User:BudjarnLambeth/Possible convention for temperament pages: Difference between revisions
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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 == | ||
| Line 6: | Line 6: | ||
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. | ||
| Line 13: | Line 15: | ||
Comma list: 66/65, 81/80, 99/98, 105/104, 120/119 | Comma list: 66/65, 81/80, 99/98, 105/104, 120/119 | ||
{{Mapping|legend=0| 1 0 -4 -13 -25 -20 12 | 0 1 4 10 18 15 -5 }} | |||
Optimal tuning ([[POTE]]): ~2 = 1200.0, ~3/2 = 697.003 | Optimal tuning ([[POTE]]): ~2 = 1200.0, ~3/2 = 697.003 | ||
| Line 21: | Line 23: | ||
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. | ||
| Line 28: | Line 30: | ||
Comma list: 66/65, 81/80, 99/98, 105/104, 120/119 | Comma list: 66/65, 81/80, 99/98, 105/104, 120/119 | ||
{{Mapping|legend=0| 1 0 -4 -13 -25 -20 12 | 0 1 4 10 18 15 -5 }} | |||
Optimal tuning ([[CTE]]): ~2 = 1200.0, ~3/2 = 696.9080 | Optimal tuning ([[CTE]]): ~2 = 1200.0, ~3/2 = 696.9080 | ||
| Line 36: | Line 38: | ||
Badness: 0.019982 | Badness: 0.019982 | ||
== 2 tunings == | == 2 or 3 tunings == | ||
List | List all tunings in a dot point list. | ||
If CWE tuning is available, list it first. | |||
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 "4+ tunings" format. | |||
=== Examples === | |||
=== 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. | ||
| Line 50: | Line 56: | ||
Comma list: 66/65, 81/80, 99/98, 105/104, 120/119 | Comma list: 66/65, 81/80, 99/98, 105/104, 120/119 | ||
{{Mapping|legend=0| 1 0 -4 -13 -25 -20 12 | 0 1 4 10 18 15 -5 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 60: | Line 66: | ||
Badness: 0.019982 | Badness: 0.019982 | ||
== 3+ tunings == | ==== Huygens ==== | ||
List | 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|legend=0| 1 0 -4 -13 -25 -20 12 | 0 1 4 10 18 15 -5 }} | |||
Optimal tunings: | |||
* [[CWE]]: ~2 = 1200.0, ~3/2 = 696.982 | |||
* [[POTE]]: ~2 = 1200.0, ~3/2 = 697.003 | |||
* [[TE]]: ~2 = 1199.582, ~3/2 = 696.761 | |||
{{Optimal ET sequence|legend=1| 12f, 31 }} | |||
Badness: 0.019982 | |||
== 4+ tunings == | |||
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. | ||
| Line 74: | Line 102: | ||
Comma list: 66/65, 81/80, 99/98, 105/104, 120/119 | Comma list: 66/65, 81/80, 99/98, 105/104, 120/119 | ||
{{Mapping|legend=0| 1 0 -4 -13 -25 -20 12 | 0 1 4 10 18 15 -5 }} | |||
Optimal tunings: | Optimal tunings: | ||
* [[ | * [[CWE]]: ~2 = 1200.0, ~3/2 = 696.982 | ||
* [[TE]]: ~2 = 1199.582, ~3/2 = 696.761 | |||
{{Databox|Other optimal tunings|defaultstate=collapsed| | {{Databox|Other optimal tunings|defaultstate=collapsed| | ||
| Line 83: | Line 112: | ||
* [[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 ==== | |||
=== 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. | ||
| Line 97: | Line 121: | ||
Comma list: 66/65, 81/80, 99/98, 105/104, 120/119 | Comma list: 66/65, 81/80, 99/98, 105/104, 120/119 | ||
{{Mapping|legend=0| 1 0 -4 -13 -25 -20 12 | 0 1 4 10 18 15 -5 }} | |||
Optimal tunings: | Optimal tunings: | ||
* [[CTE]]: ~2 = 1200.0, ~3/2 = 696.9080 | * [[CTE]]: ~2 = 1200.0, ~3/2 = 696.9080 | ||
* [[TE]]: ~2 = 1199.582, ~3/2 = 696.761 | |||
{{Databox|Other optimal tunings|defaultstate=collapsed| | {{Databox|Other optimal tunings|defaultstate=collapsed| | ||
text= | text= | ||
* [[POTE]]: ~2 = 1200.0, ~3/2 = 697.003 | * [[POTE]]: ~2 = 1200.0, ~3/2 = 697.003 | ||
* [[ | * [[CE]]: ~2 = 1198.172, ~3/2 = 696.176 | ||
* [[WE]]: ~2= 1199.555, ~3/2 = 696.745 | |||
}} | }} | ||
Latest revision as of 12:33, 24 September 2026
(This is a proposal only, it is not an actual convention at the moment.)
1 tuning
If only one tuning is listed for a temperament, and you do not yet want to add any additional ones, display it like this.
Do not remove a tuning and add your own - instead, if you want to add one, follow the "2 tunings" format.
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.
Subgroup: 2.3.5.7.11.13.17
Comma list: 66/65, 81/80, 99/98, 105/104, 120/119
Mapping: [⟨1 0 -4 -13 -25 -20 12], ⟨0 1 4 10 18 15 -5]]
Optimal tuning (POTE): ~2 = 1200.0, ~3/2 = 697.003
Badness: 0.019982
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: [⟨1 0 -4 -13 -25 -20 12], ⟨0 1 4 10 18 15 -5]]
Optimal tuning (CTE): ~2 = 1200.0, ~3/2 = 696.9080
Badness: 0.019982
2 or 3 tunings
List all tunings in a dot point list.
If CWE tuning is available, list it first.
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 "4+ tunings" format.
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.
Subgroup: 2.3.5.7.11.13.17
Comma list: 66/65, 81/80, 99/98, 105/104, 120/119
Mapping: [⟨1 0 -4 -13 -25 -20 12], ⟨0 1 4 10 18 15 -5]]
Optimal tunings:
Badness: 0.019982
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: [⟨1 0 -4 -13 -25 -20 12], ⟨0 1 4 10 18 15 -5]]
Optimal tunings:
- CWE: ~2 = 1200.0, ~3/2 = 696.982
- POTE: ~2 = 1200.0, ~3/2 = 697.003
- TE: ~2 = 1199.582, ~3/2 = 696.761
Badness: 0.019982
4+ tunings
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.
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.
Subgroup: 2.3.5.7.11.13.17
Comma list: 66/65, 81/80, 99/98, 105/104, 120/119
Mapping: [⟨1 0 -4 -13 -25 -20 12], ⟨0 1 4 10 18 15 -5]]
Optimal tunings:
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: [⟨1 0 -4 -13 -25 -20 12], ⟨0 1 4 10 18 15 -5]]
Optimal tunings:
Badness: 0.019982