# Part II. Harmonic Numbers and AB=CD pattern

Commander in Pips: All approaches to the trading of Harmonic Patterns are based on Geometry, Fib ratios and Harmonic numbers. Very often in different study materials, the teachers skip the discussion of harmonic numbers. This makes trading Harmonic numbers flawed. Knowledge of the harmonic numbers principle will give you outstanding advantage in trading Harmonic patterns. Since we’re speaking mostly about Forex and precisely about EUR/USD – we will specify them for that pair. Also, we will show how you can estimate harmonic numbers for any asset or currency – stocks, bonds, commodities etc.

Pipruit: This stuff seems interesting, but Commander, may be we should specify what “harmonic” really means?​

Commander in Pips:
Yes, I just want to do that. Dealing with harmonic numbers moves you in physics sphere of vibrations that tells us:

Harmonic - is a component of a periodic oscillation whose frequency is an integral multiple of the fundamental frequency”

Pipruit: What? How does physics touch Forex at all?​

Commander in Pips: Very simple. First, this definition tells us that something called “harmonic” could be combined in larger substance proportionally to some multiple coefficients.

Pipruit: Commander, please… Do me a favor!​

Commander in Pips: Ok, ok. If you will take a close look at any market, you will see that all swings have non-random values. They repeat and repeat again with the approximately the same value that is called the “Harmonic number” or harmonic swing of particular market. Depending on the market behavior – contracting (during range trading or consolidation) or expanding (trend move) other swings consist of some amount of the base Harmonic swing. Taking a careless view – you will see nothing, some random vibrations. If you will attempt to apply harmonic number – you’ll see amazing order and repetition of the same swings again and again.

Tell me, what do you see here?.

Chart #1 | EUR/USD Daily
Pipruit: I do not know, some upside move may be, nothing special.​

Commander in Pips: And now?

Chart #2 | EUR/USD Daily and Repetition of Harmonic Swing
All these purple lines have the same length and slope – they were cloned, dragged to these swings. Also take a look – the long downswing consists of the same harmonic swing multiply with 2. That’s what I’ve talked about when I said“some amount of harmonic swings”. When the market is expanding, like during this long move down – its move usually consists of some number of harmonic swings. Here you can see obvious repetition of the same value’s move.

Pipruit: Wow, Commander, this is a real breakout in trading science! I’m glad that we are the first who discover it!
Commander in Pips: I do not want to upset you, my friend but that property of the market was discovered in 1970s…

Pipruit: Oh, no… And why is it so useful then?
Commander in Pips: Because we will not use it blindly and will not trade it purely. We will use it in more sophisticated tactic, but it will give us great service.

Pipruit: Hm, I’m listening very carefully…
Commander in Pips: Great. So, our work has to start from this harmonic swing estimation. And it could be estimated by observation. You should take your preferable trading chart – for instance 5, 30 or 60 minutes – depending on your trading time frame and observe it.

Pipruit: What do you mean with “observe”?
Commander in Pips: You should take a look at them each day, find some repetitive swings and measure them. Your observation is better if you accurately fix it somewhere – an Excel sheet, for instance. So, after some time you’ll see that on your preferable time frame many swings have the same value. You should search for repetition of the swings and control their value. Take additional care to the nature of the swings. Repetitive swings will appear when the market is contracting – trading in the range, while when it will turn to expansion, swings become greater and they will be multiples of contracting harmonic swing, like on chart #2, when downswing was 2 x harmonic swing.

Pipruit: And how long of a time should I do that?​

Commander in Pips: I suppose 30 days will be enough.

Pipruit: And maybe there is some other way, more simple ha?​

Commander in Pips: Well this method is most accurate and preferable, but there is another one – 3% rule. You may multiply current currency rate (or asset value) by 3% - and use this as harmonic number. For instance, if the current EUR/USD rate is 1.4276. then the harmonic number – 1.4276 x 3% = 0.0428.

