Harmonic Explorer user guide

screen functions and quick start tutorial

Main Screen

1	"Source Settings" - defining a series of frequencies scroll bar "base freq." - sets the (relative) base frequency of a series of frequencies (click centre locator to set to default) radio button "harmonic" - synthesises a geometric series radio button "arithmetic" - synthesises an arithmetic series radio button "other" - future option scroll bar "higher harmonics" - adds a number of frequencies from base freq. up scroll bar "lower harmonics" - adds a number of frequencies from base freq. down (the total nr. of frequencies is printed below the "source" screen (3)) up-down button "coherence point" - selects a harmonic key ratio scroll bar "ratio" - adds a slight offset to the coherence point (this setting is applied as per the selected geometric, arithmetic or other style) button "refresh" - refreshes all screens
2	""Source" screen - shows the individual frequencies notification "count" - total number of frequencies in series checkbox "show" - screen on/off checkbox "apply gradients" - improved visualisation of larger series notification "scale default" or "scale constrained" - scale mode default or constrained with other screens (4, 5)
3	"Coherence" screen - shows the resultant wave form as per the non-linear regime checkbox "show" - screen on/off checkbox "constrain scales" - constrain the scales of screens 1, 2 and 3 on/off horizontal scroll bar - sets horizontal scale vertical scroll bar - sets vertical scale
4	"Fusion" screen - shows the resultant wave form as per the linear regime checkbox "show" - screen on/off horizontal scroll bar - sets horizontal scale vertical scroll bar - sets vertical scale
5	"Fourier" screen - shows the linear spectrum of either resultant wave form checkbox "do Fourier" - Fourier analysis on/off checkbox "show Fourier" - show actual Fourier spectrum on/off checkbox "find peaks" - find peaks in the Fourier spectrum on/off radio button "from linear regime" - spectrum analyse "Fusion" screen radio button "from non-linear regime" - spectrum analyse "Coherence" screen checkbox "Verify" (upper) - verify spectrum analysis of "Fusion" screen on/off (not active) checkbox "Verify" (lower) - verify spectrum analysis of "Coherence" screen (verification only works when "find peaks" is on) horizontal scroll bar - sets horizontal scale (click locator to set to default) vertical scroll bar - sets vertical scale frequency count notification - displays frequencies counted if "find peaks" is on button "refresh" - refreshes all screens
6	"Harmonic scan" screen - response through harmonic range beween .5 and 2.5 (applies to the currently selected number of higher harmonics only) radio button "frequency count" - plots for each ratio the number of frequencies in the Fourier spectrum radio button "frequencies" - plots for each ratio the Fourier spectrum radio button "non-linear power" - plots for each ratio the integral wave power of the "Coherence" screen radio button "linear power" - plots for each ratio the integral wave power of the "Fusion" screen (all plots are applied as per the selected geometric, arithmetic or other style) checkbox "range fitting" - keeps the frequencies within the constraints of the Fourier algorithm and normalises the result (is not effective after "start") button "clr" - clear screen button "start / stop" - start or stop harmonic scan notification "ratio" - prints current ratio while scanning notification "freq. count" - prints latest number of frequencies counted while scanning
7	"Frequencies" screen numerically prints the relative frequencies in the Fourier spectrum if "find peaks" is on

main menu - "Coherence Points"

up - down button - sets a power of "E" and starts itteration to find E

(E can be set from 0 to 12)

main menu - "Fibonacci Series"

up - down button (left) - calculates a Fibonacci number
up - down button (right) - creates a binairy Fibonacci series or "Golden Sequence",

(the "Visual Basic" code used for either algorithms are printed)

main menu - "Coherence Classes - #4 Arithmetic Coherence"

