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motion。 When the planet appears。to track。from east to west again as。perceived from Earth； the point of change is。marked 〃D〃 to indicate Mars。has。returned to direct motion。
In Figure 5。9； the planet glyph for Neptune is。Ψ。 When this。symbol is。notated on the chart； the planet is。returning to direct motion。 When Neptune enters。a period of retrograde； the glyph convention is。ΨR。 The time bullets。throughout the chart show a correlation to inflection points。within the Eurodollar's。history。 These are not fixed interval cycles。
Gann's written astrological discussions。always。use the phrase “the study of natural cycles〃。 This。is。but one simple example to offer a conceptual introduction to the study of natural cycles。 Time； or the vertical line of resistance； was。the most important trigger for Gann。 But our discussion is。not plete until confluence is。detected in the vertical； horizontal； and diagonal。 Before moving on； it's。important to notice in Figure 5。10 that a natural cycle is。not a fixed…period cycle。 It should also be understood that each ponent within vertical； horizontal； and diagonal analyses。has。its。own method of creating confluence target zones。through the use of multiple projections。 This。in turn serves。to increase the probability of each ponent。
In Figure 5。11； we see a different retrograde cycle plotted within a weekly Brent crude chart。 This。chart maps。the retrograde cycle of Mercury。 This。chart has。the dimensions。of horizontal and diagonal analysis。we need to explore next。
Running behind the chart's。data are dotted horizontal lines。 Focus on these lines。as you pare the price data directly under or above solid black。blocks。throughout the chart。 These horizontal lines are harmonic。inflection points； all radiating from a single price pivot we will look。at more closely in Figure 5。12。 At this。stage； just study the numerous。highlighted pivot points to observe how this。market is。respecting the background grid in place。 The grid does not show equal spacing between each line through the range of the chart。 Another trait； which requires。an astute eye for geometric。proportion to detect； is。a repeating pattern that forms。with increased spacing at the higher price levelspared to the grid's。spacing nearer the bottom of the chart。 There is。a logarithmic。function to the grid。 For now； accept diat the market is。showing some respect toward the horizontal grid。 We will return to the discussion of these lines。
Figure 5。11 is。partially shaded to help emphasize the diagonal lines。through the chart。 In the middle of the chart are two parallel lines。forming a channel。 The price high； near 80； demonstrates。Gann's confluence in all three dimensions。of vertical； horizontal； and diagonal。 The vertical is。time。 We see at the high a Mercury retrograde cycle。 The horizontal is。price。 The highest rectangular black。box is。highlighting the price target on the horizontal dotted line。 Diagonal is。the geometric。measure。 The price high is。testing the upper diagonal channel running through this。chart。 Furthermore； we have the posite Index forming the kiss。under the rollover of two moving averages。following divergence that was。discussed earlier for the RSI in Figure 5。3。 Look。at points。X； Y； and Z； as。well； in the posite Index； The indicator gives。permission to buy or add at the support zones。tested by the market on the dotted lines。 Momentum indicators。work。best when they are studies at specific。price targets。to offer permission to take action。 In this chart； the price high demonstrates。the point at which everything es。together at the same time and place； providing a high…confidence sell signal。 Understanding how the diagonal lines。were created is。critical to the o
because these lines。are set at precise geometric。angles。
Gann Angles
The weekly chart we just examined in Figure 5。11 was。actually a close…up of the weekly Brent crude chart in Figure 5。12。 At first glance； it looks extremely plex； but if you looked at a chart with multiple Fibonacci retracements without guidance； it too would trigger the same first impression as。a Gann chart。 Breaking down the ponents。so that one knows。what to focus。on changes。the entire plexion of these charts。
The diagonal lines。are projected Gann angles。 Many。software vendors。offer Gann angles； but they are only speed lines。unless precise angles。are used。 If you take a price low for a stock。trading under 25 and plot a line with a growth rate of 1 for one unit of time； or 1x1； you would draw a 45o angle within the chart。 On a puter screen； it would not look like a 45o angle； because the number of pixels。on the width of your screen versus。the height is。not equal。 When you use a Gann angle tool without precise angles。defined； you are only。creating speed lines。that can be used for acceleration analysis。 It is not Gann analysis。 The process。bees。more difficult when you desire a precise 45o angle in a market like the Nikkei Stock。Index—it is。not realistic。to use 1 versus。one unit of time for the rise。
But there is。a way to solve the problem。 Figure 5。12 shows。a series。of boxes。whose corners。are connected； creating a cross。within each box。 Because there are fifty…two weeks。in a year； the weekly chart is。using the square of fifty…two。 But if you look。closely at the price scale； it is。clear that one box does。not cover a price range of 52。 Multiples。or proportional divisions。can be used and the angles。within the original square of fifty…two still retained if only a single box were displayed mapping fifty…two weeks。along the horizontal； versus。52 against the vertical。 Although one large box is。not useful； four boxes。and sixteen boxes。still produce the same angled lines。across。the chart。 When the internal corners。are connected； the grid produces。both positive and negative true geometric。angles。of 45o。 Therefore； a simple solution is。to draw the Gann boxes； establish a true 45o line； and then remove the boxes。 The outside frame of each box is。a fixed cycle。 Gann would use the cycle formed by。the Gann boxes。in several ways； including further subdivision of the square by thirds。or eighths。 However； for this。discussion we will not venture down that road。
The Gann angles。of interest are the 1x1 （45o）； 1x2 （63。75o）； 1x4 （75o）； and 1x8 （82。5o）； and occasionally we need the 1x16 （86。25o）。 For declines； we again consider 1x1； then 2x1 （26。25o ）； 4x1 （15o）； 8x1 （7。5o）； and； on occasion； 16x1 （3；75o）。 Sometimes。the 1x3 and 3x1 are used with angles。of 71。25o and 18。75o respectively。 Gann discusses。these angles。as。“moving…averages〃； which can cause confusion in modern context because puters。allow us。to chart true moving averages。derived from price or indicators。 In this。discussion； referencing Gann angles。will serve us。better。
The starting placement of the Gann angles。in Figure 5。12 will raise a question because they are not projected from blatant price lows。 Gann teaches。that a sharp decline； as。an example； does。not begin a new trend upward at the price low of the decline。 The price low is。the conclusion of the prior bear market campaign。 The start of the new trend of greatest interest is。the first secondary pullback。 In Figure 5。12； Brent crude was。nearly being a 1
parabolic。rise； so the Gann angles。were projec