Harmonic Materials of Modern Music

Mitchell, William J.; Hanson, Howard

doi:10.2307/843186

Cited by 2 publications

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Several of these organization types correspond to group-theoretic ways of distributing pcs around the chroma circle according to the concept of maximal evenness (Clough and Douthett 1991). As Quinn (2001) also points out, the chromatic, whole-tone, octatonic, hexatonic, and diatonic scales correspond to Hanson's (1960) idea of interval cycles, with each of those having ics 1 through 5 respectively dominant; and 016/0167 organization corresponds to Hanson's ic6 interval cycle. The notion of different kinds of pcsets at the extremes of the dimensions invites comparison with various models of pcset families, or genera.…”

Section: Pcset Generamentioning

confidence: 99%

“…[57] Like similarity functions, multiple genera systems have been proposed; some explicitly come out of pcset theory or investigations influenced by it (e.g., Ericksson 1986;Forte 1988;Parks 1989;Quinn 1997Quinn , 2001 while others do not (e.g., Hanson, 1960;Hindemith, 1937/42;Wolpert, 1951Wolpert, , 1972. It is beyond the scope of this article to compare all of the various genera systems with the factors found to be measured by the similarity functions studied here.…”

Section: Pcset Generamentioning

confidence: 99%

See 1 more Smart Citation

Mapping the Geometries of Pitch-Class Set Similarity Measures via Multidimensional Scaling

Samplaski

2005

MTO

View full text Add to dashboard Cite

A numerical visualization technique called multidimensional scaling (MDS) was applied to the matrices of (dis)similarity ratings from six pitch-class set (pcset) similarity functions to see what types of constructs they actually measure. Three functions that use the interval-class vector (icv) for their computations (Scott and Isaacson’s ANGLE, Isaacson’s IcVSIM and ISIM2) and three that use subset imbedding (Castrén’s RECREL, Rahn’s ATMEMB and AMEMB2) were studied. The ratings of these functions for all trichords, tetrachords, and pentachords (under Tn/I-equivalence) were examined; ratings for each cardinality of set-class separately as well as contiguously grouped together (3+4, 4+5, 3+4+5) were studied. Four-dimensional geometric solutions were found for the icv-based measures while five-dimensional solutions were found for the subset-based measures, based on goodness-of-fit analysis. The configurations show one dimension clearly interpretable as diatonicism vs. chromaticism; other dimensions indicate oppositions such as ”whole-tone” vs. ”anti-wholetone” or ic3- vs. 016-saturation. Still other dimensions are less clear as to good interpretations. The overall results are generally consistent with the idea that these functions all measure constructs relating to familiar scales (diatonic, hexatonic, octatonic, etc.). The results are also compared with several systems of pcset genera. ISIM2 was found to be inconsistent with itself in terms of the geometries it produced. Several set-classes had coordinates near zero along various dimensions in the derived configurations, indicating that in a formal quantitative sense they do not possess the corresponding musical properties being measured; this may raise questions concerning the relative aesthetic worth of some such set-classes.

show abstract

Section: Pcset Generamentioning

confidence: 99%

Section: Pcset Generamentioning

confidence: 99%

Mapping the Geometries of Pitch-Class Set Similarity Measures via Multidimensional Scaling

Samplaski

2005

MTO

View full text Add to dashboard Cite

show abstract

“…He was immersed in the details of his Harmony Book (2002), with its enumeration and classification of the universe of chord types in twelve-note equal temperament. His comments on Alois Hába's Neue Harmonielehre (1927), and later books by Howard Hanson (1960) and Vincent Persichetti (1961), are thus of considerable interest. In the Wednesday afternoon lecture, Carter addresses the shift in his compositional approach in the Piano Concerto:…”

mentioning

confidence: 98%

Review of Elliott Carter Speaks: Unpublished Lectures, Edited and with an introduction by Laura Emmery (University of Illinois Press, 2021)

Link

2023

MTO

View full text Add to dashboard Cite

Conversation with Elliott Carter (1971) is well known as a key document in Carter's reception history. But the book's format initially raised a few eyebrows. Carlton Gamer, unconvinced that such a carefully edited text should be called a "conversation," responded by interviewing himself in his review (1973). When "C. G." is asked by "MYSELF" why the conversational format is "problematic," he recalls the precedent of Carter's interview with Benjamin Boretz, which was "radically re-written" prior to its publication in Perspectives of New Music "in such a way as to convey an impression of polish and erudition that was lacking in the original" (Gamer 1973, 148). (1) This tradition of editorial rewriting has been revived in different circumstances in a new book from the University of Illinois Press, Elliott Carter Speaks: Unpublished Lectures, edited and with an introduction by Laura Emmery. The book presents a trove of primary source material from Carter's lectures at the University of Minnesota (1967) that is largely unknown to Carter enthusiasts, but it does so in a way that raises fundamental questions about how that material has been altered on its way to publication. (2) [2] Understanding these questions requires some background. Carter gave the lectures that form the basis of Elliott Carter Speaks at the University of Minnesota in July 1967 as part of the university's "Summer Music at Minnesota" program (Summer Session Bulletin, 1967). (3) His visit culminated with a performance of his Piano Concerto by Jacob Lateiner and the Minneapolis Symphony Orchestra, conducted by Stanisław Skrowaczewski on Friday, July 7. (4) Recordings of most of Carter's lectures are preserved on a series of reelto-reel tapes, which were in Carter's possession when he sold his physical manuscripts and other career-related materials in 1987 to the Paul Sacher Foundation in Basel, Switzerland. (5) There, the contents were transferred to ten CDs. (6) Notes that accompany the recordings indicate that Carter gave only one lecture on Monday July 3, and two lectures each on Tuesday, Wednesday, and Thursday, July 4-6, for a total of seven lectures. The recordings of all the lectures, except the one on Wednesday afternoon, are missing their beginnings, and all but three (Monday, Wednesday afternoon, and Thursday morning) are cut off when the tape runs out or the tape machine is stopped while Carter is still speaking (see Example 1). ( 7) A newspaper article published in the Minneapolis Tribune the week before Carter's arrival says that, in addition to "three open rehearsals of the 98-100 and Link 2022, 82-83 Return to text

show abstract

Harmonic Materials of Modern Music

Cited by 2 publications

References 0 publications

Mapping the Geometries of Pitch-Class Set Similarity Measures via Multidimensional Scaling

Mapping the Geometries of Pitch-Class Set Similarity Measures via Multidimensional Scaling

Review of Elliott Carter Speaks: Unpublished Lectures, Edited and with an introduction by Laura Emmery (University of Illinois Press, 2021)

Contact Info

Product

Resources

About