# WIP: 9 Sacred Geometry Fugues for Orchestra *0.Praeludium Lunare added 5/12*



## chee_zee

View the full score and all parts WIP here:
https://drive.google.com/open?id=1O3qqPNRIsa51-TfPV0y2G-4tejJNWO2D

0. Praeludium Lunare
A full moon occurs every 29.5 days, so 59 is two full moons. 59 is a prime number DdG 29.5, Gd 59, dd 99, Crc 108,
Cc 18, CDEAd 12.369, CGE 153 , DCA 216, EB since 37 is the number of moons in 3 years, root of 111, 22, 88 etc.
37 measures divided into sections of 18 and 19 measures since 18 is the number of years in a Saros eclipse cycle,
and 19 is the years of the Metonic cycle. 9/8 time sig. 9/8 is a whole tone, and the ratio of squaring the circles of
Earth and Moon on top of each other. 59bpm since there are two full moons in 59 days.
13 is the number of Aluminum, which is what vibraphones are made of. 5,12,13 Pythagorean triangles (maid,
mother, grandmother Ixchel), with the bisecting line dividing the 5 into 2 and 3, has a length of 12.369 (the number
of full moons per annum). The countermelody is vibes playing 13, 5 12 13, 12369, ie CE, G CD CE, CDEAd etc
Moon Magic Square has a Magic Sum of 369 (ie 12.369) and a Sigma Square Sum of 3321 (EEDC), and is a 9x9.
12 hit points on the magic seal for the odd/even shadings, 4 corners and the 8 shaded even number region wraps.
Tuba assigned to 4 corners (37, 5, 45, 77; EB, G, FG, BB), Horns 1 and 2 fiber muted (ww1) for the 2 innermost
region wraps, Bsn 3rd register (ww1) for the 2 outermost region wraps. Magic Square motifs can be played in
retrograde so it won't matter necessarily which order of occurence you read these squares, the talismanic effect
will be the same.
Binary form, but unlike most Baroque binaries, the B section is in the minor subdominant not the major dominant
(fm instead of GM). The reason for this is CF is a P4 and in Keppler's analysis of the celestial spheres, the only
occurence of the musical P4 is involving the moon. I also prefer the ivm as when you get back to I it sounds even
more uplifting, which is often done in Classical era pieces.
1. Squaring the Circle
65 bpm because the interplay of 6vs5 is half the sacred secret. This is why the horns play GA pads (5vs6).
Much of the 6vs5 ideas are dealt with in Sombre Paris for Wind and Brass Septet, but in sum:
6/5 where 6 is time and 5 is space. 6660in is 555ft
"Adenine is a hexagonal ring and a pentagonal ring, as is DMT, serotonin, and melatonin
There are 59 beads on the Rosary corresponding to 53 Hail Mary's and 6 Our Fathers.
6 Gloria Patris for which there are no beads are also said in the Rosary bringing the
total number of prayers to 65.
The obverse of The Great Seal of the United States has 13 stripes (representing the
colonies), 13 stars in the "glory" above the eagle's head, 13 arrows, 13 leaves, and
13 olives. 13 x 5 = 65.
In addition the feathers on the wings, 33 on the left and 32 on the right, add up to 65.
Also, through "Pythagorean addition" 32 becomes 3+2 = 5 and 33 becomes 3+3 = 6.
The wings of the bird then represent the relationship between 6 and 5.
Multiplying Phi squared by 6/5 is Pi
1.2 x (1.6180 x 1.6180) = 3.1415
Illuminant D65 6500 Kelvins" -Scott Onstott
12/5 and 6/5 Jerusalem rectangles
The hexagram vs the pentragram, hexagon vs pentagon, 6 v 5 (Pope Sixtus V etc)
1. Phi 1.6180339887 C: CACcrEEdccB // G: GEGgrBBaggF# // a: AFAarCCbaaG(#) // E: EC#EerG#G#F#eeD# // F or f: FDFfrAAgffE or FDbFfrAbAbgffE(b)
2. Pi 3.14159265 C: ECFCGdDAG // G: BGCGdDAED // a: CADAEbBFE // E: G#EAEBf#F#C#B // F or f: AFBbFCgGDC or AbFBbFCgGDbC
3. Phi^2 2.61803398875 C: DACcrEEdccBG // G: AEGgrBBaggF#D // a: BFAarCCbaaG(#)e // E: F#C#EerG#G#f#eeD#B // F or f: GDFfrAAgffEC or GDbFfrAbAbgffE(b)C
4. Pi^2 9.86960440109 C: dcAdArFFrCrd // G: agEaErCCrGra // a: baFbFrDDrArb // E: f#eC#f#C#rAArErf# // F or f: gfDgDrBbBbrFrg or gfDbgDbrBbBbrFrg


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## dzc4627

This is music I'd put in the category of "interesting" but sounding not good at all.


