Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself.The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music.

Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself.The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music.

By the first century AD, a nomadic peoples of the Mongolians were evident in eastern Europe. Nordic elements were witnessed from the Caspian-Pamir region. At this time, there was no further push westward by the Finns, a root people of the mongalians. It wasn't until the fourth century, that a westward movement began by those who became known as the Finns. The Finno-Ugric language is derived from a people, extending from Norway into the environs of the Ob River in Siberia. It also extends into the Carpathian basin. The ancient people of this language were surrounded by tribes of people who spoke German, Slovak, and Turkish tongues. The vocabulary of the Finno-Ugric people is derived from Lithuanian, Russian, and ancient Germanic languages. Oppland, which we will read about in this document, was located in the south central area of Norway. It was from Oppland, that the Vikings, or Scandinavians migrated to France, becoming Normans, and finally tking possession of Britain. Keep in mind, though this is my family line from 165 AD, there are lines which branch out that may be picked up, and researched for many additional Peck families. The earliest records, contained herein, are generic to most of the Peck Lines. However, as the family grew in number, so did the branches. Especially, as we approach the time of splitting from England in the 17th century.. Not everyone will agree with the conclusions drawn herewith, but for me, it is an academic and historical attempt to link the present with the past. Thus, my gratitude is extended to all who helped so graciously with this enormous task. Please read the enclosed information, with a historical mind of connecting your life with those of pastgenerations. A line of people who actually, or subliminally have contributed to who you are today. A family who has had lodged within it, Christians, pastors, archdeacons, bishops, community leaders, and royalty. So who are the Pecks?