Semitone Calculator

Calculate musical intervals, frequency ratios, and pitch relationships with precision and ease.

Master music theory with our comprehensive semitone calculator. Convert between frequencies, calculate intervals, and understand the mathematical relationships in music.

Examples

Click on any example to load it into the calculator.

Perfect Fifth (A4 to E5)

perfect-fifth

Calculate the interval from A4 (440 Hz) to E5 (659.25 Hz).

Start Freq: 440 Hz

End Freq: 659.25 Hz

Major Third (C4 to E4)

major-third

Calculate the interval from C4 (261.63 Hz) to E4 (329.63 Hz).

Start Freq: 261.63 Hz

End Freq: 329.63 Hz

Octave Up (7 semitones)

octave-up

Transpose a frequency up by 7 semitones (perfect fifth).

Start Freq: 440 Hz

Semitones: 7

Minor Second Down

minor-second

Transpose a frequency down by 1 semitone (minor second).

Start Freq: 440 Hz

Semitones: -1

Other Titles
Understanding Semitone Calculator: A Comprehensive Guide
Master the mathematical foundations of music theory. Learn how semitones, frequency ratios, and musical intervals work together to create the harmonic relationships in music.

What is a Semitone and Why Does It Matter in Music?

  • Definition and Musical Foundation
  • Mathematical Relationship
  • Historical Development
A semitone is the smallest interval in Western music, representing the distance between two adjacent notes on a piano keyboard or guitar fretboard. This fundamental unit of musical measurement serves as the building block for all other intervals, scales, and harmonic relationships. Understanding semitones is essential for musicians, composers, audio engineers, and anyone working with musical pitch and frequency relationships.
The Mathematical Foundation of Semitones
The semitone is based on the twelfth root of 2 (2^(1/12) ≈ 1.059463), which means that each semitone represents a frequency ratio of approximately 1.059463:1. This mathematical relationship ensures that twelve semitones equal one octave, maintaining the fundamental principle that doubling a frequency creates the same note one octave higher. This logarithmic relationship is why musical intervals sound harmonious to the human ear.
Historical Development and Equal Temperament
The modern semitone system is based on equal temperament, which divides the octave into twelve equal parts. This system was developed to solve the problem of tuning instruments for different keys, allowing musicians to play in any key without retuning. Before equal temperament, various tuning systems like just intonation and meantone temperament were used, but they had limitations for modulation between keys.
Practical Applications in Music and Audio
Semitones are used extensively in music composition, instrument tuning, audio processing, and music education. Composers use semitone relationships to create melodies and harmonies. Audio engineers use semitones for pitch correction and audio effects. Music educators use semitones to teach interval recognition and ear training. Understanding semitones is crucial for anyone working with musical pitch and frequency relationships.

Semitone Applications in Music:

  • Piano Tuning: Each key represents one semitone difference
  • Guitar Frets: Each fret represents one semitone interval
  • Vocal Training: Singers learn to recognize semitone intervals
  • Audio Effects: Pitch shifting effects use semitone calculations

Step-by-Step Guide to Using the Semitone Calculator

  • Frequency-Based Calculations
  • Semitone-Based Transposition
  • Interval Recognition
The semitone calculator offers multiple calculation methods to suit different musical needs. Whether you're working with specific frequencies, transposing by semitone count, or identifying intervals, this tool provides accurate results for all your musical calculations.
1. Frequency-Based Interval Calculation
To calculate the interval between two frequencies, enter the starting frequency (e.g., A4 = 440 Hz) and the ending frequency (e.g., E5 = 659.25 Hz). The calculator will determine the semitone count, frequency ratio, and interval name. This method is useful for analyzing recorded music, tuning instruments, or understanding frequency relationships in audio recordings.
2. Semitone-Based Transposition
To transpose a frequency by a specific number of semitones, enter the starting frequency and the desired semitone count. Positive values transpose upward, negative values transpose downward. The calculator will provide the new frequency and interval information. This is essential for transposing music to different keys or creating harmonic variations.
3. Interval Recognition and Analysis
The calculator can identify common musical intervals and their properties. Understanding intervals like perfect fifths (7 semitones), major thirds (4 semitones), and minor seconds (1 semitone) helps musicians recognize harmonic relationships and create more sophisticated musical compositions.
4. Advanced Applications and Considerations
For professional applications, consider factors like cents (hundredths of a semitone) for precise tuning, temperament variations for historical music, and frequency ranges for different instruments. The calculator provides results in both semitones and cents for maximum precision in musical applications.

