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| {{MOS intro}} | | {{MOS intro}} |
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| 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. | | 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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| 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¢. | | 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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| | == Intervals == |
| | {{MOS intervals}} |
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| ==Modes== | | ==Modes== |
| {{MOS mode degrees}} | | {{MOS mode degrees}} |
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| ==Scale tree== | | == Scale tree == |
| {| class="wikitable center-all" | | {{MOS tuning spectrum |
| ! colspan="6" rowspan="2" |Generator
| | | 6/5 = Qintosec ↑ |
| ! colspan="2" |Cents
| | | 7/5 = Warlock |
| ! rowspan="2" | L
| | | 13/8 = Unnamed golden tuning |
| ! rowspan="2" | s
| | | 7/4 = Quinkee |
| ! rowspan="2" |L/s
| | | 2/1 = Blacksmith is optimal around here |
| ! rowspan="2" |Comments
| | | 9/4 = Trisedodge |
| |-
| | | 13/5 = Unnamed golden tuning |
| !Chroma-positive
| | | 6/1 = Cloudtone ↓ |
| !Chroma-negative
| | }} |
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| |1\10|| || || || || ||120.000||120.000||1||1||1.000||
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| |-
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| | || || || || ||6\55||130.909||109.091||6||5||1.200||Qintosec↑
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| |-
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| | || || || ||5\45|| ||133.333||106.667||5||4||1.250||
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| |-
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| | || || || || ||9\80||135.000||105.000||9||7||1.286||
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| |-
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| | || || ||4\35|| || ||137.143||102.857||4||3||1.333||
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| |-
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| | || || || || ||11\95||138.947||101.053||11||8||1.375||
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| |-
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| | || || || ||7\60|| ||140.000||100.000||7||5||1.400||Warlock
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| |- | |
| | || || || || ||10\85||141.176||98.824||10||7||1.428||
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| |-
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| | || ||3\25|| || || ||144.000||96.000||3||2||1.500|| L/s = 3/2
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| |-
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| | || || || || ||11\90||146.667||93.333||11||7||1.571||
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| |-
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| | || || || ||8\65|| ||147.692||92.308||8||5||1.600||
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| |-
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| | || || || || ||13\105||148.571||91.429||13||8||1.625||Unnamed golden tuning
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| |-
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| | || || ||5\40|| || ||150.000||90.000||5||3||1.667||
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| |-
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| | || || || || ||12\95||151.579||88.421||12||7||1.714||
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| | || || || ||7\55|| ||152.727||87.273||7||4||1.750||Quinkee
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| |-
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| | || || || || ||9\70||154.286||85.714||9||5||1.800||
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| | ||2\15|| || || || ||160.000||80.000||2||1||2.000||Basic pentawood<br>Blacksmith is optimal around here
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| |-
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| | || || || || ||9\65||166.154||73.846||9||4||2.250||Trisedodge
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| |-
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| | || || || ||7\50|| ||168.000||72.000||7||3||2.333||
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| |-
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| | || || || || ||12\85||169.412||70.588||12||5||2.400||
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| |-
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| | || || ||5\35|| || ||171.429||68.571||5||2||2.500||
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| |-
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| | || || || || ||13\90||173.333||66.667||13||5||2.600||Unnamed golden tuning
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| |- | |
| | || || || ||8\55|| ||174.545||65.455||8||3||2.667||
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| |-
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| | || || || || ||11\75||176.000||64.000||11||4||2.750||
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| |-
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| | || ||3\20|| || || ||180.000||60.000||3||1||3.000|| L/s = 3/1
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| |-
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| | || || || || ||10\65||184.615||55.385||10||3||3.333||
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| |-
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| | || || || ||7\45|| ||186.667||53.333||7||2||3.500||
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| |-
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| | || || || || ||11\70||188.571||51.429||11||3||3.667||
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| |-
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| | || || ||4\25|| || ||192.000||48.000||4||1||4.000||
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| |-
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| | || || || || ||9\55||196.364||43.636||9||2||4.500||
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| |-
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| | || || || ||5\30|| ||200.000||40.000||5||1||5.000||
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| |-
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| | || || || || ||6\35||205.714||34.286||6||1||6.000||Cloudtone↓
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| |-
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| | 1\5|| || || || || ||240.000||0.000||1||0|| → inf||
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| |}
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| [[Category:Pentawood| ]] | | [[Category:Pentawood| ]] |
| [[Category:10-tone scales]] | | [[Category:10-tone scales]] |
| <!-- main article --> | | <!-- main article --> |