Scan 17
The New Encyclopedia Of Music And Musicians, 1929
206 lines. Read by computer on 18 September 2026. No printed page number was found. See the scan on archive.org.
1telligibility of composition are conditioned upon the disposition of tones in somewhat regular plans of relative duration (various units being known as beats or pulses, measures, phrases, sections and the like), which together make up meter.
3There is no consensus of usage as to the terms rhythm and meter. One reason is that the schemes on which music is constructed usually present an intricate blend of intensity- and duration-elements. Relative accent and relative quantity are used together as an organizing and vitalizing agency. Yet the two are not identical. Each may be regarded by itself. At first sight modern music appears to rest on schemes of accents rather than of quantities (more or less in contrast with what we know of ancient music). But even in modern music accentual patterns are quantitative because built on equal beats and measures, and the balance and flow of all the larger factors (themes, motifs, etc.) are strongly quantitative because depending on the interplay of longer and shorter tones. So it has become the habit to use the term rhythm for the total scheme of accents and quantities, often with more reference to the latter than the former. Yet there might be utility in limiting rhythm, rhythmics and rhythmical more generally to matters of relative loudness, and meter, metrics and metrical more to matters of relative duration. See Meter and Rhythm.
5(2) The connection between tones as objective phenomena and the subjective experience of music as an art is made through the recognition of tone-relationship. The way in which this principle has been used has varied much at different periods and among various races. Yet some use of it is always and everywhere requisite to the practice of music as an art.
7In general, the simpler the numerical ratio between the vibration-numbers of two tones the closer is their tone-relation. Aside from the relation of the unison (1:1), the simplest ratio is 1:2 (that of the octave) and to this follow 2:3, 3:4, 3:5, 4:5, 5:6 and 5:8—all of which are accepted in modern music as consonances or concords. Ratios containing 7, 9 or any higher number (except when reducible to simpler forms) are counted as dissonances or discords. In the formation of both melody and harmony consonances supply the element of relative completeness or finality, dissonances that of incompleteness or transition. The interplay of the two elements is necessary for both interest and strength in composition.
9The relation expressed by the ratio 1:7 is anomalous in that it is harmonious to the ear, but not definitely included in the modern system. It doubtless often occurs in unaccompanied part-singing and string-music.
11For both melodic and harmonic purposes modern music assumes one or more tone-series or scale. The most important is that whose general formula is
131-2-3-4-5-6-7-8
15This has gradually become primary in artistic usage because, in its ideal form, its tones are united by a high degree of consonance and at the same time offer convenient and somewhat varied consecutive steps. The most perfect 3-tone consonance is the triad 1-3-5 and precisely the same triad occurs in 4-6-8 and 5-7-9 (or 2). The tones 5 and 4 are the nearest relatives of 1 and each serves as the root or generator of a triad like the one belonging to 1. In consequence, even 7, which is the least directly related to 1, becomes a relative in the second degree. Parallel reasoning may be applied to the several forms of the minor scale as used in modern music. Through the combination of major and minor scales, and still more through the practice of modulation (the shifting of the tone-center from 1 to some other tone and then basing a new scale on that tone), chromatic scales of twelve tones to the octave appear. In such cases many of the tones are related to 1 only in a third or fourth degree. Yet the mind comes to feel the relationship and to use it artistically. Since chromatic scales are made up of tones somewhat equally spaced and since the maintenance of pure intonation in modulatory processes is difficult and instrumentally almost impossible, the compromise scale of equal temperament has secured wide acceptance. Here the mind comes to interpret a variety of interval effects as, so to speak, symbolic of what they are not exactly and to accept them as representing what they only approximate. See Interval, Scale and Temperament.
17The following table gives in order of pitch the tones within the octave that belong to the major and minor scales, the upward and downward chromatic scales, and also the equally-tempered scale. The ratio following the serial number is that of the tone to the starting tone. The last two columns indicate the letter-name and the vibration-numbers assuming that the octave begins with middle C ( = 264).
