What is the Rule of 4ths? Exploring Its Diverse Meanings

December 4, 2025 •

4 min read

The term “rule of 4ths” can be remarkably ambiguous, depending on the context, leading to different interpretations in fields from finance to music. This article clarifies the distinct meanings behind this seemingly simple phrase to help you understand which version applies to your area of interest.

Quick Summary

The 'rule of 4ths' refers to different concepts depending on the field, such as the musical cycle of fourths, the 4% retirement withdrawal rule in finance, and the US Supreme Court's Rule of Four.

Key Points

Music Theory: In music, the 'Rule of 4ths' is the Cycle of Fourths, a sequence of notes moving by perfect fourth intervals (e.g., C-F-B♭).
Finance: The most common financial interpretation is the 4% rule, a retirement withdrawal guideline suggesting a 4% initial withdrawal rate from savings.
Photography: The Rule of Quarters is a compositional technique for visual artists, a variation of the Rule of Thirds that uses a 4x4 grid.
US Supreme Court: The Rule of Four is a procedural practice requiring four justices to agree to hear a case before it is reviewed.
Context is Key: Because the term has different meanings across multiple fields, it's crucial to understand the context to apply the correct 'rule' or concept.

The phrase “rule of 4ths” can be confusing because it is not a single, universally defined principle. In fact, it refers to different concepts in different fields. To understand which one is relevant, you must first consider the context. This guide breaks down the most prominent interpretations of the 'rule of 4ths' and 'rule of four' to provide clarity.

The Rule of 4ths in Music Theory: The Cycle of Fourths

In music, the 'rule of 4ths' is best understood as the Cycle of Fourths, a fundamental concept for understanding the relationship between the 12 chromatic notes. It is the inverse of the more widely known Circle of Fifths. Following the cycle clockwise by ascending perfect fourths moves through every key and adds one flat to the key signature at each step. This process helps musicians with:

Memorizing key signatures: The sequence C-F-B♭-E♭-A♭-D♭-G♭-B-E-A-D-G-C makes key signatures easy to remember.
Practicing scales and arpeggios: Musicians use the cycle to practice exercises through all 12 keys.
Understanding chord progressions: Many progressions rely on root movement by a fourth (or a descending fifth).

Practical Application of the Cycle of Fourths

The cycle of fourths is essential for understanding musical harmony, used in improvisation and composition. A common jazz progression like Dm7-G7-Cmaj7 shows root notes moving by a perfect fourth, creating a sense of resolution. The tuning of most standard guitars is also largely based on perfect fourths.

The Rule of 4ths in Finance: The 4% Withdrawal Rule

In personal finance, the 'rule of 4ths' most commonly refers to the 4% withdrawal rule. This guideline, created by William Bengen, suggests withdrawing 4% of a retirement portfolio in the first year and adjusting for inflation annually. It was designed for a portfolio to last at least 30 years.

How it works: For a $1,000,000 portfolio, withdraw $40,000 initially, increasing with inflation each year.
Assumptions: The original rule assumed a 30-year retirement and a 50/50 stock/bond portfolio.
Modern updates: Research suggests potential for a slightly higher initial withdrawal rate depending on market conditions.

Criticisms and Considerations for the 4% Rule

The 4% rule is popular but has critics. Concerns include its reliance on historical data, which may not predict future returns, and its suitability for longer retirements. Individual circumstances, market volatility, and changing expenses are important factors.

The Rule of 4ths in Photography: The Rule of Quarters

In photography, a 'rule of 4ths' sometimes refers to the Rule of Quarters. This variation of the Rule of Thirds divides the frame into quarters with a 4x4 grid. It allows placing subjects closer to the frame's edges, creating expansive images, especially for landscapes.

Application: Placing horizons or points of interest on quarter-lines can create dynamic compositions.
Purpose: It's a compositional tool for balance and drawing the viewer's eye, offering an alternative to the Rule of Thirds.

The Rule of Four in US Supreme Court Practice

In the US Supreme Court, the Rule of Four is an unwritten practice where at least four of the nine justices must agree to hear a case. This allows a minority of the court to bring a case forward.

Comparison of the Rule of 4ths (and Fours)


Aspect	Music Theory (Cycle of Fourths)	Finance (4% Rule)	Photography (Rule of Quarters)	US Supreme Court (Rule of Four)
Field	Music Composition, Theory	Personal Finance, Retirement	Photography, Visual Arts	US Law, Supreme Court Practice
Purpose	To understand and utilize the harmonic relationship between keys, aid practice, and guide chord progressions.	To provide a guideline for safe retirement portfolio withdrawals over approximately 30 years.	To provide a compositional tool for creating balanced and expansive visual images.	To decide which cases the Supreme Court will review, ensuring a minority can be heard.
Mechanism	A sequence of notes moving by perfect fourths (C-F-B♭...).	An annual withdrawal rate of 4% adjusted for inflation.	Dividing the frame into 16 sections using four horizontal and vertical lines.	Four justices voting to grant a writ of certiorari.
Context	Essential for musicians, especially in jazz and classical music.	A popular, though debated, rule-of-thumb for retirement planning.	A less common but useful alternative to the more widely known Rule of Thirds.	An unwritten, internal procedure for determining the court's docket.

Conclusion

Understanding the 'rule of 4ths' depends entirely on context. Whether it's the musical Cycle of Fourths, the financial 4% rule, or the photographic Rule of Quarters, each is a structured approach within its field. The shared term highlights the need for precise language. By recognizing these distinct applications, you can apply the correct 'rule of 4ths' to your specific needs. You can learn more about the 4% rule on Investopedia.

Frequently Asked Questions

The Cycle of Fourths is used to build logical and satisfying chord progressions. In jazz, for instance, many progressions are based on moving through the cycle, which creates a strong sense of resolution. It is also used as a framework for practicing musical exercises in all 12 keys.

No, the 4% rule is a guideline, not a guarantee, and its effectiveness depends on individual circumstances. Factors like the length of retirement, market volatility, portfolio diversification, and personal spending habits all affect its success.

The Circle of Fifths and the Cycle of Fourths are essentially the same circular diagram of the 12 chromatic notes. The difference is the direction you move. Moving clockwise through the Circle of Fifths is the same as moving counter-clockwise through the Cycle of Fourths.

The original 4% rule was based on a balanced portfolio of 50% stocks and 50% bonds. However, modern financial advisors note that the ideal allocation may vary based on individual risk tolerance and market conditions.

No, like the Rule of Thirds, the Rule of Quarters is a compositional guideline rather than a strict, formal rule. It offers a structured way to place subjects and create visual interest, particularly in expansive scenes.

The Rule of Four allows a minority of justices to grant a hearing for a case, preventing the majority from controlling the court's docket entirely. It is a long-standing tradition that protects the interests of different judicial viewpoints.

The musical term is '4ths' because it refers to the perfect fourth interval between musical notes. The financial term is '4%' because it specifies a 4 percent withdrawal rate. The similar phrasing is a source of ambiguity that requires context to clarify.