The clef symbol on a musical staff tells you which pitches belong on the lines and spaces of that staff.

A description of the recommended notation for use with digital signal processing modules submitted to the Connexions project.

This course describes discrete mathematics, which involves processes that consist of sequences of individual steps (as compared to calculus, which describes processes that change in a continuous manner). The principal topics presented in this course are logic and proof, induction and recursion, discrete probability, and finite state machines. Upon successful completion of this course, the student will be able to: Create compound statements, expressed in mathematical symbols or in English, to determine the truth or falseness of compound statements and to use the rules of inference to prove a conclusion statement from hypothesis statements by applying the rules of propositional and predicate calculus logic; Prove mathematical statements involving numbers by applying various proof methods, which are based on the rules of inference from logic; Prove the validity of sequences and series and the correctness or repeated processes by applying mathematical induction; Define and identify the terms, rules, and properties of set theory and use these as tools to support problem solving and reasoning in applications of logic, functions, number theory, sequences, counting, probability, trees and graphs, and automata; Calculate probabilities and apply counting rules; Solve recursive problems by applying knowledge of recursive sequences; Create graphs and trees to represent and help prove or disprove statements, make decisions or select from alternative choices to calculate probabilities, to document derivation steps, or to solve problems; Construct and analyze finite state automata, formal languages, and regular expressions. (Computer Science 202)

In standard music notation, the duration (time length) of a particular note is defined by how long it lasts compared to a whole note.

Through a progressive series of composition projects, this course investigates the sonic organization of musical works and performances, focusing on fundamental questions of unity and variety. Aesthetic issues are considered in the pragmatic context of the instructions that composers provide to achieve a desired musical result, whether these instructions are notated in prose, as graphic images, or in symbolic notation. No formal training is required. Weekly listening, reading, and composition assignments draw on a broad range of musical styles and intellectual traditions, from various cultures and historical periods.

This module introduces symbols used in music to designate pitch.

This introduction to the piano keyboard explains the layout of the piano keyboard and relates it to the musical alphabet and notation in the treble clef.

The key signature at the beginning of a musical staff lists the sharps or flats in the key.

Mathematical tools and methods for computer science and engineering. Emphasis on development of rigorous thinking, analytical skills, and mathematical sophistication while learning elementary discrete mathematics. Topics: mathematical proofs; induction and well-ordering; divisibility and congruences; asymptotic notation and growth of functions; sets, relations, functions, and graphs; counting theory; recurrences and generating functions; and discrete probability.

In standard notation, a sharp symbol raises the pitch of the natural note by a half-step; a flat symbol lowers it by a half-step.

A teacher's guide to lecturing on series and series notation.

An updated version of the Homework: Series and Series Notation module.

Fundamentals of signals, systems, and information theory with emphasis on modeling both the audio/visual message and the human recipient. Linear systems, difference equations, Z-transforms, sampling and sampling rate conversion, convolution, filtering, modulation, Fourier analysis, entropy, noise, Shannon's fundamental theorems. Additional topics may include data compression, filter design, and feature detection.

Western music is usually written on a staff. People were talking long before they invented writing. People were also making music long before anyone wrote any music down. Some musicians still play "by ear" (without written music), and some music traditions rely more on improvisation and/or "by ear" learning. But written music is very useful, for many of the same reasons that written words are useful. Music is easier to study and share if it is written down. Western music specializes in long, complex pieces for large groups of musicians singing or playing parts exactly as a composer intended. Without written music, this would be too difficult. Many different types of music notation have been invented, and some, such as tablature, are still in use. By far the most widespread way to write music, however, is on a staff. In fact, this type of written music is so ubiquitous that it is called common notation.

We introduce superfields in chapter 2 for the simpler world of three spacetime dimensions, where superfields are very similar to ordinary fields. We skip the discussion of nonsuperspace topics (background fields, gravity, etc.) which are covered in following chapters, and concentrate on a pedagogical treatment of superspace. We return to four dimensions in chapter 3, where we describe how supersymmetry is represented on superfields, and discuss all general properties of free superfields (and their relation to ordinary fields). In chapter 4 we discuss simple (N = 1) superfields in classical global supersymmetry.

We include such topics as gauge-covariant derivatives, supersymmetric models, extended supersymmetry with unextended superfields, and superforms. In chapter 5 we
extend the discussion to local supersymmetry (supergravity), relying heavily on the compensator
approach. We discuss prepotentials and covariant derivatives, the construction of actions, and show how to go from superspace to component results. The quantum aspects of global theories is the topic of chapter 6, which includes a discussion of the background field formalism, supersymmetric regularization, anomalies, and many examples of supergraph calculations. In chapter 7 we make the corresponding analysis of quantum supergravity, including many of the novel features of the quantization procedure (various types of ghosts). Chapter 8 describes supersymmetry breaking, explicit and spontaneous, including the superHiggs mechanism and the use of nonlinear realizations.

We have not discussed component supersymmetry and supergravity, realistic superGUT models with or without supergravity, and some of the geometrical aspects of classical supergravity. For the first topic the reader may consult many of the excellent reviews and lecture notes. The second is one of the current areas of active research. It is our belief that superspace methods eventually will provide a framework for streamlining the phenomenology, once we have better control of our tools. The third topic is attracting increased attention, but there are still many issues to be settled; there again, superspace methods should prove useful.

We assume the reader has a knowledge of standard quantum field theory (sufficient to do Feynman graph calculations in QCD). We have tried to make this book as pedagogical and encyclopedic as possible, but have omitted some straightforward algebraic details which are left to the reader as (necessary!) exercises.

The time signature on a musical staff tells you the meter of the music by defining both the number of beats in a measure and the type of note that fills one beat.

Explains two's complement notation.