Pipruit: Sir, but this is 428 pips! How should I use it, say, on 30-min chart?​

Commander in Pips: Don’t panic. I’m not done yet, relax.

As we’ve noted, a harmonic swing could consists of smaller swings with some multiplier. These multipliers depend on two factors – time frame and market environment (contracting or expansion). I’ll show you the major multipliers.

Multipliers based on time frame

These are the simplest ones. You should just divide or multiply harmonic swing on integer number – 1, 2, 3…10..etc. You should do this with carefully. For, instance, if we divide our number of 428 pips on 10, we will get 43 pips.

I can tell you, that observation method tells, that for 30-60min EUR/USD chart harmonic number is 37-40 pips and 37-40x2 = 74-80 pips. See, 3% rule approximately works.

And vice versa, analyzing daily chart of EUR/USD it tells that harmonic swing equals approximately 10x30-min harmonic swing or ~ 400 pips.

Pipruit: I see, and what the relationship between timeframe and daily harmonic swing? How we could know the multiplier?​

Commander in Pips: Well, here still, you will have to make some observation with major number from 3% rule (428 pips) by applying different multipliers and comparing the numbers that you’ll get with real repetitive swings on a particular time frame. But this work is simpler, because you already know what swing’s value to watch for.

Multipliers based on market environment

Here are some additional numbers appear as multipliers. The same numbers could be applied with time frame multipliers. Later we will show how it could be done.

Since the market in contraction mode shows retracements, that usually means that swings are shorter than expansion moves, we should apply some multipliers that are less than 1, and here they are:

1. 0.382 or 0.618;

2. 1.272 and 1.618;

3. 2, 3, 4, 5…etc.

So, we know that 60-min harmonic number on EUR/USD 37-40 pips. As we know, market usually moves as some initial move and retracement from it. Retracement will be smaller than move itself, hence we should apply multipliers that less than 1. If market accelerates then it could pass 1, 2, 3 or even 4 harmonic swings.

Here is how it looks like on hourly EUR/USD:

Chart #3 | EUR/USD Hourly
Here we use 40 pips harmonic number, although I still prefer 35-37 pips, but 40 is safer for stop loss placement. So, you see that in expansion mode market move up at 4 or 5 multiples of the harmonic swing, while in contracting with 2.5-3 multiplier. Please note, by the way that if we will divide 3 into 5, we will get 0.6, as 2.5/4 will give us 0.625. Both are almost 0.618.

Pipruit: This is incredible. But looks like market rarely moves precisely to 40 pips… Sometimes it’s a bit greater, sometimes smaller…​

Commander in Pips: You’re absolutely right. This is not the math – this is the live market. So, we should treat harmonic number more as an area rather than a precise number.

Now, how is to combine these numbers on larger time frame. Here is the daily chart:

Chart #4 | EUR/USD Daily
You can see, that we may apply as 428 pips harmonic move as 40 pips harmonic move. But here first one is more comfortable. For calculation of contraction purposes you may use the same 0.382, 0.618 or other multipliers to this harmonic move. For instance – applying multiplier 2 you will get target as 856 pips, rather than 973 pips in first move. But this deviation is small, compared to the move. Retracement down was 50% as precisely 1 harmonic move. In a move up you’ll get the target with 1284 pips rather than 1511. But relative to the scale of these moves harmonic numbers work almost perfectly. Also if you take a careful look at this long 1511 pips move – you’ll see that it consists of 3 1-harmonic swings.

Pipruit: Yes, indeed. So depending on time frame, first I should scale up or down the initial harmonic number, say 37-40 pips with integer multiplier – so I’ll get a more suitable harmonic number for a particular time frame. Then I can apply different multipliers that we’ve specified to calculate targets for contracting (retracements) and expansions.​

Commander in Pips: Absolutely.

