This document discusses different types of seamless korvais in Carnatic music. It begins by defining korvais and describing different levels of complexity. It then discusses natural, seamless korvais that have elegant mathematical patterns not found in textbooks. Several examples of seamless korvais are provided, including those with progressive, dovetailing, boomerang, and 3-speed patterns. The document also discusses "keyless korvais" that have aesthetic simplicity despite lacking clear mathematical relationships. Finally, it explores extensions of seamless korvais concepts to other talas like Khanda Triputa and Mishra Chapu.
Ravikiran seamless korvais academy lecdem_dec 2014 finalAnahita Ravindran
Mathematics in Music is fascinating. The world of Korvais are intriguing and interesting. A short but extremely insightful introduction into this world has been shared in this presentation.
The document discusses properties of matrix addition and scalar multiplication. It explains that to add matrices, we add corresponding elements and the matrices must have the same dimensions. Scalar multiplication involves multiplying each element of the matrix by the scalar. Some key properties covered are:
- To add matrices, we add corresponding elements and matrices must have the same dimensions.
- Scalar multiplication involves multiplying each element of the matrix by the scalar.
- Properties of addition like commutativity and distributivity apply, but multiplication is not included.
This document contains 48 permutation and combination problems with multiple choice answers. It provides an introduction and contact information for Sthitpragya Science Classes, which offers advanced mathematics preparation courses. The problems cover a range of topics including factorials, permutations, combinations, and arrangements of objects.
This document contains a worksheet on sets, relations, and mappings with 24 multiple-choice questions. It provides the name and contact information of Mishal Chauhan, an instructor who teaches advanced mathematics courses. The questions cover topics like set operations, properties of relations such as reflexive, symmetric, transitive, equivalence relations, functions, mappings and their properties like one-to-one, onto. The answers to the questions are provided at the end.
This document contains a worksheet with 83 multiple choice questions related to functions. It provides the contact information for Sthitpragya Science Classes in Gandhidham, India, which offers advanced mathematics courses. The questions cover topics such as even and odd functions, periodic functions, inverse functions, and operations on functions.
This document contains a worksheet with 34 questions related to functions. It provides the questions, options for answers, and context about an advanced mathematics class offered by Sthitpragya Science Classes in Gandhidham, India. The class covers topics for engineering entrance exams and is taught by Mishal Chauhan, who has an M.Tech from IIT Delhi. The questions test concepts like the domain and range of functions, properties of specific functions, and solving functional equations.
1) The document provides the solution to a tutorial question about expected counts in Backgammon. It calculates that the expected count on a roll is 8 1/6.
2) It then solves another Backgammon probability question, finding the probability of hitting an opponent's blot or having to enter without hitting are 15/36 and 1/3 respectively.
3) Finally, it calculates the expectations when using a "tripling cube" instead of a doubling cube in Backgammon. It finds the expectations of tripling and accepting a re-tripling is approximately -0.54, and of tripling but refusing a re-tripling is 1/6.
Here are the steps to solve this problem:
1) A is a 3×2 matrix and B is a 2×3 matrix.
2) Since the number of columns in A equals the number of rows in B, the product AB can be evaluated.
3) To find AB, multiply the elements in each row of A by the corresponding elements in each column of B and add the results:
(3 1 1)×(1 1 2)+(1 2 0)×(1 0 1)+(1 2 0)×(1 1 1)
= 3+1+0, 1+0+2, 1+0+1
= [4 2 2]
Therefore, the product AB is the
Ravikiran seamless korvais academy lecdem_dec 2014 finalAnahita Ravindran
Mathematics in Music is fascinating. The world of Korvais are intriguing and interesting. A short but extremely insightful introduction into this world has been shared in this presentation.
The document discusses properties of matrix addition and scalar multiplication. It explains that to add matrices, we add corresponding elements and the matrices must have the same dimensions. Scalar multiplication involves multiplying each element of the matrix by the scalar. Some key properties covered are:
- To add matrices, we add corresponding elements and matrices must have the same dimensions.
- Scalar multiplication involves multiplying each element of the matrix by the scalar.
- Properties of addition like commutativity and distributivity apply, but multiplication is not included.
This document contains 48 permutation and combination problems with multiple choice answers. It provides an introduction and contact information for Sthitpragya Science Classes, which offers advanced mathematics preparation courses. The problems cover a range of topics including factorials, permutations, combinations, and arrangements of objects.
This document contains a worksheet on sets, relations, and mappings with 24 multiple-choice questions. It provides the name and contact information of Mishal Chauhan, an instructor who teaches advanced mathematics courses. The questions cover topics like set operations, properties of relations such as reflexive, symmetric, transitive, equivalence relations, functions, mappings and their properties like one-to-one, onto. The answers to the questions are provided at the end.
This document contains a worksheet with 83 multiple choice questions related to functions. It provides the contact information for Sthitpragya Science Classes in Gandhidham, India, which offers advanced mathematics courses. The questions cover topics such as even and odd functions, periodic functions, inverse functions, and operations on functions.
This document contains a worksheet with 34 questions related to functions. It provides the questions, options for answers, and context about an advanced mathematics class offered by Sthitpragya Science Classes in Gandhidham, India. The class covers topics for engineering entrance exams and is taught by Mishal Chauhan, who has an M.Tech from IIT Delhi. The questions test concepts like the domain and range of functions, properties of specific functions, and solving functional equations.
1) The document provides the solution to a tutorial question about expected counts in Backgammon. It calculates that the expected count on a roll is 8 1/6.
2) It then solves another Backgammon probability question, finding the probability of hitting an opponent's blot or having to enter without hitting are 15/36 and 1/3 respectively.
3) Finally, it calculates the expectations when using a "tripling cube" instead of a doubling cube in Backgammon. It finds the expectations of tripling and accepting a re-tripling is approximately -0.54, and of tripling but refusing a re-tripling is 1/6.
