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Music and Mathematics Harmony

Pythagoras was quoted as saying, “there is geometry in the humming of the strings, there is music in the spacing of the spheres.” As poetic as this sounds, the famous Greek mathematician was actually making a direct statement about the connection between mathematics and music. In modern times, math is a subject generally associated with left brained individuals and music is a subject generally associated with right brained individuals. What most don’t realize is that the subjects go hand in hand, and have been intertwined as early as the times of Greek antiquity; “great minds took such pains to include music in their worldview and indeed saw music as the organizing principle of the universe” [rogers]. Viewing music and science as profoundly linked was the dominant and accepted way of thinking in Western and non-Western philosophers of the past. Mathematics and music are both subjects that require an abstract way of thinking and contemplation. Both subjects require recognizing and establishing patterns. It is important to note that although the subjects on a whole are more similar than usually given credit for in this day and age, they are also interdisciplinary. Math has historically been used to describe and teach music, and vice versa. Mathematics can be found etched in common musical concepts such as scales, intervals, wave frequencies, and tones. J. Ph. Rameau, a French musicologist of the eighteenth century, said it best in his Traitd de l’harmonie rdduite d ses principes naturels (1722): “Music is a science which must have determined rules. These rules must be drawn from a principle which should be evident, and this principle cannot be known without the help of mathematics. I must confess that in spite of all the experience which I have acquired in music by practising it for a fairly long period, it is nevertheless only with the help of mathematics that my ideas became disentangled and that light has succeeded to a certain darkness of which I was not aware before.” [Papadopoulos] In Greek antiquity, it was common knowledge that the schools of Aristotle, Plato, and Pythagoras deemed music a part of mathematics. A Greek mathematical treatise would typically be comprised of four topics: Number Theory, Geometry, Music, and Astronomy. Mathematics and music were strongly linked until the Renaissance, when the two subjects diverged – theoretical music becoming an independent field. Pythagoras is recognized as the first music theorist. His greatest discovery dealt with the relation of musical intervals with ratios of integers. The story is: on a trip through a brazier’s shop, Pythagoras took note of the different sounds being produced by the hammers on anvils. He realized that the pitch he was hearing depended only on the weight of the hammer. The place the hammer hit the anvil, the angle it was hit, the magnitude of the stroke – none of these factored into the pitch. This lead him to ponder about the relationship between two notes produced by two different hammers. In classical Greek music there were intervals of the octave, fifth, and fourth. He recognized that the consonant musical intervals the hammers were creating corresponded, in terms of weights, to the numerical fraction 2/1, 3/2, and 4/3, respectively. Pythagoras discovered that musical intervals, and hence all harmony, are based on mathematical ratios, ratios that also, amazingly, appear in astronomy [rogers] Thus, Pythagoras thought that the relative weights of two hammers producing an octave is 2/1, and so on. As soon as this idea occurred to him, Pythagoras went home and performed several experiments using different kinds of instruments, which confirmed the relationship between musical intervals and numerical fractions Papadopoulos musical theory constructed by Pythagoras. Two sounds from the same taut string are said to be consonant when they are pleasing to listen to simultaneously. In the Greek cultural arena of that period such sounds are produced by lengths of string that are inversely proportional to the numbers 1, 2, 3, and 4. These compose the famous Tetraktys (1 2 3 4 = 10), a diagram of figured numbers symbolising pure harmony, the “vertical hierarchy of relation between Unity and emerging multiplic Perrine Pythagoreans considered a collection of vases, filled partially with different quantities of the same liquid, and observed on them the “rapidity and the slowness of the movements of air vibrations.” By hitting these vases in pairs and listening to the harmonies produced, they were able to associate numbers to consonances. The result is again that the octaves, fifths, and fourths correspond respectively to the fractions 2/1, 3/2 and 4/3, in terms of the quotients of levels of the liquid. Papadopoulos rich musical evolution flowing from the Greek roots into the Latin world and right up to the fourteenth century of our era. In St. Augustine’s De Musica, written at the end of the fourth century, rhythms are also classified according to their proportions (the proportional notation used today came much later). Then in the ninth century, Perrine Carolingian policy in educational and ecclesiastical matters defined new practices. It encouraged the use of neumes that indicate the inflexions of the voice, but not the pitch of the sounds. The names Do, Re, Mi, Fa, Sol, etc., appeared with Guido d’Arezzo in the eleventh century, derix4ng from the syllables at the beginning of the stanzas (voces) of a hymn addressed to St John the Baptist, written around 770 A.D. The notes (claves) are also designated by letters, a practice that is still in use today in Englishspeaking countries (La = A, Ti = B, Do = C, . . . ) and in Germany (with some specificities). Finally, polyphony created new needs for harmonic mastery, the response coming from Philippe de Vitry in the fourteenth century with his Ars Nova: in this work he defined new musical notations as well as new ways of combining rhythms. However, this culmination of the pythagorean musical base that had developed over many centuries eventually degenerated in the following century because it proved to be inadequate for responding to the new aesthetic trends that were appearing as well as the practical needs of musicians Perrine Music makes use of a symbolic language, together with a rich system of notation, including diagrams which, starting from the eleventh century (in the case of Western European music), are similar to mathematical graphs of discrete functions in two-dimensional cartesian coordinates (the x-coordinate representing time and the y-coordinate representing pitch). Music theorists used these “cartesian” diagrams long before they were introduced in geometry. Musical scores from the twentieth century have a variety of forms which are close to all sorts of diagrams used in mathematics. Besides abstract language and notation, mathematical notions like symmetry, periodicity, proportion, discreteness, and continuity, among others, are omnipresent in music. Lengths of musical intervals, rhythm, duration, tempi, and several other musical notions are naturally expressed by numbers. {Papadopoulos} Logarithms The arithmetic of musical intervals involves in a very natural way the theory of logarithms.Pythagoras defined the tone as the difference between the intervals of fifth and of fourth. The point now is that the fraction associated to the tone interval is not the difference 3/2 – 4/3, but the quotient (3/2)/(4/3) = 9/8. It is natural to define the compass of a musical interval as the number (or the fractions of) octaves it contains. Thus, when we say that two notes are n octaves apart, the fraction associated to the interval that they define is 2 n. The definition of the compass can be made in terms of frequency, and in fact one usually defines the pitch as the logarithm in base 2 of the frequency. (Of course, the notion of frequency did not exist as such in antiquity, but it is clear that the ancient Greek musicologists were aware that the lowness or the highness of pitch depends on the slowness or rapidity of the air vibration that produces it, as explained in Theon’s treatise [12], Chapter XIII.) The relation of musical intervals with logarithms can also be seen by considering the lengths of strings (which in fact are inversely proportional to the frequency). For instance, if a violinist (or a lyre player in antiquity) wants to produce a note which is an octave higher than the note produced by a certain string, he must divide the length of the string by two. Thus, music theorists dealt intuitively with logarithms long before these were defined as an abstract mathematical notion. (It was only in the seventeenth century that logarithms were formally introduced in music theory, by Isaac Newton, and then by Leonhard Euier and Jacques Lambert.) The theory of musical intervals is a natural example of the practical use of logarithms, an example easily explained to children, provided they have some acquaintance with musical intervals. {Papadopoulos} Today the Music of corpuscles and solitons is taking the place of the Music of spheres and mermaids. Considerations of the multiple infinitely small (chaos?) are replacing those on the single infinitely great (the cosmos?). The bifurcation took place at the end of the eighteenth century, at the very moment when musicians were being pushed into the category of artists, whose role was to provide pleasure for the present, and mathematicians into the category of scientists, building the society of the future. Perrine Rogers, G. L. (2016). The Music of the Spheres. Music Educators Journal, 103(1), 41-48. doi:10.1177/0027432116654547 Papadopoulos, A. (2002). Mathematics and music theory: From pythagoras to rameau. The Mathematical Intelligencer, 24(1), 65-73. doi:10.1007/BF03025314 Perrine, S. (2005). Mathematics and music. a diderot mathematical forum. The Mathematical Intelligencer, 27(3), 69-73. doi:10.1007/BF02985844
Wake Technical Community College Inkblot Projective Tests Discussion.

