3+3=5?

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Welcome to LivingPianos.com, I’m Robert Estrin. Today, I’m going to tell you how three plus three equals five. You probably clicked on this because you thought it was either a mistake or that I’d lost my mind. Well, believe it or not, it’s neither of those things! I’m going to show you how three plus three equals five in certain circumstances.

Recently, I made a video about triads.

Triads are the building blocks of Western music. A triad is a chord consisting of three notes arranged in thirds. You have two thirds: one on the bottom and one on the top. However, the outer interval is a fifth! How can two thirds equal a fifth? Have you ever thought about this? Now, many of you will probably know instantly what the answer to this is, but I thought it was interesting to ponder how you can build a chord out of two thirds and end up with a fifth, because that doesn’t make mathematical sense.

The reason is that the bottom third and the top third share the same middle note.

So you have a root, a third, and a fifth, which consists of a third on the bottom and a third on the top. And that’s the simple mathematics of it. So in triads, a third plus a third equals a fifth! But the math is still right, so don’t worry about it. Don’t trade in your calculator or rack your brains over this any further. I hope this is clear. If any of you still have questions about this, put them in the comments, and I’ll be happy to answer! Thanks again for joining me, Robert Estrin, here at LivingPianos.com, Your Online Piano Resource.

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2 thoughts on “3+3=5?”


 
 

    1. The middle note of a triad gives the major or minor sound because the perfect 5th (the top note of a major or minor triad) has little character. In fact, the root of the chord contains the upper note within its harmonic structure. The sound of G is in the C below it! But the middle note adds color you can easily discern.

      In the case of diminished and augmented triads, the 5th (the top note) is not an overtone (harmonic) of the root of the chord (the bottom note). So it does dramatically effect the sound of the chord.

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