It just doesn't add up

Four perfect fifths (minus two octaves) doesn't equal a major third

If we start with a pitch of frequency **F**, the frequency of a pitch a just perfect fifth higher is **F * 3/2**.

Another fifth up takes us to **F * 3/2 * 3/2**, or **F * 9/4**.

Next is **F * 27/8**, and one more is **F * 81/16**.

A just major seventeenth (a just major third plus two octaves) is **F * 5**, or **F * 80/16**, which is a bit flatter.