Blackwood: Difference between revisions
m Text replacement - "prime-optimized" to "norm-based" |
Added Infobox Regtemp. If the perfect fifth is a whole number of periods and zero generators, it gives an error; however, I found a workaround. Someone should fix the infobox. |
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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) | |||
| Generator = 5/4 | |||
| Mapping = 5; <small><big>0</big></small> 1 0 | |||
| Ploidacot = pentaploid acot | |||
| Pergen = (P8/5, M3<sup>5</sup>) | |||
| Color name = sawa | |||
| Edo join 1 = 5 | Edo join 2 = 10 | |||
| Optimization method = CWE | |||
| Generator tuning = 391.1 | |||
| MOS scales = [[5L 5s]], [[10L 5s]] | |||
| Odd limit 1 = 5 | Mistuning 1 = 18.0 | Complexity 1 = 15 | |||
| Odd limit 2 = 9 | Mistuning 2 = 44.9 | Complexity 2 = 15 | |||
}} | |||
'''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]]. | ||