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| {{Infobox MOS | | {{Infobox MOS |
| | Name = blackwood, 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 |
| }} | | }} |
| | {{MOS intro}} |
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| 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. | | There is only one significant [[harmonic entropy]] minimum with this MOS pattern: [[limmic temperaments#5-limit_.28blackwood.29|blackwood]], in which intervals of the prime numbers 3 and 7 are all represented using steps of [[5edo|5edo]], and the generator reaches intervals of 5 like 6/5, 5/4, or 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 – 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¢. |
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| {| class="wikitable"
| | == Intervals == |
| |-
| | {{MOS intervals}} |
| ! colspan="5" | Generator
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| ! | Cents
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| ! | Comments
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| |-
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| | | 0\5
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| | | 0
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| | style="text-align:center;" |
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| |-
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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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| |-
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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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| |-
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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
| | ==Modes== |
| |-
| | {{MOS mode degrees}} |
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| | == Scale tree == |
| | |
| | {{MOS tuning spectrum |
| | |
| | | 6/5 = Qintosec ↑ |
| | |
| | | 7/5 = Warlock |
| | | 240/(1+sq<span style="line-height: 1.5;">rt(3)</span>) | | | 13/8 = Unnamed golden tuning |
| | | | | | 7/4 = Quinkee |
| |- | | | 2/1 = Blacksmith is optimal around here |
| | | | | | 9/4 = Trisedodge |
| | | | | | 13/5 = Unnamed golden tuning |
| | | | | | 6/1 = Cloudtone ↓ |
| | | 3\40
| | }} |
| | |
| | |
| | | 90
| | [[Category:Pentawood| ]] |
| | style="text-align:center;" |
| | [[Category:10-tone scales]] |
| |- | | <!-- main article --> |
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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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| |-
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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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