/7.31/7.33/7
|9/7.10/2.12/2.20/7.24/7
|23/14.29/7.31/7.33/7
|-
|-
!16th-basis
!16th-basis
|8th-, quarter- & half-basis
|8th-, quarter- & half-basis
|7/4.9/4.10/2.12/2.13/4.17/16.19/8
|7/4.9/4.10/2.12/2.13/4
|17/16.19/8
|-
|-
!18th-basis
!18th-basis
|9th- & 6th-basis
|9th- & 6th-basis
|10/2.12/2.11/3.13/9.19/9.23/18.25/6.31/9.35/9
|10/2.12/2.11/3.25/6.35/9
|13/9.19/9.23/18.31/9
|-
|-
!30th-basis
!30th-basis
|15th- & 10th-basis
|15th- & 10th-basis
|10/2.11/3.12/2.16/15.17/15.21/10.22/5.23/15.25/6.28/15.38/15.41/30.34/15.47/10
|10/2.11/3.12/2.16/15.21/10.22/5
|17/15.23/15.25/6.28/15.38/15.41/30.34/15.47/10
|-
|-
!60th-basis
!60th-basis
|15th-, 10th- & quarter-basis
|15th-, 10th- & quarter-basis
|7/4.9/4.10/2.11/3.12/2.13/4.16/15.17/15.21/10.22/5.23/15.25/6.28/15.29/20.38/15.41/30.43/15.47/10.49/30.61/20.69/20
|7/4.9/4.10/2.11/3.12/2.16/15.21/10
|13/4.17/15.22/5.23/15.25/6.28/15.29/20.38/15.41/30.43/15.47/10.49/30.61/20.69/20
|-
|-
!68th-basis
!68th-basis
|17th- & quarter-basis
|17th- & quarter-basis
|7/4.9/4.10/2.12/2.13/4.18/17.28/17.41/34.43/17.63/34.67/34.75/17.80/17
|7/4.9/4.10/2.12/2.13/4
|18/17.28/17.41/34.43/17.63/34.67/34.75/17.80/17
|-
|-
!88th-basis
!88th-basis
|11th- & 8th-basis
|11th- & 8th-basis
|7/4.9/4.10/2.12/2.13/4.14/11.15/11.16/11.17/11.18/11.19/8.23/11.25/22.28/11.47/44.53/44.63/22.67/22
|7/4.9/4.10/2.12/2.14/11.15/11.16/11
|13/4.17/11.18/11.19/8.23/11.25/22.28/11.47/44.53/44.63/22.67/22
|-
|-
!90th-basis
!90th-basis
|15th-, 10th-, 9th- & 6th-basis
|15th-, 10th-, 9th- & 6th-basis
|10/2.11/3.12/2.13/9.16/15.17/15.19/9.21/10.22/5.23/15.23/18.25/6.28/15.31/9.35/9.38/15.41/30.43/15.47/19.49/30
|10/2.11/3.12/2.16/15.21/10.22/5
|13/9.17/15.19/9.23/15.23/18.25/6.28/15.31/9.35/9.38/15.41/30.43/15.47/19.49/30
|-
|-
!140th-basis
!140th-basis
|14th-, 10th- & quarter-basis
|14th-, 10th- & quarter-basis
|7/4.9/4.9/7.10/2.12/2.13/4.20/7.23/14.24/7.29/7.29/20.31/7.33/7.61/20
|7/4.9/4.9/7.10/2.12/2.20/7.24/7
|13/4.23/14.29/7.29/20.31/7.33/7.61/20
|}
|}


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