*This blog series from FSC Science Director Ray Tomes shares the fundamentals of physics in layman's terms, showing how present theory must inevitably lead to all waves losing energy and forming harmonically related waves. The end result is a very specific detailed structure that matches the observed universe and explains many previously mysterious observations. This series was previously published.*

### Really Big Numbers

During March 2004 I decided to extend the harmonics calculations that I had done years before. Computers had got much faster since then, and I put a little effort into speeding up the calculations by taking some additional mathematical shortcuts. The speed of calculation improvement can be broken into three steps, one of which was undertaken years ago in order to even do 15-digit numbers. If I had told my computer to lay out a table like the ones in the chapter "Many Harmonics" twelve years ago, then it still wouldn't have completed the calculations that I did then. So what I did was recognising that numbers with lots of powers of 2 and less each of 3, 5 and 7 were present, I made a different shaped table with just products of powers of these numbers. The first speed up in calculating the number of ways each number can be factorised is to discover this formula:

**H(C) = sum H(I) over all I that are factors of H, except H itself**

An example is always worth a thousand words, so for example H(12) = H(1) + H(2) + H(3) + H(4) + H(6), which doesn't help us very much until we have calculated the smaller harmonics. We start with H(1)=1, not because 1 has any factors other than itself, but because if we don't, nothing else works. Where harmonic one comes from is not part of the definition, it is an assumption that will no doubt lead to speculations about God and many other things.

We know that H(2) and H(3) are 1 because 2 and 3 are primes. H(4) is 2 because it is made from H(1) and H(2). H(6) is 3 because it gets a share of H(1), H(2) and H(3). So now we can add them up and get the answer H(12)=8.

When this process is done for number to 10^50 it requires 8 nested repeats for the eight primes 2, 3, 5, 7, 11, 13, 17 and 19 just to visit each number once, and another 8 nested repeats within those to add up all the harmonics that are the numbers factors. That adds up to a really big number.

In the latest runs I reduced the calculating time by incorporating two time saving factors. The first is to recognise that 2^8*3^3*5^1 can be factorised in the same number of ways as 2^3*3^8*5^1 and 2^8*3^1*5^3 and so on. So rather than calculate all of these, if the program finds a pattern of prime indices that it has done before in a different order, then it takes a wee peak at the result and pretends it didn't copy off someone else. This doubled the speed of calculation.

The last improvement to speed was to see that when doing C(24) we get H(1) + H(2) + H(3) + H(4) + H(6) + H(8) + H(12) and that H(1) + H(2) + H(3) + H(4) + H(6) is already known and is the same as H(12) because that is how we calculated H(12). So H(24) is just 2*H(12) plus H(8). Now although this type of thing happens incredibly often in the calculations, it is extremely difficult to generalise how to do it. However, I recognised one very common situation, which is when going up by a factor of 2 and just did that one. It improved the speed by a factor of ten and enabled me to calculate to beyond 10^50 which was a desired result.

The output of my 25th March calculation was a 463 MB tabulation. This is too big to share and not a lot of use on its own. So I make available on my website several files in CSV (Comma Separated Values) format which is plain text numbers separated by commas. It can be used as input to spreadsheets by anyone who wants to play around with these numbers and calculations. One file is the mainline harmonics which is quite a small file and another is harmonics selected for being strong in their range which is rather large because otherwise it is not a lot of use.

Here is a graphic showing all the stronger harmonics up to around 10^54. Notice that at the top end the pattern goes a little funny, which is due to incompleteness of my calculations in that vicinity. This graphic and the file are reasonably complete to around 10^51 for even moderately strong harmonics and complete for the strongest ones to 10^53.

The parabolas showing the families of harmonics with ratios 2 are visible throughout the range 1 to 10^53 as are the other common musical relationships. However there are some other things going on too, most noticeably some general wave-ness in the main line harmonics. Given that a detrending formula has been used it is reasonable to ask to what extent this waviness is real and to what extent it is a product of the analysis. The answer is that the broad sweep of the graphs, which includes a slight upturn at the very high end, may be a result of the analysis. However the waviness on the scale of several powers of ten is most definitely a real thing although its exact measurement may be subject to some refinement yet. This is attested to by four different things.

