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=== Composite subgroups ===
=== Composite subgroups ===
If one ignores primes and focuses on integers in general, 26ed5 can instead be used as a strong tuning for the obscure [[subgroup]] '''5.6.12.22.32.34.41.44.46.49.53.56.59.63.67'''.
If one ignores primes and focuses on integers in general, 26ed5 can instead be used as a strong tuning for the giant [[subgroup]]:


One can also use any subset of that subgroup for example:
'''5.6.12.22.32.44.49.52.56.63.'''
* 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 6 and the primes: '''5.6.41.59.67'''


==== Tables of harmonics ====
'''72.81.91.98.104.110.117.126'''
 
Or it can be a strong tuning for any smaller subgroup that is contained within that group.
 
Just some examples of possible smaller subgroups, not exhaustive:
*Only [[basis element]]s within the 50 [[integer limit]]: 5.6.12.22.32.44.49
*Only 6 and odd basis elements: 5.6.49.63.81.91.117
*Only [[7-limit]] basis elements: 5.6.12.32.49.56.63.72.81.98.126
* Only [[11-limit]] basis elements: 5.6.12.22.32.44.49.56.63.72.81.98.110.126
====Tables of harmonics====
{{Harmonics in equal
{{Harmonics in equal
| steps = 26
| steps = 26
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}}
}}


=== Fractional subgroups ===
===Fractional subgroups===
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, 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.
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.


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


{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
|+ ''N''th-prime subgroups
|+''N''th-prime subgroups
!Family
! Family
!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)
!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
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!90th-prime
!90th-prime
|15th-, 10th-, 9th- & 6th-prime
|15th-, 10th-, 9th- & 6th-prime
|11/3.13/9.17/15.19/9
| 11/3.13/9.17/15.19/9
|23/15.23/18.31/9.41/30.43/15.47/19.49/30
|23/15.23/18.31/9.41/30.43/15.47/19.49/30
|-
|-
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|}
|}


==== ''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"
|+ ''N''th-basis subgroups
|+''N''th-basis subgroups
!Family
!Family
!Most distinctive related families
!Most distinctive related families
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|<small>13/9.17/15.19/9.22/5.23/15.23/18.25/6.28/15.31/9.35/9.38/15.41/30.43/15.47/19.49/30</small>
|<small>13/9.17/15.19/9.22/5.23/15.23/18.25/6.28/15.31/9.35/9.38/15.41/30.43/15.47/19.49/30</small>
|-
|-
!140th-basis
! 140th-basis
|14th-, 10th- & quarter-basis
|14th-, 10th- & quarter-basis
|7/4.9/4.9/7.10/2.12/2.20/7
|7/4.9/4.9/7.10/2.12/2.20/7
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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.
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 ==
==Intervals==
{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
|+
|+
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|18/17
|18/17
|47/44
|47/44
| 16/15
|16/15
|
|
| 36/34, 34/32
|36/34, 34/32
|18/17, 17/16
|18/17, 17/16
|-
|-
! 2
!2
!214.3
!214.3
|17/15
|17/15
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|6/5
|6/5
|
|
|6/5, 41/34
|6/5
|6/5, 41/34
|6/5
|-
|-
!4
!4
! 428.7
!428.7
|
|
|
|
| 14/11
|14/11
|23/18
|23/18
|9/7
|9/7
| 63/49
|63/49
| 9/7
|9/7
|-
|-
! 5
!5
!535.8
!535.8
|41/30
|41/30
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|21/10, 19/9
|21/10, 19/9
|21/10
|21/10
|46/22, (6/5)x(56/32)
|(6/5)x(56/32)
|23/11, 21/10
|21/10
|-
|-
!13
!13
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|
|
|9/4
|9/4
|
|81/36
|
|9/4
|-
|-
!14
!14
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|
|
|
|
|
|12/5
|
|12/5
|-
|-
!15
!15
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|27/10
|27/10
|27/10
|27/10
|
|81/30
|
|27/10
|-
|-
!17
!17
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|
|
|61/20
|61/20
|67/22
|
|67/22
|
|-
|-
!19
!19
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|
|
|13/4
|13/4
|
|104/32
|
|13/4
|-
|-
!20
!20
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!2464.8
!2464.8
|25/6
|25/6
|25/6
| 25/6
|25/6
|25/6
|25/6
|25/6
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|-
|-
!24
!24
!2572.0
! 2572.0
|22/5
|22/5
|75/17
|75/17
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|-
|-
!26
!26
!2786.3
! 2786.3
|5/1
|5/1
|5/1
|5/1
|5/1
| 5/1
|5/1
|5/1
|5/1
|5/1
| 5/1
|5/1
|5/1
| 5/1
|}
|}


==Scales==
==Scales==


=== 13ed5plus===
===13ed5plus===
[[Category:14-tone scales]]Inspired by the [[elevenplus]] scale of [[22edo]], the '''13ed5plus scale''' is [[13ed5]] plus a step of 26ed5 in between two of its steps.
[[Category:14-tone scales]]
Inspired by the [[elevenplus]] scale of [[22edo]], the '''13ed5plus scale''' is [[13ed5]] plus a step of 26ed5 in between two of its steps.


In other words, 13ed5plus is all of the odd-numbered steps of 26ed5, plus step 2
In other words, 13ed5plus is all of the odd-numbered steps of 26ed5, plus step 2
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|6/5
|6/5
|
|
|6/5, 41/34
|6/5
|6/5, 41/34
|6/5
|-
|-
!5
!5
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|
|
|9/4
|9/4
|
|81/36
|
|9/4
|-
|-
!15
!15
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|
|
|13/4
|13/4
|
|104/32
|
|13/4
|-
|-
!21
!21
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