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Mathematics Music 

Divine 9 revisited

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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.

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Music 

Divine 9 tuning

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SpiralsThis 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). Read More

Ukulele 

Ukelele chords II

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In part I we started the ukulele chord system by learning which notes are used in a chord. Now it’s time to find those notes on the ukulele fretboard. First we’ll have a look at which notes are where on the fretboard. Then, we can search for the chord notes. We will learn that a few shapes are sufficient to play all chords.
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Music Ukulele Uncategorized 

Ukulele chords I

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Note: this is the first part of a five-part course in moveable ukulele chords, originally published in Dutch. The other parts will follow shortly.

You can find ukulele chords in chord tables which you can find on the internet. But there are many kinds of chords like major, minor, 7th and many more, each in twelve different keys. And you can play each of these chords in a number of ways, resulting in hundreds of ukulele chords. You could learn all of these chords or use a small selection of ‘basic’ chords. A much better solution is to know what you’re doing, and learn a couple of basic shapes. Combined with a little bit of musical theory you can then find all the chords and variations you ever need yourself. In this series I’ll show you how to do just that.

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Music 

K枚hler’s Violin Repository of Dance Music

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Thee Petrucci Music Library is one of the large collections of classical sheet music on the internet. With a bit of searching you can also find some nice folk collections. In K枚hler’s Violin Repository of Dance Music you can find a few numbers of K枚hler’s The Musical Treasury (1885). In total there’s hundreds of hornpipes, quadrilles, waltzes etcetera. Written for one or two violins, but of course also playable on other instruments.