Here are the steps to solve this problem:
1) A is a 3×2 matrix and B is a 2×3 matrix.
2) Since the number of columns in A equals the number of rows in B, the product AB can be evaluated.
3) To find AB, multiply the elements in each row of A by the corresponding elements in each column of B and add the results:
(3 1 1)×(1 1 2)+(1 2 0)×(1 0 1)+(1 2 0)×(1 1 1)
= 3+1+0, 1+0+2, 1+0+1
= [4 2 2]
Therefore, the product AB is the
Class xii inverse trigonometric function worksheet (t)Mishal Chauhan
This document contains a worksheet with 38 multiple choice questions related to inverse trigonometric functions for Class XII. The worksheet was created by Sthitpragya Science Classes in Gandhidham and covers topics relevant for engineering entrance exams like JEE, BITSAT, and GUJCET. It is taught by Mishal Chauhan, who has an M.Tech from IIT Delhi. The worksheet provides practice on evaluating inverse trigonometric functions, determining their principal values, and solving equations involving inverse trigonometric functions.
Xi trigonometric functions and identities (t) part 1 Mishal Chauhan
This document contains a trigonometry worksheet with 36 multiple choice questions covering trigonometric functions and identities. It provides the contact information for Sthitpragya Science Classes in Gandhidham, India, which offers advanced mathematics courses. The questions cover topics like trigonometric ratios, trigonometric identities, trigonometric equations, and their properties.
The document contains two examples of maximum and minimum problems involving differentiation.
Example 1 asks the reader to find the minimum volume of a cone given that a sphere must fit inside it. It is found that the minimum volume occurs when the radius of the cone is 28.577 cm.
Example 2 involves finding the maximum volume of a cylinder inscribed in a sphere. The maximum volume is calculated to be 104,000 cm3, occurring when the height of the cylinder is 28.5 cm.
The document provides guidance on solving maximum and minimum problems using differentiation, illustrated through these two examples involving geometric shapes.
1. The document is a model question paper with 3 sections containing multiple choice and long answer questions on mathematics.
2. Section A contains 15 multiple choice questions worth 1 mark each. Section B contains 10 long answer questions worth 2 marks each. Section C contains 9 long answer questions worth 5 marks each and 1 compulsory question.
3. The questions cover topics in algebra, trigonometry, geometry, sequences and series, and probability.
MODULE 4- Quadratic Expression and Equationsguestcc333c
(1) The document is a math worksheet containing 20 quadratic equations to solve.
(2) It provides the steps to solve each equation, factorizing the expressions and setting each factor equal to zero to find the roots.
(3) The answers section lists the factored forms and solutions for each of the 20 equations.
This document provides a module on functions and simultaneous equations for Additional Mathematics Form 4 students in Terengganu, Malaysia. It contains 15 problems on functions and 12 problems on simultaneous equations to help students prepare for their SPM examinations. The module is published by the Terengganu Education Department and involves several teachers from technical and science schools in the state.
This document contains math tutorial questions and solutions for applying theorems about perpendicular bisectors, angle bisectors, the Pythagorean theorem, and classifying triangles by their side lengths. The questions cover finding side lengths, angle measures, and determining if sets of values could represent triangle sides. The solutions show the step-by-step work using the appropriate theorems.
Theta θ(g,x) and pi π(g,x) polynomials of hexagonal trapezoid system tb,aijcsa
A counting polynomial, called Omega Ω(G,x), was proposed by Diudea. It is defined on the ground of
“opposite edge strips” ops. Theta Θ(G,x) and Pi Π(G,x) polynomials can also be calculated by ops
counting. In this paper we compute these counting polynomials for a family of Benzenoid graphs that called
Hexagonal trapezoid system Tb,a.
This document is a module on differentiation for Additional Mathematics Form 4 students in Terengganu, Malaysia. It contains 20 practice problems on various topics related to differentiation, including finding derivatives of functions, finding maximum/minimum values, related rates, and finding equations of tangents and normals. The problems are presented without solutions for students to practice solving. The module is published by the Terengganu State Education Department.
This document provides notes and examples for multiplying binomials. It introduces the FOIL method for multiplying terms in parentheses: First, Outside, Inside, Last. Several examples are worked out step-by-step using FOIL to multiply binomial expressions like (x + 6)(x + 2), (7x + 4)(2x - 4), and (x2 + x)(x2 + 7x + 4). The last examples multiply a binomial by a trinomial and two binomials containing variables raised to higher powers.
This document provides practice problems for additional mathematics Form 4 students in Terengganu, Malaysia. It covers topics on quadratic equations and quadratic functions, with multiple choice and short answer questions. The problems are divided into three sections: quadratic equations, quadratic functions for paper 1, and quadratic functions for paper 2. The document is copyrighted material from the Terengganu State Education Department.
This document contains a review exercise with 22 multiple part questions about simplifying algebraic expressions. The questions cover topics such as identifying coefficients, determining like/unlike terms, combining like terms, and performing operations on algebraic expressions including addition, subtraction, multiplication, and division.
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems.
This document provides 15 multi-part math word problems involving indices, logarithms, and coordinate geometry. The problems cover topics such as simplifying expressions with indices, solving logarithmic and exponential equations, finding equations of lines and loci, determining properties of geometric figures defined by coordinate points, and calculating areas. Students must use their understanding of indices, logarithms, coordinate geometry, and geometric relationships to solve the problems.
The document is a mathematics textbook for Additional Mathematics Form 4. It covers topics on functions, simultaneous equations, quadratic equations, and quadratic functions. It contains examples and practice questions for students to work through with answers. The questions range from simple calculations to solving equations and inequalities involving quadratic expressions.