Pipruit: This is very interesting, but what about how to apply all of this?​

Commander in Pips: All harmonic patterns are based on some Fib ratios and harmonic swings. If you know Fib ratio and swing – you can estimate the reversal points with high precision. The most significant quality of any harmonic swing is that market will not pass it occasionally. For instance, if some harmonic pattern shows us reversal at 1.50 on EUR/USD – then we can place stop above at 1.5040 and enter. Because if market will pass higher than 1 harmonic swing – it tells that our pattern has failed and the move up will continue. That’s our major way of application of harmonic number to harmonic patterns. Harmonic swing allows us significantly reduce risk and increase precision of estimation of our entry/exit points in trades.

The second important issue tells that when the market breaks out of some range - turns to expansion from contraction, and if it moves more than 1 harmonic swing – very probable that it will pass 2 or 3 more.

Pipruit: And is harmonic swing constant over time?​

Commander in Pips: I suppose that it is not. It can change. But this change happens slowly after long-term period, so from time to time it makes sense to revalue our harmonic number by doing the same work with observations.

AB=CD Pattern

The old wisdom tells that as some tool is simpler in nature, it more useful. That’s like the AB=CD pattern. In fact, this pattern could be seen most often on all markets and all time frames. Also usually it becomes a part of a complicated patterns such as 3-Drive, Gartley “222” and Butterfly. That’s why it’s very important to fully understand it.

The structure of this pattern is relatively simple. It consists of three legs – the initial AB move, CD retracement from the AB move and a continuation or extension CD. Although I draw CD as equal to AB, it is not always like that. The BC move could have different depth than the AB leg.

BC retracement leg usually shows move to one of the Fib support/resistance, depending on Buy/Sell pattern. The most often levels that stop BC move are: 0.382; 0.5; 0618; 0.786. The depth of retracement, i.e. BC leg has very significant meaning itself. For instance BC move just to 0.382 level usually happens on strong thrusting market, and could give early notification that probably CD leg will be greater than AB. While retracement to 0.786 level is vice versa – tells that probably CD leg will not exceed AB.

When market continues move outside point “B” – CD leg begins to form and we expect that price will reach pattern’s completion point at “D”. During development of CD leg we should watch for some warning signs that could force us to skip this trade or wait for additional confirmation – we will talk about them a bit later, but now let’s specify parameters that could invalidate this pattern:

1. BC leg can’t exceed AB leg. Other words retracement could not be greater that 1.0 of AB;

2. BC can be 1.0 retracement of AB and in this case AB=CD pattern is valid, although this is rare pattern that looks like double top or bottom, but it’s valid;

3. D must exceed B so that it could be completed in point D and to be a valid AB=CD pattern.
First of all keep in mind, that AB=CD pattern will have equal AB and CD legs only in 30-40% of cases. So, do not be deceived by its name. Most times CD leg will not be perfectly symmetrical to AB. Since we talk about “Harmonic patterns” the harmony term has very significant meaning for us. And this harmony is not only in term of price swings but in time also.

Since AB and CD leg could be different let’s how it could happen:

1. CD leg is an extension of AB anywhere from 1.27 to 2.0, 3.618 or even greater (difference in terms of price).

2. CD leg could be as steeper or flatter than AB (difference in terms of time).

Pipruit: I’m confused, Sir. If there could be such differences, how we can trade it at all?​

Commander in Pips: As usual solution is hidden in details and nuances. The first important issue is the development of the BC leg, second – price action after the C point has been formed. This will allow to you make right decisions about potential AB=CD pattern. But don’t interrupt me, I will tell you about that. Then you can ask your questions.

