# Ichimoku Theories

Also known as: Time theory, Price/Wave theory, Sanjin principles.
A Trend concept (Ichimoku system) in the LuxAlgo Library, with 1 indicator implementation.

## What are the Ichimoku Theories?

The Ichimoku Theories are the three doctrines Goichi Hosoda (who wrote as Ichimoku Sanjin) built beneath the five-line chart: time theory, wave theory, and price observation theory. Hosoda treated time as the dominant dimension. Time theory rests on his basic numbers (9, 17 and 26, with longer counts composed from them), counted forward from significant highs and lows to mark windows where a trend may turn, and on equalized spans, the idea that a developing phase often mirrors the length of a completed one. The familiar 9/26/52 settings of the [Ichimoku System](https://www.luxalgo.com/library/concept/ichimoku-system/) descend from these numbers.

Wave theory classifies movement into a grammar of I waves (one leg), V waves (two) and N waves (three, the basic trending unit), with contracting and expanding forms in fuller treatments. Price observation theory turns a completed A-B-C swing into four measured targets: N projects the first leg's length from the pullback low, E stacks that leg on top of its high, V doubles the correction's depth above the prior high, and NT projects the A-to-C span upward from C. Together the theories supply the forecasting layer that line-and-cloud reading alone, including the standard [Ichimoku Signals](https://www.luxalgo.com/library/concept/ichimoku-signals/), leaves out; every projection is a candidate window or objective, not a promise.

The history explains the system's texture. Hosoda developed the framework across decades of pre-computer research, famously employing a room of students to compute the lines and counts by hand, and published only in 1969 after years of refinement; the theories circulated primarily in Japanese, so English-language treatments vary in detail and completeness. The basic numbers extend beyond the simple three: composites such as 33, 42, 65 and 76 appear in fuller expositions, built from sums and overlaps of 9, 17 and 26, and the span-equalization principle, phases mirroring the durations of completed phases, runs through the whole time doctrine.

The three theories are designed to converge. A count window arriving while the current wave completes its N structure, with price approaching one of the four calculated targets, is the framework's full alignment, and the five-line chart itself encodes the time doctrine, the 26-bar displacement of the cloud being a basic number projected forward. In practice the theories survive mostly in automated form: the Library's Ichimoku Theories implementation labels waves, runs the counts and computes the N/V/E/NT objectives mechanically, which handles the bookkeeping the doctrines demand. The honest footing: these are Hosoda's conventions, coherent and venerable, with their forecasting value resting on practitioner tradition rather than audited statistics.

## How to identify the Ichimoku theories at work

The three doctrines are applied as one workflow: label the wave, count the time, project the price.

1. Label the swing structure: identify the working A-B-C sequence and classify the wave as I, V or N under the wave grammar.
2. Run the counts: bars forward from significant highs and lows in basic-number increments, 9, 17, 26 and their composites, marking the turn windows they nominate.
3. Check equalization: compare the developing phase's duration against completed phases, since mirrored spans are the time doctrine's second signal.
4. Compute the objectives: N, V, E and NT targets from the labeled A-B-C, selecting among them by the wave's shape.
5. Weight the confluences: a count window, a completing wave and a nearby calculated target arriving together is the framework's strongest read, and each alone is only a candidate.

## How it's calculated

Hosoda's three companion theories to the Ichimoku chart: numbered time counts, wave classification, and four arithmetic price targets.

```
Label an upward N wave: A = starting swing low, B = first swing high, C = pullback low
V = B + (B - C)
N = C + (B - A)
E = B + (B - A)
NT = C + (C - A)
For a downward wave, mirror the labels and subtract the same distances instead of adding
Time theory: project change days K bars forward from a significant turn, counting the turn bar as 1, with K in {9, 17, 26} or their combinations (33, 42, 51, 65, 76, 129, ...)
Wave theory classifies moves as I, V, or N waves (one, two, or three legs); the price targets apply to completed N waves

  A: price at the wave origin (the initial swing low in an upward wave)
  B: price at the first swing high of the wave
  C: price at the pullback low between legs
  V: V target, the pullback depth projected above the first high
  N: N target, the first leg's height projected from the pullback low
  E: E target, the first leg's height projected above the first high
  NT: NT target, the rise from origin to pullback low projected above the pullback low
  K: basic number (kihon suchi), a bar count used for time projections
  I wave: a single one-leg move in wave theory
  V wave: a two-leg move, a leg and its retrace
  N wave: a three-leg move, the shape the price targets are measured from
```

These are the Sanjin principles: time, wave, and price theories behind the standard Ichimoku lines, whose 9, 26, 52 lengths come from the same basic numbers.

E is read as the extended target, where the first leg's height repeats above B.

Change days flag dates where a trend may turn or accelerate; they do not indicate direction.

