Sexturistens Klagan

Down For The Count

Recorded by Kari Malm at Baron Hill Studio Sweden and mixed by Atle.
Vocals and guitars: Mikael Öberg
Bass: Daniel Karlberg
Choir: Mikael, Ture, Daniel, Roger Polander
Drums: Christian Hell

Bad Reputation

Rain On My Parade W Vox

Block 5

Sista Beställningen

This track is constructed from all chords using the numbers 1 to 6 which meet certain criteria. Using whole numbers to construct harmony is 'Just Intonation'. Both the otonal chord (a, b, c) and the utonal chord (1/c, 1/b, 1/a) were used.

This track is intended to help composers to familiarise themselves with the chords available in 5-limit harmony.

For example, (3, 4, 5) is a (G, C, E') major triad in the second inversion. It is otonal, and its utonal counterpart is (1/5, 1/4, 1/3) = (12, 15, 20) which is (G, B', E') minor triad in the first inversion.

The rules for including a chord (a, b, c) were:
  a < b < c
  gcd(a,b,c) = 1
  4/3 <= c/a <= 4/1
  chord is otonal, which is (abc)^(1/3) < lcm(abc)^(1/2)

The final otonal harmonies found were:
1	2	4
1	3	4
1	2	3
2	5	6
2	3	5
2	4	5
2	3	4
3	5	6
3	4	5
4	5	6

The corresponding utonal harmonies were:
1	2	4
1	3	4
1	2	3
2	5	6
2	3	5
2	4	5
2	3	4
3	5	6
3	4	5
4	5	6
(note that 1 2 4 does not have a utonal counterpart)

Each harmony was used 3 times, by multiplying each chord by 6, 8 and 9, giving versions in keys of C, G and D.

They were then arranged in:
  descending order of MaxRatio = c/a
  ascending order of bass note 'a'
  descending order of middle note 'b'.

I hope that you find this track useful! Dave.

PS apologies for the lack of 11th and 13th harmonics, however those were not part of the construction schema :/

------------------------

See also:
- https://arxiv.org/a/ryan_d_1 (arXiv) for a list of my academic paper pre-prints, including my writing on music theory and Just Intonation
- http://orcid.org/0000-0002-4785-9766 (ORC ID) for my academic profile
- https://www.linkedin.com/in/davidryan59 for my LinkedIn profile

Example track of 3 note harmonies in Just Intonation constructed from the numbers 1 to 6

M.e.s- Gypsy

Alan Walker - Faded (ZeP Remix)

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Block 5

Slan Studios

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