Schottenbauer Publishing

Monday, April 13, 2015

How to Use Graphs in Music Education

Graphs can be integrated into music education from approximately fourth grade through high school, as well as college and university classes. 



The following list describes possible learning activities centered on graphs:

Possible Lesson Plans

  • Graph Reading 
    • Identifying Minimum & Maximum 
    • Determining Graph Shape 
    • Redrawing the Graph on a Different Scale 
  • Mathematical Modeling 
    • Writing the Graph's Equation 
    • Transforming the Graph's Equation 
  • Theoretical Analysis 
    • Describing the Scientific & Mathematical Concepts Related to Graph(s) 
    • Describing the Scientific & Mathematical Theories Related to Graph(s) 
    • Identifying the Theoretically Ideal Graph & Comparing to Individual Graph(s) 
    • Understanding Measurement Error & Other Types of Error 
    • Comparing & Contrasting Specific Graphs 
  • Science Writing 
    • Describing a Graph in Words 
    • Writing a Comparison & Contrast of Graphs 
    • Describing Scientific Concepts & Theories Relevant to Graphs 
    • Developing Theories Based on Graphs 
    • Re-writing Graph Titles in Scientific Format 
    • Practicing Different Styles of Writing about Graphs (e.g., Journalistic, Scientific, Practical/Colloquial) 
  • Exploratory Research 
    • Data-Mining 
    • Developing Theories Based on Graphs 
    • Exploring Open-Ended Questions (e.g., Look at this book of graphs and write about a topic of interest.) 
  • Estimation Skills 
    • Understanding Range & Order of Magnitude 
    • Developing Theoretical Comparisons from Commonly Available Data (e.g., Here is a graph of air flow while playing a note on a trombone mouthpiece. How much air would be required to play on a trumpet mouthpiece? On a tuba? Euphonium? Flugelhorn?) 

A full listing of books with graphs from Schottenbauer Publishing, indexed by book series and data type, are available in a Teacher Resource Guide from the publisher. Additional information about using graphs in class is available on the blog Graphs in Education.



Additional Information

Sunday, April 5, 2015

Understanding the Harmonic Overtone Series

The harmonic overtone series describes the science of the relationship between notes in the Western harmonic system. Harmonics are most obvious on string instruments, brass instruments, and the flute, which easily demonstrate the relationship between the lowest note, the octave above, and the perfect fifth above the octave, plus many of the other harmonic overtones in the series.



Did you know that harmonics are present in all naturally-produced notes, sounding softly in addition to the fundamental tone? It is not obvious to many listeners. A free YouTube video from the publisher, Introduction to the Harmonic Overtone Series demonstrates harmonic overtones on several instruments. A mathematical expression of the combination of harmonics is presented in graphical form in the appendices of Where Does Sound Come From? Volumes 1, 3, & 4. A mathematical analysis of several prominent tuning systems is included in the appendices of Where Does Sound Come From? Volume 2. 


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