Abstract

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The harmonic series (overtone series) is a topic that comes up in nearly every university-level music course. Yet only in a course on musical acoustics is a student likely to have access to all of the information required to gain a good understanding of the nature of the harmonic series. From a pedagogical point of view, the harmonic series can serve as a path to understanding a variety of musical concepts. This author has created a collection of Web-based multimedia resources entitled "The Harmonic Series: A path to understanding musical intervals, scales, tuning and timbre" designed to introduce the harmonic series and related concepts to musicians. In addition to the usual text and image presentation in a HyperText environment, the site contains audio examples, instructional animations, interactive applications, JavaScript calculation tools, links to related Web resources, and worksheets in pdf format. The presentation will take the following form. First, a brief overview of the site will be provided and the tools used to build the instructional animations will be briefly discussed. Second, a number of the instructional animations available on the site will be demonstrated. The Web site for this presentation is: www.music.sc.edu/fs/bain/atmi02/.

Download

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1. Download the Presentation Handout (pdf)

2. Download the PowerPoint Presentation (bain-atmi02.ppt)

Presentation Examples

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1. The Harmonic Series: A path to understanding musical intervals, scales, tuning and timbre.

   Hear the Harmonic Series

   1. Play Harmonics: 1-12, 8-16, 16-24 (See 1., above) A Sweep of the First 20+ Harmonics of A1
   2. The harmonic series vs. its approximation in 12TET
   3. Arpeggio in the harmonic series, a Csound instrument by J. C. Risset
   4. Tuvan throat singer Vasili Chazir sings ARTY-SAYIR "the far side of a dry riverbed"

2. Cents: A convenient unit for pitch interval.
3. Hear Natural (Just) Intervals
4. The Line of Fifths
5. A Pythagorean tuning of the diatonic and chromatic scales
   1. The Pythagorean comma
6. A Just Tuning of the Diatonic Scale
7. Fusion
8. Beats, roughness, and critical band

JavaScript Calculation Tools

1. Natural interval frequency ratio to cents conversion (See bottom frame).
2. 12TET Frequency Table Maker - Creates a frequency table (Hz.) for all 12TET pitches C0-B8 (C4 is middle-C). User can set the frequency of A4 (A above middle-C)

Lab/Worksheets

1. Acoustical Foundations of Tonal Theory
   1. Properties of Sound (pdf)
   2. The Harmonic Series, Pitch Notation & Natural Interval Frequency Ratios (pdf)
   3. Cents, The Line of Fifths and Scale Creation (pdf)
2. Create your own tuning

Shockwave/Flash Examples

1. The relationship between circular motion and sinusoidal waveform (swf)
2. Building a complex tone from harmonically-related sinusoidal components (swf)

Software Links

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1. Vercoe's Csound
2. Macromedia's Flash
3. Apple's QuickTime