Firstly, the detrending has only two terms which does not allow it to put so many curves in. Secondly, the very high peaks are always associated with places where the one family stands out strongly from any other families which means that the maximum energy flow is in that particular family at the peak. Thirdly, alternative detrending methods that take a less global perspective still show these peaks. Fourthly, and perhaps most importantly, the major peaks occur at the places with are furtherest away from the larger primes in the main line sequence.

This last reason makes sense, because if we are right on a large prime in the main line sequence, then the energy is split equally between two different families of harmonics and so none can stand out from the others. This may be understood in the "Flow of Energy" diagram where for harmonics around the vicinity of 6 and 8 the energy is taking different paths and they come together again at 24 making a big peak.

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*This blog series from FSC Science Director Ray Tomes shares the fundamentals of physics in layman's terms, showing how present theory must inevitably lead to all waves losing energy and forming harmonically related waves. The end result is a very specific detailed structure that matches the observed universe and explains many previously mysterious observations. This series was previously published.*

### Flow of Energy

These patterns help to see what is going on as regards how strong or energetic each harmonic is and its relation to others, but they do not make clear why it happens. For an understanding of why this happens it is helpful to look at the flow of energy between harmonics as described in the harmonics axiom. Each harmonic loses energy to exact multiples of that harmonic.

The following diagram does not attempt to be an exact representation or to show every harmonic and every flow of energy, just the flows to multiples, 2, 3, 4, and 6. Remember that more energy flows to the lower harmonics, especially 2 times. The thickness of the blue lines is representative of the amount of energy flowing. Those harmonics with little input obviously must have corresponding output.

The diagram does show that even though energy is mostly lost from harmonic 1 along the first line and only a small proportion goes downwards, eventually that proportion accumulates because it never comes back upwards. So by the time we get to 8 the next line at 24 is already stronger. Further along the leakage has made the third line predominate and so on. The green circles show the strongest harmonics which are called the main line.

Remember that some energy is also going to ratios other than 2, 3, 4 and 6 as shown here. Some of these ratios are within the diagram such as 8, 12, 16, 24, 9 ... but the direction of travel of energy is always from left to right and top to bottom. The extra flows not shown include 5, 10, 15 and others with the ratio 5. To include these in the diagram we would need to include a third dimension, putting another layer below the first with harmonics 5 times higher and another with 25 times higher. Such a diagram would then show why eventually the families related by ratios of 3 also fall away, because the family with one ratio of 5 then takes over in the main line.

Between these different ways of looking at things it should now be clear that although the initial assumptions of the harmonics theory are extremely simple, the pattern of energy made by harmonic number, or frequency, is quite elaborate. The question to be ultimately asked is whether that elaborate pattern bears any relationship to the real world around us. If it doesn't then this exercise would still be interesting in terms of mathematics and music but would not have served its purpose which is to explain the structural scales at which the universe manifests energy.

Before looking at these relationships to the universe it is necessary to look at extremely large harmonics, going not just up to a million but through more than 170 octaves to numbers with over fifty digits in them. This is required because the scales of the universe that have been observed range from tens of billion light years down to around 10^-17 metres which is below the scale of naturally (at least in our little corner of the universe) occurring sub-atomic particles. The ratio between these extremes is about 10^43 and we cannot just assume that the largest scale so far observed is the size of the universe, because the distance that we have observed to keeps on going up over time.

“This is gold, Mr. Bond. All my life I’ve been in love with its colour … its brilliance, its divine heaviness.” An infamous line from the antagonist Auric Goldfinger, in the illustrious Bond movie series by Ian Fleming, aptly personifies an appreciation of all things gold following its latest 10% surge. It has retested the $2k glass ceiling, amidst heightening geopolitical tensions, while also breaking historical macro correlations with real bond yields.

