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→Selected just intervals by error: clean up, especially 15-odd-limit tables, put image in separate section (it shows 17-limit intervals)
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"just" double harmonic - 2524252
"just" double harmonic - 2524252


==Selected just intervals by error==
== Selected just intervals by error ==
{| class="wikitable" style="text-align:center;"
 
!colspan=2|
{| class="wikitable center-all"
!prime 2
! colspan=2 |
!prime 3
! prime 2
!prime 5
! prime 3
!prime 7
! prime 5
!prime 11
! prime 7
!prime 13
! prime 11
!prime 17
! prime 13
! prime 17
|-
|-
!rowspan=2|error
! rowspan=2 | error
! absolute (¢)
! absolute (¢)
| 0.0
| 0.0
Line 765: Line 766:
| +7
| +7
|-
|-
!colspan=2|[[fifthspan]]
! colspan=2 | [[fifthspan]]
|0
| 0
| +1
| +1
| +9
| +9
Line 774: Line 775:
| -10
| -10
|}
|}
The following table shows how [[Just-24|some prominent just intervals]] are represented in 22edo (ordered by absolute error).


===Best direct mapping, even if inconsistent===
=== 15-odd-limit interval mappings ===
 
The following tables show how [[15-odd-limit intervals]] are represented in 22edo.


{| class="wikitable"
{| class="wikitable center-1 right-2"
|+ Direct mapping (even if inconsistent)
! Interval, complement
! Error (abs, [[cent|¢]])
|-
|-
! | Interval, complement
| [[9/7]], [[14/9]]
! | Error (abs., in [[cent|cents]])
| 1.280
|-
|-
| style="text-align:center;" | [[9/7|9/7]], [[14/9|14/9]]
| [[11/10]], [[20/11]]
| style="text-align:center;" | 1.280
| 1.368
|-
|-
| style="text-align:center;" | [[11/10|11/10]], [[20/11|20/11]]
| [[16/15]], [[15/8]]
| style="text-align:center;" | 1.368
| 2.640
|-
|-
| style="text-align:center;" | [[16/15|16/15]], [[15/8|15/8]]
| [[5/4]], [[8/5]]
| style="text-align:center;" | 2.640
| 4.496
|-
|-
| style="text-align:center;" | '''[[5/4|5/4]], [[8/5|8/5]]'''
| [[7/6]], [[12/7]]
| style="text-align:center;" | '''4.496'''
| 5.856
|-
|-
| style="text-align:center;" | [[7/6|7/6]], [[12/7|12/7]]
| [[11/8]], [[16/11]]
| style="text-align:center;" | 5.856
| 5.863
|-
|-
| style="text-align:center;" | '''[[11/8|11/8]], [[16/11|16/11]]'''
| [[4/3]], [[3/2]]
| style="text-align:center;" | '''5.863'''
| 7.136
|-
|-
| style="text-align:center;" | '''[[4/3|4/3]], [[3/2|3/2]]'''
| [[15/11]], [[22/15]]
| style="text-align:center;" | '''7.136'''
| 8.504
|-
|-
| style="text-align:center;" | [[15/11|15/11]], [[22/15|22/15]]
| [[15/14]], [[28/15]]
| style="text-align:center;" | 8.504
| 10.352
|-
|-
| style="text-align:center;" | [[15/14|15/14]], [[28/15|28/15]]
| [[6/5]], [[5/3]]
| style="text-align:center;" | 10.352
| 11.631
|-
|-
| style="text-align:center;" | [[6/5|6/5]], [[5/3|5/3]]
| [[8/7]], [[7/4]]
| style="text-align:center;" | 11.631
| 12.992
|-
|-
| style="text-align:center;" | '''[[8/7|8/7]], [[7/4|7/4]]'''
| [[12/11]], [[11/6]]
| style="text-align:center;" | '''12.992'''
| 12.999
|-
|-
| style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]]
| [[9/8]], [[16/9]]
| style="text-align:center;" | 12.999
| 14.272
|-
|-
| style="text-align:center;" | [[9/8|9/8]], [[16/9|16/9]]
| [[13/11]], [[22/13]]
| style="text-align:center;" | 14.272
| 16.482
|-
|-
| style="text-align:center;" | [[13/11|13/11]], [[22/13|22/13]]
| [[7/5]], [[10/7]]
| style="text-align:center;" | 16.482
| 17.488
|-
|-
| style="text-align:center;" | [[7/5|7/5]], [[10/7|10/7]]
| [[13/10]], [[20/13]]
| style="text-align:center;" | 17.488
| 17.850
|-
|-
| style="text-align:center;" | [[13/10|13/10]], [[20/13|20/13]]
| [[18/13]], [[13/9]]
| style="text-align:center;" | 17.850
| 17.928
|-
|-
| style="text-align:center;" | [[18/13|18/13]], [[13/9|13/9]]
| [[10/9]], [[9/5]]
| style="text-align:center;" | 17.928
| 18.767
|-
|-
| style="text-align:center;" | [[10/9|10/9]], [[9/5|9/5]]
| [[14/11]], [[11/7]]
| style="text-align:center;" | 18.767
| 18.856
|-
|-
| style="text-align:center;" | [[14/11|14/11]], [[11/7|11/7]]
| [[14/13]], [[13/7]]
| style="text-align:center;" | 18.856
| 19.207
|-
|-
| style="text-align:center;" | [[14/13|14/13]], [[13/7|13/7]]
| [[11/9]], [[18/11]]
| style="text-align:center;" | 19.207
| 20.135
|-
|-
| style="text-align:center;" | [[11/9|11/9]], [[18/11|18/11]]
| [[16/13]], [[13/8]]
| style="text-align:center;" | 20.135
| 22.346
|-
|-
| style="text-align:center;" | '''[[16/13|16/13]], [[13/8|13/8]]'''
| [[15/13]], [[26/15]]
| style="text-align:center;" | '''22.346'''
| 24.986
|-
|-
| style="text-align:center;" | [[15/13|15/13]], [[26/15|26/15]]
| [[13/12]], [[24/13]]
| style="text-align:center;" | 24.986
| 25.064
|-
| style="text-align:center;" | [[13/12|13/12]], [[24/13|24/13]]
| style="text-align:center;" | 25.064
|}
|}


