User:BudjarnLambeth/Possible convention for temperament pages: Difference between revisions
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Changed KE to CWE for now because the contents of "Dave Keenan & Douglas Blumeyer's guide to RTT: alternative complexities" contradict what I've heard from Mike, and it looks like there's been confusion about what exactly KE corresponds to for a long time, so for now I'll just stick with CWE to be safe. |
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(This is a proposal only, it is not | (This is a proposal only, it is not an actual convention at the moment.) | ||
== 1 tuning == | == 1 tuning == | ||
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Do not remove a tuning and add your own - instead, if you want to add one, follow the "2 tunings" format. | Do not remove a tuning and add your own - instead, if you want to add one, follow the "2 tunings" format. | ||
=== Huygens === | === Examples === | ||
==== Huygens ==== | |||
Dubbed ''huygens'' here, this extension is perhaps the most practical, as it maps 17/16 to the minor second (C-Db), and 19/16 to the minor third (C-Eb), suitable for a system generated by a mildly tempered fifth. | Dubbed ''huygens'' here, this extension is perhaps the most practical, as it maps 17/16 to the minor second (C-Db), and 19/16 to the minor third (C-Eb), suitable for a system generated by a mildly tempered fifth. | ||
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Badness: 0.019982 | Badness: 0.019982 | ||
=== Huygens === | ==== Huygens ==== | ||
Dubbed ''huygens'' here, this extension is perhaps the most practical, as it maps 17/16 to the minor second (C-Db), and 19/16 to the minor third (C-Eb), suitable for a system generated by a mildly tempered fifth. | Dubbed ''huygens'' here, this extension is perhaps the most practical, as it maps 17/16 to the minor second (C-Db), and 19/16 to the minor third (C-Eb), suitable for a system generated by a mildly tempered fifth. | ||
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List all tunings in a dot point list. | List all tunings in a dot point list. | ||
If | If CWE tuning is available, list it first. | ||
List pure-octave tunings first and tempered-octave tunings last. | List pure-octave tunings first and tempered-octave tunings last. | ||
Do not remove a tuning and add your own - instead, if you want to add more, follow the " | Do not remove a tuning and add your own - instead, if you want to add more, follow the "4+ tunings" format. | ||
=== Huygens === | === Examples === | ||
==== Huygens ==== | |||
Dubbed ''huygens'' here, this extension is perhaps the most practical, as it maps 17/16 to the minor second (C-Db), and 19/16 to the minor third (C-Eb), suitable for a system generated by a mildly tempered fifth. | Dubbed ''huygens'' here, this extension is perhaps the most practical, as it maps 17/16 to the minor second (C-Db), and 19/16 to the minor third (C-Eb), suitable for a system generated by a mildly tempered fifth. | ||
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Badness: 0.019982 | Badness: 0.019982 | ||
=== Huygens === | ==== Huygens ==== | ||
Dubbed ''huygens'' here, this extension is perhaps the most practical, as it maps 17/16 to the minor second (C-Db), and 19/16 to the minor third (C-Eb), suitable for a system generated by a mildly tempered fifth. | Dubbed ''huygens'' here, this extension is perhaps the most practical, as it maps 17/16 to the minor second (C-Db), and 19/16 to the minor third (C-Eb), suitable for a system generated by a mildly tempered fifth. | ||
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Optimal tunings: | Optimal tunings: | ||
* [[ | * [[CWE]]: ~2 = 1200.0, ~3/2 = 696.982 | ||
* [[POTE]]: ~2 = 1200.0, ~3/2 = 697.003 | * [[POTE]]: ~2 = 1200.0, ~3/2 = 697.003 | ||
* [[TE]]: ~2 = 1199.582, ~3/2 = 696.761 | * [[TE]]: ~2 = 1199.582, ~3/2 = 696.761 | ||
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List 2 tunings in a plain dot point list. List all other tunings below these, in a collapsible databox (collapsed by default). | List 2 tunings in a plain dot point list. List all other tunings below these, in a collapsible databox (collapsed by default). | ||
CWE and TE should always be included in the plain dot point list if you know them. | |||
Both lists should have pure-octave tunings at the top of the list and tempered-octave tunings at the bottom. | |||
Do not remove any other tunings that are already listed, just move them to the databox. | Do not remove any other tunings that are already listed, just move them to the databox. | ||
=== Huygens === | === Examples === | ||
==== Huygens ==== | |||
Dubbed ''huygens'' here, this extension is perhaps the most practical, as it maps 17/16 to the minor second (C-Db), and 19/16 to the minor third (C-Eb), suitable for a system generated by a mildly tempered fifth. | Dubbed ''huygens'' here, this extension is perhaps the most practical, as it maps 17/16 to the minor second (C-Db), and 19/16 to the minor third (C-Eb), suitable for a system generated by a mildly tempered fifth. | ||
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Optimal tunings: | Optimal tunings: | ||
* [[ | * [[CWE]]: ~2 = 1200.0, ~3/2 = 696.982 | ||
* [[TE]]: ~2 = 1199.582, ~3/2 = 696.761 | * [[TE]]: ~2 = 1199.582, ~3/2 = 696.761 | ||
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* [[CTE]]: ~2 = 1200.0, ~3/2 = 696.9080 | * [[CTE]]: ~2 = 1200.0, ~3/2 = 696.9080 | ||
* [[POTE]]: ~2 = 1200.0, ~3/2 = 697.003 | * [[POTE]]: ~2 = 1200.0, ~3/2 = 697.003 | ||
}} | |||
==== Huygens ==== | |||
Dubbed ''huygens'' here, this extension is perhaps the most practical, as it maps 17/16 to the minor second (C-Db), and 19/16 to the minor third (C-Eb), suitable for a system generated by a mildly tempered fifth. | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 66/65, 81/80, 99/98, 105/104, 120/119 | |||
Mapping: {{mapping| 1 0 -4 -13 -25 -20 12 | 0 1 4 10 18 15 -5 }} | |||
Optimal tunings: | |||
* [[CTE]]: ~2 = 1200.0, ~3/2 = 696.9080 | |||
* [[TE]]: ~2 = 1199.582, ~3/2 = 696.761 | |||
{{Databox|Other optimal tunings|defaultstate=collapsed| | |||
text= | |||
* [[POTE]]: ~2 = 1200.0, ~3/2 = 697.003 | |||
* [[CE]]: ~2 = 1198.172, ~3/2 = 696.176 | |||
* [[WE]]: ~2= 1199.555, ~3/2 = 696.745 | |||
}} | }} | ||