In behavioural terms, the yellow metal is reactivating a 13-year bullish pattern that visually resembles a “cup and handle” (C&H), where the cup is in the shape of a curved basing formation, symbolising trading accumulation, and the handle, which is typically marked by either a sideways or downward consolidation, that leads to the upside breakout signal. The C&H pattern, originally popularised by veteran investor William O’Neil in his classic 1988 book on technical analysis, currently signals a minimum price objective of $2,700, with overshoot risk into $3k (Figure 1). What makes this pattern of greater significance is that, if/once confirmed, it will reverse a previous widely acclaimed triple top signal, near $2070, that would have attracted much bearish consensus.

Broader upside scope for gold is evidenced by its rising tide across a basket of world currencies (XAUWCU). Its October monthly surge triggered a record new high breakout, that will likely extend the long-term uptrend by a further 80% (Figure 2).

From a macro perspective, this is ultimately a reflection of the accelerating currency debasement effect, weighed by ongoing restrictive monetary conditions and consequential secular inflationary forces ahead.

On this point, gold is sending out an interesting message, by its extraordinary divergence from real bond yields, thereby breaking a historical inverse correlation, of up to 91%, between gold and the yield of 10-year TIPS, during 2007-2021 (Figure 3).

There are several plausible factors, led by bullish market forces, supported by gold’s relative outperformance, geopolitical safe-haven flows and central bank demand. Charlie Morris, CIO of Bytetree, argues in his latest Atlas Pulse report that gold is likely experiencing a “transformational period”, whereby “TIPS are mispriced (too cheap) and understating inflation”. This aligns with our long-term structural inflation outlook, based on the Kondratieff wave. Interestingly gold remains a contrarian trade in the short-term, weighed by negative sentiment proxies, with headline news stories at decade lows, lagging ETF liquidity flows since 2020 and divergent mining stocks (Figure 4).

Looking ahead for plausible risk scenarios, it’s worth recalling gold’s historical rhyme, in periods of crisis, as highlighted in 1980 and 1973, which included the Soviet-Afghanistan War, Iranian Revolution and Arab-Israeli “Yom Kippur” war. In both analogues, gold typically spiked by up to 700%, while previously marking its inflation-adjusted peak near $2,700 (Figure 5).

The prospects of a commodity super cycle will offer broader support (Figure 6), notably the FAANG 2.0 industries, currently led by fuel, defense, and gold.

Thank you to all FSC members for all your kind feedback and insightful questions on our FSC blog series. Welcome more interaction on ron.william@cycles.org.

**Ron William, CFTe Bio**

Ron William, CFTe, is a market strategist and educator/mentor with more than 20 years of experience working for leading macro research and institutional firms, producing tactical research and trading strategies. He specializes in global, multi-asset, top-down framework, grounded in behavioural technical analysis, driven by cycles based on the *"Roadmap"* signature model of veteran market technician Robin Griffiths, published in his book “*Mapping the Markets*.”

Ron also applies a *"market & mind"* approach at IntensiChi, using the latest techniques in behavioral-risk models and neuroscience sourced from expert groups. He further supplements with mentoring/coaching, trained by the *International Coaching Federation (ICF),* and teaches a regulatory approved masterclass in Applied Behavioral Science, with investment, private banks and CFA Societies.

Ron's primary work, as part of his current institutional market advisory firm (RWA), acquired global industry recognition as winner of *“Best FX Research”* in 2020. Financial media programs and industry publications regularly feature his market insights, including “*Is the big cycle about to turn?*”, predicting the 2020 crash and alerting the *“Minsky paradigm”* of 2020 H2-2022.

Driven by high-integrity education, Ron serves as part of the education committee of the *International Federation of Technical Analysts* *(IFTA),* Development Director at the *Foundation of the Study of Cycles (FSC),* Head of SAMT’s Geneva Chapter, and an honorary member of ESTA. He is also a visiting lecturer at universities, active guest speaker for the CFA, CAIA and CISI, and senior teacher at colleges offering an accredited diploma in trading and investing.

