228 HANDBOOK OF ACOUSTICS. 

The remaining two are exceptions; for from the vibration numbers above we have 





Again, the Minor Thirds that can be formed from the notes of the diatonic scale are : 





If, as above, the vibration ratios of these intervals be calculated, it will be found that the following three are true Minor Thirds, that is, the vibration numbers of their constituent tones are in the exact ratio of 6:5: 







Of these three exceptions, we may at once dismiss j £' as being a well recognized interval, the Diminished Fifth, less by a Semitone than the Perfect Fifth, for which it is not likely to be mistaken. But it is otherwise with the other two; they are very nearly a Perfect Fifth and a true Minor Third, respectively, for as we have just seen 





The imperfection of these intervals will be best seen by sketching the Compound Tones of up to the beating partials, taking the vibration numbers given above; thus,— 