## How traders use it

- Counting time: bars are counted from major pivots in basic-number increments to flag windows where turns become more likely, and phases are checked for equalized spans; kindred in spirit to other [fixed time cycles](https://www.luxalgo.com/library/concept/fixed-time-cycles/) work.
- Framing structure: swings are labeled with the I/V/N grammar so that targets and signals are applied to a defined wave rather than to noise.
- Setting objectives: the N, V, E and NT calculations give measured targets for the current wave, usually read alongside the cloud and cross signals rather than in isolation.
- In cloud confluence: calculated targets landing at cloud edges or line levels merge the forecasting layer with the standard chart, and such overlaps are ranked above either read alone.
- Automated: implementations that label waves, run counts and project the four objectives mechanically keep the doctrines applicable at modern pace, with the trader's judgment spent on which confluences deserve action.

## Ichimoku theories vs related frameworks

- **Ichimoku System** (https://www.luxalgo.com/library/concept/ichimoku-system/): The system is the five lines and cloud most charts show; the theories are the doctrines underneath, supplying the time counts, wave grammar and price objectives the lines silently encode. Reading the chart without the theories is using the interface without the engine.
- **Ichimoku Signals** (https://www.luxalgo.com/library/concept/ichimoku-signals/): The standard signals, crosses, cloud breaks, Chikou confirmations, are present-tense reads of line positions. The theories add the forecasting layer: when a turn window is due, which wave is completing, and where the measured objectives sit. Signals time entries; theories frame expectations.
- **Fixed Time Cycles** (https://www.luxalgo.com/library/concept/fixed-time-cycles/): Hosoda's counts are a fixed-cycle tradition: constant bar intervals projected from anchors, with all the same honesty requirements about windows and confirmation. The distinctive additions are the composite number set and the span-equalization principle, which generic cycle counting lacks.

## FAQ

### What are Hosoda's basic numbers in Ichimoku?

The simple basic numbers are 9, 17 and 26, and Hosoda composed longer counts from them for extended cycles. They are used as bar counts projected forward from significant highs and lows to mark windows where a trend change becomes more likely, and they are the source of the chart's 9, 26 and 52 defaults. The counts define watch windows, not scheduled reversals.

### What are the N, V, E and NT price targets in Ichimoku?

They are Hosoda's four measured objectives, each computed from an A-B-C swing. N adds the first leg's length to the pullback low; E adds it on top of the leg's high; V adds the correction's depth back above the prior high; NT adds the A-to-C distance to C. Which one applies depends on the wave's shape, and all four are candidate targets to monitor rather than certainties.

### Why the numbers 9, 17 and 26?

Hosoda asserted them from his research rather than deriving them, and the popular explanation, that 26 approximates a trading month in Japan's old six-day week with 9 and 17 as its subdivisions, is retrofitted folklore the primary sources do not clearly confirm. What can be said: the numbers were fixed by decades of manual testing on Japanese markets, and their descendants parameterize every Ichimoku chart drawn today. Treat them as the framework's axioms.

### What is span equalization in time theory?

The principle that market phases tend to mirror the durations of completed phases: an advance running roughly as long as the prior advance, a correction consuming about the time of the one before. Practitioners compare the developing phase's bar count against recent completed spans and treat approaching equality as a maturing signal, converging evidence for the same windows the basic-number counts nominate. It is a symmetry heuristic, applied with tolerance rather than precision.

### What are the P and Y waves in wave theory?

The expanded grammar's consolidation forms: P waves contract, successive swings narrowing toward an apex like a converging triangle, and Y waves expand, each swing exceeding the last in a broadening structure. They classify the sideways passages the basic I/V/N trending grammar leaves out, and their resolution hands the count back to the directional waves. Fuller Japanese treatments elaborate them; abbreviated Western summaries often omit them entirely.

### Do Hosoda's targets and counts actually work?

No audited statistics exist, and the framework's age means survivorship does some of the advocacy. What the doctrines demonstrably provide is a disciplined structure: defined waves, pre-computed objectives, scheduled attention windows, and a confluence logic for combining them, which beats improvisation whether or not the specific numbers carry power. The defensible use treats N/V/E/NT levels and count windows as candidates requiring price confirmation, exactly as the tradition itself teaches.

## Implementations in the Library

- Ichimoku Theories (LuxAlgo): https://www.luxalgo.com/library/indicator/ichimoku-theories/

## Related concepts

- Ichimoku System: https://www.luxalgo.com/library/concept/ichimoku-system/
- Ichimoku Signals: https://www.luxalgo.com/library/concept/ichimoku-signals/

---

Source: https://www.luxalgo.com/library/concept/ichimoku-theories/ (LuxAlgo Library, the encyclopedia of trading & technical analysis). Free to use with attribution: https://www.luxalgo.com/library/license/