Musical Techniques

Frequencies and Harmony

Dominique Paret, Serge Sibony

• Publisher: Wiley-ISTE
• Year: 2017
• ISBN:
  9781119388623
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

This book is built to start from elementary and fundamental bases to the first degrees of harmony. It provides many theoretical and technical bases of music, presenting in detail relations between physics and music (harmonics, frequency and time spectrum, dissonance, etc.), physiological relations with human body and education.

PART 1
Laying the Foundations

Introduction to Part 1

This first part examines the fundamental and classic concepts of music theory, which, in many places, are supplemented by physical-, physiological-, societal- and technical aspects, so we can begin to look at the idea of harmony within a clearly-defined context (notably western structures).

This part is divided into five chapters, always related directly or indirectly to harmony:

• – the first gives a concrete recap of the characteristics and performances of the human auditory system;
• – the second describes the types of modes of creation and generation which gave rise to notes, and are at the heart of numerous problems;
• – the third is a mini-recreation in relation to the notions of timbres, and also attempts to resolve certain confusions;
• – the fourth makes a long and detailed point about the vast extent underlying the terms of intervals;
• – the fifth and final chapter in this first part looks at fine quantification of the intervals to be defined for the concepts of consonance, dissonance and harshness.

1
Sounds, Creation and Generation of Notes

To begin this book, which has the ambitious aim of serving as a passport to harmony in the musical domain, it is perfectly normal to offer a recap of a few elementary aspects, which are absolutely necessary for the workings of our auditory apparatus (ear + brain + education + civilization + etc.) which will, ultimately, be the adjudicator of all this work. Thus… 1; 2; 1, 2, 3, 4!

1.1. Physical and physiological notions of a sound

1.1.1. Auditory apparatus

In acoustic science, sound is a vibration propagating through gases, liquids and solids. For humans, generally, it is the vibration of a mass of air, driven by a tiny variation in air pressure, with varying rapidity, which, via the outer ear, vibrates the membrane of the hearer’s eardrums and stimulates nerve endings situated in the inner ear (see Figure 1.1).

1.1.1.1. Outer ear

The auditory canal in the “outer” ear is in the shame of an acoustic horn, decreasing in diameter as we approach the bottom – i.e. the eardrum.

1.1.1.2. Middle ear

The middle ear contains the eardrum and three tiny bones, respectively called the hammer, anvil and the stirrup, which, together, make up the “ossicular chain”. The hammer and the anvil form a fairly inflexible joint called the “incudomalleolar joint”. The vibrations of masses of air in the auditory canal cause the eardrum to vibrate. These mechanical vibrations are then transmitted along the ossicular chain mentioned above, and then into the inner ear through the oval window.

Figure 1.1. Diagram of the human auditory apparatus (source: Wikipedia). For a color version of this figure, please see www.iste.co.uk/paret/musical.zip

The mode of simplified propagation of vibrations in the inner ear is essentially as follows: the lines of the concentric zones of iso-amplitude of certain frequencies are parallel to the “handle” (shaft) of the hammer, with, for the membrane of the eardrum, zones of vibration with greater amplitude than the handle.

As the middle ear forms a cavity, overly high external pressure may perforate the eardrum. In order to ensure and re-establish a pressure balance on both sides of the eardrum (inner/outer), the middle ear is connected to the outside world (the nasal cavities) via the Eustachian tubes.

1.1.1.3. Inner ear

The inner ear contains not only the organ of hearing, but also the vestibule and the semicircular ducts, the organ of balance (not shown in the figure), responsible for perception of the head’s angular position and its acceleration. Microscopic motions of the stirrup are transmitted to the “cochlea” via the oval window and the vestibule.

The cochlea is a hollow organ filled with a fluid called endolymph. It is lined with sensory hair cells (having microscopic hairs – cilia – which serve as sensors), which cannot regenerate once lost. They have tuft-like protruding structures: stereocilia. These cells are arranged all along a membrane (the basilar membrane), which divides the cochlea into two chambers. Together, the hair cells and the membranes to which they connect make up the “organ of Corti”.

The basilar membrane and the hair cells are set in motion by the vibrations transmitted through the middle ear. Along the cochlea, each cell has a preferential frequency to which it responds, so that on receiving the information, the brain can differentiate the frequencies (the pitches) maki...

Table of contents

• Cover
• Table of Contents
• Title
• Copyright
• Preface
• Introduction
• PART 1: Laying the Foundations
• PART 2: Scales and Modes
• PART 3: Introduction to the Concept of Harmony: Chords
• PART 4: Harmonic Progressions
• Appendix: Acoustic (Harmonious) Effects
• Glossary
• Bibliography
• Index
• End User License Agreement