This time last year broad risk markets accelerated their corrective wave, notably S&P500, marked by a near -20% peak-to-trough drawdown (mid-August & late-October). Will seasonality headwinds strike again? The month of September is a negative outlier due to a range of factors, as published in previous FSC blogs. Bottom-line, it’s historically the worst performing, generating a lowest monthly return of -0.6% and lowest probability of a positive return of 46% - according to a back test of S&P500 during 1964-2022 *(Figure 1).*

While this annual timing pattern is one of the most reliable and worst performing, it’s not a certainty, more so, given the near 50% hit ratio. Additionally, as with all heuristic models, there are exceptions, with best/worst sample periods to the historical average of 9%, -12% and STD of 4.4%. Also important, is to blend quantitative statistical analysis with qualitative charting methods, to offer valuable context. For example, the broader negative seasonality pattern is a three-stage process, aligned with our *“Roadmap signature”* of a “price fall, oversold rally, followed by the rest of the fall” *(Figure 2).*

In the latest market setup, S&P500 peaked into late-July, marked by a key-day reversal, followed by a sharp decline, predicted in earlier FSC blogs. Currently, the market breaking down. A sustained corrective wave unlocks further downside risk into 4220 and 4130. Expect the worst period of September’s seasonality pattern to trigger in the backend *(Figure 3),* with likely rollover into October, which traditionally marks a final capitulation ‘true low’- often associated with the market anniversary of a fall-crash signature.

Recall 1987 Black Monday, 9/11 and the failure of Lehman ahead of the 2008 GFC, all occurred in this period, each resulting in big selloffs. The so-called September effect could be particularly chilling this year due to a confluence of macro event risks. These include rising crude oil prices, inflation risks and China’s pressured economy.

Review our follow-up theme on a *“Crude Oil reawakening…”,* and interview, highlighting a recovery base pattern targeting $105 and consequential impact to inflation. The uncomfortable combination of rallying oil and US10YR at new cycle highs, is disrupting the goldilocks soft-landing scenario and triggering a rotation into the “persisting inflation & sticky rates” narrative, adding further pressure on equities and valuations.

Interestingly, my industry peers remain split. Sharing the bearish camp, veteran technical anlayst Milton Berg warns of a potential 50% crash as severe recession sets in. Real vision hosted an interview with us together, in late 2022, featuring big picture views still in play. Meanwhile, leading the bull-case, BofA strategist Stephen Suttmeier cited in a note *“the best setup for both September and the rest of the year is when S&P500 rallies between 10-20% [in H1]” (Figure 4). *However, be mindful the S&P500 remains historically fragile, both in terms asymmetric risk and ongoing narrow leadership *(Figure 4).* Stay alert!

Thank you to all FSC members for all your kind feedback and insightful questions on our FSC blog series. I welcome more interaction on ron.william@cycles.org.

**Ron William, CFTe Bio**

Ron William, CFTe, is a market strategist and educator/mentor with more than 20 years of experience working for leading macro research and institutional firms, producing tactical research and trading strategies. He specializes in global, multi-asset, top-down framework, grounded in behavioural technical analysis, driven by cycles based on the *"Roadmap"* signature model of veteran market technician Robin Griffiths, published in his book “*Mapping the Markets*.”

Ron also applies a *"market & mind"* approach at IntensiChi, using the latest techniques in behavioral-risk models and neuroscience sourced from expert groups. He further supplements with mentoring/coaching, trained by the *International Coaching Federation (ICF),* and teaches a regulatory approved masterclass in Applied Behavioral Science, with investment, private banks and CFA Societies.

Ron's primary work, as part of his current institutional market advisory firm (RWA), acquired global industry recognition as winner of *“Best FX Research”* in 2020. Financial media programs and industry publications regularly feature his market insights, including “*Is the big cycle about to turn?*”, predicting the 2020 crash and alerting the *“Minsky paradigm”* of 2020 H2-2022.

