This is “Scales and Scale-Steps”, section 3.1 from the book Music Theory (v. 1.0).
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In examining the notation of pitch, we observe that notes climbed or “scaled” the lines and spaces of staves from low to high. Ordered sequential collections of these pitches are called scales (Italian: scala-“ladder”).
Scales are comprised of five or more pitches arranged in sequential patterns of whole steps and half steps spanning an octave species. We label scales as to the number of differing elements they contain:
Four-note sequences are called tetrachords (Greek: “four tones”). In this context, they are regarded as constituent components of larger scale patterns.
Since scales are orderings of whole steps and half steps, these serve as the foundation “building-blocks” for scale construction. As we learn to construct and identify scales, we do so by recognizing their content in terms of tones (whole steps) and semi-tones (half steps).Although tone and semi-tone are proper names, whole step and half step are commonly used terms. In some instances you may encounter the terms whole tone and half tone also. For now, avoid calling whole steps and half steps by any other name, for example, “major-seconds” or “minor–seconds.” Proper interval identification for whole steps and half steps shall be addressed in Chapter 5 "Intervals".
Throughout the history of music, various systems of referential tuning have evolved, been adopted, been modified, and been discarded in favor of other systems. It is not within the purview of this discussion to examine these various and sundry systems of tuning.An exceptionally clear and concise discussion of the history and theory of tuning systems may be found in Chapters 1 and 2 of Chromaticism: Theory and Practice, Howard Boatwright, Walnut Grove Press, 1994.
For our purposes, we shall limit the discussion to the standardized tuning system known as equal temperamentThe current system of tuning whereby pitches have been adjusted to allow division of the octave into twelve equal portions.. Music in the transitional period between the Renaissance and Baroque employed different tuning systems that limited compositional resources. A “compromise” tuning system was proposed and gradually adopted, whereby pitches were slightly altered enabling the division of the octave into twelve equal portions or semi-tones (half steps). This “evenly-tuned,” or “equal-tempered” system allowed composers to employ the full resources of the chromatic collection.This will come into focus in Chapter 4 "Key Sense, Key Signatures, and The Cycle of Fifths" and Chapter 5 "Intervals".
Therefore, the source collection for Western music is the Chromatic ScaleThe source set or collection for pitch materials as defined within equal temperament..The Chromatic Scale, so called because it contains all the pitch “colors,” is also known as the Duodecuple scale (Latin: duo-deca, “two and ten”). It is also labeled the Non-Selective Scale, so-called because, all pitches being of equal quality, no one pitch asserts itself over the others.
Figure 3.1 The Chromatic Scale
The Chromatic Scale(click to see video)
The Chromatic Scale is comprised entirely of half steps. When constructing this, it is customary to use sharps when ascending and to use enharmonically equivalent flats when descending.
Music of the mid-17th Century through end of the 19th Century saw the formulation of a more or less unified system of composition and its supportive theory. A lingua franca of music was established, essentially a common language shared by all musicians. Music of the period (roughly!) from Corelli through Brahms is called the Common Practice PeriodMusic from roughly the 17th- through the 19th Centuries. Also may be referred to as Tonal Music., or the Common Practice style.
One of the fundamental attributes of this Common Practice style was the use of two scale types. These two types, Major and Minor were “distilled” from the multiple scale types employed in early music. Major and Minor scales became the predominant resource for Common Practice music. These scale types shall become essential tools for many of the acquired tasks and skill-sets in the study of music. Understanding and recognizing these constructs is a fundamental and necessary attribute of the music student.
The student should understand: