Journal of Mathematics and Music最新文献

{"title":"Three-string inharmonic networks","authors":"Saba Goodarzi, W. Sethares","doi":"10.1080/17459737.2022.2136776","DOIUrl":"https://doi.org/10.1080/17459737.2022.2136776","url":null,"abstract":"This paper studies the resonant frequencies of three-string networks by examining the roots of the relevant spectral equation. A collection of scaling laws are established which relate the frequencies to structured changes in the lengths, densities, and tensions of the strings. Asymptotic properties of the system are derived, and several situations where transcritical bifurcations occur are detailed. Numerical optimization is used to solve the inverse problem (where a desired set of frequencies is specified and the parameters of the system are adjusted to best realize the specification). The intrinsic dissonance of the overtones provides an approximate way to measure the inherent inharmonicity of the sound.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"35 1","pages":"388 - 402"},"PeriodicalIF":1.1,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88457514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Type and class vectors and matrices in ℤ n . Application to ℤ6, ℤ7, and ℤ12","authors":"Luis Nuño","doi":"10.1080/17459737.2022.2120214","DOIUrl":"https://doi.org/10.1080/17459737.2022.2120214","url":null,"abstract":"In post-tonal theory, set classes are normally elements of and are characterized by their interval-class vector. Those being non-inversionally-symmetrical can be split into two set types related by inversion, which can be characterized by their trichord-type vector. In this paper, I consider the general case of set classes and types in and their -class and -type vectors, ranging from to , which are properly grouped into matrices. As well, three relevant cases are considered: (hexachords), (heptatonic scales), and (chromatic scale), where all those type and class matrices are computed and provided in supplementary files; and, in the first two cases, also in the form of tables. This completes the corresponding information given in previous publications on this subject and can directly be used by researchers and composers. Moreover, two computer programs, written in MATLAB, are provided for obtaining the above-mentioned and other related matrices in the general case of . Additionally, several theorems on type and class matrices are provided, including a complete version of the hexachord theorem. These theorems allow us to obtain the type and class matrices by different procedures, thus providing a broader perspective and better understanding of the theory.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"64 1","pages":"244 - 265"},"PeriodicalIF":1.1,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86197849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Letters on P-Relations, 1992–1997","authors":"J. Douthett, Richard Cohn, Dani Zanuttini-Frank","doi":"10.1080/17459737.2022.2157060","DOIUrl":"https://doi.org/10.1080/17459737.2022.2157060","url":null,"abstract":"Jack Douthett wrote a number of letters to John Clough and Richard Cohn concerning Cohn's “P-Relations,” single-semitone voice-leading relationships. The ideas in these letters led to graph-theoretic and geometric models. The following selection has been edited and prepared for publication by Richard Cohn and Dani Zanuttini-Frank.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"35 1","pages":"263 - 292"},"PeriodicalIF":1.1,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81714883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Jack Douthett’s letters","authors":"Richard Cohn","doi":"10.1080/17459737.2022.2157061","DOIUrl":"https://doi.org/10.1080/17459737.2022.2157061","url":null,"abstract":"This publication transcribes seven previously unpublished letters from Jack Douthett. The earliest four letters, from 1992–94, were written to John Clough, who was the Slee Professor of Music Theory at SUNY Buffalo from the early 1980s to 2001. They are hand-written, mailed by postal service, and are among the founding documents of the sub-field that emerged in the 1990s that has come to be known under the catch-all label of “neo-Riemannian theory.” The three remaining letters, word processed and circulated via email to a working group of researchers known informally as the “Buffalo group,” are from 1997 and 2000, and responded to emerging work of a remarkable cohort of PhD students then working on neo-Riemannian topics. The first three letters were the first of a flurry of eleven that were precipitated by some ideas that I sketched over lunch with John and Jack in late October 1992 at the Society for Music Theory annual meeting in Kansas City, and subsequently detailed in a written document that I mailed to them shortly thereafter.1 In that document, I defined (1) a “P relation” when two pitchclass sets are connected by single-semitonal displacement, for example {C, E, G} P {C, E, G }, (2) a “P property” for any Tn/TnI set class2 that contains P-related pairs, and (3) a “PP property” for any set class that partitions into cycles of three or more P-related pairs. These definitions, which are presented more systematically at the end of this introduction, supported my central finding: that the structures that co-anchor the European tonal system, major/minor triads and major/minor scales, together with their complements, uniquely possess the PP property (nontrivially).3 In that document, I also identified set classes with the PP property in universes with fewer than twelve elements, and advanced some theorems about the relation of the PP property to other properties and relations central to theories of atonality and diatonicism. Douthett’s first response, from 11/24/92, is primarily concerned with connections between my central finding and his research with Clough on maximally even sets (Clough and Douthett 1991). That letter is primarily algebraic, but ends with a graph-theoretic turn that is developed a few days later in the brief letter of 11/30/92, and emerges in mature form in the longer letter of 12/12/92, where the two graphs that became respectively known as “Cube Dance” and “Power Towers” are first described. These three letters, together with eight subsequent letters from the","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"44 