Some Observations on Pm,n Relations within Set Classes
Identifieur interne : 000E46 ( Istex/Corpus ); précédent : 000E45; suivant : 000E47Some Observations on Pm,n Relations within Set Classes
Auteurs : Michael RussSource :
- Music Analysis [ 0262-5245 ] ; 2007-03.
English descriptors
- Teeft :
- Adjacent integers, Atonal, Blackwell, Blackwell publishing, Boris godunov, Callender, Cardinality, Chorale, Chord, Class comments, Cohn, Cohn functions, Contrary motion, David lewin, Diatonic, Different ways, Diminution, Dominant sevenths, Douth2, Douthett, Dyad, Easy piano pieces, Form relations, Generalized chord spaces, Harmonic, Hexachord, Hexachords, Hungarian peasant songs, Interval, Interval class, Interval string, Interval strings, Interval vectors, Invariant subset, Invariant subsets, Invariant tetrachord, Invariant tetrachords, Invariant trichord, Inversion, Italic, Journal compilation, Large number, Larger cardinality, Lewin, Major scale, Maximally, Michael russ, Minor triad, More relations, Music analysis, Music theory, Musorgsky, Mystic chord, Octatonic, Parsimonious, Parsimony, Pentachordal, Pentachords, Perturbation, Pitch class, Pitch classes, Power towers, Prime form, Prime forms, Progression, Relation results, Retrograde rotation, Richard cohn, Right hand, Rus, Same class, Same time, Scriabin, Semitonal, Semitone, Seventh chords, Similar motion, Single relation, Single semitonal perturbation, Small number, Subset, Such relations, Tetrachord, Tetrachordal, Tetrachords, Tonality, Transposition, Triad, Trichord, Trichords, Tymoczko, Voices move, Whole step, Whole tone, Whole tones, Wind instruments.
Abstract
It is well known (from Riemann, Lewin, Cohn and others) that two voices of a triad (set class 3–11) may be held and one moved ‘parsimoniously’ by a tone or semitone to produce another triad; or two voices of a dominant and half‐diminished seventh (set class 4–27) may be held while two voices are displaced by a semitone to produce another dominant or half‐diminished seventh (Lewin's ‘DOUTH2’ relation). This article takes 4–27 as its starting point and first explores examples of such parsimonious voice‐leading between sets of the same class in nineteenth‐century music (notably Brahms, Chopin and Musorgsky). The discussion introduces the idea of a diminution existing between forms of 4–27 when the two voices do not proceed simultaneously. The capability of tetrachords of other classes as well as set classes of larger cardinality to engage in parsimonious voice‐leading either by semitone or whole tone is then explored (with examples drawn from the music of Bartók, Mahler, Scriabin and Stravinsky). The type and degree of parsimony are indicated by the Pm,n designations developed by Douthett and Steinbach, and the article examines the ways in which the capacity of sets to behave in this manner may be predicted from interval strings and invariant subsets.
