Partch’s Tonality Diamond related to my Moodswinger Color Schedule

When I first saw the tonality diamond of Harry Partch I couldn’t really figure out how it was constructed and what the logical aspect of it was.

Here’s a step my step guide which explains its relation with the color dotted system I use on my Moodswinger and other instruments. Note that this color dotted system has no relation with the color dotted system Partch used.

In 2006 I saw an internet site of a guy called Steven Rowatt using a color system. I couldn’t trace how it was constructed. Later I found out he used Partch’s color system. Partch used colors for equal values in the lower half of his fractions, I do to, but I always work from a different direction. Partch works with frequency ratios, I work with string part ratios. So my octave is 1/2 instead of 2/1.

The picture on top of this article is found on:

http://farm1.static.flickr.com/151/338779527_0843ed01d1.jpg?v=0

Where a man is also constructing some kind of piano with the system. When I started to develop my color system I also used the 2 color indication, but this appeared to unhandy, so I simplified it to a one color serie following the direction of a rainbow, starting with grey and than red, because otherwise it would lead to unhandy colors in dark rooms. You can’t recognize green from cyan for instance if the light is yellow, so I had to be sure those values wouldn’t too often led to confusion while playing.

This is the Partch diamond:

If I invert the mentioned values it becomes:

I have a tendency to think for the point of view from the overtones and therefore I prefer to think of 1/4 instead of 3/4. So if we take the mathmatical complement values of the string lengths we get:

Not all of them function well on my Moodswinger. When the denominator exceeds 9 the resonance decreases too much and the overtone becomes to high in relation to the ratios mentioned in picture 2. The sound of the instrument is the combination of the pitches of pic 2 and 3 together (creating the multiphonic clock sound). So I included my 8 limit color system in the picture below. The more complex fractions are colored in logical family colors related to diagonal family ratios. 1/10 fits logical with 1/5 for instance, so it becomes 15% Yellow.

Now at least the diagram makes sense to me, hopefully also to you partly. There is much more truth in Partch’s diamond, but this is at least one aspect which is clarified with this color inclusion.

Remarkable for me personally was the absence of the octave in the diagram. I always thought is was in. Also funny is the inverse appearance of the perfect fifth and perfect fourth. The only two notes which appear twice in the schedule. Sometimes the schedule is pictured with a vertical line right next to the grey row, indicating the utonality and otonailty section. Apparantly both notes take the inverse role of eachother in the two systems.

What also surprised me was the absense and random occurrence of the higher fractions. I expected a more logical pattern without too difficult fractions like the 9/20, which is not consonant at all. I had expected the series 1/13 – 6/13 or otherwise the series 1/15 – 7/15. Also 1/14 is missing.

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