The document contains 27 multi-part math problems involving expanding, factorizing, and expressing algebraic expressions as fractions. The problems cover topics such as expanding products of binomials, factoring quadratics and expressions involving multiple terms, rationalizing denominators, and simplifying algebraic fractions.
This short document promotes creating presentations using Haiku Deck, a tool for making slideshows. It encourages the reader to get started making their own Haiku Deck presentation and sharing it on SlideShare. In just one sentence, it pitches the idea of using Haiku Deck to easily create engaging slideshows.
Music photography aims to promote and entertain by documenting live music performances. These photographs are used in magazines and on social media to help fans remember concerts and bring feelings of nostalgia. Fine art photography explores the photographer's personal vision rather than just capturing a moment. Fine art photographers develop themes for exhibitions and make money by selling their photographs. Gregory Crewdson specializes in tableau scenes depicting American homes that are inspired by films and leave aspects open to the viewer's interpretation.
Ahmed Mohammed Kamel Sayed Ahmed is an Egyptian national currently residing in Saudi Arabia. He is seeking a career in customer service, marketing, public relations or tourism. His previous work experience includes several sales representative roles in Saudi Arabia and Egypt from 2005 to the present. He speaks Arabic and English fluently and has a Bachelor's degree in Travel and Tourism from Cairo University from 2002.
Class xii inverse trigonometric function worksheet (t)Mishal Chauhan
This document contains a worksheet with 38 multiple choice questions related to inverse trigonometric functions for Class XII. The worksheet was created by Sthitpragya Science Classes in Gandhidham and covers topics relevant for engineering entrance exams like JEE, BITSAT, and GUJCET. It is taught by Mishal Chauhan, who has an M.Tech from IIT Delhi. The worksheet provides practice on evaluating inverse trigonometric functions, determining their principal values, and solving equations involving inverse trigonometric functions.
Xi trigonometric functions and identities (t) part 1 Mishal Chauhan
This document contains a trigonometry worksheet with 36 multiple choice questions covering trigonometric functions and identities. It provides the contact information for Sthitpragya Science Classes in Gandhidham, India, which offers advanced mathematics courses. The questions cover topics like trigonometric ratios, trigonometric identities, trigonometric equations, and their properties.
The document contains two examples of maximum and minimum problems involving differentiation.
Example 1 asks the reader to find the minimum volume of a cone given that a sphere must fit inside it. It is found that the minimum volume occurs when the radius of the cone is 28.577 cm.
Example 2 involves finding the maximum volume of a cylinder inscribed in a sphere. The maximum volume is calculated to be 104,000 cm3, occurring when the height of the cylinder is 28.5 cm.
The document provides guidance on solving maximum and minimum problems using differentiation, illustrated through these two examples involving geometric shapes.
1. The document is a model question paper with 3 sections containing multiple choice and long answer questions on mathematics.
2. Section A contains 15 multiple choice questions worth 1 mark each. Section B contains 10 long answer questions worth 2 marks each. Section C contains 9 long answer questions worth 5 marks each and 1 compulsory question.
3. The questions cover topics in algebra, trigonometry, geometry, sequences and series, and probability.
MODULE 4- Quadratic Expression and Equationsguestcc333c
(1) The document is a math worksheet containing 20 quadratic equations to solve.
(2) It provides the steps to solve each equation, factorizing the expressions and setting each factor equal to zero to find the roots.
(3) The answers section lists the factored forms and solutions for each of the 20 equations.
This document provides a module on functions and simultaneous equations for Additional Mathematics Form 4 students in Terengganu, Malaysia. It contains 15 problems on functions and 12 problems on simultaneous equations to help students prepare for their SPM examinations. The module is published by the Terengganu Education Department and involves several teachers from technical and science schools in the state.
This document contains math tutorial questions and solutions for applying theorems about perpendicular bisectors, angle bisectors, the Pythagorean theorem, and classifying triangles by their side lengths. The questions cover finding side lengths, angle measures, and determining if sets of values could represent triangle sides. The solutions show the step-by-step work using the appropriate theorems.
Theta θ(g,x) and pi π(g,x) polynomials of hexagonal trapezoid system tb,aijcsa
A counting polynomial, called Omega Ω(G,x), was proposed by Diudea. It is defined on the ground of
“opposite edge strips” ops. Theta Θ(G,x) and Pi Π(G,x) polynomials can also be calculated by ops
counting. In this paper we compute these counting polynomials for a family of Benzenoid graphs that called
Hexagonal trapezoid system Tb,a.
This document is a module on differentiation for Additional Mathematics Form 4 students in Terengganu, Malaysia. It contains 20 practice problems on various topics related to differentiation, including finding derivatives of functions, finding maximum/minimum values, related rates, and finding equations of tangents and normals. The problems are presented without solutions for students to practice solving. The module is published by the Terengganu State Education Department.
This document provides notes and examples for multiplying binomials. It introduces the FOIL method for multiplying terms in parentheses: First, Outside, Inside, Last. Several examples are worked out step-by-step using FOIL to multiply binomial expressions like (x + 6)(x + 2), (7x + 4)(2x - 4), and (x2 + x)(x2 + 7x + 4). The last examples multiply a binomial by a trinomial and two binomials containing variables raised to higher powers.
This document provides practice problems for additional mathematics Form 4 students in Terengganu, Malaysia. It covers topics on quadratic equations and quadratic functions, with multiple choice and short answer questions. The problems are divided into three sections: quadratic equations, quadratic functions for paper 1, and quadratic functions for paper 2. The document is copyrighted material from the Terengganu State Education Department.
This document contains a review exercise with 22 multiple part questions about simplifying algebraic expressions. The questions cover topics such as identifying coefficients, determining like/unlike terms, combining like terms, and performing operations on algebraic expressions including addition, subtraction, multiplication, and division.
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems.
