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| | {{Interwiki |
| | | de = |
| | | en = 5L 5s |
| | | es = Escala Blackwood |
| | | ja = |
| | }} |
| {{Infobox MOS | | {{Infobox MOS |
| | Name = pentasymmetric | | | 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 |
| }} | | }} |
| == Name ==
| | {{MOS intro}} |
| The [[TAMNAMS]] temperament-agnostic name is '''pentasymmetric'''. The name "blackwood" is also used, although this is a misnomer as [[blackwood]] is an abstract temperament, not a concrete scale (a more proper name is "blackwood[10]").
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| == As a temperament ==
| | 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]]. |
| 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. | | |
| | 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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| | == Scale properties == |
| | {{TAMNAMS use}} |
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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).
| | === Intervals === |
| | {{MOS intervals}} |
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| == Scale tree == | | === Modes === |
| {| class="wikitable" | | {{MOS mode degrees}} |
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| ! colspan="5" | Generator
| | === Scale tree === |
| ! | Cents
| | {{MOS tuning spectrum |
| ! | Comments
| | | 6/5 = [[Qintosec]] ↑ |
| |-
| | | 7/5 = [[Warlock]] |
| | | 0\5
| | | 13/8 = Unnamed golden tuning (148.328{{c}}) |
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| | | 7/4 = [[Quinkee]] |
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| | | 2/1 = [[Blackwood]] (optimal around here) |
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| | | 9/4 = [[Trisedodge]] |
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| | | 13/5 = Unnamed golden tuning (173.666{{c}}) |
| | | 0
| | | 6/1 = [[Cloudtone]] ↓ |
| | style="text-align:center;" |
| | }} |
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| | | 1\30
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| | | 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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| | | 1\20
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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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| | | 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 --> |
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| | [[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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| | | 5\65
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| | | 92.31
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| | style="text-align:center;" | Golden blackwood
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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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