The Concept of Musical Consonance: A Link between Music and Psychoacoustics

1984 ◽  
Vol 1 (3) ◽  
pp. 276-295 ◽  
Author(s):  
Ernst Terhardt
Keyword(s):  
Present Author ◽  
Musical Experience ◽  
Tonal Music ◽  
Specific Component ◽  
Two Component ◽  
Sensory Consonance ◽  
Definition Of ◽  
Musical Sounds

This paper is a presentation of the essentials of a new concept and foundation of musical consonance described by the present author in German in Acustica 36,121-137 (1976). Musical consonance is considered from the terminological, musical, conceptual, and psychoacoustic aspects. An appropriate definition of musical consonance is given, based on the principles governing tonal music. Recent results on psychoacoustic evaluation of consonance, which at first glance appear to be in conflict with musical experience, can be reconciled by a two-component concept of musical consonance. The first component is called sensory consonance; it represents the graded absence of annoying factors and is not confined to musical sounds, that is, not music specific. The second component of musical consonance is called harmony; it represents the typical, musicspecific principles of tonal affinity, compatibility, and fundamental-note relation (root). This concept is discussed in the context of Helmholtz's work on Konsonanz and Klangverwandtschaft. Helmholtz's work turns out to be an excellent basis of modern solutions to the consonance problem, as much of it still is valid, while the remainder can readily be replaced by more appropriate new solutions. The psychoacoustic foundations of sensory consonance, as provided by modern psychoacoustics, are largely identical with those found by Helmholtz. With regard to harmony, that is, the music-specific component of musical consonance, a new psychoacoustic foundation is provided by the established principles of virtualpitch perception. Several consequences and prospects of the concept for musical science are briefly considered.

THE MOUFANG LAWS, GLOBAL AND LOCAL

2009 ◽  
Vol 08 (04) ◽  
pp. 477-492 ◽  
Author(s):  
J. D. PHILLIPS
Keyword(s):  
Present Author ◽  
Inverse Property ◽  
Loop Theory ◽  
Traditional Definition ◽  
Moufang Loops ◽  
Definition Of ◽  
Global And Local

There are many possible ways to define Moufang element. We show that the traditional definition is not the most felicitious — for instance, the set of all Moufang elements in an arbitrary loop, qua the traditional definition, need not form a subloop. We offer a new definition of Moufang element that ensures that the set of all Moufang elements in an arbitrary loop is a subloop. Moreover, this definition is "maximally algebraic" with respect to autotopisms. We also give an application of this new definition by showing that a flexible A-element in an inverse property loop is, in fact, a Moufang element, thus sharpening a well-known result of Kinyon, Kunen, and the present author [6]. Finally, we prove that divisible, Moufang groupoids are Moufang loops, thus sharpening a result of Kunen [9], one of the first computer-generated proofs in loop theory.

Music as Epistemic Construct: From Sonic Experience to Musical Sense-Making

2020 ◽  
Vol 30 ◽  
pp. 56-60
Author(s):  
Mark Reybrouck
Keyword(s):  
Real Time ◽  
Mental Representation ◽  
Knowledge Construction ◽  
Virtual Space ◽  
Sense Making ◽  
Musical Experience ◽  
Dynamic Tension ◽  
Cognitive Economy ◽  
Discrete Processing ◽  
Definition Of

Taking an epistemological stance towards music in a real-time listening situation entails a definition of music as a temporal and sounding art. This means that music cannot be described in abstract and detached terms as something “out there” in a virtual space but rather as something that impinges upon our senses in an actual “here and now.” Musical sense-making, therefore, should be considered a kind of ongoing knowledge construction with a dynamic tension between actual sensation and mental representation of sounding events. Four major dichotomies may be considered in this regard: the focal versus synoptic overview of the sounding music, the continuous/discrete processing of the sounds, the distinction between sensory experience versus cognitive economy, and the in-time/outside-of-time distinction. The author argues that a deliberate combination of these diverging approaches makes the musical experience a richer one.

The Identification and Decomposition of Hierarchical Tasks

1977 ◽  
Vol 14 (3) ◽  
pp. 189-212 ◽  
Author(s):  
John W. Cotton ◽  
John P. Gallagher ◽  
Sandra P. Marshall
Keyword(s):  
Mathematical Model ◽  
Experimental Design ◽  
Experimental Evidence ◽  
Hierarchical Structure ◽  
Alternate Route ◽  
Component Task ◽  
Two Component ◽  
Hierarchical Ordering ◽  
Definition Of

The definition of hierarchical structure is reviewed, together with psychometric and experimental evidence regarding the existence of specific structures. Exceptions to hierarchical ordering are frequent enough to merit consideration of an assumption that skill on an item may simply transfer to the next higher item rather than being fully prerequisite to it. In some cases an alternate route hierarchy may occur, with persons either learning an item and then the next item or learning both at the same time. A mathematical model including hierarchical and nonhierarchical options fir a two-component task is presented; an experimental design appropriate to testing the model and related transfer hypotheses is also presented.

