Blackwood: Difference between revisions
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m Recategorize. Like catler, this is best considered blackwood family only |
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: ''This article is about the regular temperament. For the musician, see [[Easley Blackwood Jr.]] | {{Interwiki | ||
| en = Blackwood | |||
'''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]] 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]]. | | de = Blackwood-Limmisch | ||
}} | |||
: ''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]]. | |||
The main interest in this temperament is in its [[mos scale]]s, featuring [[5L 5s|pentawood (5L 5s)]]. 15edo provides an excellent tuning for this temperament as well as for pentawood. | The main interest in this temperament is in its [[mos scale]]s, featuring [[5L 5s|pentawood (5L 5s)]]. 15edo provides an excellent tuning for this temperament as well as for pentawood. | ||
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Blackwood was named in honor of [[Easley Blackwood Jr.]] | Blackwood was named in honor of [[Easley Blackwood Jr.]] | ||
See [[ | See [[Blackwood family #Blackwood]] for technical data. | ||
__TOC__ | |||
{{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" | | ||
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{| 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" | | ||
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| POBE: ~5/4 = 395.3830{{c}} | | POBE: ~5/4 = 395.3830{{c}} | ||
|} | |} | ||
=== Tuning spectrum === | |||
{| class="wikitable center-all left-4" | |||
|- | |||
! Edo<br>generator | |||
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]* | |||
! Generator (¢) | |||
! Comments | |||
|- | |||
| | |||
| 15/14 | |||
| 359.443 | |||
| | |||
|- | |||
| 3\10 | |||
| | |||
| 360.000 | |||
| Lower bound of 7- and 9-odd-limit diamond monotone | |||
|- | |||
| | |||
| 15/8 | |||
| 368.269 | |||
| -1/5-limma | |||
|- | |||
|11\35 | |||
| | |||
| 377.143 | |||
|35b val | |||
|- | |||
| | |||
| 7/5 | |||
| 377.488 | |||
| | |||
|- | |||
| 8\25 | |||
| | |||
| 384.000 | |||
| | |||
|- | |||
| | |||
| 5/4 | |||
| 386.314 | |||
| Untempered, 5- and 7-limit CTE, etc. | |||
|- | |||
| | |||
| 25/24 | |||
| 395.336 | |||
| 1/10-limma | |||
|- | |||
| | |||
| 21/20 | |||
| 395.533 | |||
| | |||
|- | |||
| | |||
| | |||
|397.163 | |||
|DR-optimized 4:5:6 tuning | |||
|- | |||
| 5\15 | |||
| | |||
| 400.000 | |||
| | |||
|- | |||
| | |||
| 5/3 | |||
| 404.359 | |||
| 1/5-limma | |||
|- | |||
| 7\20 | |||
| | |||
| 420.000 | |||
| 20c val | |||
|- | |||
| | |||
| 9/5 | |||
| 422.404 | |||
| 2/5-limma | |||
|- | |||
| 2\5 | |||
| | |||
| 480.000 | |||
| Upper bound of 7- and 9-odd-limit diamond monotone | |||
|} | |||
<nowiki/>* Besides the octave | |||
== Music == | |||
; [[E8 Heterotic]] | |||
* [https://www.youtube.com/watch?v=67hj_bs_9e4 ''Cyberfunk''] (2020) – in Blackwood[10], 15edo tuning | |||
; [[Sevish]] | |||
* From ''[[Harmony Hacker]]'' (2017) | |||
** "[[Freathy]]" – in Blackwood[10], TOP tuning | |||
** "[[So Thankful]]" – in Blackwood[10], 15edo tuning | |||
== See also == | == See also == | ||
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[[Category:Blackwood| ]] <!-- main article --> | [[Category:Blackwood| ]] <!-- main article --> | ||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||
[[Category: | [[Category:Exotemperaments]] | ||
[[Category: | [[Category:Blackwood family]] | ||