Hemfiness temperaments: Difference between revisions
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'''Hemfiness''' rank-two temperaments temper out the ''hemfiness'' comma, 4096000/4084101 = {{monzo|15 -5 3 -5}} (saquinru-atriyo), the amount by which a stack of three [[5/4]]s and five [[32/21]]s exceed four octaves. | {{Technical data page}} | ||
'''Hemfiness''' rank-two temperaments temper out the ''hemfiness'' comma, [[4096000/4084101]] = {{monzo|15 -5 3 -5}} (saquinru-atriyo), the amount by which a stack of three [[5/4]]s and five [[32/21]]s exceed four octaves. | |||
Temperaments dicussed elsewhere include: | Temperaments dicussed elsewhere include: | ||
| Line 15: | Line 16: | ||
* [[Meantone family #Jerome|Jerome]] | * [[Meantone family #Jerome|Jerome]] | ||
* [[Archytas clan #Progress|Progress]] | * [[Archytas clan #Progress|Progress]] | ||
* [[Wizmic microtemperaments # | * [[Wizmic microtemperaments #Witcher|Witcher]] | ||
== Undesemi == | == Undesemi == | ||
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[[Mapping]]: [{{val|1 5 5 1}}, {{val|0 -51 -40 27}}] | [[Mapping]]: [{{val|1 5 5 1}}, {{val|0 -51 -40 27}}] | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~8575/8192 = 80.347 | ||
{{ | {{Optimal ET sequence|legend=1| 15, …, 194, 209, 224, 463, 687, 1150d }} | ||
[[Badness]]: 0.178777 | [[Badness]]: 0.178777 | ||
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POTE generator: ~22/21 = 80.347 | POTE generator: ~22/21 = 80.347 | ||
Optimal ET sequence: {{Optimal ET sequence| 15, …, 194, 209, 224, 463, 1150de }} | |||
Badness: 0.042318 | Badness: 0.042318 | ||
[[ | == Piracy == | ||
{{see also|Very high accuracy temperaments #Pirate}} | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 4096000/4084101, 48828125/48771072 | |||
[[Mapping]]: [{{val|1 -6 0 9}}, {{val|0 49 15 -40}}] | |||
[[Optimal tuning]] ([[POTE]]): ~4096/3675 = 185.7609 | |||
{{Optimal ET sequence|legend=1| 71, 84, 155, 239, 323, 885, 1208d, 1531d }} | |||
[[Badness]]: 0.159305 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 6250/6237, 12005/11979, 16384/16335 | |||
Mapping: [{{val|1 -6 0 9 16}}, {{val|0 49 15 -40 -81}}] | |||
Optimal tuning (POTE): ~49/44 = 185.7671 | |||
Optimal ET sequence: {{Optimal ET sequence| 84, 155, 239, 562e, 801e }} | |||
Badness: 0.092173 | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 625/624, 2080/2079, 2205/2197, 12005/11979 | |||
Mapping: [{{val|1 -6 0 9 16 2}}, {{val|0 49 15 -40 -81 11}}] | |||
Optimal tuning (POTE): ~49/44 = 185.7663 | |||
Optimal ET sequence: {{Optimal ET sequence| 84, 155, 239f }} | |||
Badness: 0.063719 | |||
==== Pirateship ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 364/363, 1716/1715, 4096/4095, 6250/6237 | |||
Mapping: [{{val|1 -6 0 9 16 15}}, {{val|0 49 15 -40 -81 -73}}] | |||
Optimal tuning (POTE): ~39/35 = 185.7621 | |||
Optimal ET sequence: {{Optimal ET sequence| 84, 155f, 239, 323e }} | |||
Badness: 0.073523 | |||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Latest revision as of 00:31, 24 June 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
Hemfiness rank-two temperaments temper out the hemfiness comma, 4096000/4084101 = [15 -5 3 -5⟩ (saquinru-atriyo), the amount by which a stack of three 5/4s and five 32/21s exceed four octaves.
Temperaments dicussed elsewhere include:
- Hemififths
- Nessafof
- Gamera
- Superkleismic
- Quanharuk
- Merman
- Decipentic
- Oquatonic
- Stockhausenic
- Secant
- Thuja
- Jerome
- Progress
- Witcher
Undesemi
Subgroup: 2.3.5.7
Comma list: 4096000/4084101, 95703125/95551488
Mapping: [⟨1 5 5 1], ⟨0 -51 -40 27]]
Optimal tuning (POTE): ~8575/8192 = 80.347
Optimal ET sequence: 15, …, 194, 209, 224, 463, 687, 1150d
Badness: 0.178777
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 180224/180075
Mapping: [⟨1 5 5 1 5], ⟨0 -51 -40 27 -23]]
POTE generator: ~22/21 = 80.347
Optimal ET sequence: 15, …, 194, 209, 224, 463, 1150de
Badness: 0.042318
Piracy
Subgroup: 2.3.5.7
Comma list: 4096000/4084101, 48828125/48771072
Mapping: [⟨1 -6 0 9], ⟨0 49 15 -40]]
Optimal tuning (POTE): ~4096/3675 = 185.7609
Optimal ET sequence: 71, 84, 155, 239, 323, 885, 1208d, 1531d
Badness: 0.159305
11-limit
Subgroup: 2.3.5.7.11
Comma list: 6250/6237, 12005/11979, 16384/16335
Mapping: [⟨1 -6 0 9 16], ⟨0 49 15 -40 -81]]
Optimal tuning (POTE): ~49/44 = 185.7671
Optimal ET sequence: 84, 155, 239, 562e, 801e
Badness: 0.092173
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 2080/2079, 2205/2197, 12005/11979
Mapping: [⟨1 -6 0 9 16 2], ⟨0 49 15 -40 -81 11]]
Optimal tuning (POTE): ~49/44 = 185.7663
Optimal ET sequence: 84, 155, 239f
Badness: 0.063719
Pirateship
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 1716/1715, 4096/4095, 6250/6237
Mapping: [⟨1 -6 0 9 16 15], ⟨0 49 15 -40 -81 -73]]
Optimal tuning (POTE): ~39/35 = 185.7621
Optimal ET sequence: 84, 155f, 239, 323e
Badness: 0.073523