scholarly journals Religiøs argumentation som religionsfænomenologisk forskningsområde

1992 ◽  
Author(s):  
Mikael Aktor
Keyword(s):  
Mystical Experience ◽  
Point Of View ◽  
Essential Difference ◽  
Specific Character ◽  
Concrete Material ◽  
Material World ◽  
Basic Point ◽  
Two Component ◽  
The World ◽  
Definition Of

This article is a reflection on the specific character of religious assertations and religious arguments. The basic point of view is that these religious practices should not be investigated as isolated religious phenomena sui generis, but on the contrary, that they are conditioned by and derived from common linguistic and epistemological practices that relate to the concrete material world. Religious assertations join together finction and description of the world, whereas religious arguments refer todata which are either quasi-empiric (a holy scripture  for instance) or quasi-public (a mystical experience for instance). in four text examples these derivations are investigated in the light of a two-component definition of religion, which stresses the concept of an essential difference as well as the concept of a possibility of a passage to an fro between essentially differenct categories.

scholarly journals 導言: 確定死亡之醫學及哲學問題

1999 ◽  
Vol 2 (3) ◽  
pp. 1-28
Author(s):  
Ping-cheung LO
Keyword(s):  
Brain Death ◽  
Present Author ◽  
Biomedical Ethics ◽  
The Body ◽  
Philosophical Issue ◽  
Whole Brain ◽  
Definition Of Death ◽  
Definition Of ◽  
Whole Brain Death ◽  
Defining Death

LANGUAGE NOTE | Document text in Chinese; abstract also in English.確定死亡要分開三個層次：死亡的定義、死亡的判準、死亡的測試；當中既有醫學問題﹒也有哲學問題。“全腦死亡”（簡稱腦死亡）的提出，並非要修改傳統對死亡的定義；全腦死亡只是一個新的死亡判準，在死亡的測試上既可用新的腦功能測試，但也不排斥傳統的心肺功能測試，視情況而定。因此，全腦死亡判準，並沒有提出一個新的死亡觀來取代舊的死亡觀。反對全腦死亡判準的意見走向二個極端。有些人認為全腦死亡只是一個人的死亡的必要但非充分條件，還需心肺死亡配合才構成充分條件。但另一些人則認為，全腦死亡是作為萬物之靈的人之死亡的既非充分也非必要條件；真正的必要（或甚至充分）條件是上腦（大腦）死亡。要徹底處理這些醫學爭論問題，無可避免地我們要問“死亡是甚麼？”“生命是甚麼？”及進一步追問“人是甚麼？”這些哲學問題。This essays begins by noting the brief history of "updating" death since the Harvard Medical School Report in 1968. The deficiencies of this report are noted and the background of the President's Commission's Report on "Defining Death" are briefly explained. The author then discusses and endorses the three-fold distinction in the determination of death as suggested by other scholars, viz., the definition of, the criterion of, and the tests for death. While the test for death is basically a medical issue, and that the definition of death is basically a philosophical issue, the criterion of death is both medical and philosophical.Since the People's Republic of China does not have any brain death legislation, and since some recent Chinese biomedical ethics textbooks have an inaccurate understanding of brain death, the present author summarizes the major theses of "Defining Death" by the President's Commission of 1981. It is pointed out that the idea of "brain death" does not indicate a new definition of death; it only advocates a new criterion of death, and a new way of testing death (neurological) in addition to the conventional way of testing death (cardiac-pulmonary). Hence the precise idea of "brain death" is not as radical as some Chinese interpreters think it to be.This essay also analyzes the criticism of brain death criterion both from the left and from the right. The Jewish position, as articulated by Hans Jonas and others, that brain death is not the sufficient condition of human death is explained. The present author points out that Jonas' idea that the argument for brain death is value-laden is vindicated by many Chinese writings on biomedical ethics. The position in the other extreme, viz., whole brain death is not even a necessary condition of the death of persons, is also explained. The arguments in its favor and against it are both critically analyzed. The serious mistake of many Chinese writings of equating the condition of persistent vegetative state with whole brain death is criticized. The author also notes that according to Buddhist views, pvs patients still possess some degree of consciousness and hence should not be deemed dead.The philosophical issue of "what is death?" necessarily leads to another issue, viz., what is the nature of human life? The ancient Chinese discussions of the nature of the soul (shen) and the body-mind (xing-shen) problem are briefly discussed. The author points out the relevance of these discussions to the contemporary reflection on the nature of human death.DOWNLOAD HISTORY | This article has been downloaded 27 times in Digital Commons before migrating into this platform.

