It bridges the gap between the natural sciences and music theory and, nearly a century after its first publication, it is still a standard text for the study of physiological acoustics — the scientific basis of musical theory. It is also a treasury of knowledge for musicians and students of music and a major work in the realm of aesthetics, making important contributions to physics, anatomy, and physiology in its establishment of the physical theory of music. Difficult scientific concepts are explained simply and easily for the general reader.The first two parts of this book deal with the physics and physiology of music. Part I explains the sensation of sound in general, vibrations, sympathetic resonances, and other phenomena. Part II cover combinational tones and beats, and develops Helmholtz's famous theory explaining why harmonious chords are in the ratios of small whole numbers (a problem unsolved since Pythagoras).Part III contains the author's theory on the aesthetic relationship of musical tones. After a survey of the different principles of musical styles in history (tonal systems of Pythagoras, the Church, the Chinese, Arabs, Persians, and others), he makes a detailed study of our own tonal system (keys, discords, progression of parts).Important points in this 576-page work are profusely illustrated with graphs, diagrams, tables, and musical examples. 33 appendices discuss pitch, acoustics, and music, and include a very valuable table and study of the history of pitch in Europe from the fourteenth to the nineteenth centuries.

    ca. 165), a convert to Christianity from traditional Greek religion. The Dialogue purports to be a two-day dialogue that took place in Asia Minor between Justin and Trypho, a Hellenized Jew. Justin argues extensively on the basis of lengthy Old Testament quotations that Christ is the Messiah and God incarnate, and that the Christian community is the new Israel. In the beginning of the work Justin recounts how he converted to Christianity.The Dialogue remains of great, and varying, interest. It has important information on the development of Jewish-Christian relations, on the development of the text of the Old Testament, and on the existence and character of the early Jewish Christian community. Justin's story of how he became a Christian is one of our earliest conversion accounts. The Dialogue is an ideal textbook for classes investigating the development of religion in Late Antiquity since it touches on many aspects of religion in the Roman Empire.This edition of the Dialogue with Trypho is a revision of Thomas B. Falls's translation, which appeared in Fathers of the Church, vol. 6. Thomas P. Halton has emended the translation in light of the 1997 critical edition by Miroslav Marcovich, and he has provided extensive annotation to recent scholarship on the Dialogue. Michael Slusser has edited the volume to bring it into conformity with the new Selections from Fathers of the Church series.ABOUT THE TRANSLATOR:Thomas P. Halton is Professor Emeritus of Greek and Latin at the Catholic University of America. He has served as the general editor of the Fathers of the Church series since 1983.

    Donald E. Knuth so loved the Bible that he dedicated five years of his life to creating this masterpiece. With it, you will learn about each 3:16 verse of the Bible, how it came to be written, and how it contributes to the wholeness of the Bible.

    His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.