I’ve received a few questions about the details of the mathematics in my Divine 9 post, and why the Divine 9 theory qualifies as pseudo-science. In this post I’ll skip the musical part of the Divine 9 tuning, and will focus on the arguments about the divinity of the number 9.
Let’s start with the pseudo-science part. The usual scientific principle is to start with the facts, and then trying to draw a conclusion. Scientists try to find counter-examples to disprove their own theory. Pseudo-science just starts with a conclusion and tries to find facts supporting this conclusion, ignoring facts that don’t fit with the result. Now let me try to explain why the Divine 9 theory qualifies as pseudo-science.
If you take a look at the Divine 9 music site, you’ll read about the importance of the number 9 and how it should show up everywhere in nature. In fact, this connection with nature is based on spirals, the Fibonacci sequence, and the golden ratio. So far, so good. Both the Fibonacci sequence and the related golden ratio (I’ll get into the details), really do show up in nature. Interesting, but not that spectacular, since both nature and the Fibonacci sequence follow simple rules. Where it goes wrong is where the number 9 is lifted to a divine status. On the Divine 9 site, Gert Kramer gives examples of how the number 9 keeps showing up. Musical examples are John Lennon’s ‘Revolution 9’ and the fact that Beethoven wrote 9 symphonies. Conveniently, wikipedia maintains a list of song titles with a number in the title. Counting titles I don’t see a preference for 9. And though pi shows up, the golden ratio is missing. Wikipedia also features a list of symphony composers. Again, there are many composers who didn’t write exactly 9 symphonies.
There’s only so many ads I can take before I get curious. After too many pop-ups about how to become rich I had a look at the Euro Millionaire System. I’m not brave (or stupid) enough to really give it a go, but the system itself is completely wrong. The ‘magic system’ contains a few mathematical tricks that help to convince you that you can’t go wrong, but actually don’t make sense. With the Euro Millionaire System you’re supposed to bet on binary options, using two simple strategies: one to choose which of the two options you have to bet on (up or down), the other to choose the amount of money you wager. I am not a stock expert, but let me try to explain how binary options work. The Euro Millionaire System video refers to Stockpair, a platform for binary options. The idea is that you guess whether for example the euro/dollar exchange rate goes up or down in the next 15 minutes. If you’re right you earn yourself some money, if not you loose. Not too different from playing roulette, except that one could argue that the exchange rate over a short period of time isn’t completely random. The payout however is much lower than in a casino.
This week I stumbled upon what’s called the Divine 9 tuning, which should be an alternative to Equal Temperament. The Divine 9 website claims that this temperament is based on the order principles of nature itself, and looks more like a new age site than a music site. It keeps mentioning the importance of the number 9 and how this is derived straight from spirals using the Fibonacci sequence (including Egyptian gods, Chinese dragons and ‘Cosmic creation principles’). The Divine 9 tuning is supposed to use this number to give it it’s specific properties.
There’s nothing wrong with trying out different tunings, but the Divine 9 tuning somehow annoys me. More because of its presentation than because of the tuning itself. First of all I’m not sure whether it’s really an alternative to Equal Temperament. Secondly, the mathematics behind the importance of the number 9 and its relationship with nature is flawed. Finally, the way the number nine is part of the Divine 9 tuning is very artificial, and has hardly any influence on the tuning itself. From what I’ve heard of music played in Divine 9 tuning it sounds pleasant, but so does for example Pythagorean tuning (yes, my digital piano can play Pythagorean). I haven’t checked in which keys the Divine 9 example are, but I doubt it sounds that good in all 12 keys (which is exactly why we use equal temperament on a piano). Continue reading