Babbitt’s Beguiling Surfaces, Improvised Inside; Part II: Diversities

2019 ◽  
Vol 5 (2) ◽  
Author(s):  
Joshua Banks Mailman
Keyword(s):  
Visual Art ◽  
Partial Ordering ◽  
Computational Formula ◽  
Jazz Improvisation ◽  
Background Structure ◽  
Partial Orderings ◽  
Compositional Structures ◽  
Late Works ◽  
Inside Part

Babbitt’s pre-compositional structures (partial orderings) serve as a series of game-like rules affecting the composition of surface details we hear. Especially in Babbitt’s late works (post-1980) these partial ordering rules vary drastically in terms of how much freedom they allow. This variance can be modeled mathematically (a computational formula is explained and visualized). This video (the second of a three-part video essay) reveals, in an excerpt from Babbitt’s 1987 sax and piano work Whirled Series, an intricate web of referential details (serial and tonal) that are improvised from the trillions of possibilities enabled by its background structure (partial ordering). The advantages of this peculiar improvisatory compositional situation in which Babbitt places himself are compared to visual art, chord-based bebop jazz improvisation, and to current ethics-infused philosophies of improvisation.

Babbitt’s Beguiling Surfaces, Improvised Inside; Part III: Opportunities

2019 ◽  
Vol 5 (3) ◽  
Author(s):  
Joshua Banks Mailman
Keyword(s):  
Music Composition ◽  
Jazz Improvisation ◽  
The Third ◽  
Partial Orderings ◽  
Compositional Structures ◽  
Surface Patterns ◽  
Inside Part ◽  
Musical Activities

Babbitt’s relatively early composition Semi-Simple Variations (1956) presents intriguing surface patterns that are not determined by its pre-compositional plan, but rather result from subsequent “improvised” decisions that are strategic. This video (the third of a three-part video essay) considers Babbitt’s own conversational pronouncements (in radio interviews) together with some particulars of his life-long musical activities, that together suggest uncanny affiliations to jazz improvisation. As a result of Babbitt’s creative reconceptualizing of planning and spontaneity in music, his pre-compositional structures (partial orderings) fit in an unexpected way into (or reformulate) the ecosystem relating music composition to the physical means of its performance.

Babbitt’s Beguiling Surfaces, Improvised Inside; Part I: Freedoms

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Joshua Banks Mailman
Keyword(s):  
Partial Ordering ◽  
Personal Traits ◽  
Milton Babbitt ◽  
Iconic Figure ◽  
Inside Part

Milton Babbitt has been a controversial and iconic figure, which has indirectly led to fallacious assumptions about how his music is made, and therefore to fundamental misconceptions about how it might be heard and appreciated. This video (the first of a three-part video essay) reconsiders his music in light of both his personal traits and a more precise examination of the constraints and freedoms entailed by his unusual and often misunderstood compositional practices, which are based inherently on partial ordering (as well as pitch repetition), which enables a surprising amount of freedom to compose the surface details we hear. The opening of Babbitt’s Composition for Four Instruments (1948) and three recompositions (based on re-ordering of pitches) demonstrate the freedoms intrinsic to partial ordering.

Natural Partial Orders

1968 ◽  
Vol 20 ◽  
pp. 535-554 ◽  
Author(s):  
R. A. Dean ◽  
Gordon Keller
Keyword(s):  
Partial Orders ◽  
Partial Ordering ◽  
Finite Set ◽  
Partial Orderings

Let n be an ordinal. A partial ordering P of the ordinals T = T(n) = {w: w < n} is called natural if x P y implies x ⩽ y.A natural partial ordering, hereafter abbreviated NPO, of T(n) is thus a coarsening of the natural total ordering of the ordinals. Every partial ordering of a finite set 5 is isomorphic to a natural partial ordering. This is a consequence of the theorem of Szpielrajn (5) which states that every partial ordering of a set may be refined to a total ordering. In this paper we consider only natural partial orderings. In the first section we obtain theorems about the lattice of all NPO's of T(n).

CLASSIFICATION OF MULTIVARIATE LIFE DISTRIBUTIONS BASED ON PARTIAL ORDERING

2002 ◽  
Vol 16 (1) ◽  
pp. 129-137 ◽  
Author(s):  
Dilip Roy
Keyword(s):  
Present Article ◽  
Failure Rate ◽  
Partial Ordering ◽  
Increasing Failure Rate ◽  
Multivariate Generalization ◽  
Partial Orderings ◽  
Life Distributions ◽  
New Better Than Used ◽  
Better Than

Barlow and Proschan presented some interesting connections between univariate classifications of life distributions and partial orderings where equivalent definitions for increasing failure rate (IFR), increasing failure rate average (IFRA), and new better than used (NBU) classes were given in terms of convex, star-shaped, and superadditive orderings. Some related results are given by Ross and Shaked and Shanthikumar. The introduction of a multivariate generalization of partial orderings is the object of the present article. Based on that concept of multivariate partial orderings, we also propose multivariate classifications of life distributions and present a study on more IFR-ness.

Partial Orderings of Distributions Based on Right-Spread Functions

1998 ◽  
Vol 35 (1) ◽  
pp. 221-228 ◽  
Author(s):  
J. M. Fernandez-Ponce ◽  
S. C. Kochar ◽  
J. Muñoz-Perez
Keyword(s):  
Probability Distributions ◽  
Partial Ordering ◽  
Dispersion Measure ◽  
Dispersive Ordering ◽  
Partial Orderings

In this paper we introduce a quantile dispersion measure. We use it to characterize different classes of ageing distributions. Based on the quantile dispersion measure, we propose a new partial ordering for comparing the spread or dispersion in two probability distributions. This new partial ordering is weaker than the well known dispersive ordering and it retains most of its interesting properties.

