Tags: Mobile edit Mobile web edit |
|
| (11 intermediate revisions by 4 users not shown) |
| Line 1: |
Line 1: |
| {{Technical data page}} | | {{Technical data page}} |
| Below are listed some '''very low accuracy temperaments'''. Temperaments with exceedingly low accuracy such as these tend to [[tempering out|temper out]] very large intervals such as [[9/8]], [[10/9]], [[32/27]], or [[15/14]], equating wildly different interval sizes with [[semitone (interval size measure)|semitone]]-level or even greater [[error]]s. A lot of temperaments listed here don't have [[diamond monotone]] tunings because of their sheer inaccuracy. As a result, all of them are right on or even beyond the edge of what can be sensibly called a temperament at all; that is to say, they are [[exotemperament]]s. | | Below are listed some '''very low accuracy temperaments'''. Temperaments with exceedingly low accuracy such as these tend to [[tempering out|temper out]] very large intervals such as [[9/8]], [[10/9]], [[32/27]], or [[15/14]], equating wildly different interval sizes with [[semitone (interval size measure)|semitone]]-level or even greater [[error]]s, and often swapping the sizes of simple ratios compared to just intonation. As a result, all of them are right on or even beyond the edge of what can be sensibly called a temperament at all; that is to say, they are [[exotemperament]]s. |
|
| |
|
| == Antitonic == | | == Antitonic == |
| Line 185: |
Line 185: |
| * CWE: ~2 = 1200.000{{c}}, ~3/2 = 800.996{{c}} | | * CWE: ~2 = 1200.000{{c}}, ~3/2 = 800.996{{c}} |
|
| |
|
| {{Optimal ET sequence|legend=0| 2c, 3d }} | | {{Optimal ET sequence|legend=0| 1c, 3d }} |
|
| |
|
| Badness (Sintel): 0.720 | | Badness (Sintel): 0.720 |
| Line 294: |
Line 294: |
|
| |
|
| == Quad == | | == Quad == |
| Quad is identical to 4et in the 5-limit, but has an independent generator for prime 7. | | Quad is identical to [[4edo|4et]] in the 5-limit, but has an independent generator for prime 7. |
|
| |
|
| [[Subgroup]]: 2.3.5.7 | | [[Subgroup]]: 2.3.5.7 |
| Line 311: |
Line 311: |
|
| |
|
| [[Badness]] (Sintel): 1.16 | | [[Badness]] (Sintel): 1.16 |
| | |
| | == Quint == |
| | Quint preserves the 5-limit mapping of 5edo, and harmonic 7 is mapped to an independent generator. As harmonic 7 is way more accurately approximated than 5 by 5edo, this temperament provides little improvement to 5edo's 7-limit tuning, so in what way this temperament is useful remains unexplained. It would make much more sense to, for example, preserve the 2.3.7-subgroup structure of 5edo and give prime 5 an independent generator instead, which is exactly what [[blackwood]] does. |
| | |
| | [[Subgroup]]: 2.3.5.7 |
| | |
| | [[Comma list]]: 16/15, 27/25 |
| | |
| | {{Mapping|legend=1| 5 8 12 0 | 0 0 0 1 }} |
| | |
| | : Mapping generators: ~6/5, ~7 |
| | |
| | [[Optimal tuning]]s: |
| | * [[WE]]: ~6/5 = 236.416, ~7/4 = 1002.701 (~28/27 = 57.038) <!-- Please review, last digit may be wrong --> |
| | : [[error map]]: {{val| -17.921 -10.628 +50.676 -1.966 }} |
| | * [[CWE]]: ~6/5 = 240.000, ~7/4 = 1005.135 (~28/27 = 45.135) |
| | : error map: {{val| 0.000 +18.045 +93.686 +36.309 }} |
| | |
| | {{Optimal ET sequence|legend=1| 5, 15ccd }} |
| | |
| | [[Badness]] (Sintel): 1.22 |
|
| |
|
| == Geryon == | | == Geryon == |
| Line 425: |
Line 446: |
|
| |
|
| == Plutus == | | == Plutus == |
| | {{Distinguish| Pluto }} |
| {{See also| Meantone family }} | | {{See also| Meantone family }} |
|
| |
|
| Line 556: |
Line 578: |
|
| |
|
| [[Badness]] (Sintel): 1.52 | | [[Badness]] (Sintel): 1.52 |
|
| |
| == Bixby ==
| |
| {{Main| Bixby }}
| |
|
| |
| [[Subgroup]]: 2.3.5
| |
|
| |
| [[Comma list]]: [[4/3]]
| |
|
| |
| {{Mapping|legend=1| 1 2 0 | 0 0 1 }}
| |
|
| |
| [[Optimal tuning]]s:
| |
| * [[WE]]: ~2 = 1020.058{{c}}, ~5/4 = 674.394{{c}}
| |
| : [[error map]]: {{val| -179.942 +138.161 -71.803 }}
| |
| * [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 629.521{{c}}
| |
| : error map: {{val| 0.000 +498.045 +243.208 }}
| |
|
| |
| {{Optimal ET sequence|legend=1| 1c, 2b, 3bbcc }}
| |
|
| |
| [[Badness]] (Sintel): 0.424
| |
|
| |
| == Archon ==
| |
| {{Main| Archon }}
| |
|
| |
| [[Subgroup]]: 2.3.5
| |
|
| |
| [[Comma list]]: [[5/4]]
| |
|
| |
| {{Mapping|legend=1| 1 0 2 | 0 1 0 }}
| |
|
| |
| [[Optimal tuning]]s:
| |
| * [[WE]]: ~2 = 1268.274{{c}}, ~3/2 = 612.921{{c}}
| |
| : [[error map]]: {{val| +68.274 -20.760 -249.765 }}
| |
| * [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 614.055{{c}}
| |
| : error map: {{val| 0.000 -87.900 -386.314 }}
| |
|
| |
| {{Optimal ET sequence|legend=1| 2c }}
| |
|
| |
| [[Badness]] (Sintel): 0.474
| |
|
| |
| == Seesaw ==
| |
| {{Main| Seesaw }}
| |
| Seesaw tempers out the [[6/5|classic minor third (6/5)]], equating the [[5/1|fifth]] and [[6/1|sixth harmonic]]s. It was named by [[User:Xenllium|Xenllium]] in 2026.
