Visualized Just Intonation in the perfect third and fifth

Visualized Just Intonation in the perfect third and fifth
September 4, 2018 mahal
In Blog

To hear a perfect third, the two frequencies are in the ratio of 5:4. For example a Kammerton A at 440Hz has its perfect third at 550Hz. The equally tempered third is by 14cents wider, meaning the first tone is lower or the second tone is higher than a just third.

Depending on the instrument and it’s overtones, this is sometimes not so easy to hear. While implementing Werckmeister we use the Hilbert Scope built into Piano Tuner to visualize it:


With a frequency ratio of 5:4 the Terz looks just beautiful:


With a slight deviation of 0.2 cents the loop still shows but it starts to rotate:


In the equal temperament, it doesn’t show any more the internal beauty of a harmonic series.:



The same goes for the perfect fifth which has a frequency ratio of 3:2

In equal temperament, the deviation is only 2 cents so the Quint beats very slowly:

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