Driven by high-integrity education, Ron serves as part of the education committee of the *International Federation of Technical Analysts* *(IFTA),* Development Director at the *Foundation of the Study of Cycles (FSC),* Head of SAMT’s Geneva Chapter, and an honorary member of ESTA. He is also a visiting lecturer at universities, active guest speaker for the CFA, CAIA and CISI, and senior teacher at colleges offering an accredited diploma in trading and investing.

*This blog series from FSC Science Director Ray Tomes shares the fundamentals of physics in layman's terms, showing how present theory must inevitably lead to all waves losing energy and forming harmonically related waves. The end result is a very specific detailed structure that matches the observed universe and explains many previously mysterious observations. This series was previously published.*

### Families of Harmonics

When several main line harmonics in a row are at ratios of 2 relative to each other, those families of harmonics do not stop just because they are not in the main line. For example, looking at 144 and 288 in the main line, we can trace a smooth curve back through 72, 36, 18 and 9 and forward through 576, 1152, 2304 and further on into the weaker harmonics jungle. These harmonics that are linked by ratios of 2 are called families of harmonics, and they can help us to see the fascinating structure present. In music all of the notes linked by ratios of 2 are given the same name, such as C, although they may be called C4, C5 and C6 so that we know which C is meant. The families are just like the musical notes, and adjacent families, which are different by only a ratio of 3, are like the most common musical modulations of adding or taking away a sharp or flat in music.

The first family goes 1, 2, 4, 8, 16, ... or just the powers of 2. Initially these are the strongest harmonics but at 8 the harmonics dip below the next family, their cousins, 3, 6, 12, 24, 48, 96, 192, ... which are all powers of 2 times 3. Again these are the strongest harmonics from 12 to 48 but then 96 falls below the line of the next family. This process keeps repeating with families that are powers of 2 times 3, 3^2, 3^3, 3^4 and so on. It can be seen that the peaks of these coloured parabolas occur between 12 and 24, then 144 and 288, and so on. This supports the view that a ratio of 3 happens for every 2.38 ratios of 2 because that also would fall between those same numbers.

However something else happens to our coloured lines as we move from left to right, the peaks of these parabolas are themselves making a parabola and as a result they stop being the highest harmonics of all. A new unmarked family of 720, 1440, 2880, 5760, ... takes over the lead. This family is of the form 2^n*3^2*5 and second cousin 5 has joined the fray.

The curved lines are getting a bit more crowded now, so the new families, which all have a factor of 5, have been added in darker colours. These new families again each make parabolas and the cousin families again extend this with a parabola of parabolas. At the right edge of the graph some of the strong harmonics are not members of any of the coloured families, but belong to a new cousins involving the ratio 7.

It is possible to make parabolas through harmonics that are linked by ratios of 3 rather than 2 also. An example would be 16, 48, 144, 432, ... and many others. Such groups fall away a little faster in each direction than the families based on ratios of 2. If we do the same thing with ratios of 5 or 7 then they fall away faster still. That is why repeated ratios of 2 and 3 happen in music but not with the higher primes.

### Main Line Harmonics

The term "main line harmonics" is used for the harmonics shown in larger font in the above diagram. They are the series of harmonics starting from 1 that are always related to each other by a prime number ratio and which are the very strongest harmonics. There are some marginal cases to this definition as we might have chosen either 5760 or 8640 to lie between 2880 and 17280. Either way the ratios would be the primes 2, 3 or 3, 2; but 8640 was chosen as being a little stronger than 5760. Such a decision might be influenced by the formula for detrending the harmonics.

The purpose in highlighting these main line harmonics and the prime ratios between them is that the prime ratios contain a pattern which is almost regular. The early main line harmonics are 1, 2, 4, 12, 24, 48, 144, 288, 1440, 2880, 8640, 17280, 34560, 69120, 207360, 414720, ... and these have ratios between them of 2, 2, 3, 2, 2, 3, 2, 5, 2, 3, 2, 2, 2, 3, 2, ... and so on. It can be seen that there is one ratio of 3 for every two or three ratios of 2 and that the other primes occur much less often.