Constraint on the Multi-Component CKP Hierarchy and Recursion Operators

2016 ◽  
Vol 71 (6) ◽  
pp. 487-492
Author(s):  
Tao Song ◽  
Chuanzhong Li ◽  
Jingsong He
Keyword(s):  
Recursion Operators ◽  
Two Component ◽  
Ckp Hierarchy ◽  
Definition Of

AbstractIn this article, we give the definition of the multi-component constrained CKP (McCKP) and two-component constrained CKP (cCKP) hierarchies (under the condition N=2). Then we give recursion operators for the two-component cCKP hierarchy. At last, we give the constrained condition from the two-component cCKP hierarchies to cCKP hierarchy.

scholarly journals Annealing Kinetic Model Using Fast and Slow Metastable Defects for Hydrogenated-Amorphous-Silicon-Based Solar Cells

2007 ◽  
Vol 2007 ◽  
pp. 1-8 ◽  
Author(s):  
Seung Yeop Myong
Keyword(s):  
Solar Cells ◽  
Kinetic Model ◽  
Amorphous Silicon ◽  
Hydrogenated Amorphous Silicon ◽  
Microscopic Mechanism ◽  
Two Component ◽  
Field Annealing ◽  
Annealing Kinetic ◽  
Definition Of ◽  
Hydrogenated Amorphous

The two-component kinetic model employing “fast” and “slow” metastable defects for the annealing behaviors in pin-type hydrogenated-amorphous-silicon- (a-Si:H-) based solar cells is simulated using a normalized fill factor. Reported annealing data on pin-type a-Si:H-based solar cells are revisited and fitted using the model to confirm its validity. It is verified that the two-component model is suitable for fitting the various experimental phenomena. In addition, the activation energy for annealing of the solar cells depends on the definition of the recovery time. From the thermally activated and high electric field annealing behaviors, the plausible microscopic mechanism on the defect removal process is discussed.

scholarly journals Letters

1989 ◽  
Vol 6 (3) ◽  
pp. 307-308
Author(s):  
Harold Jones
Keyword(s):  
Good Deal ◽  
Musical Experience ◽  
Tonal Music ◽  
Musical Education ◽  
Harmonic Language ◽  
Romantic Era ◽  
Gradus Ad Parnassum ◽  
Figured Bass ◽  
The One ◽  
Made In

Laura Campbell's article (Vol. 5, No. 3, November 1988) seems a little ambivalent. On the one hand she proposes a ‘method’ for harmonising chorales in the style of J. S. Bach; on the other she seems to suggest that this is not in any case an appropriate task for the student.By implication this raises once again the whole question of the value of ‘imitative’ work as an agent of musical education. Does it teach anything other than knowledge of the particular style involved and if not, does it matter? To take a style even more remote from everyday musical experience, that of Palestrina, I am sure that those of us who devoted a good deal of time to it as students did gain much useful practice in the writing of smooth vocal lines applicable in fields as distant from the idiom of Palestrina as the arrangement of modern light music. In the same way the budding composer can learn from Bach-style chorale harmonisation something of the way in which harmonic considerations interact with the writing of interesting vocal lines, and the compromises that have to be made in the process of fusing the two together. It is true that the principal benefit of this activity is knowledge of Bach's methods in chorale harmonisation, but the same is true of what is now known as ‘pastiche’ work in any idiom; the idea that one can learn a sort of all-purpose abstract harmonic language which can be applied mutatis mutandis to all tonal music from the Baroque to the late Romantic era has now fallen into disrepute. It is worth noting that Haydn, Mozart, Beethoven and Bruckner all considered it worth their while to work at Fux's Gradus ad Parnassum, a sort of archetypal ‘pastiche’ method. Figured bass, incidentally, is not primarily a method of teaching, but a shorthand performing notation.

A NUMERICAL INVARIANT FOR TWO COMPONENT SPATIAL GRAPHS

2010 ◽  
Vol 19 (09) ◽  
pp. 1125-1134
Author(s):  
SUMIKO HORIUCHI ◽  
YOSHIYUKI OHYAMA
Keyword(s):  
Finite Type ◽  
Absolute Value ◽  
Numerical Invariant ◽  
Linking Number ◽  
Type Invariant ◽  
Spatial Graphs ◽  
Two Component ◽  
The Absolute ◽  
Definition Of

We define an invariant for two component spatial graphs. Although the definition of the invariant is alike a linking number, it is different from the absolute value of a linking number. We show that the invariant is not a finite type invariant.

scholarly journals Limit linear series for curves not of compact type

2019 ◽  
Vol 2019 (753) ◽  
pp. 57-88 ◽  
Author(s):  
Brian Osserman
Keyword(s):  
Moduli Space ◽  
Linear Series ◽  
Restricted Class ◽  
Compact Type ◽  
Nodal Curves ◽  
Equivalent Definition ◽  
Two Component ◽  
Limit Linear Series ◽  
Definition Of

AbstractWe introduce a notion of limit linear series for nodal curves which are not of compact type. We give a construction of a moduli space of limit linear series, which works also in smoothing families, and we prove a corresponding specialization result. For a more restricted class of curves which simultaneously generalizes two-component curves and curves of compact type, we give an equivalent definition of limit linear series, which is visibly a generalization of the Eisenbud–Harris definition. Finally, for the same class of curves, we prove a smoothing theorem which constitutes an improvement over known results even in the compact-type case.

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