Music and Modular Arithmetic and their Similarities

For many â€Å"right-brained† people, like myself, math is not an enjoyable concept. Aside from just counting, it seems that there is no correlation between people who practice differential calculus and people who practice Violin Concertos. When I am working on learning a piece of music, the only numbers I need to know are measure numbers and note numbers. But without realizing it, there is a pattern of numbers that is present in most all music, a basic scale. Though it is different for each key, most pieces stick to a basic eight note scale. Musicians understand the concept of the musical alphabet. It begins at A and ends on G and is repeated over and over. But this concept of the musical alphabet is the concept of modular arithmetic. If a piece is in the key of C major, the C~scale would begin on C and go up. Each semitone between the beginning C and the next octave could be numbered 1 to 12. However, at the number 13, the scale starts over at C again. The next whole tone, D , would be numbered 14. But there are only 12 notes in the chromatic scale so this new, higher D is 14-12 which equals 2. Therefore, 14 is 2 modulated 12. This diagram shows a three octave scale beginning on a C and ending on an E. The original line of numbers is how all the notes would be counted without repetition. Each new line of numbers begins at 1 again at a new octave C. So without knowing it, musicians have incorporated modular arithmetic into the very fabric of musical theory through the musicalShow MoreRelatedManaging Information Technology (7th Edition)239873 Words   |  960 PagesRole of the Operating Manager in Information Systems 10 PART I Information Technology Chapter 2 Computer Systems 17 19 Basic Components of Computer Systems 20 Underlying Structure 20 Input/Output 20 Computer Memory 21 Arithmetic/Logical Unit Computer Files Control Unit 23 23 25 The Stored-Program Concept 25 Types of Computer Systems 28 Microcomputers 29 Midrange Systems 30 Mainframe Computers Supercomputers 33 34 Key Types of SoftwareRead MoreStephen P. Robbins Timothy A. Judge (2011) Organizational Behaviour 15th Edition New Jersey: Prentice Hall393164 Words   |  1573 Pagesdilemma. Some researchers propose that managers need to make a concerted effort to adapt their organizational culture to match the culture of the countries in which they operate. These authors note that within any country, there is a great deal of similarity in management practices that is likely the result of culture or values. If a country’s basic outlook is highly individualistic, then organizational culture should also emphasize individual contributions and efforts. Conversely, if national cultureRead MoreIntroduction to Materials Management169665 Words   |  679 Pagesto be established. Although marketing naturally looks at products from the customers’ point of view of functionality and application, manufacturing looks at products in terms of processes. Thus, firms need to establish product groups based on the similarity of manufacturing processes. Manufacturing must provide the capacity to produce the goods needed. It is concerned more with the demand for the specific kinds of capacity n eeded to make the products than with the demand for the product. Capacity isRead MoreStrategic Marketing Management337596 Words   |  1351 Pagesto an analysis of the firm’s competitive position. A detailed discussion of how this can be done appears in Chapter 6. In essence, however, this involves a combination of strategic group analysis in which competitors are mapped in terms of their similarities, dissimilarities, their capabilities and the strategies they follow, and market share analysis to highlight their relative degrees of market power. 5 This information is then used as the basis for identifying in detail how environmental forces