Url:
DOI: 10.1111/j.1468-2249.2007.00251.x
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ISTEX:B81019B07BED8DE7B8D7E4CFDC3BDE942ECF441ELe document en format XML
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This article takes 4–27 as its starting point and first explores examples of such parsimonious voice‐leading between sets of the same class in nineteenth‐century music (notably Brahms, Chopin and Musorgsky). The discussion introduces the idea of a diminution existing between forms of 4–27 when the two voices do not proceed simultaneously. The capability of tetrachords of other classes as well as set classes of larger cardinality to engage in parsimonious voice‐leading either by semitone or whole tone is then explored (with examples drawn from the music of Bartók, Mahler, Scriabin and Stravinsky). The type and degree of parsimony are indicated by the P<hi rend="subscript">m,n</hi> designations developed by Douthett and Steinbach, and the article examines the ways in which the capacity of sets to behave in this manner may be predicted from interval strings and invariant subsets.</p></abstract><textClass><keywords rend="tocHeading1"><term>Original Articles</term></keywords></textClass><langUsage><language ident="en"></language></langUsage></profileDesc><revisionDesc><change xml:id="refBibs-istex" who="#ISTEX-API" when="2018-06-14">References added</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/B81019B07BED8DE7B8D7E4CFDC3BDE942ECF441E/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Wiley, elements deleted: body"><istex:xmlDeclaration>version="1.0" encoding="UTF-8" standalone="yes"</istex:xmlDeclaration><istex:document><component version="2.0" type="serialArticle" xml:lang="en"><header><publicationMeta level="product"><publisherInfo><publisherName>Blackwell Publishing Ltd</publisherName><publisherLoc>Oxford, UK</publisherLoc></publisherInfo><doi origin="wiley" registered="yes">10.1111/(ISSN)1468-2249</doi><issn type="print">0262-5245</issn><issn type="electronic">1468-2249</issn><idGroup><id type="product" value="MUSA"></id><id type="publisherDivision" value="ST"></id></idGroup><titleGroup><title type="main" sort="MUSIC ANALYSIS">Music Analysis</title></titleGroup></publicationMeta><publicationMeta level="part" position="03001"><doi origin="wiley">10.1111/musa.2008.26.issue-1-2</doi><numberingGroup><numbering type="journalVolume" number="26">26</numbering><numbering type="journalIssue">1‐2</numbering></numberingGroup><coverDate startDate="2007-03">March‐July 2007</coverDate></publicationMeta><publicationMeta level="unit" type="article" position="6" status="forIssue"><doi origin="wiley">10.1111/j.1468-2249.2007.00251.x</doi><idGroup><id type="unit" value="MUSA251"></id></idGroup><countGroup><count type="pageTotal" number="48"></count></countGroup><titleGroup><title type="tocHeading1">Original Articles</title></titleGroup><copyright>© 2007 The Author. Journal compilation © 2007 Blackwell Publishing Ltd</copyright><eventGroup><event type="firstOnline" date="2008-07-08"></event><event type="publishedOnlineFinalForm" date="2008-07-08"></event><event type="xmlConverted" agent="Converter:BPG_TO_WML3G version:2.3.5 mode:FullText source:FullText result:FullText" date="2010-04-07"></event><event type="xmlConverted" agent="Converter:WILEY_ML3G_TO_WILEY_ML3GV2 version:3.8.8" date="2014-02-03"></event><event type="xmlConverted" agent="Converter:WML3G_To_WML3G version:4.1.7 mode:FullText,remove_FC" date="2014-10-31"></event></eventGroup><numberingGroup><numbering type="pageFirst" number="111">111</numbering><numbering type="pageLast" number="158">158</numbering></numberingGroup><linkGroup><link type="toTypesetVersion" href="file:MUSA.MUSA251.pdf"></link></linkGroup></publicationMeta><contentMeta><countGroup><count type="figureTotal" number="20"></count><count type="tableTotal" number="14"></count><count type="formulaTotal" number="0"></count><count type="referenceTotal" number="0"></count><count type="wordTotal" number="0"></count></countGroup><titleGroup><title type="main">S<sc>ome</sc> O<sc>bservations on</sc> P<sub><sc>m</sc>,<sc>n</sc></sub> R<sc>elations within</sc> S<sc>et</sc> C<sc>lasses</sc></title><title type="shortAuthors">MICHAEL RUSS</title><title type="short">P<sub><sc>m</sc>,<sc>n</sc></sub> R<sc>elations within</sc> S<sc>et</sc> C<sc>lasses</sc></title></titleGroup><creators><creator creatorRole="author" xml:id="cr1" affiliationRef="#a1"><personName><givenNames>MICHAEL</givenNames><familyName>RUSS</familyName></personName></creator></creators><affiliationGroup><affiliation xml:id="a1"><unparsedAffiliation>University of Huddersfield</unparsedAffiliation></affiliation></affiliationGroup><abstractGroup><abstract type="main" xml:lang="en"><title type="main">ABSTRACT</title><p>It