Modal logicModal logic is a kind of logic used to represent statements about necessity and possibility. It plays a major role in philosophy and related fields as a tool for understanding concepts such as knowledge, obligation, and causation. For instance, in epistemic modal logic, the formula can be used to represent the statement that is known. In deontic modal logic, that same formula can represent that is a moral obligation. Modal logic considers the inferences that modal statements give rise to.
Music theoryMusic theory is the study of the practices and possibilities of music. The Oxford Companion to Music describes three interrelated uses of the term "music theory": The first is the "rudiments", that are needed to understand music notation (key signatures, time signatures, and rhythmic notation); the second is learning scholars' views on music from antiquity to the present; the third is a sub-topic of musicology that "seeks to define processes and general principles in music".
Mode (music)In music theory, the term mode or modus is used in a number of distinct senses, depending on context. Its most common use may be described as a type of musical scale coupled with a set of characteristic melodic and harmonic behaviors. It is applied to major and minor keys as well as the seven diatonic modes (including the former as Ionian and Aeolian) which are defined by their starting note or tonic. (Olivier Messiaen's modes of limited transposition are strictly a scale type.
Modal μ-calculusIn theoretical computer science, the modal μ-calculus (Lμ, Lμ, sometimes just μ-calculus, although this can have a more general meaning) is an extension of propositional modal logic (with many modalities) by adding the least fixed point operator μ and the greatest fixed point operator ν, thus a fixed-point logic. The (propositional, modal) μ-calculus originates with Dana Scott and Jaco de Bakker, and was further developed by Dexter Kozen into the version most used nowadays.
Modal operatorA modal connective (or modal operator) is a logical connective for modal logic. It is an operator which forms propositions from propositions. In general, a modal operator has the "formal" property of being non-truth-functional in the following sense: The truth-value of composite formulae sometimes depend on factors other than the actual truth-value of their components. In the case of alethic modal logic, a modal operator can be said to be truth-functional in another sense, namely, that of being sensitive only to the distribution of truth-values across possible worlds, actual or not.
Diatonic and chromaticDiatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, especially when applied to contrasting features of the common practice music of the period 1600–1900. These terms may mean different things in different contexts. Very often, diatonic refers to musical elements derived from the modes and transpositions of the "white note scale" C–D–E–F–G–A–B.
Pitch classIn music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart; for example, the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave position." Important to musical set theory, a pitch class is "all pitches related to each other by octave, enharmonic equivalence, or both." Thus, using scientific pitch notation, the pitch class "C" is the set {Cn : n is an integer} = {..., C−2, C−1, C0, C1, C2, C3 ...}.
Chromatic scaleThe chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely, pitch classes) used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce the chromatic scale, while other instruments capable of continuously variable pitch, such as the trombone and violin, can also produce microtones, or notes between those available on a piano. Most music uses subsets of the chromatic scale such as diatonic scales.
Musical analysisMusical analysis is the study of musical structure in either compositions or performances. According to music theorist Ian Bent, music analysis "is the means of answering directly the question 'How does it work?'". The method employed to answer this question, and indeed exactly what is meant by the question, differs from analyst to analyst, and according to the purpose of the analysis. According to Bent, "its emergence as an approach and method can be traced back to the 1750s.
Common practice periodIn European art music, the common-practice period is the era of the tonal system. Most of its features persisted from the mid-Baroque period through the Classical and Romantic periods, roughly from 1650 to 1900. There was much stylistic evolution during these centuries, with patterns and conventions flourishing and then declining, such as the sonata form. The most prominent, unifying feature throughout the period is a harmonic language to which music theorists can today apply Roman numeral chord analysis.
Set theory (music)Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonal music. Other theorists, such as Allen Forte, further developed the theory for analyzing atonal music, drawing on the twelve-tone theory of Milton Babbitt. The concepts of musical set theory are very general and can be applied to tonal and atonal styles in any equal temperament tuning system, and to some extent more generally than that.
Musical noteIn music, a note is the representation of a musical sound. Notes can represent the pitch and duration of a sound in musical notation. A note can also represent a pitch class. Notes are the building blocks of much written music: discretizations of musical phenomena that facilitate performance, comprehension, and analysis. The term note can be used in both generic and specific senses: one might say either "the piece 'Happy Birthday to You' begins with two notes having the same pitch", or "the piece begins with two repetitions of the same note".
Modality (linguistics)In linguistics and philosophy, modality refers to the ways language can express various relationships to reality or truth. For instance, a modal expression may convey that something is likely, desirable, or permissible. Quintessential modal expressions include modal auxiliaries such as "could", "should", or "must"; modal adverbs such as "possibly" or "necessarily"; and modal adjectives such as "conceivable" or "probable".
Scale (music)In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale. Often, especially in the context of the common practice period, most or all of the melody and harmony of a musical work is built using the notes of a single scale, which can be conveniently represented on a staff with a standard key signature.
Sheet musicSheet music is a handwritten or printed form of musical notation that uses musical symbols to indicate the pitches, rhythms, or chords of a song or instrumental musical piece. Like its analogs – printed books or pamphlets in English, Arabic, or other languages – the medium of sheet music typically is paper (or, in earlier centuries, papyrus or parchment).
WoodWood is a structural tissue found in the stems and roots of trees and other woody plants. It is an organic material - a natural composite of cellulose fibers that are strong in tension and embedded in a matrix of lignin that resists compression. Wood is sometimes defined as only the secondary xylem in the stems of trees, or it is defined more broadly to include the same type of tissue elsewhere such as in the roots of trees or shrubs. In a living tree it performs a support function, enabling woody plants to grow large or to stand up by themselves.
Pitch (music)Pitch is a perceptual property of sounds that allows their ordering on a frequency-related scale, or more commonly, pitch is the quality that makes it possible to judge sounds as "higher" and "lower" in the sense associated with musical melodies. Pitch is a major auditory attribute of musical tones, along with duration, loudness, and timbre. Pitch may be quantified as a frequency, but pitch is not a purely objective physical property; it is a subjective psychoacoustical attribute of sound.
SleepSleep is a state of reduced mental and physical activity in which consciousness is altered and sensory activity is inhibited to a certain extent. During sleep, there is a decrease in muscle activity, and interactions with the surrounding environment. While sleep differs from wakefulness in terms of the ability to react to stimuli, it still involves active brain patterns, making it more reactive than a coma or disorders of consciousness. Sleep occurs in repeating periods, during which the body alternates between two distinct modes: REM and non-REM sleep.
Engineered woodEngineered wood, also called mass timber, composite wood, man-made wood, or manufactured board, includes a range of derivative wood products which are manufactured by binding or fixing the strands, particles, fibres, or veneers or boards of wood, together with adhesives, or other methods of fixation to form composite material. The panels vary in size but can range upwards of and in the case of cross-laminated timber (CLT) can be of any thickness from a few inches to or more.
Wood preservationWood easily degrades without sufficient preservation. Apart from structural wood preservation measures, there are a number of different chemical preservatives and processes (also known as timber treatment, lumber treatment or pressure treatment) that can extend the life of wood, timber, and their associated products, including engineered wood. These generally increase the durability and resistance from being destroyed by insects or fungi. As proposed by Richardson, treatment of wood has been practiced for almost as long as the use of wood itself.