| |
|
| |
| [[Subgroup]]: 2.3.5
| |
|
| |
| [[Comma list]]: 6/5
| |
|
| |
| {{Mapping|legend=1| 1 0 1 | 0 1 1 }}
| |
|
| |
| [[Optimal tuning]]s:
| |
| * [[WE]]: ~2 = 1155.569{{c}}, ~3/2 = 643.349{{c}}
| |
| : [[error map]]: {{val| -44.431 -103.037 +168.173 }}
| |
| * [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 627.511{{c}}
| |
| : error map: {{val| 0.000 -74.444 +241.197 }}
| |
|
| |
| {{Optimal ET sequence|legend=1| 2 }}
| |
|
| |
| [[Badness]] (Sintel): 0.367
| |
|
| |
| === 2.3.5.11 subgroup ===
| |
| This temperament is extended to the 2.3.5.11 subgroup naturally, tempering out both [[11/10]] and [[12/11]], undecimal neutral seconds.
| |
|
| |
| Subgroup: 2.3.5.11
| |
|
| |
| Comma list: 6/5, 11/10
| |
|
| |
| Mapping: {{mapping| 1 0 1 2 | 0 1 1 1 }}
| |
|
| |
| Optimal tunings:
| |
| * WE: ~2 = 1156.418{{c}}, ~3/2 = 643.202{{c}}
| |
| * CWE: ~2 = 1200.000{{c}}, ~3/2 = 627.023{{c}}
| |
|
| |
| {{Optimal ET sequence|legend=0| 2 }}
| |
|
| |
| Badness (Sintel): 0.499
| |
|
| |
| === Heavy windmill ===
| |
| Heavy windmill tempers out [[9/7]] and [[15/14]] in the 7-limit.
| |
|
| |
| Subgroup: 2.3.5.7
| |
|
| |
| Comma list: 6/5, 9/7
| |
|
| |
| Mapping: {{mapping| 1 0 1 0 | 0 1 1 2 }}
| |
|
| |
| Optimal tunings:
| |
| * WE: ~2 = 1161.600{{c}}, ~3/2 = 571.169{{c}}
| |
| * CWE: ~2 = 1200.000{{c}}, ~3/2 = 559.563{{c}}
| |
|
| |
| {{Optimal ET sequence|legend=0| 2 }}
| |
|
| |
| Badness (Sintel): 0.676
| |
|
| |
| ==== 11-limit ====
| |
| Subgroup: 2.3.5.7.11
| |
|
| |
| Comma list: 6/5, 9/7, 11/10
| |
|
| |
| Mapping: {{mapping| 1 0 1 0 2 | 0 1 1 2 1 }}
| |
|
| |
| Optimal tunings:
| |
| * WE: ~2 = 1166.584{{c}}, ~3/2 = 568.073{{c}}
| |
| * CWE: ~2 = 1200.000{{c}}, ~3/2 = 558.941{{c}}
| |
|
| |
| {{Optimal ET sequence|legend=0| 2 }}
| |
|
| |
| Badness (Sintel): 0.774
| |
|
| |
| === Light windmill ===
| |
| Light windmill tempers out [[8/7]] and [[21/20]] in the 7-limit.
| |
|
| |
| Subgroup: 2.3.5.7
| |
|
| |
| Comma list: 6/5, 8/7
| |
|
| |
| Mapping: {{mapping| 1 0 1 3 | 0 1 1 0 }}
| |
|
| |
| Optimal tunings:
| |
| * WE: ~2 = 1134.018{{c}}, ~3/2 = 670.285{{c}}
| |
| * CWE: ~2 = 1200.000{{c}}, ~3/2 = 667.893{{c}}
| |
|
| |
| {{Optimal ET sequence|legend=0| 2 }}
| |
|
| |
| Badness (Sintel): 0.629
| |
|
| |
| ==== 11-limit ====
| |
| Subgroup: 2.3.5.7.11
| |
|
| |
| Comma list: 6/5, 8/7, 11/10
| |
|
| |
| Mapping: {{mapping| 1 0 1 3 2 | 0 1 1 0 1 }}
| |
|
| |
| Optimal tunings:
| |
| * WE: ~2 = 1136.109{{c}}, ~3/2 = 672.403{{c}}
| |
| * CWE: ~2 = 1200.000{{c}}, ~3/2 = 668.374{{c}}
| |
|
| |
| {{Optimal ET sequence|legend=0| 2 }}
| |
|
| |
| Badness (Sintel): 0.681
| |
|
| |
| [[Category:Temperament collections]]
| |