A new ordering for stochastic majorization: theory and applications

1992 ◽  
Vol 24 (03) ◽  
pp. 604-634 ◽  
Author(s):  
Cheng-Shang Chang
Keyword(s):  
Sample Path ◽  
Stochastic Ordering ◽  
Partial Ordering ◽  
Scheduling Problems ◽  
Unified Approach ◽  
Finite Buffers ◽  
Routing And Scheduling ◽  
Partial Orderings ◽  
Stochastic Load ◽  
Stochastic Majorization

In this paper, we develop a unified approach for stochastic load balancing on various multiserver systems. We expand the four partial orderings defined in Marshall and Olkin, by defining a new ordering based on the set of functions that are symmetric, L-subadditive and convex in each variable. This new partial ordering is shown to be equivalent to the previous four orderings for comparing deterministic vectors but differs for random vectors. Sample-path criteria and a probability enumeration method for the new stochastic ordering are established and the ordering is applied to various fork-join queues, routing and scheduling problems. Our results generalize previous work and can be extended to multivariate stochastic majorization which includes tandem queues and queues with finite buffers.

Some results on the relative ageing of two life distributions

1994 ◽  
Vol 31 (4) ◽  
pp. 991-1003 ◽  
Author(s):  
Debasis Sengupta ◽  
Jayant V. Deshpande
Keyword(s):  
Hazard Ratio ◽  
Partial Ordering ◽  
Closure Properties ◽  
Partial Orderings ◽  
Life Distributions ◽  
Crossing Hazards ◽  
Moment Bounds

Kalashnikov and Rachev (1986) have proposed a partial ordering of life distributions which is equivalent to an increasing hazard ratio, when the ratio exists. This model can represent the phenomenon of crossing hazards, which has received considerable attention in recent years. In this paper we study this and two other models of relative ageing. Their connections with common partial orderings in the reliability literature are discussed. We examine the closure properties of the three orderings under several operations. Finally, we give reliability and moment bounds for a distribution when it is ordered with respect to a known distribution.

scholarly journals Ramsey Properties of Countably Infinite Partial Orderings

10.37236/3151 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Marcia J. Groszek
Keyword(s):  
Natural Number ◽  
Large Class ◽  
Bipartite Graphs ◽  
Partial Ordering ◽  
Partial Orderings ◽  
Countably Infinite

A partial ordering $\mathbb P$ is chain-Ramsey if, for every natural number $n$ and every coloring of the $n$-element chains from $\mathbb P$ in finitely many colors, there is a monochromatic subordering $\mathbb Q$ isomorphic to $\mathbb P$.  Chain-Ramsey partial orderings stratify naturally into levels.  We show that a countably infinite partial ordering with finite levels is chain-Ramsey if and only if it is biembeddable with one of a canonical collection of examples constructed from certain edge-Ramsey families of finite bipartite graphs.  A similar analysis applies to a large class of countably infinite partial orderings with infinite levels.

0# and some forcing principles

1986 ◽  
Vol 51 (1) ◽  
pp. 39-46 ◽  
Author(s):  
Matthew Foreman ◽  
Menachem Magidor ◽  
Saharon Shelah
Keyword(s):  
Real Number ◽  
Large Cardinals ◽  
Singular Limit ◽  
Partial Ordering ◽  
The Other ◽  
List Type ◽  
Consistency Strength ◽  
Axiom Of Determinacy ◽  
Partial Orderings ◽  
The Universe

It has been considered desirable by many set theorists to find maximality properties which state that the universe has in some sense “many sets”. The properties isolated thus far have tended to be consistent with each other (as far as we know). For example it is a widely held view that the existence of a supercompact cardinal is consistent with the axiom of determinacy holding in L(R). This consistency has been held to be evidence for the truth of these properties. It is with this in mind that the first author suggested the following:Maximality Principle If P is a partial ordering and G ⊆ P is a V-generic ultrafilter then eithera) there is a real number r ∈ V [G] with r ∉ V, orb) there is an ordinal α such that α is a cardinal in V but not in V[G].This maximality principle applied to garden variety partial orderings has startling results for the structure of V.For example, if for some , then P = 〈{p: p ⊆ κ, ∣p∣ < κ}, ⊆〉 neither adds a real nor collapses a cardinal. Thus from the maximality principle we can deduce that the G. C. H. fails everywhere and there are no inaccessible cardinals. (Hence this principle contradicts large cardinals.) Similarly one can show that there are no Suslin trees on any cardinal κ. These consequences help justify the title “maximality principle”.Since the maximality principle implies that the G. C. H. fails at strong singular limit cardinals it has consistency strength at least that of “many large cardinals”. (See [M].) On the other hand it is not known to be consistent, relative to any assumptions.

Infinite chains and antichains in computable partial Orderings

2001 ◽  
Vol 66 (2) ◽  
pp. 923-934 ◽  
Author(s):  
E. Herrmann
Keyword(s):  
Partial Ordering ◽  
Partial Orderings

AbstractWe show that every infinite computable partial ordering has either an infinite chain or an infinite antichain. Our main result is that this cannot be improved: We construct an infinite computable partial ordering that has neither an infinite chain nor an infinite antichain.

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