1	Analysing mode radio button "find sequences" - searches and prints arithmetic series in the "Golden Sequence" (screen 6A, B) radio button: "group max" - finds and prints the longest series in each group (screen 6C) radio button: "group average" - prints the average series length in each group (screen 6C) radio button: "group total" - prints the total series lengths in each group (screen 6C)
2	range setting scroll bar "range" - sets the starting group, at the left of the screen
3	group filter checkbox "Fibonacci" - prints Fibonacci spaced series checkbox "Fibonacci octaves" - prints Fibonacci higher octaves spaced series checkbox "Primes" - prints prime number spaced series checkbox "Primes" - prints prime number spaced series (applies only for counting modes, screen 6C))
4	various printing settings checkbox "Show Golden Sequence" - prints Golden Sequence spaced freq's in background (screen 6A, B) checkbox "Colour mode" - articulates the Golden Sequence (screen 6A, B) ckeckbox "Auto width" - creates bar graph (applies only for counting modes, screen 6C)
5	horizontal and vertical scaling scrollbar "sequence spacing" - sets spacings between series in sequence mode (screen 6A, B) scrollbar "group spacing" - sets spacings between groups for all modes scrollbar (vertical) - sets vertical scale for all modes
6	Arithmetic Coherence Screens Screen A - grouped series Screen B - grouped series and Golden Sequence grid and colouring Screen C - group counts

quick start tutorial

note: leave all settings default unless specified otherwise

[ results and additional comments are printed in blue ]

