62 THE STUDY OF SPEECH CURVES. 



For most melody work such a table will suffice, except when the waves 

 are so long that a difference of 0.1mm. shows in the frequency column in 

 tenths of a vibration. In these cases the results must l)e worked out in 

 tenths; for example, a wave measuring 167 tenths of a milhmeter has a 

 period of 0.01167s. and a frequency of 85.5, while a wave 168 tenths long 

 gives 0.01176s. and 85.0, etc. 



For portions without waves the length is multiplied by the time 

 equation and the result is written across both columns to show that the 

 number does not indicate a wave-period, but another kind of duration 

 (surd, pause, etc.). 



To plot the melody curve some time equation is assigned to the X-axis 

 of the plot. In order to have all curves uniform it would be well to adopt 

 certain relations as standard ones: say for X, lmm.=0.001s. ; for Y, 

 1mm. = 1 vibration. The speech curve may be supposed to be laid along 

 the X-axis and stretched or contracted to suit the case. At the beginning 

 of each wave an ordinate is erected proportional to the frequency. 



To obtain the wave-lengths the period must be divided by the number 

 of seconds per millimeter for the X-axis of the plot. Thus for a plot with 

 lmm. = 0.0010s. the periods must be divided by 0.0010, for lmm.=0.0005s. 

 by 0.0005, etc. For example, let lmm. = 0.001s. for the X-axis and 1mm. 

 = 1 vibration for the Y-axis, and let the melody of the series of waves 50, 

 54, 55, 56, 59 tenths of a millimeter be plotted. At zero, a dot is placed 

 286mm. (see table on preceding page) above the X-axis. Then a distance 

 along X is laid off equal to the length of the first wave in order to find the 

 beginning of the second wave. The period or wave-length in seconds from 

 the first wave is (see the table) 0.00350s.; for 1mm. = 0.001s., this gives a 

 wave-length of 3.5mm. The distance 3.5mm. is laid off to find the begin- 

 ning of the second wave. Here a dot is placed at 265mm. above the X- 

 axis. The length of the second wave 5.4mm. is then laid off to find the 

 beginning of the third wave. Here a dot is placed 260mm. above, etc. In 

 this way we proceed, placing a "frequency dot" over the beginning of each 

 wave and laying off its length to find the beginning of the next wave, thus, 

 frequency 255, length 5.6; frequency 242, length 5.9. The series of fre- 

 quency dots thus obtained is the " melody plot." 



The separate dots may be connected by straight lines, and a general 

 smooth curve of melody may be drawn among them ; in this way the demands 

 of detailed study and also of general view are met. Where only a general 

 view is wanted it is sufficient to draw the smooth curve. 



To illustrate the methods to be followed in the study of melody I will 

 show how the plots were interpreted in several investigations, namely, of 



