probably easier to sing on a synth than in real life ;)

Here is a simple piece for choir based on this balanced string principle with the connected trinity of intervals played together so if a string of length = 1 is divided into a string length = 1/r1 & 1/r2 then 1/r1 + 1/r2 = 1 so r1 = r2/(r2-1) &r2 = r1/(r1-1)
The trinity of frequencies, fundamental = 1 & r1 & r2 are sounded together in this piece in order, from one end of a hypothetical string to the other, then repeated. Kept it simple as a demonstration.
These abstract intervals seem harmonious and balanced in a way 
Heres the scale i used double checking i hadn't made an error, so very sure this is what it sounds like
Letting sum1 =(r1+1)
Sum2 = (r2+2)
diff1 = (r1-1)
diff2 = (r2-1)

r1 = 8/7 = 231.174c  r2 = 3600c


When diff2/sum1 = 3
r1 = 2/sqroot(3) = 249.022c r2= 3479.962c
 
r1 = 7/6= 266.8708 r2=3368.826

r1 = 6/5 = 315.641 r2= 3101.955

When 3*sum1 = sum2
r1 = (1+sqroot(7))/3 = 337.504cents r2= 2996.598

When diff2/sum1 = 2
r1 = sqroot(3/2) = 350.977cents r2=2935.345

r1 = 5/4 = 386.3137 r2=2786.314

When 3*(r1) = 1/diff1
r1 = (1+sqrt(7/3))/2 = 405.271cents r2=2712.496

When 2*diff1 = (r1)/sum1
r1 = (1+sqroot(17)/4 = 428.422cents r2=2627.43


r1 = 4/3 = 498.048 r2=2400

When 2*(r1) = 1/(diff1)
r1 = (1+sqrt(3))/2= 539.981cents r2=2279.962 yes

When (1/diff1) - (r1)/sum1 = 2
the same as saying r2/sum1 = 3/2
r1 = (1+sqroot(10))/3 = 566.893cents r2=2208.502

When 1/sum1 = diff1
r1 = sqroot(2) = 600.000cents r2= 2125.864 yes

When 3*r1 = sum2
r1 = (5+sqroot(13))/6 = 624.366cents r2= 2068.415


r1 = 3/2 = 701.955cents r2=1901.955


When r1 = 1/diff1 {Golden ratio phi}
r1 = (1+sqroot(5))/2 = 833.090cents r2= 1666.180


r1 = 5/3 = 884.3586 r2=1586.314


When diff2 / diff1 = 2
r1 = 1+1/sqroot(2) = 925.864cents r2= 1525.864


When sum1 = 2*diff2
r1 = sqroot(3) = 950.978cents r2= 1490.959


When diff1/diff2 = 2/sum2

r1 = (3+sqr(17))/4 = 999.008cents r2= 1427.430

When 3*diff1 = 2*diff2
r1 = 1+sqroot(2/3) = 1033.390cents r2=1384.367

When 3*diff2 = 4*diff1
r1 = 1+sqroot(3)/2 = 1079.962cents r2=1328.984

Trinity Abstract (balanced divisions )

http://www.dubbhism.com/2014/02/out-now-ligon-sevish-dubshot-23.html#4209590400367778973

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I'm tired of making this work. I'll finish it eventually, but it's taking such a long time that I'm getting frustrated.

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I can't think of anything more nightmarish than being in a terrible situation while others watching without acting.

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Dirigent - Matthias Kuhn
Flöte & Altflöte - Bettina Berger
Oboe & Lupophon - Martin Bliggenstorfer
Klarinette - Nils Kohler
Bass- & Kontrabassklarinette - Richard Haynes
Fagott & Kontrafagot - Elise Jacoberger
Horn - Deepa Goonetilleke
Trompete - Paul Hübner
Posaune - Kevin Austin
Tuba - Simon Lamothe-Falardeau
Harfe - Vera Schnider
Violine - Maximilian Haft
Violine - Mark Menzies
Viola - Laurent Camatte
Violoncello - Jan-Filip Ťupa
Kontrabass - Caleb Salgado

www.ensembleproton.ch

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This is a piece composed by my friend Aaron. I perform it as a wedding greeting. All the best to you Aaron and Doro :) I really hope its contemplative attitude will not depress you...

----
see also the composer's rendering of the piece: https://soundcloud.com/uz1kt3k/2013-prelude-in-e-flat-minor?in=uz1kt3k/sets/prelude-fugue-in-e-flat-minor

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Find the album https://magneticflame.bandcamp.com/album/nimus

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Trinity Abstract (balanced divisions )

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