is well known (from Riemann, Lewin, Cohn and others) that two voices of a triad (set class 3–11) may be held and one moved ‘parsimoniously’ by a tone or semitone to produce another triad; or two voices of a dominant and half‐diminished seventh (set class 4–27) may be held while two voices are displaced by a semitone to produce another dominant or half‐diminished seventh (Lewin's ‘DOUTH2’ relation). This article takes 4–27 as its starting point and first explores examples of such parsimonious voice‐leading between sets of the same class in nineteenth‐century music (notably Brahms, Chopin and Musorgsky). The discussion introduces the idea of a diminution existing between forms of 4–27 when the two voices do not proceed simultaneously. The capability of tetrachords of other classes as well as set classes of larger cardinality to engage in parsimonious voice‐leading either by semitone or whole tone is then explored (with examples drawn from the music of Bartók, Mahler, Scriabin and Stravinsky). The type and degree of parsimony are indicated by the P<sub>m,n</sub> designations developed by Douthett and Steinbach, and the article examines the ways in which the capacity of sets to behave in this manner may be predicted from interval strings and invariant subsets.</p></abstract></abstractGroup></contentMeta></header></component></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Some Observations on Pm,n Relations within Set Classes</title></titleInfo><titleInfo type="abbreviated" lang="en"><title>Pm,n Relations within Set Classes</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Some Observations on Pm,n Relations within Set Classes</title></titleInfo><name type="personal"><namePart type="given">MICHAEL</namePart><namePart type="family">RUSS</namePart><affiliation>University of Huddersfield</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="article" displayLabel="article" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-6N5SZHKN-D">article</genre><originInfo><publisher>Blackwell Publishing Ltd</publisher><place><placeTerm type="text">Oxford, UK</placeTerm></place><dateIssued encoding="w3cdtf">2007-03</dateIssued><copyrightDate encoding="w3cdtf">2007</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><extent unit="figures">20</extent><extent unit="tables">14</extent><extent unit="formulas">0</extent><extent unit="references">0</extent><extent unit="words">0</extent></physicalDescription><abstract lang="en">It is well known (from Riemann, Lewin, Cohn and others) that two voices of a triad (set class 3–11) may be held and one moved ‘parsimoniously’ by a tone or semitone to produce another triad; or two voices of a dominant and half‐diminished seventh (set class 4–27) may be held while two voices are displaced by a semitone to produce another dominant or half‐diminished seventh (Lewin's ‘DOUTH2’ relation). This article takes 4–27 as its starting point and first explores examples of such parsimonious voice‐leading between sets of the same class in nineteenth‐century music (notably Brahms, Chopin and Musorgsky). The discussion introduces the idea of a diminution existing between forms of 4–27 when the two voices do not proceed simultaneously. The capability of tetrachords of other classes as well as set classes of larger cardinality to engage in parsimonious voice‐leading either by semitone or whole tone is then explored (with examples drawn from the music of Bartók, Mahler, Scriabin and Stravinsky). The type and degree of parsimony are indicated by the Pm,n designations developed by Douthett and Steinbach, and the article examines the ways in which the capacity of sets to behave in this manner may be predicted from interval strings and invariant subsets.</abstract><relatedItem type="host"><titleInfo><title>Music Analysis</title></titleInfo><genre type="journal" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre><identifier type="ISSN">0262-5245</identifier><identifier type="eISSN">1468-2249</identifier><identifier type="DOI">10.1111/(ISSN)1468-2249</identifier><identifier type="PublisherID">MUSA</identifier><part><date>2007</date><detail type="volume"><caption>vol.</caption><number>26</number></detail><detail type="issue"><caption>no.</caption><number>1‐2</number></detail><extent unit="pages"><start>111</start><end>158</end><total>48</total></extent></part></relatedItem><identifier type="istex">B81019B07BED8DE7B8D7E4CFDC3BDE942ECF441E</identifier><identifier type="ark">ark:/67375/WNG-4NG2K4Q3-5</identifier><identifier type="DOI">10.1111/j.1468-2249.2007.00251.x</identifier><identifier type="ArticleID">MUSA251</identifier><accessCondition type="use and reproduction" contentType="copyright">© 2007 The Author. 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