DEFINITION OF THE CONSONANT INTERVALS. 185
The following beats will be generated between these Differentials,
202 — 198 = 4 \
303 — 299 = 4 [ beats per second.
703 — 699 = 4 )
The Major Third between tones consisting of the first three partials is guarded therefore by three sets of Differential Tones of the 1st order.
Summary of Definition of Intervals. Simple Tones.
Octave. 1st Differential in unison with lower tone. Fifth. 1st „ ,, ,, 2nd Differential.
Fourth. 1st ,, ,, ,, 3rd ,,
Any departure from true intonation produces beats between these unisons.
Other intervals practically undefined. i
Ordinary Compound Tones.
The Octave, Fifth and Fourth defined as above, but also and chiefly as follows,
Octave. 2nd partial of lower tone unisonant with 1st partial of higher. Fifth. 3rd ,, „ „ „ ,, 2nd ,,
Fourth. 4th ,, „ „ „ ,, 3rd ,, „
Major Third. 5th ,, ,, ,, ,, 4th ,, ,,
Minor Third. 6th ,, ,, ,, ,, 5th ,, ,,
and generally, in any interval the unisonant or defining partials are given by the numbers which denote its vibration ratio.
If the lower of the two tones of any interval be out of tune by 1 vibration per second, the number of beats generated (by lowest pair of defining partials) is the same as the greater of the two numbers which denote its vibration ratio ; if the higher tone be out of tune by the same amount, the number of beats is the smaller of these two numbers.