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| == Uncle == | | == Uncle == |
| : ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum#Uncle_(5-limit)|Syntonic–diatonic equivalence continuum]].'' | | : ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Uncle (5-limit)]].'' |
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| Uncle tempers out 256/245, mapping the interval class of 5 to -6 generator steps, as a major 2-step in oneirotonic or a diminished fifth in diatonic. | | Uncle tempers out 256/245, mapping the interval class of 5 to -6 generator steps, as a major 2-step in oneirotonic or a diminished fifth in diatonic. |
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| == Octokaidecal == | | == Octokaidecal == |
| The 5-limit [[restriction]] of octokaidecal is supersharp, which tempers out [[800/729]], the difference between the [[27/20]] wolf fourth and the [[40/27]] wolf fifth, splitting the octave into two 27/20~40/27 semioctaves. It generally requires a very sharp fifth, even sharper than 3\5, as a generator. This means that five steps from the [[generator sequence #JI scales obtained from guided generator sequences|Zarlino generator sequence]] starting with 6/5 are tempered to one and a half octaves. The only reasonable 7-limit extension adds 28/27 and 50/49 to the comma list, taking advantage of the existing semioctave.
| | : ''For the 5-limit versions, see [[Miscellaneous 5-limit temperaments #Supersharp]].'' |
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| === 5-limit (supersharp) ===
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| [[Subgroup]]: 2.3.5
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| [[Comma list]]: 800/729
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| {{Mapping|legend=1| 2 0 -5 | 0 1 3 }}
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| : mapping generators: ~27/20, ~3
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| [[Optimal tuning]]s:
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| * [[WE]]: ~27/20 = 596.986{{c}}, ~3/2 = 725.434{{c}} (~10/9 = 128.448{{c}})
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| : [[error map]]: {{val| -6.029 +17.450 -13.027 }}
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| * [[CWE]]: ~27/20 = 600.000{{c}}, ~3/2 = 726.548{{c}} (~10/9 = 126.548{{c}})
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| : error map: {{val| 0.000 +24.593 -6.670 }}
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| {{Optimal ET sequence|legend=1| 8, 10, 18, 28b }}
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| [[Badness]] (Sintel): 2.88
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| === 7-limit ===
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| [[Subgroup]]: 2.3.5.7 | | [[Subgroup]]: 2.3.5.7 |
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