At one time I conjectured that the primes occurred with inverse frequency p*log(p) and because it it difficult to calculate very high harmonics this conjecture was used as a substitute for the actual calculations beyond the known limits. However with increasing computer speed and a few mathematical tricks it has been possible to calculate the harmonics out beyond 10^50 now and to find that the conjecture is not correct and gets gradually less accurate at higher order as the larger primes get further apart than expected. If this conjecture were correct, then a three would occur for every 2.38 twos, a five would occur for every 5.8 twos and a seven for every 9.8 twos. On that basis a 7 should be due to happen next and it does.

These proportions of 2s, 3s, 5s and 7s are quite consistent with musical practice. Pythagoras only used 2s and 3s in his musical scale, however Galilei, the father of the famous Galileo, showed that a major third is really 5/4 and not 81/64 as Pythagoras had assumed. Actually both of these ratios do occur but it is most often Galilei's ratio that happens in music. It has been expressed, for example by the mathematician Euler, that the ratio 7 is a bit too harsh to be used in musical ratios. However it is used in Indian music and in Blues music and should definitely be considered as a valid musical ratio, Part of the reason that it is not used more is not that it is naturally harsh but that it does not fit in with the present music notation which really is biased to the equitempered scale which only deals comfortably with ratios involving 2, 3 and 5. The proportional frequency of occurrence of 2, 3, 5 and 7 according to the harmonics theory gives a meaningful answer to the question that Euler asked concerning the concordance of sounds, a subject which has been studied by music theoreticians since Euler's time.

According to the expanded cycle framework that I use, originally based on the “Roadmap signature” model of veteran strategist and mentor Robin Griffiths (Figure 1 ABC), **the U.S. economy remains in a late-stage pending recession, but is now shifting into 2024 as part of a multi-year transition**.

The Kondratieff wave which, drives trends of interest rates, predicted the bottom in 2020 and structural rise in 2022, marking a winter season amplified by a great debt burden *(Figure 2).*

The same k-wave is part of a ‘creative destruction’ force that predicts long periods of innovation. It confirms that we are now in a **sixth innovation ‘echo’ wave** - **since the Industrial Revolution,** **that is likely to last 20-25 years,** largely driven by technological developments in AI and robotics *(Figure 3).*

Primarily for this reason, the latest AI boom proved stronger than expected, with YTD performance quadrupling for some leading stocks *(Figure 4),* NVIDIA hitting the $trillion valuation and market internals historically more divergent even than Y2K and 2008 GFC. The warning about *“The Perils of ‘Painting the Tape’”* remains!

**Watch S&P500 equal-weighted, as it nears YTD peak levels, into historic +2STD threshold** *(Figure 5).* Only above here would signal broader market rotation and stronger risk appetite.

Alternatively, failure implies pending mean-reversion risk, further weighed by **negative seasonality, typically led by a peak into August and fall-crash pattern into September-October ***(Figure 6).* More seasonality analysis to follow in future FSC blogs.

Thank you to all FSC members for all your kind feedback and insightful questions on our FSC blog series. I welcome more interaction on ron.william@cycles.org.

**Ron William, CFTe Bio**

Ron William, CFTe, is a market strategist and educator/mentor with more than 20 years of experience working for leading macro research and institutional firms, producing tactical research and trading strategies. He specializes in global, multi-asset, top-down framework, grounded in behavioural technical analysis, driven by cycles based on the *"Roadmap"* signature model of veteran market technician Robin Griffiths, published in his book “*Mapping the Markets*.”

Ron also applies a *"market & mind"* approach at IntensiChi, using the latest techniques in behavioral-risk models and neuroscience sourced from expert groups. He further supplements with mentoring/coaching, trained by the *International Coaching Federation (ICF),* and teaches a regulatory approved masterclass in Applied Behavioral Science, with investment, private banks and CFA Societies.

