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Arts & Humanities Independent Learning Assignment Music

The Twelve Note Conspiracy: Exploring Methods of Comparison Between Various Equal Divisions of the Octave

This essay was written by upper-sixth former Stan Lawrence, and was the winner of the Arts category for the 2020 Independent Learning Assignment. The following provides a short abstract to the full essay.

Estimated read time of abstract: 4 minutes

Estimated read time of essay: 18 minutes

This essay was written by upper-sixth former Stan Lawrence, and was the winner of the Arts category for the 2020 Independent Learning Assignment. The following provides a short abstract to the full essay, which can be found at the bottom.

Estimated read time of abstract: 4 minutes
Estimated read time of essay: 18 minutes

For the last few hundred years, Western music has mainly used a system called 12 tone equal temperament. This means it has 12 equally spaced tones before it reaches the same pitch as the first again, an octave up. This system is ingrained in our musical culture and isn’t often questioned, at least in mainstream music. However, some musicians maintain that there isn’t any particular reason why this status quo should be continued. The microtonal composer Harry Partch even goes as far as to say that 12EDO (Equal Division of the Octave) is a “musical conspiracy.” 

When I started thinking about what to do for my ILA, I realised that there were uncountable EDOs – you can split an octave into however many divisions you want – so I wanted a method of comparison to work out which EDOs I might like to compose with. In my full project, I compared different EDOs in three different ways: to see how close each EDO is to a tuning system that exists in nature (to create a temperament); a mathematical approach which attempted to work out whether each EDO would be useful or unusual for a composer; and finally, a more qualitative approach. I rejected the first two approaches for being a suitable way to compare them. I abandoned the first because it assumes sovereignty of natural scales built on the harmonic series, so therefore seems to commit the naturalistic fallacy. Then I rejected the second approach as the main reason for using different EDOs is to find new sounds – so I agree with the ancient Greek philosopher Aristoxenus when he wrote “Intervals should be judged by the ear alone, not by arithmetical relations.” 

So, I decided the third qualitative method was the most suitable for comparison of EDOs. For this method I decided I would do an arrangement of the same piece (a very famous Mozart Sonata) in different EDOs then try and describe and compare the overall sound of each arrangement. However, if there were more than 12 divisions in the EDO the arrangement would have to be variations on a themeThis was because as if I simply chose the notes that were closest to the original melody in our familiar 12-tone system then this wouldn’t be using all the notes in that EDO and so wouldn’t get an overall sense of the sound of that EDO. 

All these recordings are on my Soundcloud – soundcloud.com/stanlawrence – there is a playlist called the 12 Note Conspiracy with these (and a few more that I mentioned in my full project): 

  • 7EDO: this sounds most similar to Mozart’s original composition as it has the same number of notes as a major (not chromatic) scale. But it is noticeably “out of tune.” 
  • 19EDO – this is a noticeably busier version than the 7EDO as I had to put more ornaments and reharmonisations (when one changes the original harmony of a piece) in to cover all 19 notes.  
  • 23EDO – this is further away from 12EDO (the normal system) than 19EDO so has quite an other-worldly feel (also known as xenharmony) 

Conclusions 

As the arrangements were specifically variations on a theme (as this gets past the problem of not using that EDO to its fullest extent), this means that I couldn’t say exactly how the EDOs are different. But comparing my three arrangements to the original 12EDO version, it is clear for me that they all have different moods – in general terms I can say that 19EDO has a richer sound than the transparent sound of 23EDO. However, it is hard to put my finger on exactly how to describe them (and therefore compare them effectively) as they all seem so alien and piercingly out of tune for someone like me, who has been entrenched in 12EDO my whole life. It may be hard to break out of unconsciously hearing things in relation to 12EDO therefore a comparison of different EDOs may be predicated on a lifetime of listening to alternative EDOs and Xenharmony.  

Furthermore, when I made the arrangements of the Mozart Sonata I was effectively squeezing a 12-tone piece with 12-tone harmony into non-12 tone systems. Therefore, while EDOs can to a certain extent accommodate normative harmony, this can be hardly said to be using these systems to their fullest extent – arguably having new harmonies is one of the biggest advantages of these systems. 

However, having said that, I do feel like I have learnt what the overarching sound of a few different EDOs is, albeit in very vague terms. Importantly, I think I have learnt which EDOs I might like to compose with out of the ones I compared – and as this was my primary aim, I think it was a moderate success. I wrote a composition in 19EDO called Stars in the Sea (also on Soundcloud), which sums up what I have learnt about the sort of sounds that can be made in this particular EDO. It was quite an eye-opening experience to compose in a system that barely fits at all with my understanding of harmony. I find it incredibly fascinating and inspiring that there are whole other systems of music that have barely been explored – the possibilities are endless!  

To view Stan’s full article, follow this link below.

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