Choose one of the projective tests described in the text and discuss its use during psychotherapy. The tests to choose from are: Ink blot test, Thematic Apperception test, and Human Figure Drawing test.Explain what is accomplished with the test. Evaluate the test you chose, giving both its strengths and weaknesses.Write about a dream you have had and give an example of a psychoanalytic interpretation of it. Why do people dream, according to Freud? Summarize the research findings on dreams that challenge Freud’s theory of dreaming.Please use 500 words or more .
Wake Technical Community College Inkblot Projective Tests Discussion

New England College Blockchain Technology in Banking Industry Essay

New England College Blockchain Technology in Banking Industry Essay.

Industry experts believe blockchain is a technology that has the potential to affect the business of most IT professionals in the next five years. Pick an industry you feel will be most affected by blockchain and how blockchain may be used in that industry. As an IT manager, how would you embrace blockchain? For instance, how would training occur for your team, what strategies might you use, what security methods may you recommend be used?Your paper should meet the following requirements:Be approximately four to six pages in length, not including the required cover page and reference page.Follow APA7 guidelines. Your paper should include an introduction, a body with fully developed content, and a conclusion.Support your answers with the readings from the course and at least two scholarly journal articles to support your positions, claims, and observations, in addition to your textbook. The UC Library is a great place to find resources.Be clearly and well-written, concise, and logical, using excellent grammar and style techniques. You are being graded in part on the quality of your writing.
New England College Blockchain Technology in Banking Industry Essay

