Inspiring communication Featuring remarkable people communicating passionately and persuasively, TED Talks provide inspiring ideas and an unparalleled source of authentic language. Keynote invites learners to explore life-changing stories for a deeper understanding of the world, developing the confidence and skills needed to express themselves powerfully and proficiently in English.

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Preface What you are now reading is the written version of an electronic document that explains the mathematical principles for different musical temperaments. The electronic version contains many music examples that you can listen to while you are working with this document at a computer. The written version obviously cannot offer this possibility. It serves therefore merely as a parallel study aid and guide and cannot replace actually working with the electronic text. Musical Temperaments Contents • V II Contents Introduction and Fundamental Properties 1 Pitch and Frequency 1 Preliminary Remarks 1 Frequencies and Intervals 2 Tuning Systems and Frequencies 5 Musical Scales in Different Tunings 5 Pure Tuning 5 Intervals and Triads in Pure Tuning 12 Pythagorean Tuning 23 Intervals and Triads in Pythagorean Tuning 31 Meantone Tuning 34 Intervals and Triads in Meantone Tuning 39 Equal Temperament (Tuning) 42 Intervals and Triads in Equal Temperament (Tuning) 47 Summary 50 Appendices 53 Pictorial explanations 53 Tables of Frequencies and Intervals 54 Operating Instructions 62 Glossary 67 Musical Temperaments Introduction and Fundamental Properties • 1 Introduction and Fundamental Properties Pitch and Frequency Preliminary Remarks It is well known that tones consist of periodically recurring phenomena, that is, beats repeating in a regular pattern. The number of repetitions of beats per second is measured in Hertz: 440 Hertz mean 440 beats per second. This number is also called the frequency of a beat.

Through life-changing stories, respected thinkers and authentic presentations, Keynote promotes a deeper understanding of the world and gives students the courage and means to express themselves in English. Communication, collaboration and creative thinking drive students towards real 21st century outcomes and encourage them to respond to ideas and find their own voice. Both students and teachers will emerge with new confidence, new ideas and a new determination to communicate in this increasingly information-rich world of Global English.

Inspiring communication Featuring remarkable people communicating passionately and persuasively, TED Talks provide inspiring ideas and an unparalleled source of authentic language. Keynote invites learners to explore life-changing stories for a deeper understanding of the world, developing the confidence and skills needed to express themselves powerfully and proficiently in English.

This book provides novel concepts and techniques for air traffic management (ATM) and communications, navigation, and surveillance (CNS) systems. The book consists of selected papers from the 6th ENRI International Workshop on ATM/CNS (EIWAC2019) held in Tokyo in October 2019, the theme of which was “Exploring Ideas for World Aviation Challenges”. Included are key topics to realize safer and more efficient skies in the future, linked to the integrated conference theme consisting of long-term visions based on presentations from various fields. The book is dedicated not only to researchers, academicians, and university students, but also to engineers in the industry, air navigation service providers (ANSPs), and regulators of aviation.