Commander in Pips: So, there are some signs in the CD leg that give us a clue will CD leg be an expansion of AB or not:

1. If right after the C point, a gap takes place in the direction of D point or somewhere on the way to D point, it could be an early warning sign that probably the CD leg will be extension of AB;

2. If right after C point, a long ranged bar (twice normal size) takes place in the direction of the D point or somewhere on the way to the D point, it could be an early warning sign that probably CD leg will be extension of AB;

3. If Gap and/or long ranged bar occur right near the D point (assuming that AB=CD) this is also the sign that CD could be extension of AB;

4. Ideally AB should be equal to CD as in price as in time. So, if AB leg forms in 10 bars so the CD leg also should form in 10 bars. This gives AB=CD pattern strength and increased odds that the market could show reversal at the D point – temporary or permanent;

5. If the CD leg has greater slope than AB, then probably it could be a 1.27, 1.618 or even greater extension of AB leg;

6. Also keep an eye on BC depth not as itself but in comparing with the AB move. If, say, AB up move takes 20 bars and BC takes 10 and has reached only 0.382 of AB - it tells that the market is absorbing the sell-off at high price and when sellers pressure will weaken – market could show a solid up thrust – the CD leg could be extended leg.

7. If BC reaches 0.618 or 0.786 then probably there is a good chances that AB and CD will be equal.

To calculate target of AB-CD pattern you may apply the following formula:

D-point = C + (B-A) x extension ratio​

Extension ratio could be one of the 1.0; 1.272; 1.618; 2.0; 2.24; 3.0; 3.168 etc. Usually 1.272; 1.618 and 2.0 are used.

Now attention – very important rule:

“You should treat an as AB=CD as any harmonic pattern from probability standpoint but not from certainty. It means that applying a solid money management and stop losses are a must here. It’s needless to say about having a deep understanding of the pattern itself”

Trading AB=CD and other harmonic patterns

Pipruit: Finally I’ll see some real market examples. I’m so tired from all that theory.​

Commander in Pips: Not only examples. Here you will meet with money management for the first time in our school.

Also I have to say that the trading approach to AB=CD pattern spreads over all the other patterns, because there is no difference due what exactly pattern we open the trade. Pattern itself just shows us the direction to enter – Buy or Sell, but money management will be quite the same. So here we will show how to trade harmonic patterns, and will stop on this in details in later parts, when we will speak about other harmonic patterns, although we will need particularly necessity to do that.

Pipruit: I see. ​

Commander in Pips:So, as we’ve said AB=CD pattern could appear and, hence, be traded at any time frame and any market, including Forex. Our approach to trading harmonic patterns is based on two principles:

1. Reduce risk as soon as it become possible;

2. Book profit – remember that we trade to make profit and not to catch huge moves or prove that you’re right about current environment.

3. We will risk max with 2% of all assets in single trade. Suppose that we have 5000 USD account.
And here how we can do this:

Chart #5 | EUR/USD 60-min
Here we see excellent example of AB=CD “Buy” pattern, it has nice harmony in time and steepness of AB and CD leg. Target of this AB=CD is 1.4486. Hence, knowing harmonic number of 35-40 pips we should place stop below 1.4486-0.0037 = 1.4449, because we assume that market will pass this distance below target of AB=CD occasionally. If it will do this, then something is wrong and it will tell us about potential acceleration to the downside.

Ok, we need to open double position, but so that our overall risk was not much then 2% from 5000 USD. Come on, calculate what should be our lot size, so that can open 2 lots and overall potential loss will not exceed 2% of capital.

Pipruit: Let’s see. Let’s suppose that our potential loss is 40 pips. Our total acceptable loss in this trade – 5000*2% = 100 USD. And we need to open 2 lots – our lot should be 100/0.0040/2= 12500 USD or 0.125 standard lot, hence overall position – 0.25 lots.​

Commander in Pips: Excellent. 0.25*100 000*0.0040 = 100 USD – you’re absolutely right. So, we enter Long around 1.4486 with 0.25 lot and put our stop loss at 1.4446.

Our initial target is the 0.618 resistance from the whole AD move – 1.4572. Here we will close 0.125 lot. Our profit will be: (1.4572-1.4486)*0.125*100 000 = 107.5 USD. After that we shift stop loss on the rest of position to breakeven and shift it to riskless trade, according to our first rule – “Reduce risk as soon as possible”.

