About “Tartini tone”

About “Tartini tone”
The otherday I have written about “Tartini Tone” in my article “The Road to Equal Temperament”.
A difference tone (Tartini tone) is a tone with a frequency equal to the difference between the frequencies of the two tones that is heard when two different tones are played simultaneously. For example, a sound of 100 Hz and 101 Hz at the same time produces one beat per second, while a sound of 100 Hz and 104 Hz produces four beats per second. A difference as small as this is perceived by the human ear as a beat, not a sound. However, when the difference in frequency becomes large to some extent, the beats becomes perceived as a tone with the unique pitch. To explain this in musical notes, it looks like this (Figure 1)
For the sake of clarity, let’s assume that the note at 100 Hz is the Do of the F clef. Then the Do one octave higher is 200Hz. So above it is 300Hz, and the Do above it is 400Hz, the Mi above it is 500Hz, the So above it is 600Hz, and the Si♭ above it is 700Hz. You can see that the difference in frequency between the two adjacent notes is all 100Hz. This means that if you play those two adjacent notes at the same time, you will hear the sound of the F clef Do (100Hz). This is actually audible, so you can try it on a violin or recorder or the others.
The chord obtained at this frequency ratio is a genuine chord. A genuine chord is a chord made of the Pythagorean fifth degree and of the major third meantone degree. The major third of the meantone is about 13.5 cents narrower than the major third of the equal temperament (in essence, the modern piano tuning system). The perfect fifth degree of the meantone is about 3.5 cents narrower than the perfect fifth degree of the equal temperament. In other words, the major third in Meantone is a genuine pitch with no beat, while the fifth degree in Meantone is a fifth degree with even more beat than the equal temperament. This means that in the Baroque era, the beauty of the major third took precedence over the beauty of the perfect fifth. #baroque #tartini #片山俊幸