This document provides 15 multi-part math word problems involving indices, logarithms, and coordinate geometry. The problems cover topics such as simplifying expressions with indices, solving logarithmic and exponential equations, finding equations of lines and loci, determining properties of geometric figures defined by coordinate points, and calculating areas. Students must use their understanding of indices, logarithms, coordinate geometry, and geometric relationships to solve the problems.
The document is a mathematics textbook for Additional Mathematics Form 4. It covers topics on functions, simultaneous equations, quadratic equations, and quadratic functions. It contains examples and practice questions for students to work through with answers. The questions range from simple calculations to solving equations and inequalities involving quadratic expressions.
The document contains 27 multi-part math problems involving expanding, factorizing, and expressing algebraic expressions as fractions. The problems cover topics such as expanding products of binomials, factoring quadratics and expressions involving multiple terms, rationalizing denominators, and simplifying algebraic fractions.
This short document promotes creating presentations using Haiku Deck, a tool for making slideshows. It encourages the reader to get started making their own Haiku Deck presentation and sharing it on SlideShare. In just one sentence, it pitches the idea of using Haiku Deck to easily create engaging slideshows.
Music photography aims to promote and entertain by documenting live music performances. These photographs are used in magazines and on social media to help fans remember concerts and bring feelings of nostalgia. Fine art photography explores the photographer's personal vision rather than just capturing a moment. Fine art photographers develop themes for exhibitions and make money by selling their photographs. Gregory Crewdson specializes in tableau scenes depicting American homes that are inspired by films and leave aspects open to the viewer's interpretation.
Ahmed Mohammed Kamel Sayed Ahmed is an Egyptian national currently residing in Saudi Arabia. He is seeking a career in customer service, marketing, public relations or tourism. His previous work experience includes several sales representative roles in Saudi Arabia and Egypt from 2005 to the present. He speaks Arabic and English fluently and has a Bachelor's degree in Travel and Tourism from Cairo University from 2002.
http://www.odysseedesjeux.fr
3e Festival Jeux&Cie d'Epinal -14 mars 2014
Jeu et image par Wilfried BOUILLET
Résumé :
I. L'imagerie du jeu
Problématique : quelle est la nature de l’imagerie dans le jeu ?
L’imagerie n’est pas une réalité autonome mais le reflet de la correspondance entre de 2 logiques : la logique ludique et la logique graphique.
II. Le jeu comme image ou objet-vu
Problématique : A quel point l’imagerie structure l’acte de jouer ?
L’imagerie détermine une zone de jeu, c'est-à-dire le monde :
- avec ses limites (son dedans et son dehors)
- avec sa géographie (lieux de placements et réseaux de déplacements)
III. Le jeu comme image vivante
Problématique : Comment cela fonctionne ?
Le jeu, contrairement à d’autres productions culturelles, ne reste pas fixe/fixé.
En effet, la série des événements et la nature de l’achèvement sont toujours uniques (singulier).
D’aucuns nomment cela l’incertitude : mais il est plutôt question d’une création partagée.
The document appears to be an information sheet about the IELTS writing exam. It includes frequently asked questions about the exam format, how essays are scored, and tips for achieving a high score. Key details provided include that the writing section consists of two tasks - a 150 word essay responding to a prompt and a 250 word essay expressing an opinion. Scoring is based on task achievement, coherence, vocabulary use, and grammar. Candidates are advised to practice with sample questions and model answers in order to familiarize themselves with the expected structure and style.
Here are the top 10 reasons why more than 125,000 merchants worldwide have chosen magento to build their ecommerce website. Go through this eye catching presentation to know why it has become one of the most leading open source ecommerce platforms.
MADE YOUR CAREER PATHWAY THROUGH VARIOUS MBA SPECIALISATIONJaro Education
If you work in or are planning a career in any of the many communication fields such as media, journalism, advertising, or public relations, then an MBA degree with a specialisation in communications is the obvious choice for you.You will also learn important communication skills such as critical thinking, interviewing, speech writing, and public relations, and gain confidence in public speaking, persuasion, and learn how to be an organisational communicator.
This document contains a 3-page excerpt from the textbook "Elementary Mathematics" by W W L Chen and X T Duong. The excerpt discusses basic algebra concepts including:
- The real number system and subsets like natural numbers, integers, rational numbers, irrational numbers
- Rules of arithmetic operations like addition, subtraction, multiplication, division
- Properties of square roots
- Distributive laws for multiplication
- Arithmetic of fractions including addition and subtraction of fractions.
This document contains a sample question paper for Class XII Mathematics. It has 5 sections (A-E). Section A contains 18 multiple choice questions and 2 assertion-reason questions worth 1 mark each. Section B has 5 very short answer questions worth 2 marks each. Section C contains 6 short answer questions worth 3 marks each. Section D has 4 long answer questions worth 5 marks each. Section E contains 3 case study/passage based questions worth 4 marks each with internal subparts. The document provides sample questions on topics including trigonometry, calculus, matrices, probability, linear programming and more.
This document contains 10 math questions related to trigonometric functions, sets, relations and functions, complex numbers, sequences and series, straight lines, conic sections. The questions range from proving identities and equations to finding specific values based on given information. They require various trigonometric, algebraic and geometric problem solving skills at a higher-order thinking level.
The document contains instructions for a math exam for Class XII. It states that the paper contains 50 multiple choice questions (MCQs), and to darken the appropriate circle on the answer sheet. Each correct answer receives 4 marks, incorrect answers receive -1 mark, and unattempted questions receive 0 marks. It wishes the student good luck for their bright future.
The document provides examples and explanations of adding, subtracting, multiplying, and expanding polynomials. It demonstrates multiplying polynomials using the FOIL (First, Outer, Inner, Last) method and provides examples of sum and difference of squares, square of a binomial, cube of a binomial, and multiplying three binomials. Common patterns that arise when multiplying polynomials are identified.