Pipruit: And why we couldn’t do that earlier?​

Commander in Pips: Generally because our profit from the first half compensates our potential loss from total position. But you may think about it also, when the market has passed harmonic swing (about 40 pips) in your favor. Treat trades with harmonic patterns in terms of harmonic swings. The major problem with that is placing too tight stop will make your position too sensitive to possible splashes and will not allow the market to breath. That’s why I suggest moving stop to breakeven a bit later.

Our second target – 0.786 resistance from AD move – 1.4598. We’ve got fill, so our profit here is:

(1.4598-1.4486)*0.125*100 000 = 140 USD. And this is risk-free trade. So, overall result 140+107.5 = 247.50 USD or 99 pips on 0.25 lot.

Pipruit: And why we should move stop to breakeven at all? Second question – why have we closed half of position but not total position at 0.618 or not hold total position till 0.786?​

Commander in Pips: The major answer on all questions is “because of probability”. Our primary task is to make profit. That’s why we do that at the first target area. If the market suddenly returns back – our potential profitable trade could turn to loss, and we do not want it. For the same reason we shift our stop to breakeven when we take profit from the first half of position. If market will return back – our second half will loose nothing, but our first half has given us the profit already.

Speaking about taking profit at the whole position at 0.618 target – also nice approach. I have to say that this is in fact an alternative way to manage position. In some cases, when the market returns back – it gives better results, otherwise - when market continues its move up, worse results. But this way is appropriate also.

We did not hold total position till 0.786 because 0.618 is resistance and the market has chances to not reach 0.786. But as you remember, our primary task is to make profit and not to catch long moves. Hence answer is the same – probability.

Pipruit: Hm. But the market has shown strong upward continuation after that. We could get much more profit…​

Commander in Pips: May be, but you do not know it in advance. We have to take profits when available, and do not worry what the market does after it has reached your profit objective. Whistle on the road to the bank and don’t care about market moves after your trade has been completed with profit. But this does not mean that you should take profit prior to where your trading plan suggests to do that – do not break your initial trading plan. But be calm when it has been accomplished.

Here is example of similar possibility but with AB=CD “sell” pattern:

Chart #6 | EUR/USD 15-min
The market has accomplished this pattern almost pips to pips.

Pipruit: And why do we use just a 20 pips stop loss here?​

Commander in Pips: Generally because we solidly reduce trading time frame to 15-min chart. Hence, it allows us reduce harmonic swing value for 2 times. Still experience in trading of harmonic patterns is very important as always. In the beginning you can work only with larger values of harmonic swing, just separate AB=CD’s that could give you nice profit compared to potential stop-loss. Later you will better understand when it makes sense to reduce harmonic swing or not. It also depends from the size of AB=CD. On chart #6, by the way, we could apply even 40 pips stop loss, and it will give us nice risk/reward ratio>1. Also after some practice you will better choose targets – probably sometimes you will hold onto your position much longer; sometimes you will fix profits at 0.5 or even 0.382 levels.

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Bernhard33
10 years ago,
Registered user
thank you very much for this incredible good stuff Sive. I just turned a loss to a win today with knowing of the harmonic numbers:
I was short in audusd and got a retraicement. knowing harmonic numbers i waited and see it was a winner :)
Hamza Samiullah
7 years ago,
Registered user
Some points about harmonic numbers are confusing.... We can find harmonic number by multiplying current price by 3% then suppose got 428 pips.. then at which timeframe it would be applicable???
O
One-fm
5 years ago,
Registered user
it is getting clearer. Thanks.
Z
zhilone32
5 years ago,
Registered user
Please sir, can u send me video on how to use this harmonic Number, is too complicated to me
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Moyses Lopes
4 years ago,
Registered user
Hi, guys!
Thank you for your generosity! Just to point a little typewriting error, in the second paragraph about AB=CD pattern: “The structure of this pattern is relatively simple. It consists of three legs – the initial AB move, CD retracement from the AB move and a continuation or extension CD.” I think you mean “BC retracement”, correct? Best regards!
F