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## Captainnumber36

dzc4627 said:


> This is music I'd put in the category of "interesting" but sounding not good at all.


I agree .


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## chee_zee

I disagree. .........................


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## Phil loves classical

I have to say I find it fascinating. With the right production, it would sound quite impressive. There is a theatrical moment ear the end of the 1st track that I would put less emphasis on. Also one earlier in the 2nd. They sound too recognizable or associative and distract from the main thing. The 2nd track really seemed to build something by the end I thought.

Is it serial? It's unlike anything I've ever heard


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## chee_zee

Phil loves classical said:


> I have to say I find it fascinating. With the right production, it would sound quite impressive. There is a theatrical moment ear the end of the 1st track that I would put less emphasis on. Also one earlier in the 2nd. They sound too recognizable or associative and distract from the main thing. The 2nd track really seemed to build something by the end I thought.
> 
> Is it serial? It's unlike anything I've ever heard


It follows similar generative processes as serialism. The way I base it is that the pitches are semi-predetermined but not rhythms.

pi is 3.1459 in C is ECFGd (the octave above being lowercase).

the decimal gps location for the great pyramid is 29.979200, 31.134200 N and E

So DddBdDrr (rest), ECCEFDrr

For instance, take my Sombre Paris for Wind Septet. m88 has the clarinet playing the gps coordinates to the Grande Arch in Paris. Go to 2m33s in the recording to hear.

If you can manipulate the rhythms you can create quite neat sounding pandiatonic music with this system (it's all in what you want to assign the numbers too). With my fugue series I'm focusing on pandiatonicism in the vein of baroque fugal modulation practices. For inverting a fugue subject, 9 becomes the 7 below your base point, so if 1 is C4, 9 is d5, then when making the inversion of this subject that 9 would go from d5 to b3. You could set this stuff to octatonic scales of your choice or perhaps 9 note scale, or 10 notes if you want 0 to be a pitch rather than a rest (usually I take 0 as a rest for the length of a beat for whatever time sig I'm in, so again it's all in what you assign the numbers to and what you do with that raw material)









Sombre Paris recording





And apologies for my inferior samples haha


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## chee_zee

From the first fugue m23 at 1m21s we can see the first full statement of the 4 themes used; the 2 subjects and 2 countersubjects (although really treated formally as the equivalent to 1 subject with 3 countersubjects to more accurate to baroque fugue terminology).













Tuba mute embouchure, trumpet metal straight mute, and Hn 1 only, stopped, so their timbrel fullness is closer to that of the other instruments here so the real world blend would be about the same, it kinda looks from this extract that the brass would be way too dominate (strings mostly doubling the ww here)


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## Phil loves classical

chee_zee said:


> It follows similar generative processes as serialism. The way I base it is that the pitches are semi-predetermined but not rhythms.
> 
> pi is 3.1459 in C is ECFGd (the octave above being lowercase).
> 
> the decimal gps location for the great pyramid is 29.979200, 31.134200 N and E
> 
> So DddBdDrr (rest), ECCEFDrr
> 
> For instance, take my Sombre Paris for Wind Septet. m88 has the clarinet playing the gps coordinates to the Grande Arch in Paris. Go to 2m33s in the recording to hear.
> 
> If you can manipulate the rhythms you can create quite neat sounding pandiatonic music with this system (it's all in what you want to assign the numbers too). With my fugue series I'm focusing on pandiatonicism in the vein of baroque fugal modulation practices. For inverting a fugue subject, 9 becomes the 7 below your base point, so if 1 is C4, 9 is d5, then when making the inversion of this subject that 9 would go from d5 to b3. You could set this stuff to octatonic scales of your choice or perhaps 9 note scale, or 10 notes if you want 0 to be a pitch rather than a rest (usually I take 0 as a rest for the length of a beat for whatever time sig I'm in, so again it's all in what you assign the numbers to and what you do with that raw material)
> 
> View attachment 103891
> 
> 
> Sombre Paris recording
> 
> 
> 
> 
> 
> And apologies for my inferior samples haha


It is basically chance- generated tones then. When you mentioned in the first post the moon, etc. and geometry in the title I was wondering if the tones were generated by geometry somehow through inflection, etc. But what you did with the rhythms and everything was pretty impressive


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## chee_zee

Just to update that there was a performance/recording in October of '18 by the Musica Nova Orchestra at the Musical Instrument Museum. The first fugue, "Squaring the Circle" was played.


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