The document summarizes the history of solving cubic equations and the discovery of complex numbers. It describes how del Ferro, Tartaglia, and Bombelli contributed to solving cubic equations of the form x3 = bx + c. Bombelli realized that taking the cube root of a negative number results in an "imaginary" number containing the square root of -1. He used this insight to find all three cube roots of a complex number. Modern algebra approaches finding the cube roots of a complex number using polar form and trisecting angles. This allowed solving any cubic equation with three real or complex solutions. The document traces the conceptual breakthroughs that led to the acceptance and understanding of imaginary and complex numbers.
This document contains math problems involving ratios, proportions, functions, and sets. It asks the student to:
1) Find missing values in ratios and proportions.
2) Represent sets, relations, and functions using diagrams like arrow diagrams and Cartesian diagrams.
3) Identify properties of functions like their domain, codomain, and range.
4) Graph linear and quadratic functions and find features like the x- and y-intercepts.
5) Solve proportions and equations involving ratios.
So in summary, the document provides exercises to practice fundamental concepts involving ratios, proportions, functions, and sets through problems requiring calculations, diagrammatic representation, graphing, and solving equations.
This document contains a summary of key concepts in polynomials including:
1) Definitions of terms like variable, term, coefficient, degree, constant and zero polynomials.
2) The Remainder Theorem and how it relates the remainder of polynomial division to the factor theorem.
3) The Factor Theorem and how it can be used to determine if a polynomial is a factor of another.
4) Examples of factoring polynomials and using the Factor Theorem.
5) A list of 15 common algebraic identities involving polynomials.
This document discusses algebraic identities and factorizing polynomials. It begins by defining polynomials and their classification based on number of terms and degree. Some common algebraic identities involving addition, subtraction, and multiplication of polynomials are presented. These identities can be used to factorize polynomials. The document then describes an activity to verify the identity (a + b)3 = a3 + 3ab(a + b) + b3 using cubes and cuboids. A similar activity is presented for the identity (a - b)3 = a3 - 3ab(a - b) - b3.
This document contains 54 multiple choice questions related to polynomials and their properties. Some key questions asked about:
- Finding the degree of polynomials
- Identifying the number of real zeros of polynomials
- Factoring polynomials
- Evaluating polynomials for given values
- Identifying coefficients and constants in polynomial expressions
- Relating the zeros of a polynomial to its factors
The questions cover topics like polynomial definitions, operations, factorization, finding zeros, and other properties of polynomials.
The document provides instructions and questions for a game show involving solving combination inequalities. Contestants can use lifelines like eliminating answers or asking the host for help. Questions are worth $40,000 each and involve solving inequality expressions using functions, difference/quotient functions, and graphing calculators. Correct answers are provided for practice problems.
B.Sc (Pass) Nautical & Engineering Model Question 2 Mathematics Second Paper
(Differential Calculus, Integral Calculus, Two-dimensional & Three- dimensional Geometry)
This document contains a chapter on functions with 30 math exercises. The exercises involve evaluating functions, determining domains and ranges, analyzing graphs of functions, and solving word problems involving functions.
Similar to Chitravina Ravikiran- SeamLess korvais - Music Academy Lec-Dem - 2014 (14)
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
How to Fix the Import Error in the Odoo 17Celine George
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2. Prelude
Numbers have fascinated man for millennia.
India’s contributions in this area is mammoth in general.
It is therefore unsurprising that Indian rhythm has led the
way in world music when it comes to musical mathematics.
Even between Indian’s two major classical systems,
Carnatic culture stands out for not just rhythmic virtuosity
but in its sophisticated approach towards structured
mathematical patterns.
3. Korvai Types
Level I: Any number taken after appropriate units after
samam to end as required. Ex: (3+3, 5+3, 7)x3 after 1. My
very first attempt at a korvai at age 5…
Level II: Taken from samam to end at samam with 1 or 2
karvais between patterns to fill out the remaining units (in
say 32/64/28/40 units in Adi 1/2 kalais, Mishra
chapu/Khanda chapu etc)
Level III: Same as II but to end a few units after or before
samam.
Level IV: Same as I or II but with different gatis thrown in.
All these can be termed as man-made korvais
4. Natural Korvais – seamless elegance
Seamless korvai – DEFINITION: Patterns (of usually two or more parts) from samam to
samam/landing point of song that do not have remainder indivisible by 3 in talas or landings
indivisible by 3.
In other words, these do not have remainder of any number of units not divisible by 3 (like 2
or 4) which have to be patched up as 1 or 2 karvais it in between patterns. These have a grace
or sophistication in the numbers that are obvious only when one is inspired.
Intellectually, they require multi-layered thinking rather than just conventional approaches.
Some of them involve precise and logical patterns but not found in mathematical text
books.
I literally stumbled upon most them as some of them are not accessible through intuitive
methods.
A couple of them have been in vogue for decades – 6, 8, 10 (or 8+8+8) as first part then 3x5,
2x5, (1x5) x3.
Typically, they are in one gati though there are exceptions (but overuse of multiple gati will
make it a different concept.)
5. Seamless korvais – amazing options
ADI 2 kalais = 64 units
Challenges: To get 3 khandams (3x5) in Part B, Part A has to be 49. Similarly,
for 3x6, 3x7 or 3x9 in B, we need A to be 46, 43 or 37, none of which is
divisible by 3. So, simple approaches will not work.
1. Simple progressive: These are most obvious types.
Ex 1: 7+3 (karvais), 6+3….. 1+3 as first part (A) and 5x3 as the second
part (B).
