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== Bohpier ==
== Bohpier ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Bohpier]].''
{{main|Bohpier}}
{{main|Bohpier}}


'''[[Bohpier]]''' is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen-Pierce equal temperament]].
'''[[Bohpier]]''' is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen-Pierce equal temperament]].


=== 5-limit (satheyo) ===
Subgroup: 2.3.5
[[Comma list]]: 1220703125/1162261467
[[Mapping]]: [{{val| 1 0 0 }}, {{val| 0 13 19 }}]
[[POTE generator]]: ~27/25 = 146.476
[[Minimax tuning]]:
* 5-odd-limit: ~27/25 = {{monzo| 0 0 1/19 }}
: Eigenmonzos (unchanged intervals): 2, 5/4
[[Tuning ranges]]:
* 5-odd-limit [[diamond monotone]]: ~27/25 = [144.000, 150.000] (3\25 to 1\8)
* 5-odd-limit [[diamond tradeoff]]: ~27/25 = [146.304, 147.393]
* 5-odd-limit diamond monotone and tradeoff: ~27/25 = [146.304, 147.393]
{{Val list|legend=1| 8, 41, 131, 172, 213c }}
[[Badness]]: 0.860534
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


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* 9-odd-limit: ~27/25 = {{monzo| 0 1/13 }}
* 9-odd-limit: ~27/25 = {{monzo| 0 1/13 }}
: Eigenmonzos (unchanged intervals): 2, 4/3
: Eigenmonzos (unchanged intervals): 2, 4/3
[[Tuning ranges]]:
* 7-odd-limit [[diamond monotone]]: ~27/25 = [145.455, 150.000] (4\33 to 1\8)
* 9-odd-limit diamond monotone: ~27/25 = [145.455, 146.939] (4\33 to 6\49)
* 7-odd-limit [[diamond tradeoff]]: ~27/25 = [145.628, 147.393]
* 9-odd-limit diamond tradeoff: ~27/25 = [145.028, 147.393]
* 7-odd-limit diamond monotone and tradeoff: ~27/25 = [145.628, 147.393]
* 9-odd-limit diamond monotone and tradeoff: ~27/25 = [145.455, 146.939]


{{Val list|legend=1| 41, 131, 172, 213c }}
{{Val list|legend=1| 41, 131, 172, 213c }}
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* 11-odd-limit: ~12/11 = {{monzo| 1/7 1/7 0 0 -1/14 }}
* 11-odd-limit: ~12/11 = {{monzo| 1/7 1/7 0 0 -1/14 }}
: Eigenmonzos (unchanged intervals): 2, 11/9
: Eigenmonzos (unchanged intervals): 2, 11/9
Tuning ranges:
* 11-odd-limit diamond monotone: ~12/11 = [145.455, 146.939] (4\33 to 6\49)
* 11-odd-limit diamond tradeoff: ~12/11 = [145.028, 150.637]
* 11-odd-limit diamond monotone and tradeoff: ~12/11 = [145.455, 146.939]


Optimal GPV sequence: {{Val list| 41, 90e, 131e }}
Optimal GPV sequence: {{Val list| 41, 90e, 131e }}
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* 13- and 15-odd-limit: ~12/11 = {{monzo| 0 0 1/19 }}
* 13- and 15-odd-limit: ~12/11 = {{monzo| 0 0 1/19 }}
: Eigenmonzos (unchanged intervals): 2, 5/4
: Eigenmonzos (unchanged intervals): 2, 5/4
Tuning ranges:
* 13-odd-limit diamond monotone: ~12/11 = [145.455, 146.939] (4\33 to 6\49)
* 15-odd-limit diamond monotone: ~12/11 = [146.341, 146.939] (5\41 to 6\49)
* 13- and 15-odd-limit diamond tradeoff: ~12/11 = [138.573, 150.637]
* 13-odd-limit diamond monotone and tradeoff: ~12/11 = [145.455, 146.939]
* 15-odd-limit diamond monotone and tradeoff: ~12/11 = [146.341, 146.939]


Optimal GPV sequence: {{Val list| 41, 90ef, 131ef, 221bdeff }}
Optimal GPV sequence: {{Val list| 41, 90ef, 131ef, 221bdeff }}
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