Ron's primary work, as part of his current institutional market advisory firm (RWA), acquired global industry recognition as winner of *“Best FX Research”* in 2020. Financial media programs and industry publications regularly feature his market insights, including “*Is the big cycle about to turn?*”, predicting the 2020 crash and alerting the *“Minsky paradigm”* of 2020 H2-2022.

Driven by high-integrity education, Ron serves as part of the education committee of the *International Federation of Technical Analysts* *(IFTA),* Development Director at the *Foundation of the Study of Cycles (FSC),* Head of SAMT’s Geneva Chapter, and an honorary member of ESTA. He is also a visiting lecturer at universities, active guest speaker for the CFA, CAIA and CISI, and senior teacher at colleges offering an accredited diploma in trading and investing.

### Outstanding Harmonics

To further delve into the pattern of the harmonics, it is necessary to solve the problem of detrending the upward sweep of C(H), which grows ever faster with increasing H. For example, the harmonic 34560 has no less than 622592 ways of being factorised, so if it were placed on the graph of C(H)/H above, it would be at 18.01... which is way out the top and past your ceiling. And further up there are numbers with 36 digits that have a number of ways of being factorised that has 57 digits, so it would be more than out of the graph, it would be out past Sirius!

I might add as an aside that it takes a bit of computer time to calculate these harmonics. When I was doing this in the early days of the Harmonics theory I had this *new fast* computer with an 80286 chip in it that could calculate harmonics up to 15 digits or so if left alone for a few days. With the advance in computer speed and a few programming and mathematical tricks it is now possible to calculate beyond 50 digit harmonics. It doesn't do *all* of them, only the strong ones and the other ones necessary to calculate the strong ones.

In has taken some considerable effort to find a formula that detrends this sweeping growth. After using a variety of techniques to separate the different parts of what is going on, in March 2004 a formula that fitted the trend in the strongest harmonics was found. It works reasonably well up to fifty digit harmonics but might require a little tinkering beyond there. The trend in C(H) for the outstanding harmonics is estimated as Cest(H) = (H^1.7323)/(10.18^sqrt(log10(H)). The following graphs have been detrended by dividing C(H) by this Cest(H). This leaves two other parts of the variations in C(H) untouched. They are the variations in C over several octaves of H, and the detailed patterns within the octaves.

The result of this detrending is that we are free to look for the effects that are visible to us in the energy patterns of the universe because we will be comparing the energy at similar scales and not trying to compare galaxies to atoms which is beyond the present scope.

One other thing will be done to allow the musical pattern to be more easily seen, and that is to use a log scale for the harmonic number H, meaning that each doubling of H will take the same horizontal space. This will also avoid the graph going past Sirius in the horizontal direction. A doubling of H is what is called an octave in music, or going up from one note such as C to the next C. Now let's look at our harmonics in terms of whether they are outstanding harmonics in their range for harmonics from one to a million on a log scale.

It is clear that as the harmonic number gets higher the complexity increases. The number of weak harmonics grows very rapidly and although the strong harmonics stand out very much from these weak ones they are much further apart. There is less complexity among the strongest harmonics, with ratios of 2, 3, 4, 6, 12 and 3/2, 4/3, 5/4, 9/8 and others being frequently present between strong harmonics. These are the musical ratios. This diagram is nothing more or less than an enormous chord spanning some 20 octaves and including within it all the commonly known musical chords and scales. This aspect will be examined in detail later.

Sound the alarm! The recent escape-velocity melt-up in mega cap tech, is likely to suffer the perils of "painting the tape," based on **historic divergences in market internals, greater than Y2K TMT and 2008 GFC**. Jesse Livermore, a famous trader of the early 20th century and publisher of the classic trading bible *Reminiscences of a Stock Operator* was known for taking advantage of a previous version of this market anomaly. Generations later, the term evolved to describe artificial and unsustainable market rises that would typically carry large asymmetric risk. However, as many astute professionals know, this is only a **market setup and not a timing signal**.

