Cluster MOS: Difference between revisions
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Rather than simply denoting one of a list of rank-2 temperaments, the phrase "cluster scale" is also associated with a compositional philosophy. It is often said that temperaments such as slendric are melodically "bad" or have "bad MOS structure", because some MOS (in this case slendric[5]) is "too equal" and the next higher MOSes are "too unequal". But this can be thought of as a feature rather than a bug. Rather than forcing them into the MOS framework, one can think of cluster scales as having two hierarchical levels of melodic structure: the "step" (a step of the quasi-equal MOS), and the "chroma", and a chroma is so much smaller than a step that the steps seldom go out of order no matter how many chromas are involved. | Rather than simply denoting one of a list of rank-2 temperaments, the phrase "cluster scale" is also associated with a compositional philosophy. It is often said that temperaments such as slendric are melodically "bad" or have "bad MOS structure", because some MOS (in this case slendric[5]) is "too equal" and the next higher MOSes are "too unequal". But this can be thought of as a feature rather than a bug. Rather than forcing them into the MOS framework, one can think of cluster scales as having two hierarchical levels of melodic structure: the "step" (a step of the quasi-equal MOS), and the "chroma", and a chroma is so much smaller than a step that the steps seldom go out of order no matter how many chromas are involved. | ||
=Examples= | == Examples of cluster temperaments === | ||
==Slendric== | === Slendric === | ||
Main article: [[Slendric|Slendric]] | Main article: [[Slendric|Slendric]] | ||
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Slendric has two quite different extensions that are both also cluster scales: | Slendric has two quite different extensions that are both also cluster scales: | ||
===Mothra=== | ====Mothra==== | ||
Main article: [[Mothra|Mothra]] | Main article: [[Mothra|Mothra]] | ||
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*[http://sevish.com/scaleworkshop/index.htm?name=31edo%20mothra&data=38.70967741935484%0A77.41935483870968%0A116.12903225806451%0A154.83870967741936%0A193.5483870967742%0A232.25806451612902%0A270.9677419354839%0A309.6774193548387%0A348.38709677419354%0A387.0967741935484%0A425.80645161290323%0A464.51612903225805%0A503.2258064516129%0A541.9354838709678%0A580.6451612903226%0A619.3548387096774%0A658.0645161290323%0A696.7741935483871%0A735.483870967742%0A774.1935483870968%0A812.9032258064516%0A851.6129032258065%0A890.3225806451613%0A929.0322580645161%0A967.741935483871%0A1006.4516129032259%0A1045.1612903225807%0A1083.8709677419356%0A1122.5806451612902%0A1161.2903225806451%0A1200.&vert=-5&horiz=6&midi=16 Play Mothra in 31edo] | *[http://sevish.com/scaleworkshop/index.htm?name=31edo%20mothra&data=38.70967741935484%0A77.41935483870968%0A116.12903225806451%0A154.83870967741936%0A193.5483870967742%0A232.25806451612902%0A270.9677419354839%0A309.6774193548387%0A348.38709677419354%0A387.0967741935484%0A425.80645161290323%0A464.51612903225805%0A503.2258064516129%0A541.9354838709678%0A580.6451612903226%0A619.3548387096774%0A658.0645161290323%0A696.7741935483871%0A735.483870967742%0A774.1935483870968%0A812.9032258064516%0A851.6129032258065%0A890.3225806451613%0A929.0322580645161%0A967.741935483871%0A1006.4516129032259%0A1045.1612903225807%0A1083.8709677419356%0A1122.5806451612902%0A1161.2903225806451%0A1200.&vert=-5&horiz=6&midi=16 Play Mothra in 31edo] | ||
===Rodan=== | ====Rodan==== | ||
Main article: [[Rodan|Rodan]] | Main article: [[Rodan|Rodan]] | ||
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|} | |} | ||
==Modus (of the tetracot family)== | === Modus (of the tetracot family) === | ||
Main article: [[Modus|Modus]] | Main article: [[Modus|Modus]] | ||
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* [http://sevish.com/scaleworkshop/index.htm?name=34edo%20modus&data=35.294117647058826%0A70.58823529411765%0A105.88235294117648%0A141.1764705882353%0A176.47058823529414%0A211.76470588235296%0A247.05882352941177%0A282.3529411764706%0A317.64705882352945%0A352.9411764705883%0A388.2352941176471%0A423.5294117647059%0A458.82352941176475%0A494.11764705882354%0A529.4117647058824%0A564.7058823529412%0A600.%0A635.2941176470589%0A670.5882352941177%0A705.8823529411766%0A741.1764705882354%0A776.4705882352941%0A811.764705882353%0A847.0588235294118%0A882.3529411764706%0A917.6470588235295%0A952.9411764705883%0A988.2352941176471%0A1023.529411764706%0A1058.8235294117649%0A1094.1176470588236%0A1129.4117647058824%0A1164.7058823529412%0A1200.&vert=-4&horiz=5 Play Modus in 34edo] | * [http://sevish.com/scaleworkshop/index.htm?name=34edo%20modus&data=35.294117647058826%0A70.58823529411765%0A105.88235294117648%0A141.1764705882353%0A176.47058823529414%0A211.76470588235296%0A247.05882352941177%0A282.3529411764706%0A317.64705882352945%0A352.9411764705883%0A388.2352941176471%0A423.5294117647059%0A458.82352941176475%0A494.11764705882354%0A529.4117647058824%0A564.7058823529412%0A600.%0A635.2941176470589%0A670.5882352941177%0A705.8823529411766%0A741.1764705882354%0A776.4705882352941%0A811.764705882353%0A847.0588235294118%0A882.3529411764706%0A917.6470588235295%0A952.9411764705883%0A988.2352941176471%0A1023.529411764706%0A1058.8235294117649%0A1094.1176470588236%0A1129.4117647058824%0A1164.7058823529412%0A1200.&vert=-4&horiz=5 Play Modus in 34edo] | ||
==Miracle== | === Miracle === | ||
Main article: [[Miracle|Miracle]] | Main article: [[Miracle|Miracle]] | ||
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|} | |} | ||
==Porcupine(fish)== | === Porcupine(fish) === | ||
Main article: [[Porcupine|Porcupine]] | Main article: [[Porcupine|Porcupine]] | ||
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|} | |} | ||
==17-limit valentino== | === 17-limit valentino === | ||
Chroma: 49/48~55/54~56/55~64/63~65/64~85/84~119/117~128/125~143/140~153/150 | Chroma: 49/48~55/54~56/55~64/63~65/64~85/84~119/117~128/125~143/140~153/150 | ||
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|} | |} | ||
==2.3.5.11.13 hitchcock== | === 2.3.5.11.13 hitchcock === | ||
Unlike amity itself, this 2.3.5.11.13 amity extension is a cluster temperament because the intervals between 6/5 and 5/4 are mapped to 11/9 and 16/13. | Unlike amity itself, this 2.3.5.11.13 amity extension is a cluster temperament because the intervals between 6/5 and 5/4 are mapped to 11/9 and 16/13. | ||