Miaplacidus: Difference between revisions
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'''Miaplacidus''' is a [[tritave]]-repeating [[rank-2 temperament]] that tempers out the comma 5859375/5764801 in the 3.5.7 subgroup, the amount by which 4 [[15/7]]'s exceed [[9/7]]. It thus tunes the chord 7:9:15 accurately. Having a generator of ~[[15/7]], it possesses [[MOS scale]]s of the families 3L 4s<3/1>, 3L 7s<3/1>, 3L 10s<3/1>, and 13L 3s<3/1>. Good tunings for this temperament are [[13edt]], [[16edt]], and [[29edt]]. | '''Miaplacidus''' is a [[tritave]]-repeating [[rank-2 temperament]] that tempers out the comma 5859375/5764801 in the 3.5.7 subgroup, the amount by which 4 [[15/7]]'s exceed [[9/7]]. It thus tunes the chord 7:9:15 accurately. Having a generator of ~[[15/7]], it possesses [[MOS scale]]s of the families 3L 4s<3/1>, 3L 7s<3/1>, 3L 10s<3/1>, and 13L 3s<3/1>. Good tunings for this temperament are [[13edt]], [[16edt]], and [[29edt]]. | ||
== Interval chain (POTE tuning) == | == Interval chain (POTE tuning) == | ||
{|class="wikitable" | {|class="wikitable" | ||
|- | |- | ||
!Generators up | ! Generators up | ||
!Cents | ! Cents | ||
!Generators down | ! Generators down | ||
!Cents | ! Cents | ||
|- | |- | ||
|0 | | 0 | ||
|0.00 | | 0.00 | ||
|0 | | 0 | ||
|0.00 | | 0.00 | ||
|- | |- | ||
|1 | | 1 | ||
|1316.10 | | 1316.10 | ||
|1 | | 1 | ||
|585.86 | | 585.86 | ||
|- | |- | ||
|2 | | 2 | ||
|730.24 | | 730.24 | ||
|2 | | 2 | ||
|1171.72 | | 1171.72 | ||
|- | |- | ||
|3 | | 3 | ||
|144.38 | | 144.38 | ||
|3 | | 3 | ||
|1757.58 | | 1757.58 | ||
|- | |- | ||
|4 | | 4 | ||
|1460.48 | | 1460.48 | ||
|4 | | 4 | ||
|441.48 | | 441.48 | ||
|- | |- | ||
|5 | | 5 | ||
|874.62 | | 874.62 | ||
|5 | | 5 | ||
|1027.34 | | 1027.34 | ||
|} | |} | ||
[[Category: | [[Category:Miaplacidus| ]] <-- main article --> | ||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||
[[Category:Non-octave temperaments]] | |||
{{ | {{Stub}} | ||
Latest revision as of 14:42, 28 May 2026
Miaplacidus is a tritave-repeating rank-2 temperament that tempers out the comma 5859375/5764801 in the 3.5.7 subgroup, the amount by which 4 15/7's exceed 9/7. It thus tunes the chord 7:9:15 accurately. Having a generator of ~15/7, it possesses MOS scales of the families 3L 4s<3/1>, 3L 7s<3/1>, 3L 10s<3/1>, and 13L 3s<3/1>. Good tunings for this temperament are 13edt, 16edt, and 29edt.
Interval chain (POTE tuning)
| Generators up | Cents | Generators down | Cents |
|---|---|---|---|
| 0 | 0.00 | 0 | 0.00 |
| 1 | 1316.10 | 1 | 585.86 |
| 2 | 730.24 | 2 | 1171.72 |
| 3 | 144.38 | 3 | 1757.58 |
| 4 | 1460.48 | 4 | 441.48 |
| 5 | 874.62 | 5 | 1027.34 |
<-- main article -->
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