Future E Business Challenges And Opportunities Information Technology Essay

essay help online E-business changed the way business was being done over the years. It created more and more avenues and opportunities. E-business changed the competitive platform. While the old competitive barriers are diminishing it created new entry and competitive barriers. The hard competitive barriers are becoming weak while the soft competitive barriers became more and more prominent. It is believed that not even 50% of the potential of e-business is to be unleashed yet. This definitely indicates that e-business has lot more to offer. E-business has appealed the businesses and customers from all segments. E-business increased the connectivity among different businesses. The integration among departments, different businesses, and different sectors through e-business made it possible to offer variety of services to customers. The new technologies, high speed internet made the transactions possible. Improved integration and interoperability needs of next generation e-business systems are met by new e-business solution architectures. New technologies of data storage, distributed access and cloud computing allowed advantages like access of information. Trading knowledge, online information transaction, bidding for even small articles, integrated online solutions and many more business applications have become possible with the blessing of technologies. While e-business has revolutionized global economy and information management, it also improved services and reach of businesses. There is high possibility that e-business will overtake the traditional way of doing business in coming years. New business, technology and organizational architectures have emerged and will emerged to support e-business. Web 2.0, web 3.0 and other developments seem to revolutionize whole e-business spectrum. E-business is the journey of empowering business which has wheels of technology, strategies and processes. The robust, stable and adaptive framework is required to absorb new innovations. In this chapter we will discuss various environments that can provide opportunity for e-business to unleash its potential. While doing this we will also discuss about the constraints. E-business is adopted in many sectors – and can go beyond those sectors. The collaboration of business components, different sectors and technologies while creating new opportunities posed many new challenges. The focus still remains the strategic and technological aspects of e-business. The legal issues, intellectual property related issues, security and regulatory issues will definitely focus of future e-business. While addressing the technical and social issues e-business related to strike the balance. It is a way of living, life style and way of doing business. Hence future e-business is holistic and more systemic where it is not a technology but it is life style and business style appealing to masses. 15.2 New technologies knocking on the door: Technologies are evolving at a faster pace than social evolution. Last three centuries witnessed this technology change and last three decades experience the technology movement changing the lifestyle of every individual. The people reluctant to use debit card due to security concerns have started freely using credit cards, started paying electronically and online. Technologies evolved and that revolutionized the speed of Internet, downloads and communication. On line movie releases, online book releases are no longer remained a friction. The faster, cheaper and relatively more secured transactions fueled the growth of e-business. E-tourism, e-libraries grown by many folds in last five years. The new technologies like 3G, web 3.0, advanced processors and new frameworks promised the better business experience. The new technologies like cloud computing and 3G even helped to change the old paradigm of e-business like: – One needs to own the infrastructure – One needs to pay monthly – There is nothing like on demand The new paradigms like collaborative on-demand services, transaction based payments, sharing of space and information along with processor, memory have changed the business paradigm. The new paradigm and new technologies helped to develop new ways of management, strategic and implementation enabling to overcome hurdles in adoption and diffusion of e-business. So this is now prompting e-business not only to be looked as technology innovation but also as a business innovation. E-business readiness, environment readiness is increasing and with new technologies knocking at the door it is expected to grow e-business many folds. Technologies are drivers for this change and are also prepare platform to support new strategic and business concepts. It is expected that the availability of broad band to end user will increase further to 1000 million and that will develop a socially acceptable communication lifestyle. The new technology development in safeguarding sensitive information has created many business opportunities. The next generation technologies will improve privacy protection, strengthen security, provide personalized services and access controls and will change the face of the business and social transactions. The explosion of social networking and their possible integration with business and information transactions would help to create a collaborative and integrated e-business platform creating many business opportunities. But this will definitely lead to many questions and challenges like systemic, social and ethical issues. It will pose the challenges like impact of different activities on other systems, social infrastructure. The new technologies knocking at the door can like new security frameworks can help to solve these problems. 15.3 Business with limited infrastructure: The new technologies and on demand services, on demand storage, on demand infrastructure and even on demand information can allow to set a business with limited infrastructure. The integrated and collaborative approaches allow setting business with limited infrastructure. The processing power can be shared, memory and storage can be shared, and bandwidth can also be shared. This allow service provider to provide you infrastructure on demand – i.e. when you need (for specific time slots), how much you need (a small amount to huge one). Any way this may raise a few security concerns about information and business data. That can also be resolved by technology allowing you to have your private and controlled but shared and collaborative frameworks. 