User:BudjarnLambeth/Possible convention for temperament pages

Revision as of 00:46, 20 March 2024 by BudjarnLambeth (talk | contribs) (Additional suggested changes)

(This is a proposal only, it is not yet an actual convention, do not do this yet.)

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.

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

Optimal ET sequence12f, 31

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

Optimal ET sequence12f, 31

Badness: 0.019982

2 tunings

List both tunings in a dot point list.

If KE 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 "3+ tunings" format.

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:

  • CTE: ~2 = 1200.0, ~3/2 = 696.9080
  • POTE: ~2 = 1200.0, ~3/2 = 697.003

Optimal ET sequence12f, 31

Badness: 0.019982

3+ tunings

List 1 or 2 tunings in a plain dot point list. List at least 2 other tunings below these, in a collapsible databox (collapsed by default).

KE and TE should always be included in the plain dot point list when they are available. Both lists should have pure-octave tunings first and tempered-octave tunings last.

Do not remove any other tunings that are already listed, just move them to the databox.

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:

  • KE: ~2 = 1200.0, ~3/2 = 696.982
  • TE: ~2 = 1199.582, ~3/2 = 696.761
Other optimal tunings
  • CTE: ~2 = 1200.0, ~3/2 = 696.9080
  • POTE: ~2 = 1200.0, ~3/2 = 697.003

Optimal ET sequence12f, 31

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:

  • KE: ~2 = 1200.0, ~3/2 = 696.982
  • CTE: ~2 = 1200.0, ~3/2 = 696.9080
Other optimal tunings
  • POTE: ~2 = 1200.0, ~3/2 = 697.003
  • TE: ~2 = 1199.582, ~3/2 = 696.761

Optimal ET sequence12f, 31

Badness: 0.019982