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| Line 110: |
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| | 11/4 = 2.75 || 11/7 = 1.{{overline|571428}} || [[Magus]] || {{monzo| 24 1 -11 }} | | | 11/4 = 2.75 || 11/7 = 1.{{overline|571428}} || [[Magus]] || {{monzo| 24 1 -11 }} |
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| Because 3et is a record equal temperament in the 2.5 subgroup, there is another way to conceptualize this continuum. The characteristic 2.5-subgroup comma is 128/125, and the interval with a single factor of 3 is 25/24. As such, Godtone has conceptualized this continuum as ''augmented–dicot equivalence continuum''. See [[{{PAGENAME}}/Godtone's approach]].
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| Others prefer conceptualizing this continuum in terms of {{nowrap| ''k'' {{=}} {{sfrac|1|''n'' − 2}} }} such that temperaments satisfy {{nowrap|(25/24)<sup>''k''</sup> {{=}} 16/15}}. This gives rise to the name ''chromatic–diatonic equivalence continuum'', where both ''chromatic'' and ''diatonic'' refer to the classical versions of semitones. The just value of ''k'' is approximately 1.58097…
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| {| class="wikitable center-1"
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| |+ style="font-size: 105%;" | Temperaments with integer ''k''
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| |-
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| ! rowspan="2" | ''k''
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| ! rowspan="2" | Temperament
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| ! colspan="2" | Comma
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| |-
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| ! Ratio
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| ! Monzo
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| |-
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| | -1
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| | [[Very low accuracy temperaments #Antonian|Antonian]]
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| | [[10/9]]
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| | {{Monzo| 1 -2 1 }}
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| |-
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| | 0
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| | [[Father]]
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| | [[16/15]]
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| | {{Monzo| 4 -1 -1 }}
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| |-
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| | 1
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| | [[Augmented (temperament)|Augmented]]
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| | [[128/125]]
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| | {{Monzo| 7 0 -3 }}
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| |-
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| | 2
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| | [[Magic]]
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| | [[3125/3072]]
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| | {{Monzo| 10 1 -5 }}
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| |-
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| | 3
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| | [[Wesley]]
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| | 78125/73728
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| | {{monzo| 13 2 -7 }}
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| |-
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| | 4
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| | 3 & 33c
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| | 1953125/1769472
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| | {{Monzo| 16 3 -9 }}
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| |-
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| | …
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| | …
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| | …
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| | …
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| |-
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| | ∞
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| | [[Dicot]]
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| | [[25/24]]
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| | {{Monzo| -3 -1 2 }}
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| |}
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| == 3 & 33c ==
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| This low-accuracy high-complexity temperament corresponds to {{nowrap| ''n'' {{=}} 9/4 }} and {{nowrap| ''m'' {{=}} 9/5 }}.
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| [[Subgroup]]: 2.3.5
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| [[Comma list]]: 1953125/1769472
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| {{Mapping|legend=1| 3 2 6 | 0 3 1 }}
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| : mapping generators: ~125/96, ~5/4
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| [[Optimal tuning]]s:
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| * [[WE]]: ~125/96 = 401.2633{{c}}, ~5/4 = 367.0585{{c}} (~25/24 = 34.2047{{c}})
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| : [[error map]]: {{val| +3.790 +1.747 -11.676 }}
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| * [[CWE]]: ~125/96 = 400.0000{{c}}, ~5/4 = 366.8103{{c}} (~25/24 = 33.1897{{c}})
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| : error map: {{val| 0.000 -1.524 -19.503 }}
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| {{Optimal ET sequence|legend=1| 3, …, 33c, 36c, 69cc }}
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| [[Badness]] (Sintel): 16.0
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| == Mutt (5-limit) == | | == Mutt (5-limit) == |