Calculation Examples:

  • Perfect Fifth: 440 Hz to 659.25 Hz = 7 semitones (ratio 1.5:1)
  • Major Third: 261.63 Hz to 329.63 Hz = 4 semitones (ratio 1.25:1)
  • Octave: Any frequency doubled = 12 semitones (ratio 2:1)
  • Minor Second: 440 Hz to 466.16 Hz = 1 semitone (ratio 1.059:1)

Real-World Applications and Musical Context

  • Music Composition and Arrangement
  • Audio Engineering and Production
  • Instrument Tuning and Maintenance
Semitone calculations are essential in numerous professional and educational musical contexts. From composition and performance to audio engineering and instrument maintenance, understanding semitone relationships enhances musical quality and technical precision.
Music Composition and Harmonic Analysis
Composers use semitone relationships to create harmonic progressions, melodic intervals, and chord structures. Understanding the mathematical relationships between notes helps composers make informed decisions about voice leading, chord voicings, and harmonic tension. The semitone calculator aids in analyzing existing music and creating new compositions with precise interval relationships.
Audio Engineering and Digital Audio Processing
Audio engineers use semitone calculations for pitch correction, harmonization effects, and audio manipulation. Digital audio workstations (DAWs) often use semitone-based pitch shifting, and understanding these relationships helps engineers achieve natural-sounding results. The calculator is particularly useful for setting up pitch correction software and creating harmonization effects.
Instrument Tuning and Maintenance
Professional musicians and instrument technicians use semitone calculations for precise tuning and maintenance. Understanding frequency relationships helps in setting up instruments, adjusting intonation, and maintaining consistent pitch across different registers. The calculator provides the mathematical foundation for accurate instrument setup and tuning.
Music Education and Ear Training
Music educators use semitone relationships to teach interval recognition, scale construction, and harmonic theory. Students learning to recognize intervals by ear benefit from understanding the mathematical relationships between notes. The calculator serves as a practical tool for demonstrating these relationships in the classroom.

Professional Applications:

  • Studio Recording: Pitch correction and harmonization effects
  • Live Performance: Real-time pitch shifting and transposition
  • Music Education: Teaching interval recognition and theory
  • Instrument Repair: Precise tuning and intonation adjustment

Common Misconceptions and Correct Methods

  • Equal Temperament vs. Just Intonation
  • Frequency vs. Pitch Perception
  • Mathematical Precision vs. Musical Context
Understanding semitone calculations requires clarity about common misconceptions and the relationship between mathematical precision and musical practice. Different tuning systems, frequency perception, and musical context all affect how semitones are understood and applied.
Equal Temperament vs. Historical Tuning Systems
The modern semitone system uses equal temperament, where all semitones are mathematically equal. However, historical tuning systems like just intonation used pure frequency ratios that created more harmonious intervals but limited modulation between keys. Understanding this difference is crucial for historical performance practice and certain musical styles.
Frequency vs. Perceived Pitch
While frequency is a physical measurement, perceived pitch can vary based on context, timbre, and individual hearing. The same frequency ratio may sound different depending on the frequency range, instrument type, and musical context. The calculator provides mathematical relationships, but musical interpretation requires additional consideration.
Precision vs. Musical Practice
Mathematical precision in semitone calculations doesn't always translate directly to musical practice. Musicians often make subtle adjustments based on musical context, ensemble tuning, and expressive needs. The calculator provides the theoretical foundation, but musical application requires artistic judgment and practical experience.
Cents and Microtonal Music
For maximum precision, musicians and audio engineers work with cents (hundredths of a semitone). This level of precision is essential for fine-tuning, historical performance practice, and microtonal music. The calculator provides results in both semitones and cents for applications requiring high precision.

Tuning System Differences:

  • Equal Temperament: All semitones = 100 cents (modern standard)
  • Just Intonation: Pure ratios (3:2 for perfect fifth = 702 cents)
  • Pythagorean: Based on perfect fifths (perfect fifth = 708 cents)
  • Meantone: Compromised thirds (major third = 386 cents)

Mathematical Derivation and Advanced Concepts

  • Logarithmic Nature of Pitch
  • Frequency Ratio Calculations
  • Cents and Microtonal Precision
The mathematical foundation of semitones is based on logarithmic relationships that reflect how humans perceive pitch. Understanding these mathematical principles provides deeper insight into musical relationships and enables more sophisticated applications in music and audio.
Logarithmic Nature of Musical Pitch
Human pitch perception is logarithmic, meaning we perceive equal ratios of frequencies as equal intervals. This is why doubling a frequency creates the same note one octave higher, regardless of the starting frequency. The semitone system reflects this logarithmic nature, with each semitone representing an equal ratio rather than an equal frequency difference.
Frequency Ratio Calculations
The frequency ratio between two notes separated by n semitones is calculated as: ratio = 2^(n/12). For example, a perfect fifth (7 semitones) has a ratio of 2^(7/12) ≈ 1.498, which is very close to the pure ratio of 3:2 (1.5). This mathematical relationship ensures that musical intervals maintain their harmonic character across different frequency ranges.
Cents and Microtonal Precision
Cents provide a more precise measurement than semitones, with one semitone equal to 100 cents. The formula for cents is: cents = 1200 × log2(f2/f1). This precision is essential for fine-tuning, historical performance practice, and microtonal music. The calculator provides results in both semitones and cents for maximum utility.
Advanced Applications and Extensions
Beyond basic semitone calculations, these mathematical principles extend to more advanced musical concepts. Microtonal music uses intervals smaller than semitones, while extended just intonation explores complex frequency relationships. Understanding the mathematical foundation enables exploration of these advanced musical territories.

Mathematical Relationships:

  • Semitone Ratio: 2^(1/12) ≈ 1.059463 (frequency multiplier)
  • Perfect Fifth: 2^(7/12) ≈ 1.498 (close to pure 3:2 ratio)
  • Major Third: 2^(4/12) ≈ 1.260 (close to pure 5:4 ratio)
  • Octave: 2^(12/12) = 2.000 (exact doubling of frequency)