What’s changed now is the intersection of technical, macro, and political factors. Technically, several key ratios are now at a critical tipping point. One headline example is the growth/value ratio of Nasdaq 100 to Russell 2000, recently hitting its Y2K TMT record bubble peak (Fig 1). Breadth divergences not only in the broad market, but in Tech itself, with the no. of falling tech stocks now back at yearly lows (Figure 2). Remember, this is against the backdrop of the narrowest breadth measure since Y2K TMT and 2008 GFC. Currently, the growth/value ratio is unwinding sharply lower, with small cap marginal outperformance, fuelled by record call volumes in IWM (Figure 3).

Goldman Sachs points to changing macro sentiment, as the soft-landing narrative is once again gaining traction (Fig 1) and safe-haven flows into mega-cap tech unwind. This follows the overheated debt-ceiling political drama, now resolved, with President Biden claiming a “crisis averted”.

However, many remain concerned about elevated risk factors, notably **FED TGA, Reverse Repo and $3 trillion gorilla debt supply issuance** (Fig 7) vs. lack of demand (Fig 8), with foreign holdings of USTs reaching the lowest in 19 years! This concern is further amplified by diminishing availability of UST buyers.

The AI boom proved stronger than expected, with YTD performance quadrupling for some leading stocks (Fig 1) and NVIDIA hitting the trillion $ valuation. Perhaps most ominously, the recent exuberance has come at a time of tightening financial conditions as *AI trumped The Fed* (Fig 2).

While there will undoubtedly be individual stocks that deliver accelerated growth from spending on AI this year, it is **unlikely to be enough to change the trajectory of the overall earnings trend in a meaningful way**. Instead, it may pressure margins further, as companies decide to invest in AI despite decelerating economic growth, as predicted by our Roadmap cycle model. Looking ahead, upside potential remains, as highlighted by L&G ETF AIAI base pattern and high score, relative to the world (Fig 3).

Moreover, the Foundation for the Study of Cycles (FSC) model signals imminent downside risk for Nasdaq (Fig 12). Sentiment flows are polarised (Fig 13 & 14), **implying the rally had been front-loaded and could now prove to be seen as pump and perhaps ‘dump’ next?** Interestingly the 3x short Nasdaq 100 ETF (SQQQ) is currently taking in the most cash ever YTD.

A barbell strategy, with downside protection is likely the next game in town during H2 2023. Be selective with risk assets, consider profit-taking, while building up defensive plays, such as gold, cash, quality bonds and non-correlated portfolio risk.

In behavioural terms, it’s **time to switch from FOMO to FOLO**. The performance equity curve (Fig 15) demonstrates that fear (FOLO) beats greed (FOMO) in volatile markets. Take note of this well known market wisdom shared by many pioneers. Warren Buffett warns of the importance of risk management in his biblical reference to the Noah’s Ark principle “predicting rain doesn’t count, building arks does”. While Stanley Drukenmiller recalls his worst trading mistake during the Y2K - due to FOMO extremes and the need “to play."

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Thank you to all FSC members for all your kind feedback and insightful questions on our FSC blog series. Welcome more interaction on ron.william@cycles.org.

**Ron William, CFTe Bio**

*"Roadmap"* signature model of veteran market technician Robin Griffiths, published in his book “*Mapping the Markets*.”

*"market & mind"* approach at IntensiChi, using the latest techniques in behavioral-risk models and neuroscience sourced from expert groups. He further supplements with mentoring/coaching, trained by the *International Coaching Federation (ICF),* and teaches a regulatory approved masterclass in Applied Behavioral Science, with investment, private banks and CFA Societies.

*“Best FX Research”* in 2020. Financial media programs and industry publications regularly feature his market insights, including “*Is the big cycle about to turn?*”, predicting the 2020 crash and alerting the *“Minsky paradigm”* of 2020 H2-2022.

*International Federation of Technical Analysts* *(IFTA),* Development Director at the *Foundation of the Study of Cycles (FSC),* Head of SAMT’s Geneva Chapter, and an honorary member of ESTA. He is also a visiting lecturer at universities, active guest speaker for the CFA, CAIA and CISI, and senior teacher at colleges offering an accredited diploma in trading and investing.