===Patent val mapping===
{| class="wikitable center-1 right-2"
 
|+ Patent val mapping
{| class="wikitable"
! Interval, complement
! Error (abs, [[cent|¢]])
|-
|-
! | Interval, complement
| [[9/7]], [[14/9]]
! | Error (abs., in [[cent|cents]])
| 1.280
|-
|-
| style="text-align:center;" | [[9/7|9/7]], [[14/9|14/9]]
| [[11/10]], [[20/11]]
| style="text-align:center;" | 1.280
| 1.368
|-
|-
| style="text-align:center;" | [[11/10|11/10]], [[20/11|20/11]]
| [[16/15]], [[15/8]]
| style="text-align:center;" | 1.368
| 2.640
|-
|-
| style="text-align:center;" | [[16/15|16/15]], [[15/8|15/8]]
| [[5/4]], [[8/5]]
| style="text-align:center;" | 2.640
| 4.496
|-
|-
| style="text-align:center;" | '''[[5/4|5/4]], [[8/5|8/5]]'''
| [[7/6]], [[12/7]]
| style="text-align:center;" | '''4.496'''
| 5.856
|-
|-
| style="text-align:center;" | [[7/6|7/6]], [[12/7|12/7]]
| [[11/8]], [[16/11]]
| style="text-align:center;" | 5.856
| 5.863
|-
|-
| style="text-align:center;" | '''[[11/8|11/8]], [[16/11|16/11]]'''
| [[4/3]], [[3/2]]
| style="text-align:center;" | '''5.863'''
| 7.136
|-
|-
| style="text-align:center;" | '''[[4/3|4/3]], [[3/2|3/2]]'''
| [[15/11]], [[22/15]]
| style="text-align:center;" | '''7.136'''
| 8.504
|-
|-
| style="text-align:center;" | [[15/11|15/11]], [[22/15|22/15]]
| [[15/14]], [[28/15]]
| style="text-align:center;" | 8.504
| 10.352
|-
|-
| style="text-align:center;" | [[15/14|15/14]], [[28/15|28/15]]
| [[6/5]], [[5/3]]
| style="text-align:center;" | 10.352
| 11.631
|-
|-
| style="text-align:center;" | [[6/5|6/5]], [[5/3|5/3]]
| [[8/7]], [[7/4]]
| style="text-align:center;" | 11.631
| 12.992
|-
|-
| style="text-align:center;" | '''[[8/7|8/7]], [[7/4|7/4]]'''
| [[12/11]], [[11/6]]
| style="text-align:center;" | '''12.992'''
| 12.999
|-
|-
| style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]]
| [[9/8]], [[16/9]]
| style="text-align:center;" | 12.999
| 14.272
|-
|-
| style="text-align:center;" | [[9/8|9/8]], [[16/9|16/9]]
| [[13/11]], [[22/13]]
| style="text-align:center;" | 14.272
| 16.482
|-
|-
| style="text-align:center;" | [[13/11|13/11]], [[22/13|22/13]]
| [[7/5]], [[10/7]]
| style="text-align:center;" | 16.482
| 17.488
|-
|-
| style="text-align:center;" | [[7/5|7/5]], [[10/7|10/7]]
| [[13/10]], [[20/13]]
| style="text-align:center;" | 17.488
| 17.850
|-
|-
| style="text-align:center;" | [[13/10|13/10]], [[20/13|20/13]]
| [[10/9]], [[9/5]]
| style="text-align:center;" | 17.850
| 18.767
|-
|-
| style="text-align:center;" | [[10/9|10/9]], [[9/5|9/5]]
| [[14/11]], [[11/7]]
| style="text-align:center;" | 18.767
| 18.856
|-
|-
| style="text-align:center;" | [[14/11|14/11]], [[11/7|11/7]]
| [[11/9]], [[18/11]]
| style="text-align:center;" | 18.856
| 20.135
|-
|-
| style="text-align:center;" | [[11/9|11/9]], [[18/11|18/11]]
| [[16/13]], [[13/8]]
| style="text-align:center;" | 20.135
| 22.346
|-
|-
| style="text-align:center;" | '''[[16/13|16/13]], [[13/8|13/8]]'''
| [[15/13]], [[26/15]]
| style="text-align:center;" | '''22.346'''
| 24.986
|-
|-
| style="text-align:center;" | [[15/13|15/13]], [[26/15|26/15]]
| [[13/12]], [[24/13]]
| style="text-align:center;" | 24.986
| 29.482
|-
|-
| style="text-align:center;" | [[13/12|13/12]], [[24/13|24/13]]
| [[14/13]], [[13/7]]
| style="text-align:center;" | 29.482
| 35.338
|-
|-
| style="text-align:center;" | [[14/13|14/13]], [[13/7|13/7]]
| [[18/13]], [[13/9]]
| style="text-align:center;" | 35.338
| 36.618
|-
| style="text-align:center;" | [[18/13|18/13]], [[13/9|13/9]]
| style="text-align:center;" | 36.618
|}
|}
=== Selected 17-limit intervals ===


[[File:22ed2-001e.svg|alt=alt : Your browser has no SVG support.]]
[[File:22ed2-001e.svg|alt=alt : Your browser has no SVG support.]]
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