“Dreams of the Great Old Ones”
From Playlist : Lovecraft Dark Ambient
The sequel to my 2021 “Lovecraft Ambience” is another suite of soundscapes designed to play in the background, as a complement to H.P. Lovecraft inspired board games, card games, role-playing or reading. Whereas Volume 1 focused upon outright fear, this collection is focused upon the theme of dreams and nightmares. I have striven to find a very difficult balance between hypnotic, soporific ambience and an underlying sense of dread, portent and impending doom.
The use of microtonal instrument tunings is the source of the “other-worldly” strangeness of these sounds – I used a scale based on the Fibonacci Golden Ratio.
Lovecraft Ambience 2 – Tracks in MP3 Format
The Math Behind the Sound
Traditionally, western music is based on a doubling of frequency. This relationship between pitches is called an “octave” . Because the system is based upon doubling, it necessarily follows that the scale is logarithmic, each step being an integral power of 2 – the multiplying goes by the scheme:
So, no matter what frequency you begin at, after (say) four equal steps of octaves, you are hearing a frequency that is 16 times higher than where you began. But octaves are (to the human ear) a very large change in pitch, so over history musicians have sought ways to further subdivide the octave.
Early approaches such as the “Pythagorean” method sought to divide the range of ratios between 1 and 2 using integer fractions such as:
|3/2 = 1.5||4/3 = 1.33…||9/8 = 1.125||etc.|
This worked well up to a point, but sometimes generated some quite dissonant sounds. Eventually Western musicians settled on using an “equal- temperament” scale whereby the octave was divided into 12 equal intervals, the ratio between successive pitches being the 12th root of 2, or a ratio of approximately 1.05946 (a semitone).
Musicians interested in microtonal tunings choose to further subdivide the semitone interval into 100 equal parts, called cents. Thus a cent is the 1200th root of 2, or a ratio of approximately 1.0005777895.
833 Cent Scales
In the 1970’s Heinz Bohlen questioned the standard 12-TET approach and investigated whether other tunings might be viable. He took as axiomatic that when two pitches are sounded together, one hears combination tones. So for example, when 1:1 and 2:1 (octave) are sounded together, we also hear 3:2 (the fifth). I am not a musician so I don’t know if this is true. Bohlen, however, thought about this and looked to the extreme case of “stacking” combination tones (here listed with equivalent cents values), creating a series which converges on 883.09 cents:
|3:2=884.359||5:3=813.686||8:5=840.528||13:8=830.253||21:13=834.175||……. and so on.|
Had Bohlen been a mathematician, he would instantly have recognised this as a Fibonacci sequence, converging on the Golden Ratio 0.618034.. or, the solution to the equation:
1+x = 1/x
Bohlen developed a scale based on stacking the Golden Ratio, together with a bit of manual adjustment to create this scale:
I suspect that Bholen’s 833 cent scale reflects a musical awareness, and I am unsure what justifies the somewhat arbitrary introduction of an extra two pitches selected from stacked fourths and fifths. However, I am convinced that there is some quality of the 0.618033.. ratio that makes it musically very interesting, so I chose to employ an 833 Cent type of scale for the “Lovecraft Ambience 2” soundscape collection.
Sevish Archibald is a groundbreaking microtonal musician. In 2017 he published an article “The Golden Ratio as a Musical Scale“, which first gave me an understanding of 833 cents . There are obviously many possible approaches (one of them being stacking intervals as per Bohlen above) – but Sevish proposes what I refer to as an “iterative” approach. In this method, scales are developed by subdividing the 833 cent interval using (again) the Golden Ratio. This creates two new intervals of approximately 515 and 318 cents. The process is applied iteratively. In the diagram I show the 12-TET scale of 1200 cents for comparison:
The scale therefore has a “fractal” quality – in that, the closer you look, the more you see of the same kind of structure.
Sevish kindly did the math and offered up a scale as follows:
I can appreciate that choosing to forego the 3rd iteration 786 in favour of the 4th iteration 122 makes sense musically – however, I had an intuition that sticking to a “pure” 3rd iteration 8 interval scale might produce something more appropriate for my own project which is based on greater use of dissonance – and therefore I settled upon this scale as the basis for my work:
196.665952 = 293.10 Hz (D4)
318.212189 = 314.42 Hz (Eb4)
439.758426 = 337.29 Hz
514.878128 = 352.25 Hz
636.424365 = 377.87 Hz
711.544067 = 394.62 Hz (G4)
786.663769 = 412.12 Hz (Ab4)
833.090296 = 423.33 Hz
(The frequencies listed are what would be heard if you began at a standard tuning for C4 of 261.63 Hz).
For one of the tracks in the Lovecraft Ambience 2 collection, I used the full 4th iteration 16-tone scale:
Downloads – 833 Cent Scales
If you want to play with these scales in your own soft synthesisers, here are the files in Scala format (after downloading, just rename the file extension to .scl ) You can use Scala software to convert to other formats such as .tun or .mid if required. I offer the “inverted” versions as well, where the intervals are broken in the inverse ratio.