1. Synthesising a frequency series (screen 2)	- switch "show" in screens 3 and 4 off, leave source screen (2) on - switch "do Fourier" off in screen 5 - disable "constrain scales" in screen 3 - add a few higher and lower harmonics with the scrollbars [ screen 2 will show the individual frequencies ] - add more harmonics and toggle "show gradients" [ screen 2 will show the enhanced printing of a larger number of frequencies ] - play with the base frequency, and reset to default with the centre locator - reduce the number of harmonics, and play with the coherence point - do the same, using the arithmetic mode (radio button) instead [ screen 2 will give an impression of the different spacings and ratio's ]
2. Linear and non-linear regimes (screen 3 and 4)	- set the number of higher and lower harmonics to zero - enable the "Coherence" and "Fusion" screen (check "show") - enable "constrain scales", then click centre locator in screen 3 or 4 [ all scales are lined up and the screens show their respective results ] - select "harmonic" style (radio button) - add one by one a few harmonics and check the screens [ the difference between the linear and non-linear regimes can be seen ] - add more harmonics, and play with the scaling and base frequency [ the non-linear result wave is compressing into singular spikes ] - select "arithmetic" style (radio button) [ this style is probably less relevant for coherence analysis ]
3. Checking out the Fourier analysis (screen 5)	- set the number of higher and lower harmonics to zero - set the coherence point to #1 (Golden Mean) - enable the Fourier analysis (check "do Fourier") - select "from linear regime" and leave it so (radio button in screen 5) - select "harmonic" style (radio button) - add step by step a few higher harmonics, and check the Fourier screen - add step by step a few lower harmonics [ the Fourier has recovered the original frequencies from the composed wave, in this case a golden mean harmonic or geometric cascade ] - select "arithmetic" style (radio button) - play with the harmonics [ the Fourier shows an arithmetically spaced cascade (Golden Mean times base freq. spacings) ] - enable "find peaks" and play with the harmonics and source style - check the frequeny count notification, and the frequencies screen 97) [ the Fourier screen shows both the original transform, and a peak indication, the "frequencies" screen shows a summary of the frequencies found] - disable "show Fourier" [ the Fourier screen shows only the peak indication ]
4. Spectrum analysis of non-linear regime	- enable "find peaks", enable or disable "show Fourier" as you wish - select the "harmonic" style ( ! ) - select in the Fourier screen "from non-linear regime" - disable "Verify" for non-linear - play with the harmonics - if needed, reduce the base frequency to keep within the Fourier range [the Fourier screen will show an apparently randomly distributed spectrum, whereas the number of frequencies seems to be overduely increasing] - enable "Verify" for non-linear, and play with the source frequencies [ the bar below the Fourier screen will try to match the spectrum with a spacing algorithm based upon the Golden Sequence - if there is no match, usually the spectrum is either too compressed, or out of range ] - play with the source frequencies to test the "Verify" algorithm
4. Harmonic scan (screen 6)	- leave "range fitting" disabled - select "harmonic" style for the source frequencies - select "frequencies" - set "higher harmonics" to 5 - set base frequency to apprx. 20% - click "start" [the harmonic scan plots the Fouries spectrum (vertical) for a harmonic range from 0.5 to apprx. 2.5. It is seen that at the natural coherence ratios, many frequencies are merging, where the maximum compression is at Golden Mean ratio. Depending on your source settings, the scan may run out of the peak detection or Fourier range creating noise resp. in the beginning or end of the range. This problem is solved by enabling "range fitting". (the harmonic scan may take up to a minute or so, depending on the speed of your computer; the lower harmonics are ignored by the harmonic scan) ] - enable "range fitting" and leave the number of higher harmonics as is - click "clr" to clear screen - click "start", and check both the harmonic scan and the Fourier [ the harmonic scan now a) keeps the frequencies within range of the peak detection and the Fourier and b) normalises it to the maximum frequency, to fit the screen. Rangefitting ignores the base frequency setting] - play with a higher or lower number of harmonics - disable "range fitting" - select "frequency count" - set "higher harmonics" to 5 - click "start" [ the harmonic scan shows the reduced number of frequencies around the coherence points ] - check out the frequency count using range fitting and a different nr. of harmonics - select "non-linear power" - set "higher harmonics" around 5 - click "start" [ the harmonic scan in the non-linear regime shows an increased integral wave power around the coherence points, in particular around Golden Mean (note that range fitting does not apply to the power scans; the base frequency is not critical) ] - select "linear power" - set "higher harmonics" around 5 - click "start" [ the harmonic scan in the linear regime shows no particular response around the coherence points ]
5. Main Menu - Window - Coherence points	- click the up / down button to set a value for the power of "E" [ the equation is solved by itteration, giving the coherence points or -ratio's in the non-linear regime where frequencies are reduced in number and interdigitation is perfected ("implosion") - typically E^1 gives the Golden Mean ratio ]
5. Main Menu - Window - Fibonacci series	- click the left up / down button to find a Fibonacci number [ the classical Fibonacci series is evolved, starting with "0" and "1", where F(n+1) = F(n) + F (n-1), or F(n+1) = round( F(n) Phi ) for all n > 1 ] - click the right up / down button to create the "Golden Sequence" binairy Fibonacci series [ the Golden Sequence is evolved, starting with "0" and "1", where S(n+1) = S(n) "followed by" S(n-1), or S(n+1) = 2^(n-1) * S(n) + S(n-1) ]
6. Main Menu - Window - Coherence Classes - #4 Arithemetic coherence	- select the analysing mode "sequences" (default) (1) - click the "refresh" button to update the screen [ within the selected step-size range, the Golden Sequence is scanned for unbroken arithmetic series, the result is plotted in alternating colours for each step through the Golden Sequence ] - play with the range (2) to find more series - play with the sequence- and group spacing (5) [ the longer the steps are, the more series there are in a group until the end of the first series ] - enable "show Golden Sequence" (default) - increase the vertical scale until the frequencies are visible [ as a reminder, these frequencies are the linear Fourier spectrum of a perfect Golden Mean non-linear cascade - spaced as per the Golden Sequence. If the vertical scale is set properly, you can see in detail how the aritmetic series are matched ] - enable "Colour mode" (4) - if necessary increase the vertical scale a bit more [ highlights the short spaces, bringing out the Golden Sequence more clearly ] - select the analysing mode "group average" (1) - if needed adjust the vertical scale [ in the counting mode, the counting scale is applied ] - play with the group spacing [ in the counting mode, the sequence spacing is not effective ] - enable "Auto width" (4) [ creates a bar graph ] - test the other analysing modes "group max" and "group total" [ the group total shows an equally distributed count, as the lenght of the series is decreasing for greater steps, while at the same time the number of series in a group is increasing ] - enable and disable the different group filters [ this allows easy insight into which series are most likely to constitute naturally sustainable class 4 symmetry operations, a merger of the linear and non-linear regimes creating cosmology and biology ]