Blackwood: Difference between revisions
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{{interwiki | |||
| de = Blackwood-Limmisch | |||
| en = Blackwood | |||
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: ''This article is about the regular temperament. For the musician, see [[Easley Blackwood Jr.]] For the scale structure sometimes associated with it, see [[5L 5s]].'' | : ''This article is about the regular temperament. For the musician, see [[Easley Blackwood Jr.]] For the scale structure sometimes associated with it, see [[5L 5s]].'' | ||
{{Infobox regtemp | |||
| Title = Blackwood | |||
| Subgroups = 2.3.5, 2.3.5.7 | |||
| Comma basis = [[256/243]] (2.3.5); <br>[[28/27]], [[49/48]] (2.3.5.7) | |||
| Edo join 1 = 5 | Edo join 2 = 10 | |||
| Mapping = 5; 0 1 0 | |||
| Generators = 5/4 | |||
| Generators tuning = 391.1 | |||
| Optimization method = CWE | |||
| Pergen = (P8/5, ^1) | |||
| Color name = Sawati | |||
| MOS scales = [[5L 5s]], [[10L 5s]] | |||
| Odd limit 1 = 5 | Mistuning 1 = 18.0 | Complexity 1 = 10 | |||
| Odd limit 2 = 9 | Mistuning 2 = 44.9 | Complexity 2 = 10 | |||
}} | |||
'''Blackwood''' is a [[regular temperament|temperament]] that takes [[5edo]]'s [[circle of fifths]] for the [[3-limit]], but adds multiple copies to improve the tuning of the [[5-limit]]. In the fundamental sense, it is the 5-limit temperament that [[tempering out|tempers out]] the [[Pythagorean limma]], and it extends to the [[7-limit]] (sometimes known as ''blacksmith'') by recognizing that 4\5 is a good [[7/4|harmonic seventh]], thus tempering out [[28/27]], [[49/48]], and [[64/63]], making it a member of [[trienstonic clan]], [[semaphoresmic clan]], and [[archytas clan]]. | '''Blackwood''' is a [[regular temperament|temperament]] that takes [[5edo]]'s [[circle of fifths]] for the [[3-limit]], but adds multiple copies to improve the tuning of the [[5-limit]]. In the fundamental sense, it is the 5-limit temperament that [[tempering out|tempers out]] the [[Pythagorean limma]], and it extends to the [[7-limit]] (sometimes known as ''blacksmith'') by recognizing that 4\5 is a good [[7/4|harmonic seventh]], thus tempering out [[28/27]], [[49/48]], and [[64/63]], making it a member of [[trienstonic clan]], [[semaphoresmic clan]], and [[archytas clan]]. | ||
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See [[Limmic temperaments #Blackwood]] for technical data. | See [[Limmic temperaments #Blackwood]] for technical data. | ||
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{{Clear}} | |||
== Interval chain == | == Interval chain == | ||
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== Tunings == | == Tunings == | ||
{| class="wikitable mw-collapsible mw-collapsed" | {| class="wikitable mw-collapsible mw-collapsed" | ||
|+ style="font-size: 105%; white-space: nowrap;" | 5-limit | |+ style="font-size: 105%; white-space: nowrap;" | 5-limit norm-based tunings | ||
|- | |- | ||
! rowspan="2" | | ! rowspan="2" | | ||
| Line 92: | Line 112: | ||
{| class="wikitable mw-collapsible mw-collapsed" | {| class="wikitable mw-collapsible mw-collapsed" | ||
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit | |+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings | ||
|- | |- | ||
! rowspan="2" | | ! rowspan="2" | | ||
| Line 139: | Line 159: | ||
| 368.269 | | 368.269 | ||
| -1/5-limma | | -1/5-limma | ||
|- | |||
|11\35 | |||
| | |||
| 377.143 | |||
|35b val | |||
|- | |- | ||
| | | | ||
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| 395.533 | | 395.533 | ||
| | | | ||
|- | |||
| | |||
| | |||
|397.163 | |||
|DR-optimized 4:5:6 tuning | |||
|- | |- | ||
| 5\15 | | 5\15 | ||