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| | {{Interwiki |
| | | de = |
| | | en = 5L 5s |
| | | es = Escala Blackwood |
| | | ja = |
| | }} |
| {{Infobox MOS | | {{Infobox MOS |
| | Name = blackwood | | | Name = pentawood |
| | Periods = 5 | | | Periods = 5 |
| | nLargeSteps = 5 | | | nLargeSteps = 5 |
| | nSmallSteps = 5 | | | nSmallSteps = 5 |
| | Equalized = 1 | | | Equalized = 1 |
| | Paucitonic = 0 | | | Collapsed = 0 |
| | Pattern = LsLsLsLsLs | | | Pattern = LsLsLsLsLs |
| }} | | }} |
| | {{MOS intro}} |
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| '''5L 5s''' refers to the structure of octave-equivalent [[MOS]] scales with period 1\5 (one degree of [[5edo]] = 240¢) and generators ranging from 1\10 (one degree of [[10edo]] = 120¢) to 1\5 (240¢). In the case of 10edo, L and s are the same size; in the case of 5edo, s becomes so small it disappears (and all that remains are the five equal L's). There is only one significant harmonic entropy minimum with this MOS pattern: [[Archytas_clan|blackwood]], in which intervals of the prime numbers 3 and 7 are all represented using steps of [[5edo|5edo]], and the generator gets you to intervals of 5 like 6/5, 5/4, or 7/5. Hence from a regular temperament perspective, this MOS pattern is essentially synonymous with blackwood.
| | There is only one significant [[harmonic entropy]] minimum with this mos pattern: [[blackwood]], in which intervals of the prime numbers [[3/1|3]] and [[7/1|7]] are all represented using steps of [[5edo]], and the generator reaches intervals of [[5/1|5]], such as [[6/5]], [[5/4]], and [[7/5]]. |
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| The true MOS, LsLsLsLsLs, is always proper because there is only one small step per period, but because there are 5 periods in an octave, there are a wealth of near-MOSes in which multiples of the period (that is, intervals of an even number of steps) are the only generic intervals that come in more than two different flavors. Specifically, there are 6 others: LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss. In the blackwood temperament, these are right on the boundary of being [[Rothenberg_propriety|proper]] (because 1\15 is in the middle of the range of good blackwood generators).
| | In addition to the true mos form (LsLsLsLsLs and sLsLsLsLsL), there are 6 near-mos forms, which are also single-alteration [[modmos]] scales – LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss – in which the period and its multiples (intervals of 2, 4, 6, and 8 mossteps) have more than two varieties. These forms are proper if the bright generator is less than 160{{c}}. |
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| {| class="wikitable" | | == Scale properties == |
| |-
| | {{TAMNAMS use}} |
| ! colspan="5" | Generator
| | |
| ! | Cents
| | === Intervals === |
| ! | Comments
| | {{MOS intervals}} |
| |-
| | |
| | | 0\5
| | === Modes === |
| | |
| | {{MOS mode degrees}} |
| | |
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| | |
| | === Scale tree === |
| | | | | {{MOS tuning spectrum |
| | | 0
| | | 6/5 = [[Qintosec]] ↑ |
| | style="text-align:center;" |
| | | 7/5 = [[Warlock]] |
| |- | | | 13/8 = Unnamed golden tuning (148.328{{c}}) |
| | |
| | | 7/4 = [[Quinkee]] |
| | |
| | | 2/1 = [[Blackwood]] (optimal around here) |
| | |
| | | 9/4 = [[Trisedodge]] |
| | | | | | 13/5 = Unnamed golden tuning (173.666{{c}}) |
| | | 1\30
| | | 6/1 = [[Cloudtone]] ↓ |
| | | 40
| | }} |
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| |-
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| | | 1\25
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| | | 48
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| |-
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| | | 240/(1+pi)
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| | | | |
| |- | |
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| | | 1\20
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| | | | |
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| | | 60
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| | style="text-align:center;" |
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| |-
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| | | 240/(1+e)
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| |-
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| | | 2\35
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| | | 68.57
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| |-
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| | | 3\50
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| | | 72
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| |-
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| | | 1\15
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| | | 80
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| | style="text-align:center;" | Blackwood is around here
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| Optimum rank range (L/s=2/1) for MOS
| | [[Category:Pentawood| ]] <!-- main article --> |
| |-
| | [[Category:10-tone scales]] |
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| | | 240/(1+sq<span style="line-height: 1.5;">rt(3)</span>)
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| |-
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| | | 3\40
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| | | 90
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| | style="text-align:center;" |
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| |-
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| | | 5\65
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| | | 92.31
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| | style="text-align:center;" | Golden blackwood
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| |-
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| | | 240/(1+pi/2)
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| |-
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| | | 2\25
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| | | 96
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| | style="text-align:center;" |
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| |3\35
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| |102.86
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| |-
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| |4\45
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| |103.33
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| |-
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| | | 1\10
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| | | 120
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| | style="text-align:center;" |
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| |}
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