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Music Notation and Terminology

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<h2>CHAPTER VII</h2> <h2>Scales</h2> 76. A scale (from scala, a Latin word meaning ladder; Ger. Ton-leiter) is an ascending or descending series of tones, progressing according to some definite system, and all bearing (in the case of tonality scales at least) a very intimate relation to the first tone—the key-tone or tonic. (See , Sec. 78; also note 1 at bottom of p. 38.) <div class="blockquot">Many different kinds of scales have existed in various musical eras, the point of resemblance among them all being the fact that they have all more or less recognized the octave as the natural limit of the series. The difference among the various scales has been in the selection of intervals between the scale-tones, and, consequently, in the number of tones within the octave. Thus e.g., in our major scale the intervals between the tones are all whole-steps except two (which are half-steps), and the result is a scale of eight tones (including in this number both the key-tone and its octave): but in the so-called pentatonic scale of the Chinese and other older civilizations we find larger intervals (e.g., the step-and-a-half), and consequently a smaller number of tones within the octave. Thus in the scale upon which many of the older Scotch folk songs are based the intervals are arranged as follows: </div> <table border="0" cellpadding="5" cellspacing="0" summary=""> <tbody> <tr> <td style="font-size: 150%">1</td> <td>whole step</td> <td style="font-size: 150%">2</td> <td>whole step</td> <td style="font-size: 150%">3</td> <td>step-and- a-half</td> <td style="font-size: 150%">4</td> <td>whole step</td> <td style="font-size: 150%">5</td> <td>step-and- a-half</td> <td style="font-size: 150%">6</td> </tr> </tbody> </table> <div class="blockquot">The result is a scale of six tones, corresponding approximately with C—D—E—G—A—C in our modern system. The term pentatonic is thus seen to be a misnomer since the sixth tone is necessary for the completion of the series, just as the eighth tone is essential in our diatonic scales. The following Chinese tune (called "Jasmine") is based on the pentatonic scale. </div>   <ANTIMG src="images/jasmine.jpg" width-obs="650" height-obs="177" alt="Jasmine" title="Jasmine" /> [Listen]   77. In studying the theory of the scale the student should bear in mind the fact that a scale is not an arbitrary series of tones which some one has invented, and which others are required to make use of. It is rather the result of accustoming the ear to certain melodic combinations (which were originally hit upon by accident), and finally analyzing and systematizing these combinations into a certain definite order or arrangement. The application of this idea may be verified when it is recalled that most primitive peoples have invented melodies of some sort, but that only in modern times, and particularly since the development of instrumental music, have these melodies been analyzed, and the scale upon which they have been based, discovered, the inventors of the melodies being themselves wholly ignorant of the existence of such scales. 78. A key is a number of tones grouping themselves naturally (both melodically and harmonically) about a central tone—the key tone. The word tonality is often used synonymously with key in this sense. <div class="blockquot">The difference between key and scale is therefore this, that while both key and scale employ the same tone material, by key we mean the material in general, without any particular order or arrangement in mind, while by scale we mean the same tones, but now arranged into a regular ascending or descending series. It should be noted in this connection also that not all scales present an equally good opportunity of having their tones used as a basis for tonality or key-feeling: neither the chromatic nor the whole-step scale possess the necessary characteristics for being used as tonality scales in the same sense that our major and minor scales are so used. </div> 79. There are three general classes of scales extant at the present time, viz.: (1) Diatonic; (2) Chromatic; (3) Whole-tone.[13] 80. The word diatonic means "through the tones" (i.e., through the tones of the key), and is applied to both major and minor scales of our modern tonality system. In general a diatonic scale may be defined as one which proceeds by half-steps and whole-steps. There is, however, one exception to this principle, viz., in the progression six to seven in the harmonic minor scale, which is of course a step-and-a-half. (See , Sec. 86.) 81. A major diatonic scale is one in which the intervals between the tones are arranged as follows: <table border="0" cellpadding="5" cellspacing="0" summary=""> <tbody> <tr> <td style="font-size: 150%">1</td> <td>whole step</td> <td style="font-size: 150%">2</td> <td>whole step</td> <td style="font-size: 150%">3</td> <td>half step</td> <td style="font-size: 150%">4</td> <td>whole step</td> <td style="font-size: 150%">5</td> <td>whole step</td> <td style="font-size: 150%">6</td> <td>whole step</td> <td style="font-size: 150%">7</td> <td>half step</td> <td style="font-size: 150%">8</td> </tr> </tbody> </table> In other words, a major diatonic scale is one in which the intervals between three and four, and between seven and eight are half-steps, all the others being whole-steps. A composition based on this scale is said to be written in the major mode, or in a major key. The major diatonic scale may begin on any one of the twelve pitches C, C♯ or D♭, D, D♯ or E♭, E, F, F♯ or G♭, G, G♯ or A♭, A, A♯ or B♭, B, but in each case it is the same scale because the intervals between its tones are the same. We have then one major scale only, but this scale may be written in many different positions, and may be sung or played beginning on any one of a number of different pitches. 82. It is interesting to note that the major scale consists of two identical series of four tones each; i.e., the first four tones of the scale are separated from one another by exactly the same intervals and these intervals appear in exactly the same order as in the case of the last four tones of the scale. Fig. 53 will make this clear. The first four tones of any diatonic scale (major or minor) are often referred to as the lower tetrachord[14] and the upper four tones as the upper tetrachord.   <ANTIMG src="images/fig53.jpg" width-obs="500" height-obs="108" alt="Fig. 53" title="Fig. 53" /> [Listen]   It is interesting further to note that the upper tetrachord of any sharp scale is always used without change as the lower tetrachord of the next major scale involving sharps, while the lower tetrachord of any flat scale is used as the upper tetrachord of the next flat scale. See Figs. 54 and 55.   <ANTIMG src="images/fig54-55.jpg" width-obs="500" height-obs="229" alt="Figs. 54-55" title="Figs. 54-55" /> [Listen]   83. From the standpoint of staff notation the major scale may be written in fifteen different positions, as follows:   <ANTIMG src="images/scales.jpg" width-obs="650" height-obs="555" alt="scales" title="scales" /> <ANTIMG src="images/scales2.jpg" width-obs="650" height-obs="835" alt="scales" title="scales" /> [Listen]   It will be observed that in the above series of scales those beginning on F♯ and G♭ call for the same keys on the piano, i.e., while the notation is different, the actual tones of the scale are the same. The scales of C♯ and D♭ likewise employ the same tones. When two scales thus employ the same tones but differ in notation they are said to be enharmonic, (cf. , Sec. 93.) <div class="blockquot">Note.—The student is advised to adopt some uniform method of writing scales, preferably the one followed in those given above, the necessary sharps and flats appearing before the notes in the scale and then repeated collectively at the end as a signature. He is also advised to repeat these scales and signatures over and over until absolute familiarity is attained. E.g., E—F♯—G♯—A—B—C♯—D♯—E; signature, four sharps, F, C, G, and D. </div> <hr style="width: 65%;" /> <div style="break-after:column;"></div>

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