1","pages":"260 - 262"},"PeriodicalIF":1.1,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80642189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Partitions, their classes, and multicolour evenness","authors":"J. Douthett, P. Steinbach, R. Peck, R. Krantz","doi":"10.1080/17459737.2022.2124461","DOIUrl":"https://doi.org/10.1080/17459737.2022.2124461","url":null,"abstract":"We extend the theory of maximally even sets to determine the evenness of partitions of the chromatic universe . Interactions measure the average evenness of colour sets (partitioning sets) of . For 2-colour partitions the Clough-Douthett maximal-evenness algorithm determines maximally even partitions. But to measure the evenness of non-maximally even partitions, it is necessary to use computational methods. Moreover, for more than two colour sets there is no simple algorithm that determines maximally even partitions. Again, we rely on computational methods. We also explore collections of partitions and partition-classes (orbits under a dihedral group) and construct tables that order partition-classes according to the evenness of their partitions. We use Bell numbers, Stirling numbers of the second kind, and integer partitions to enumerate relevant combinatorial objects related to our investigation.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"1639 1","pages":"303 - 345"},"PeriodicalIF":1.1,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76285326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Turning the volvelle: Exploring Jack Douthett's voice leading dynamics","authors":"Roger Asensi Arranz, T. Noll","doi":"10.1080/17459737.2022.2157059","DOIUrl":"https://doi.org/10.1080/17459737.2022.2157059","url":null,"abstract":"This paper explores Jack Douthett's model of dynamical voice leading on the level of harmonic states. It investigates global contiguous and stroboscopic dynamical systems on the entire state space and introduces a measure of effectiveness for the trajectories under consideration. Special attention is paid to the harmonic state spaces behind second-order Clough-Myerson scales, such as diatonic triads and seventh chords. Finally, a set of trajectories as a tiling of exemplifies the connection with the Spectral Conjecture.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"40 2 1","pages":"346 - 366"},"PeriodicalIF":1.1,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83769444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Letters on Hook's group, 2000","authors":"J. Douthett, Richard Cohn, Dani Zanuttini-Frank","doi":"10.1080/17459737.2022.2143590","DOIUrl":"https://doi.org/10.1080/17459737.2022.2143590","url":null,"abstract":"After encountering Julian Hook's work on uniform triadic transformations, Jack Douthett wrote letters to John Clough suggesting further group-theoretic generalizations of Hook's idea. These letters have been edited and prepared for publication by Richard Cohn and Dani Zanuttini-Frank.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"602 1","pages":"295 - 302"},"PeriodicalIF":1.1,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77349626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Jack Douthett and mathematical music theory","authors":"Jason Yust","doi":"10.1080/17459737.2022.2143589","DOIUrl":"https://doi.org/10.1080/17459737.2022.2143589","url":null,"abstract":"Jack Douthett's work over three decades was central to defining an era in mathematical theory. The present special issue attests to his abiding influence over the field, as well as the energy he brought to research in all areas of mathematical music theory through his collaborations, correspondence, and relationships.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"6 1","pages":"249 - 252"},"PeriodicalIF":1.1,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79600429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Two letters by Jack Douthett on uniform triadic transformations","authors":"Julian L. Hook","doi":"10.1080/17459737.2022.2157062","DOIUrl":"https://doi.org/10.1080/17459737.2022.2157062","url":null,"abstract":"Two letters that Jack wrote soon after I introduced uniform triadic transformations in 1999 exemplify the energy with which he threw himself into work on subjects that stirred his interest. As I note in a tribute elsewhere in this issue (Krantz 2022), I first met Jack at a meeting of the Society for Music Theory in the fall of 1999 – a conference at which I also presented my work on UTTs (later published in Hook 2002). By April of 2000, Jack had distributed two substantial letters with his evolving thoughts on the subject. The wreath-product structure of the UTT group, the simply transitive subgroups of that group, and “skew groups” (which combine mode-preserving transformations of one kind with mode-reversing transformations of another kind) were subjects of special fascination to him from the start, as they remained a few years later when we produced our joint paper on applications of UTTs to serialism (Hook and Douthett 2008). The second letter is particularly notable for a few ideas that have not been pursued elsewhere. Here Jack relates UTTs to the seventh-chord transformations that he had studied with Peter Steinbach (Douthett and Steinbach 1998), and also to Jonathan Kochavi’s work (Kochavi 1998) on contextual inversions (presenting what Jack calls “Kochavi diagrams” for some groups of UTTs). He also refines my embryonic suggestion for generalizing UTTs to situations where there are more than two classes of objects (such as inversionally related chord qualities).","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"30 1","pages":"293 - 294"},"PeriodicalIF":1.1,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88047746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Colleague, collaborator, friend Jack Douthett (1942–2021)","authors":"R. Krantz","doi":"10.1080/17459737.2022.2140214","DOIUrl":"https://doi.org/10.1080/17459737.2022.2140214","url":null,"abstract":"Remembrances of Jack Douthett from his students and colleagues.","PeriodicalId":50138,"journal":{"name":"Journal of Mathematics and Music","volume":"43 1","pages":"254 - 259"},"PeriodicalIF":1.1,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86022956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}