15.4 From e-paper to E-gadgets: The traditional gadgets with no communication abilities are replaced by e-gadgets – those are intelligent and have communication abilities. These communication abilities of e-gadgets help the growth of e-business. These gadgets allow different transactions, they can communicate among themselves and build knowledge and information base. E-paper are the range of display and other electronic technologies those are designed to give feel of real paper and gives the experience similar to actual paper reading. Stable images, wider viewing angle and no blinking helps to make e-paper reading much more comfortable compared to images on regular computer screens. E-papers, e-gadgets change the overall transaction experience of users involved in e-business. Similarly advanced gadgets, connectivity, integration allows the communication among different stakeholders. The overall ease of communication and ability to transact electronically expected to evolve the business communication to next level. 15.5 Changing the way business is done: From the years together the way business used to be done has evolved. Initially from the simple exchange of useful amenities the business began and created value for every trader in the village. As this type of exchange was not possible always and hence there was need of common currency. This introduced different coins. These coins were different for different kingdoms and there was no way to exchange across the small kingdoms. Slowly there was standardization and security embedded in currency. This evolved to common currencies, conversion rates and later to some standard currencies like Euro that can be traded across countries. The user experience and business growth have been the driving factor for evolution of business. Electronic technology evolved the traditional businesses. The information availability, advanced communication means and technologies like credit cards made it possible to transact remotely and without actual currency exchange. In coming years the further evolution of technology can address the issues in transaction experience and security concerns in these transaction. Next level of integration between the traditional and modern ways of business will change the way business is done. The more intelligent and user friendly gadgets will not only help users but also to businessmen. 15.6 Getting ready for new technologies: No innovation is possible unless society, environment and business is ready for new technology or for that innovation. It demands the understanding of technology and utilities by users and further users can see value and minimal risk in new technologies. There are some other factors like individual should able to identify himself with the technology use, he should be acquainted to technology and can see the value in it. Society gets ready for new technology based on infrastructure, availability and positioning of technology. 15.7 Challenges and New Trends: The communication and the ability to communicate has been strength of human being. These communications can create social and emotional bonding. Every evolution and change in e-business has introduced new means to communicate and transact. These new means to transact also introduce new challenges. The concepts and paradigms of personalization and parameters of security changed. Though the law is catching up with the online business world – still there are many challenges like dealing with intellectual property related issues, regulatory policies, taxation policies and most importantly restriction of information access and censorship. These issues not only create business implication but many times lead to social unrest. Many ethical issues and business issues create complications those can lead to long term negative social and business impacts. The electronic acceptance of agreement still has numerous issues and IT acts needs to be technology aware to deal with them. While legal system is stretched between social issues and business issues with reference to new business technology – e-business definitely has potential to provide better mechanism for financial transactions. As per Narayan Murthy – “Technology will solve many social issues and irregularities in days to come” 15.8 Ethical and regulatory issues: The protection of intellectual property through security mechanisms and through legal infrastructure remains the challenge in front of E-business. Ethical and regulatory issues and technology and legal infrastructure to solve these issues will remain point of focus and dominate the further evolution in e-business. As the dependency of users and businesses on e-business infrastructure — the various attacks and anti-competitive activities will increase. In this case user needs technological and legal protection. The social and environmental impact of technology and use of e-business need to be understood. Even the management of electronic waste and other waste material, impacts of huge data centers on environment are a few more issues those will be focused as part of ethical practices. The cautious approach towards selection of technology and testing them and applying them with ethical and regulatory issues in mind can help in building sustainable e-business. 15.9 Summary: E-business is neither technology nor management it is a paradigm of doing the business. It changed the paradigm and assumptions with witch the business used to be done. It revolutionized the transaction processes and created more avenues for transaction. It even created platforms for new social networking, knowledge acquisition and infrastructure use. E-business changed life, business and assumption. Every change comes with opportunities and challenges. Along with business opportunities and value created for user – e-business has posed many security related, society related, ethical and transactional challenges. The next generation technologies and future e-businesses are focused on user experience and technological parameters have to go much beyond that to address these concerns. E-business is business and social paradigm with huge opportunities and many challenges and unanswered question. The quest for the business excellence will drive the technology growth and penetration of e-business across the globe in coming years. Concept review Questions: 1. Discuss challenges in e-business implementation 2. Discuss role of new technology in driving next generation e-business 3. Discuss e-business as a business and transaction paradigm Critical thinking exercise: 1. List five important technologies in e-business and impact 2. Discuss social networking and e-business 3. Discuss three pressing ethical issues in e-business Project work: 1. List the growth of e-business and penetration in five developing and five developed countries with reasons 2. Draw a conceptual next generation e-business framework

