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Gentle region: Difference between revisions

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''This is the version of Oct 30, 2012. For an alternative version see: [[Gentle_region_(extended_version)|Gentle region (extended version)]]''
''This is the version of Oct 30, 2012. For an alternative version see: [[Gentle region (extended version)]]''


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[[Margo_Schulter|Margo Schulter]], in a [http://launch.groups.yahoo.com/group/tuning/message/38721 tuning list posting], defined the "gentle region" of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later [http://launch.groups.yahoo.com/group/tuning/message/105172 amending that] to from 1.49 to 3.04 cents sharp. We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of [[29edo|29edo]], [[46edo|46edo]], [[75edo|75edo]], [[104edo|104edo]], [[109edo|109edo]], [[121edo|121edo]], [[145edo|133edo]], [[155edo|155edo]], [[162edo|162edo]], [[167edo|167edo]], [[179edo|179edo]], [[191edo|191edo]], [[201edo|201edo]], [[213edo|213edo]], [[225edo|225edo]] and [[237edo|237edo]], plus [[63edo|63edo]] and [[80edo|80edo]] in the extended region.
[[Margo Schulter]], in a [http://launch.groups.yahoo.com/group/tuning/message/38721 tuning list posting], defined the "gentle region" of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later [http://launch.groups.yahoo.com/group/tuning/message/105172 amending that] to from 1.49 to 3.04 cents sharp. We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of [[29edo]], [[46edo]], [[75edo]], [[104edo]], [[109edo]], [[121edo]], [[145edo]], [[155edo]], [[162edo]], [[167edo]], [[179edo]], [[191edo]], [[201edo]], [[213edo]], [[225edo]] and [[237edo]], plus [[63edo]] and [[80edo]] in the extended region.


{| class="wikitable"
{| class="wikitable"
|-
|-
| | 17\29
| 17\29
| |  
|  
| |  
|  
| |  
|  
| | 703.448
| 703.448
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 61\104
| 61\104
| | 703.846
| 703.846
| |  
|  
|-
|-
| |  
|  
| |  
|  
| | 44\75
| 44\75
| |  
|  
| | 704
| 704
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 71\121
| 71\121
| | 704.132
| 704.132
| |  
|  
|-
|-
| |  
|  
| | 27\46
| 27\46
| |  
|  
| |  
|  
| | 704.348
| 704.348
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 64\109
| 64\109
| | 704.587
| 704.587
| | Boundary of smaller "gentle region"
| Boundary of smaller "gentle region"
|-
|-
| |  
|  
| |  
|  
| | 37\63
| 37\63
| |  
|  
| | 704.762
| 704.762
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 47\80
| 47\80
| | 705
| 705
| | Boundary of larger "gentle region"
| Boundary of larger "gentle region"
|-
|-
| | 10\17
| 10\17
| |  
|  
| |  
|  
| |  
|  
| | 705.882
| 705.882
| |  
|  
|}
|}
== See also ==
* [[Interseptimal]]
[[Category:edo]]
[[Category:edo]]
[[Category:fifth]]
[[Category:fifth]]
[[Category:gentle]]
[[Category:gentle]]
[[Category:sharp]]
[[Category:sharp]]
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