The Science of Tone Quality

Tone quality is essential to all musical performance, but is not usually taught systematically in traditional music education. Rather than building an awareness of tone across instruments, individuals taking lesson in strings, woodwinds, brass may be offered individual suggestions for improving tone on their own instrument. Usually, their instrument is a student or intermediate model. If fortunate to take private lessons, students may also be provided exemplary tone quality examples from a specialist teacher performing on a professional instrument. In ensemble, students may be urged to "match tone quality" across their section, even when performing on different makes and models of instruments, which offer various tone quality. Options for learning about tone quality are even more limited on the piano, which is a common tool for music education.

How can educators and students learn about tone quality across the spectrum of band and orchestral instruments? A set of educational materials from Schottenbauer Publishing offer opportunities for learning multiple aspects of tone quality, including:

• Identifying tone quality in band and orchestral instruments
• Understanding the math and science of tone quality
• Linking instrumental skills to auditory and math/science skills

To meet the first goal, the student can obtain recordings of multiple instruments, including common examples of good and poor tone quality. By listening carefully to comparison and contrast examples, and reading descriptions of each sample in words, students can develop and hone skills for identifying good tone. The multimedia set Ear Training: Tone Quality (Level 1) from MusicaNeo contains over 250 computer audio files with performance samples from common musical instruments, including strings, woodwinds, brass, and percussion. The series is accompanied by a brief lead sheet with exercises for improving tone quality, as well as an audio file with a computer realization of the exercises.  

To meet the second goal, the student can obtain graphs of tone quality samples from multiple instruments, including common examples of good and poor tone quality. By comparing these tone samples visually, and by reading descriptions of each sample in words, students can develop a mathematical/graphical understanding of good tone. The book series Where Does Sound Come From? and the anthology The Science of Music provide graphs with performance samples from common musical instruments, including strings, woodwinds, brass, and percussion. The graph below provides one example of the contents of these book series.

To meet the third goal, students can record their own musical performance on a microphone at the computer, and analyze the sound wave using a free program such as Audacity. Students can follow procedures from the free blog article Easy Science of Music Experiment to analyze their tone quality.

These educational tools can be integrated into music education curricula from late elementary school through high school and college/university, in classrooms, after-school enrichment programs, individual lessons, independent study, and/or homeschool. Additional information is available on the Schottenbauer Publishing website, and from the links below. A free pamphlet from the publisher is also available on the website.

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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.


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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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Bow Science and Exercises: Clear, Concise Instruction for Students of All Ages

Students who seek rapid development of bowing skills can find clear instruction in a newly published series of books by M. Schottenbauer, Ph.D., Bow Science & Exercises for Violin & Viola. This growing series of books contains progressive levels of information and advice, including instruction in basic math and physics, plus convenient exercises which may rapidly advance control over the bow arm, hand, and fingers. 

Sample pages (Copyright 2014, All Rights Reserved) are located on the slides below, which highlight features from the book:

A brief YouTube video about the book series is also available.

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Unbeatable Specials

With Kindle Unlimited ($9.99/month) at Amazon.com, you can read all e-books from Schottenbauer Publishing for no extra charge! Amazon offers Free 30-Day Trials of Kindle Unlimited. With this deal, trial members can read all Schottenbauer Publishing e-books free! This includes the Bow Science & Exercise Series, plus all the geometry workbooks, "The World in a Graph," "Alphabets of the World," all the e-book puzzles, and the educational novels by M. Schottenbauer, Ph.D.

Science of Music Performance: Motion, Force, and Breathing

The science of music performance is fascinating, for those who take the time and effort to obtain useful data. Fortunately, a large collection of scientific graphs and data on the science of music performance is now available in a series of books by M. Schottenbauer, Ph.D., How Do You Play That Thingamabob? The Science of Music Performance. Graphs in the series focus on the forces and motions required to produce sound. As such, they complement another series of books on the science of music by the same author, Where Does Sound Come From? This latter series focuses on the science of music, that is, the physics of the sounds which are arising from the musical instruments.

The graphs below demonstrate a selection of data from each volume of How Do You Play That Thingamabob? The Science of Music Performance.

Discussion Questions

1. In Graph 1, what is the range of motion? Does one hand move further than the other, in any direction? 
2. In Graph 2, what is the differential of force required to depress the different keys? On a practical level, what does this difference require of the instrumentalist?
3. In Graph 3, what is the difference in the air flow rate during the crescendo and diminuendo? Describe the difference in terms of (a) the average difference, (b) the maximum difference, (c) the minimum difference, and (d) the difference in variation.

Additional graphs on the science of music and music performance can be found in a free pamphlet from the publisher, and the following book series by M. Schottenbauer, Ph.D. The books below contain data from common band and orchestral instruments, plus recorders, keyboard, voice, and conducting.  

• Where Does Sound Come From?

• How Do You Play That Thingamabob? The Science of Music Performance

• The Science of Music: An Anthology of 28 Graphs for Kids,Teens, & Curious Adult

• Bow Science & Exercises for the Violin & Viola

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The Science of the Harmonic Overtone Series

The harmonic overtone series is a basic concept in music education which explains how many musical instruments function. It is easiest to explain the harmonic overtone series with science and math. New teaching tools from Schottenbauer Publishing offer students a refreshing insight into the working of the harmonic overtone series. 

The graphs below are excerpted from Volume 1 of Where Does Sound Come From?, as well as a free pamphlet from the publisher. These graphs show graphs of sound pressure from two notes performed on a soprano recorder.

Discussion Questions

1. Describe at least 2 differences between these two graphs.
2. What types of information are contained in each graph?
3. If possible, identify the frequency, wavelength, and/or amplitude of the wave in each graph.
4. Is it possible to determine the pitch of the note from either graph? If so, how?
5. Is it possible to determine the sound level (decibels) of the note from either graph? If so, how?
6. Are these two graphs related in the harmonic overtone series? If so, how?
7. Write a mathematical equation to describe the wave pattern in the bottom graph.

In addition to these graphs, a free YouTube video from the same publisher provides a brief lecture, as well as samples of the harmonic overtone series on flute, trumpet, trombone, and violin. 

Students may learn more about the harmonic overtone series in a multimedia training program titled Ear Training: Harmonic Overtone Series. Additional information is available on the Music Theory & Ear Training blog.

Additional graphs on the science of music and music performance can be found in a free pamphlet from the publisher, and the following book series by M. Schottenbauer, Ph.D. The books below contain data from common band and orchestral instruments, plus recorders, keyboard, voice, and conducting. 

• Where Does Sound Come From?

• How Do You Play That Thingamabob? The Science of Music Performance

• The Science of Music: An Anthology of 28 Graphs for Kids,Teens, & Curious Adult

• Bow Science & Exercises for the Violin & Viola

Additional Information

Schottenbauer Publishing

Free Education Resources