19<table>
20 <tr>
21 <th>1</th>
22 <th>1/1</th>
23 <th>Unison or prime</th>
24 <th>C</th>
25 <th>264</th>
26 </tr>
27 <tr>
28 <th>1#</th>
29 <th>25/24</th>
30 <th>Augmented prime</th>
31 <th>C#</th>
32 <th>275</th>
33 </tr>
34 <tr>
35 <th>1# = 2b</th>
36 <th>1 tempered semitone</th>
37 <th>C# = Db</th>
38 <th>279</th>
39 </tr>
40 <tr>
41 <th>2b</th>
42 <th>16/15</th>
43 <th>Minor second</th>
44 <th>Db</th>
45 <th>281</th>
46 </tr>
47 <tr>
48 <th>2</th>
49 <th>10/9</th>
50 <th>Major second (small)</th>
51 <th>D</th>
52 <th>293</th>
53 </tr>
54 <tr>
55 <th>2</th>
56 <th>9/8</th>
57 <th>Major second (large)</th>
58 <th>D</th>
59 <th>297</th>
60 </tr>
61 <tr>
62 <th>2#</th>
63 <th>75/64</th>
64 <th>Augmented second</th>
65 <th>D#</th>
66 <th>309</th>
67 </tr>
68 <tr>
69 <th>2# = 3b</th>
70 <th>3 tempered semitones</th>
71 <th>D# = Eb</th>
72 <th>313</th>
73 </tr>
74 <tr>
75 <th>3b</th>
76 <th>6/5</th>
77 <th>Minor third</th>
78 <th>Eb</th>
79 <th>316</th>
80 </tr>
81 <tr>
82 <th>3</th>
83 <th>5/4</th>
84 <th>Major third</th>
85 <th>E</th>
86 <th>330</th>
87 </tr>
88 <tr>
89 <th>3</th>
90 <th>4/3</th>
91 <th>Perfect fourth</th>
92 <th>F</th>
93 <th>352</th>
94 </tr>
95 <tr>
96 <th>4</th>
97 <th>4/3</th>
98 <th>Perfect fourth</th>
99 <th>F</th>
100 <th>352</th>
101 </tr>
102 <tr>
103 <th>4#</th>
104 <th>25/18</th>
105 <th>Augmented fourth</th>
106 <th>F#</th>
107 <th>366</th>
108 </tr>
109 <tr>
110 <th>4# = 5b</th>
111 <th>5 tempered semitones</th>
112 <th>F# = Gb</th>
113 <th>375</th>
114 </tr>
115 <tr>
116 <th>5b</th>
117 <th>64/45</th>
118 <th>Diminished fifth</th>
119 <th>Gb</th>
120 <th>380</th>
121 </tr>
122 <tr>
123 <th>5</th>
124 <th>3/2</th>
125 <th>Perfect fifth</th>
126 <th>G</th>
127 <th>395</th>
128 </tr>
129 <tr>
130 <th>5#</th>
131 <th>25/16</th>
132 <th>Augmented fifth</th>
133 <th>G#</th>
134 <th>412</th>
135 </tr>
136 <tr>
137 <th>5# = 6b</th>
138 <th>8 tempered semitones</th>
139 <th>G# = Ab</th>
140 <th>419</th>
141 </tr>
142 <tr>
143 <th>6b</th>
144 <th>8/5</th>
145 <th>Minor sixth</th>
146 <th>Ab</th>
147 <th>422</th>
148 </tr>
149 <tr>
150 <th>6</th>
151 <th>5/3</th>
152 <th>Major sixth</th>
153 <th>A</th>
154 <th>440</th>
155 </tr>
156 <tr>
157 <th>6</th>
158 <th>9 tempered semitones</th>
159 <th>A</th>
160 <th>443</th>
161 </tr>
162 <tr>
163 <th>6#</th>
164 <th>125/72</th>
165 <th>Augmented sixth</th>
166 <th>A#</th>
167 <th>458</th>
168 </tr>
169 <tr>
170 <th>6# = 7b</th>
171 <th>10 tempered semitones</th>
172 <th>A# = Bb</th>
173 <th>470</th>
174 </tr>
175 <tr>
176 <th>7b</th>
177 <th>16/9</th>
178 <th>Minor seventh (small)</th>
179 <th>Bb</th>
180 <th>469</th>
181 </tr>
182 <tr>
183 <th>7b</th>
184 <th>9/5</th>
185 <th>Minor seventh (large)</th>
186 <th>Bb</th>
187 <th>475</th>
188 </tr>
189 <tr>
190 <th>7</th>
191 <th>15/8</th>
192 <th>Major seventh</th>
193 <th>B</th>
194 <th>495</th>
195 </tr>
196 <tr>
197 <th>7</th>
198 <th>2/1</th>
199 <th>Perfect octave</th>
200 <th>C</th>
201 <th>528</th>
202 </tr>
203</table>
205See diagram under Scale.
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