18 HJALMAR THUREN. 
measure some of the tones, partly owing to the indistinctness of 
these, partly because the duration of the tone was too short, which 
especially was frequently the case with transitional tones. 
The singer generally sang the same intervals throughout the 
melody. Where differences of any importance occur, this is noted. 
Scepticism has been expressed from various sides with regard 
to the use of tone-calculations as here proposed. It may be frankly 
admitted, that calculation of sound-waves is far from being able to 
give us as certain results in vocal music as in instrumental, and 
that the numbers everywhere can only be considered as approxi- 
mately accurate. But between this admission and the denial of anv 
importance to the calculation of the wave-frequency of a song, there 
is a wide step. That the intervals in songs of primitive races do 
not often correspond to those in European is indeed a fact, which 
even ordinary travellers have noticed. And this fact can not be 
reduced by saying, that these primitive people are unmusical — as 
Julien Tiersot has maintained quite recently with regard to Indian 
melodies, in a very superficial attack against those who are specially 
engaged in the study of wave-frequency. * 
There is hardly any doubt that the cents tables, which have now 
been worked out for so much primitive music, will in time constitute 
an important material for the comparative study of music, while 
hitherto it has been necessary to treat with some reserve melodies 
written down from the ear alone — often by casual recorders. 
The accompanying table gives a summary of intervals occur- 
ring in the material (44 melodies) worked out tonometrically. The 
ordinary numbers indicate intervals between adjacent tones of the 
scale of the melody, the numbers italicised indicate intervals of the 
melody, calculated from the tonus currens, and the numbers under- 
lined the intervals calculated from other tones of the melody. In 
the last two cases when an interval has already been given, it is 
not again indicated. ? means that the scale contains an interval 
which cannot be determined tonometrically. > 
C, E flat, G, as the distance between the deepest and highest tone is 751 cents. 
The interval lies midway between a fifth and a minor sixth. 
These examples belong however to the exceptional cases. As a rule there is 
no doubt as to the notation of the melody. 
1 Sammelbände а. Intern. Musikgesellschaft, XI, 5. 172—73 (1909—10). 
2 As will be seen from the scales which are printed in front of each melody in 
our collection, there is often an intermediate note between the prima and third. 
0 +0.06 0,37 The G is only of little importance in the 
fes ne Nos 8B | SNE —e— melody; it occurs only as an intermediary 
INOS AL ae 
5 AL fone and fs sung as a rule so quickly 
i te i 
406 251 
and indistinctly, that the determination 
