sus4

Here’s an interesting effect in Dynamic Tuning.

Using the Max/MSP implementation of Dynamic Tuning found here, first

• Slide the slider on the lower left of the screen rightward to “fully tempered”
• Set the tuning slider to 696.6 cents (1/4-comma meantone or 31-tet)
• Play a major triad on your QWERTY keyboard (e.g., the buttons labeled H-K-U)
• While the triad is sounding, slide the tuning slider up to its maximum (720 cents, 5-tet)
• Hold the slider there a moment, and then slide it back to where it started (696.6 cents)

What did you hear?

What I hear is:

• A nice, pure-sounding major triad, then
• A sus4, then
• A major triad again.

How’d that happen?

Well, when you push the slider up from 696.6 cents to 720 cents, you’re widening the tempered perfect fifth accordingly. The pitch of the major third (and the placement of the fifth harmonic of the tempered timbre) is higher than that of the root by four tempered perfect fifths minus two octaves. That means that the major third is widening from

• ((4 * 696.6) - (2 * 1200) = (2786.4 - 2400) =) 386.4 cents, which is a nearly-just major third, to
• ((4 * 720.0) - (2 * 1200) = (2880.0 - 2400) =) 480.0 cents, which is 18 cents flat from a just perfect fourth.

Just by wiggling the tuning slider, you can go from a very restful major triad to a tense sus4 – with the sharpened P5 adding to the tension – and back again.

Cool! :-)