(srgmpdn s,, rgmpdn s,, gmpdn s,, mpdn s,, pdn s,,
dn s,, ns,,) as A and (grsnd rsndp dpmgr) as B
6. Simple progressive contd
Ex 2: 7+2…0+2 as A and B is 5x3 in tishra gati. (A can also
be in srotovaha yati)
(srgmpdn s, rgmpdn s, gmpdn s, mpdn s, pdn s, dn s, ns, s,) as
A and (grsnd rsndp dpmgr) as B in tishra gati.
2.Progressive with addition in multiple parts:
A= (2,3,4)+(2,3,4,5)+(2,3,4,5,6); B=7x3.
(s, ns, dns,) + (s, ns, dns, pdns,) + (s, ns, dns, pdns, mpdns,) as
A and (g,r,snd r,s,ndp d,p,mgr) as B
7. Seamless korvais – amazing options
3. Inverted progression in 3 parts:
A=3,3,3 + 5X1, B= 3,3+7X2, C= 3+9X3
(g,, r,, s,, + grsns) as A and( r,, s,, + g,r,sns r,s,ndn) as B
and (s,, + g,r,grsns r,s,rsndp d,p,dpmgr) as C
Another example:
A=2,2,3 + 7x1; B=2,3 + 7x2; C=3 + 7x3(tishra gati)
8. 4. Progressive in second part: A= 6, 6, 6; B = (3x9) + (2x7) + (1x5). Impressive when B is
rendered 3 times with A alternating between the 9, 7 and 5s.
( gr,s,, rs,n,, sn,d,,) + (g,, ,,, r,, ,,, g,, r,, s,, n,, d,, r,, ,,, s,, ,,, r,, s,, n,, d,, p,,
s,, ,,, n,, ,,, s,, n,, d,, p,, m,,) first time
then (gm,p,, mp,d,, pd,n,,) + (g, ,, m, ,, p, d, p, m, ,, p, ,, d, n, d, p, ,, d, ,,
n, s, n,) as second time
and (gr,s,, rs,n,, sn,d,, ) +( grsnd rsndp dpmgr) as third time
5. Progressive in each part:
A = (5x3karvais)+(5x2karvais)+5x1;
B= (6x3karvais)+(6x2karvais)+6x2
C = (7x3karvais)+(7x2karvais)+7x3
9. Seamless korvais – amazing options
5. 3-speed korvais (example for 4 after samam):
(A=7, 2+7, 4+7; B=9x3)x3 karvais;
(A=7, 2+7, 4+7; B=9x3)x2 karvais;
A=7, 2+7, 4+7; B=9x3
(g,, ,,, r,, ,,, s,, ,,, ,,, s,, n,, g,, ,,, r,, ,,, s,, ,,, ,,, d,,n,,s,,n,, g,, ,,, r,, ,,, s,, ,,, ,,,) as
A and (g,, ,,, r,, ,,, g,, r,, s,, n,, d,, r,, ,, s,, ,, r,, s,, n,, d,, p,, s,, ,,, n,, ,,, s,, n,, d,,
p,, m,,) as B;
(g, ,, m, ,, p, ,, ,, p, m, g, ,, m, ,, p, ,, ,, n,d,p,m, g, ,, m, ,, p, ,, ,, ) as A and
(g,m,g,m,p,d,p, m,p,m,p,d,n,d, p,d,p,d,n,s,n,) as B;
(g,r,s,, sn g,r,s,, dnsn g,r,s,,) as A and (g,r,grsnd r,s,rsndp d,p,dpmgr) as B
10. Another example, employing second part progression
also (samam to samam):
6+2, 5+2, 4+2, 3+2, (3x5)x3; 6+2, 5+2, 4+2, 3+2,
(2x7)x3; 6+2, 5+2, 4+2, 3+2, (1x9)x3
11. Seamless korvais – dovetailing patterns
The beauty of these are part of A will dovetail into B in a seamless manner.
(a) G,R,S,, R,S,N,, - G,R,SND - GR,S,, RS,N,, - GR,SND - GRS,, RSN,, - GRSND
RSNDP SNDPM
(b) GR, S, N, S,,, R,,, - GRSND – R,SN, S,,, R,,, - GRSND – SN, S,,, R,,, - GRSND
RSNDP SNDPM
(c) G,,,,, R,,,,, G,, R,, S,, N,, D,, - G,,, R,,, G, R, S, N, D, - G,R, GRSND RSNDP
SNDPM
(d) G,,, R,,, S,,, N,,, D – GRSND – R,, S,, N,, D,, P – RSNDP – S,N,D,P,D - GRSND
RSNDP SNDPM
It would be obvious that some are 13+5, 13+5 and 13+(3 times 5) in various
ways. If song starts after +6, various manifestations of 15+5, 15+5 and 15+(3
times 5) can be created.
12. Seamless korvais – Boomerang patterns
Let’s look at the sequence of numbers: (a) 7, 12, 15, 16….
(b) 6, 10, 12, 12... What are the next numbers?
Typically, these are not part of general math textbooks and do not make
sense to most mathematicians. But they are fine examples of how Carnatic
music can transcend science and math. Remarkably, the series will turn back
on itself. I call these Double layered progressive sequences which
boomerang. The first few numbers are formed using multiplication
progression in (a) are: 7x1, 6x2, 5x3, 4x4. Thus, the next few numbers are
15, 12 and 7. Similarly, in (b), they are 10 and 6.
An example of a korvai with this: A= 6x2, 5x3, 4x4; B = 7x3
(Ta….. Ki…..), (Ta,,,, ki,,,, ta,,,,) , (Ta,,, ka,,, di,,, mi,,,) as A and (Ta.di.kitatom
Ta.di.kitatom Ta.di.kitatom ) as B
13. • Another ex: A= 7, 12, 15, 16, 15, 12 or 7x1, 6x2, 5x3, 4x4,
5x3, 6x2 and B= 3 mishrams C= 3x10 (which can be said as
ta.. Ti.. Ki ta. Tom (to give an illusion of 7)
(g,,,,,, r,,,,,s,,,,, n,,,,d,,,,p,,,, m,,,g,,,r,,,s,,, r,,g,,m,,p,,d,,
m,p,d,n,s,r,) as A and (g,r,snd r,s,ndp p,d,nsr) as B and
(g,,r,,sn,d r,,s,,nd,p s,,n,,dp,m ) as C
14. The concept of Keyless korvais
At times, one stumbles upon korvais with no apparent mathematical relationship.
