Fractal Tone Monochord Octave: to derive tone for musical scales and chords. Decreelor Decre€) (10 points from the 3rd tone, and 28 points from the 4tb 1. Length of Monochord: 1 rneter (100 cm) in length, this length gives sustancial tone for an "A"110 or "G'098. It also lets you divide and plot points for the string ratios easily into 100 (2ll = 50,312= 66.6,413 =75 and so on). It gives comfort for about three octaves of determining scales with. 2. Octave: in this instance is 50 cm, and contains the'{nfinite Complement Ratio Symmetry" point (between 29.5 and 20.5) to be spoken in depth later. Naturally, half the length of the Monochord yields the Octave (or the distance from 1/1 to 2ll). The Octave is but a blank canvas in which you are to develop a system to draw tones from (hopefully not abstract); from these tOneS yOu derive Scales, and then Chords. (Note: shifting the octave (with a set scate) on ascending and descending 3/2's is an old Chinese method that can be applied when playing) J. 11L1 2/1, 4lL,8ll: this is the nature of the Octave, continually halving the next paft of the string. The 1/1 is a determined tone, say "A"110vps (vibrations per second), then 2/1, (point which string is now beating 2beats to the 1/1's 1 beat) would give you an ".L"220vps,4ll 440vps (4 beats to the 1/1'S I beat) and SO Ofl. (Note: 3/2, point which string has 3beats to 1/1's 2beats, and so tike for others) 4. The Fractal: is an equilateral triangle created by dividing the Octave into 3 equal lengths, then constructing your first triangle on the center length, then dividing the remaining lengths on each side, into 3 again, and then constructing an equilateral triangle (in the center length) amongst those. In doing this 3 times is what is meant by the "third degree", once more is the "46"(this is the point where visuaiiy it is awkward to continue fractal division further, given the length of the rnonochord, 100cm). The upward points on the fractal are to graduate the degrees of tone. 5. 1/L Nut, 4/3,715,10/7r614 (3/2),211(Lll new Octave), Bridge: (notice on the drawing that the encroaching octaves never touch the Bridge, halving itself downwardly indefiniteiy). 1/1 is a tone that is decided on, I chose "4110" in my examples. Then, the rest of the notes from the points of graduation follow that tone. The Nut is merely the tensioner gizmo of the string. The remaining ratios are to demonstrate an explanation for the "Infinite Complement Ratio Symmetry (2/1 Inversion)tt, a term of my owfl. (r{ote: a monochord is symmetricat in that the Bridge and Nut could be flip flopped) 6. Octavets Ratio Center of "Definite Physical Symmetry": this is simply the center point of the octave if it was divided in two. If you measured the distance from 1/1 to 211 (50cm), and halved it (25cm), then the 413 is this point. (Note: the Fractat is not centered upon this point) 7. Octave's Center of "Infinite Complement Ratio Symmetry (2/1 Inversion)": this is the point from which the explanation for the word "Complement" in the book "Genesis of a Music" by Harry Partch (page 70) springs to life from. Here is the definition; lComplement: that ratio which. added to another ratio (multiplied). makes 2i 1: for example. 4i3 is the complement of 3/2: 4/3x3i2=2/1. In conventional terms. the "inversion" of an interval - a "perfect fourth" (4/3) is the inversion of a "perfect fifth" (3/2).] To me, this point that exists between any inversion ratios should not be thought of as a point, but as an infinite space between them (the smaller the space the higher the ratios, the greater the space the lower the ratios). And, from that space working in Opposite difeCtions Outwardly. (Nore: the Fractat is cenrered upon this point) 1 meter or 100 cm 29.5 cm--l-- 20.5 cm I I i,, 10 points from the 3rd Degree for a movable bridge to graduate tone to define scales 28 points from the 4th Degree for a movable bridge to graduate tone to define scales 2t1 Bridge 4t3 (l/1 New Octave) Octave's Fractal Tone Ratio Center Monochord Octave of / r'Definite Physical Sym metry to derive tone for \ musical scales Octave's Center Created by of Geordan Mitchett "Infinite Complement Ratio Symmetry'' @Z@L (2ll inversion) 1 meter or 100 cm 2-i la <- 20.5 cm I' 29.5 cm -,i ('\ I z Ut r-.}l < t': tl Fractals existance centered upon the Physical Symmetry" F"Definite jjr, I a,n(i ',') \ Determination of the Fractal centered upon the "Infinite Complement Ratio Symmetry" (2ll.inversion) Result of Determining determination the Fractal position on the "Infinite Complement Ratio Symmetry" 3n5197 2/1, Inverse Determined Fractal 55 cps 110 cps 220 cps 880 cps ffiffiffiffi ffiffiffifr 10 tones to the 2/I Inversion Octave Fractal Octave KeyBoard Layout in c( A)) 10 tone from the 3rd degree 9l2r/02 | /'- FiuL^ '/VL ,7D7 t0{o-1 8 t d = l8g 1,,/'_tl ] 'f r,/ f*-'iTeru't Z,'q - V Zo*, Fod-eto ,7oT I o b alt I 'tl :.tit * :l , ; 414 -+ n ,1t4 +- 4 ,414 **5 r1. ,414" . 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