Florida International University Mod 13 Helping English Language Learners Paper

Florida International University Mod 13 Helping English Language Learners Paper.

I’m working on a literature question and need support to help me understand better.

This 45-minute webcast offers practical information on how to teach English language learners effective comprehension skills
Dr. Cynthia Lundgren is an assistant professor at The Center for Second Language Teaching and Learning at Hamline University’s Graduate School of Education in St. Paul, MN. In this interview, Dr. Lundgren offers a blueprint for administrators who are serving a new or changing population of ELLs. Topics covered include creating a welcoming culture, assessment, language instruction, staffing, and professional development. In addition, Dr. Lundgren has contributed to the following resources from Colorín Colorado:
Kristina Robertson is an ELL specialist with extensive experience as a classroom teacher and professional development leader. Kristina is the current Titles Coordinator for the Burnsville-Eagan-Savage School District in Minnesota. Kristina is a contributor to our Bright Ideas section (Links to an external site.) and is featured in a Colorín Colorado 
Delia Pompa is the moderator of this webcast. She is the Vice President of the Center for Community Educational Excellence, at the National Council of La Raza.
Use the following prompts to guide your submission:

Some activities that can be used to help ELL students tap into their prior knowledge of a topic.
Ms. Gonazlez classroom at Webster Elementary School.  How is her program unique and very helpful for ELLs?  How does she use cognates? What is some of the extra help she gives her students? What role does their native language play in their transfer to reading and writing in English?
The reading skills that transfer from the first to second language 
ELLs learning comprehension strategies that will help with their academic English in the Heritage Elementary School in Portland Oregon.  Discuss the different strategies that are used to help the ELL students.
Reciprocal teaching at Frank Love Elementary  School in Seattle Washington.  How does it work?
Consider a classroom reading book you recently used. What vocabulary or concepts were presented in the book that could cause confusion for ELL learners? What could you do to scaffold the read aloud experience that would benefit ELL learners?
The final thoughts of the moderators of the Webcast.

Florida International University Mod 13 Helping English Language Learners Paper

ISOL 535 University of the Cumberlands Block Encryption in CBC Using 3DES Discussion

ISOL 535 University of the Cumberlands Block Encryption in CBC Using 3DES Discussion.

For this project you will solve the problem presented using Figure 7.17 located in our text and write a 2-3 page report that includes the following:2-3 pages of content minimum (does not include cover, abstract or references pages)Paper must conform to full APA guidelines to include a cover page, abstract, headers, introduction, body paragraphs with appropriate headings/subheadings, conclusion, and a reference page.All sources must be cited and references. Remember, unless the statement is common knowledge, you must cite and reference your sources.You must use at least one peer-reviewed source Ensure you follow academic integrity policies. Problem: You want to build a hardware device to do block encryption in the cipher block chaining (CBC) mode using an algorithm stronger than DES. 3DES is a good candidate. Figure 7.17 shows two possibilities, both of which follow from the definition of CBC. Which of the two would you choose and why: For security?For performance? You must fully explain your justification and reasoning.
ISOL 535 University of the Cumberlands Block Encryption in CBC Using 3DES Discussion