These cannot be logically deciphered or developed by locking on to their key (usually
the average of their various parts/2nd repeat out of 3). Yet, these are elegant beyond
words in their simplicity.
1. A 3-part korvai over 2 cycles (128 units): A stunning set of patterns
found in nature.
A= [(5+2), (4+2), (3+2)] + (3x5);
[( gmpdn s,) (mpdn s,) (pdn s,)] + grsnd rsndp sndpm as A
B = [(5+2), (4+2), (3+2), (2+2)] + (3x7)
[( gmpdn s,) (mpdn s,) (pdn s,) (dn s,)] + (g,r,snd r,s,ndp d,p,mgr) as B and
C = [(5+2), (4+2),(3+2), (2+2), (1+2)] + (3x9).
[( gmpdn s,) (mpdn s,) (pdn s,) (dn s,) (n s,)] + (g,r,grsnd r,s,rsndp
d,p,dpmgr) as C
15. 2. A 3-part Korvai in 3 speeds: The amazing aesthetics of
this is mind-boggling – simple when rendered but looks a
jungle of numbers when expressed as below!
A = (8+3)x3 + (1x5)x3
B = (6+3)x2 + (2x7) x 2
C = (4+3)x1 + (3x9) x1
(Ta.. … Di.. … Ta.. Ka.. Di.. Na.. Tam.. … …) + (Ta.. Di.. Ki.. Ta..tom.. ) – A
(Di. .. Ta. Ka. Di. Na. tam. .. ) +( Ta. .. Di. .. Ki. Ta. Tom. Ta. .. Di. .. Ki. Ta.
Tom.) – B
( Takadina Tam..) +( Ta.di.tatikitatom Ta.di.tatikitatom Ta.di.tatikitatom) -
C
16. Keyless korvais extensions to other talas
Keyless methods give scope to execute amazing finishes in seemingly impossible
situations. For instance, a tala like Khanda Triputa @ 8 units per beat (72 units) or
Rupakam, which is already divisible by 3, can hardly offer scope for a samam to +
2 or + 4 finish… Let’s look at a couple of aesthetic solutions.
1. Khanda triputa – samam to +2 (out of 8) in 2 cycles
A= [(5+2), (4+2), (3+2), (2+2)] + (3x5), B = [(5+2), (4+2), (3+2), (2+2), (1+2)] +
(3x8), C = [(5+2), (4+2), (3+2), (2+2), (1+2), (0+2)] + (3x11).
[Takatakita tam. Takadina tam. Takita tam. Taka tam.] + (Tadikitatom
Tadikitatom Tadikitatom) – A
[Takatakita tam. Takadina tam. Takita tam. Taka tam. TaTam.] + (Tadi . Ki .
Ta . tom Tadi . Ki . Ta . tom Tadi . Ki . Ta . tom ) - B
[Takatakita tam. Takadina tam. Takita tam. Taka tam. TaTam. Tam.] +
(Ta di .. Ki.. Ta.. Tom Ta di .. Ki.. Ta.. Tom Ta di .. Ki.. Ta.. Tom ) - C
17. 2. A 3-part Korvai in 3 speeds for same landing as above
A = (11+3)x3 + (1x5)x3 (Can be rendered as G, R, GRSN DPD
N,, - GRSND in a raga like Vachaspati)
B = (9+3)x2 + (2x7) x 2
C = (7+3)x1 + (3x9) x1
A = (g,, ,,, r,, ,,, g,, r,, s,, n,, d,, p,, d,, n,, ,, ,,) +( g,, r,, s,, n,, d,,)
B = ( r, ,, g, r, s, n, d, p, d, n, ,, ,, ) + (g,,, r,,, s, n, d, r,,,s,,,n,d,p,)
C= (grsndpd n,,) + (g,r,grsnd r,s,rsndp s,n,sndpm)
3. Khanda triputa – samam to +3 (out of 8)
[A= 7+3 (karvais), 6+3…..1+3, 0+3 B= 7x3] (To be rendered 3 times or change
B as 5x3, 7x3 and 9x3 each time etc).
A= Takadimitakita tam.. Takadimitaka tam.. Takatakita tam.. Takadina tam..
Takita tam.. Taka tam.. Ta tam.. Tam..)
B = (Ta.di.kitatom Ta.di.kitatom Ta.di.kitatom )
18. Keyless korvais extensions to other talas
4. Mishra Chapu: Samam to -1
[(5x4)+1]x3, [(4x4)+1]x3, [(3x4)+1]x3, [(2x4)+1]x3,
[(1x4)+1]x3 (for landings like Suvaasita nava javanti in Shri
matrubhootam)
(Ta…. Di…. Ki…. Ta…. Tom Ta…. Di…. Ki…. Ta…. Tom Ta…. Di…. Ki…. Ta…. Tom ),
(Ta... Di... Ki… Ta… Tom Ta... Di... Ki… Ta… Tom Ta... Di... Ki… Ta… Tom ),
(Ta.. Di.. Ki.. Ta.. Tom Ta.. Di.. Ki.. Ta.. Tom Ta.. Di.. Ki.. Ta.. Tom),
(Ta. Di. Ki. Ta. Tom Ta. Di. Ki. Ta. Tom Ta. Di. Ki. Ta. Tom) ,
(Tadikitatom Tadikitatom Tadikitatom )
19. 5. Roopakam: Samam to +2
A= [(5+2), (4+2), (3+2)] + (3x5), B = [(5+2), (4+2), (3+2), (2+2)]
+ (3x9), C = [(5+2), (4+2), (3+2), (2+2), (1+2)] + (3x13).
(The 3x(5/9/13) can be rendered as just 3x5 all 3 times. Or as
3x9, 3x13, 3x17 etc.
20. Seamless korvais for other talas
ADI 1 kalai (32 units)
Most korvais in this smaller space require patch work. Some of the most famous
ones are even mathematically incorrect. (ta, tom… taka tom.. Takita tom.. + 3x5).
1. Simple progressive: A few years ago, I had introduced
A = 2, 3, 4, 5; B = 6x3.
(Tam. TaTam. TakaTam. TakiTaTam.) – A
(Tadi.kitatom Tadi.kitatom Tadi.kitatom ) - B
21. 2.Single part apparently wrong but actually correct
korvai:
GR,-GRS,-GRSN,-GRSNP,-GRSNPG,-GRSNPGR
Typical hearing will make it seem like 1+2 karvais… 5+2
karvais and final phrase illogically being 7. In reality, it
is 2+1, 3+1…6+1 ending in 7.
22. Seamless korvais for other talas… contd
ADI 1 kalais = 32 units
3. An elegant solution in 3 cycles for songs starting after 6
(34 units/cycle)
A = (3x5) x3; B= (2x6)x3; C = (1x7) x3
(G,, r,, s,, n,, d,, r,, s,, n,, d,, p,, d,, p,, m,, g,, r,,) – A
(g, m, ,, p, d, p, m, p, ,, d, n, d, p, d, ,, n, s, n,) – B
(gr,,snd rs,,ndp dp,,mgr) - C
23. 4. Several other progressive solutions work beautifully for samam to
songs starting after 6:
7+7 (karvais), 6+7….2+7 +1 (landing on the song)
The same one can be rendered with 6 karvais for songs starting on samam.
5. A simple 3-speed solution for 6 after samam:
A = (6x3 + 5x3)x3; B = (6x3 + 5x3)x2
C = (6x3 + 5x3)x1
24. Seamless korvais for other talas… contd
ADI 1 kalais = 32 units
6. A progressive 3-speed korvai for 6 after samam:
(7+7+3; 5)x3 karvais; (GR,S,N, DP,D,N, S,, - GRSND)X3
(6+6+3; 5)x2 karvais;
5+5+3; 5,5,5
(G,, r,, ,,, s,, ,,, n,, ,,, + d,, p,, ,,, d,, ,,, n,, ,,, + s,, ,,, ,,, ; g,, r,, s,, n,, d,,) for the
first part
(g, r, ,, s, n, ,, + d, p, ,, d, n, ,, + s, ,, ,, ; g, r, s, n, d, ) for second part
(grsn, + dpdn, + s,,) ; grsnd rsndp dpmgr for third part
25. Roopakam from samam to +3
A= [6, (2+6), (4+6)] B = (5 x 4 karvais + 3x5)
C = [6, (2+6), (4+6)] D = (7 x 4 karvais + 3x7)
E= [6, (2+6), (4+6)] B = (9 x 4 karvais + 3x9)
Note: A, C and E can be any combination divisible by 12
26. Seamless korvais in other gatis
Just as many korvais for Adi can be extended to other talas, they can be extended
to other gatis too. For instance, Adi - Khanda gati (double speed) = 80 units
Eg: GR, SN, DP, DN, S,, - G, R, SND – RS, ND, PM, P D, N,,- R,S |
,NDP – SN, DP, MG, MP, D,, - G | ,R,SND – R,S,NDP – S,N,DPM ||
But there are highly interesting possibilities which are original
for this like the one I had presented in my solo concert at the
Academy 2-3 years ago: A = (4x5) + (3x7) + (2x9); B= 5+7+9
(Ta… Ka… Ta… Ki… Ta… ) + ( Ta.. .. Di.. .. Ki.. Ta.. Tom..) + (Ta. .. Di. ..
Ta. Di. Ki. Ta. Tom. ) as A
And (Tadikitatom Ta.di.kitatom Ta.di.Tadikitatom) as B
28. Seamless korvais with other approaches
I had remarked in a mrdanga arangetram about how most of our music is
elementary arithmetic and why percussionists must focus on aesthetics once they
have got the patterns right. This got me into thinking about experimenting with
korvais that represent some other math concepts such as a couple below:
1. Fibonachi series: Leonardo of Pisa, known as Fibonacci in 1200 AD but
attributed to a much earlier Indian mathematician Pingala (450-200 BC). The
series is any two initial numbers like 3, 4 which are added to get 7. Now, add
the last two numbers (4+7) to get 11 and so forth. A korvai in that sequence
(in say, Kalyani):
A = G,, - R,,, - G,R,SND – GRSNDPMGRSN – DN,R,, GM,D,, MD,N,, B= G,R,SND –
R,S,NDP – D,P,MGR
2. A simple korvai using squares of numbers as first part (3)2+(4)2+(5)2:
A= G,,R,,S,, - G,,, R,,, S,,, N,,, - G,,,, R,,,, S,,,, N,,,, D,,,,
B= 3 mishrams in tishra gati double speed.
29. Creating Seamless korvais
It now would be obvious that anyone can create seamless korvais with the
thinking and methods I have shared.
I have used mostly familiar sounding easy patterns to create these, mainly
with melodic aesthetics in mind.
I have shown only a few small samples here, even from the ones I have
discovered/presented.
Pure rhythmic seamless korvais can deal with typical patterns suited for
percussion.
This is a vast exciting new world with tremendous scope to expand the
horizons both melodically and rhythmically.
Each door I’ve opened leads to exhilarating worlds…
Happy exploring!!!