Semitone Calculator
Calculate semitone intervals, frequency ratios, and note relationships for music theory and instrument tuning with our free tool.
Calculate Your Semitone Calculator
What is a Semitone?
A semitone (also called a half step) is the smallest musical interval commonly used in Western tonal music. It represents the distance between two adjacent notes on a piano keyboard, including the distance between a white key and an adjacent black key. For example, the distance from C to C# (or Db) is one semitone.
The Mathematical Foundation of Semitones
In modern equal temperament tuning, an octave is divided into 12 equal semitones. Since an octave represents a doubling of frequency, each semitone corresponds to a frequency ratio of 2^(1/12) or approximately 1.05946.
This mathematical relationship means that if you have a note with frequency f, the note one semitone higher has a frequency of f × 2^(1/12), and the note one semitone lower has a frequency of f ÷ 2^(1/12).
Semitones and Musical Intervals
Common musical intervals are measured in semitones:
- Minor 2nd: 1 semitone (e.g., C to Db)
- Major 2nd: 2 semitones (e.g., C to D)
- Minor 3rd: 3 semitones (e.g., C to Eb)
- Major 3rd: 4 semitones (e.g., C to E)
- Perfect 4th: 5 semitones (e.g., C to F)
- Tritone: 6 semitones (e.g., C to F#/Gb)
- Perfect 5th: 7 semitones (e.g., C to G)
- Minor 6th: 8 semitones (e.g., C to Ab)
- Major 6th: 9 semitones (e.g., C to A)
- Minor 7th: 10 semitones (e.g., C to Bb)
- Major 7th: 11 semitones (e.g., C to B)
- Octave: 12 semitones (e.g., C to C)
Applications of Semitone Calculations
Instrument Tuning
Understanding semitones is crucial for tuning musical instruments. Every semitone increase corresponds to a specific frequency multiplication factor, allowing precise tuning calculations.
Transposition
Musicians use semitone calculations to transpose music from one key to another. By counting the number of semitones between the original and target keys, they can shift all notes in a piece accordingly.
Digital Audio Processing
In digital audio production, pitch-shifting algorithms rely on semitone calculations to alter the pitch of recordings. Understanding the frequency ratios between semitones ensures accurate pitch modifications.
Harmonization
Composers and arrangers use semitone relationships to create harmonies. Different chord types are defined by specific semitone patterns (e.g., a major triad has intervals of 4 and 3 semitones from the root).
Different Tuning Systems
While equal temperament (with 12 equal semitones per octave) is standard in modern Western music, other tuning systems exist:
- Just intonation: Based on pure frequency ratios, resulting in unequal semitones
- Pythagorean tuning: Based on perfect fifths, with slightly different semitone sizes
- Quarter-tone systems: Dividing the octave into 24 quarter-tones (half-semitones)
- Microtonal systems: Using intervals smaller than a semitone
Cultural Variations
Different musical traditions around the world use various interval divisions:
- Arabic maqam: Uses quarter-tones (half-semitones)
- Indian classical music: Uses a 22-shruti system with intervals smaller than semitones
- Indonesian gamelan: Uses completely different scale systems not based on equal semitones
Understanding semitones provides a foundation for exploring music theory, composition, and the mathematical relationships that govern harmony across different musical traditions.
Related Calculators
Frequently Asked Questions
A semitone (also called a half step) is the smallest musical interval commonly used in Western music. It represents the distance between two adjacent notes on a piano keyboard. For example, the interval from C to C# (or Db) is one semitone, as is the interval from E to F. In equal temperament tuning, a semitone represents a frequency ratio of approximately 1.059 (specifically 2^(1/12)), meaning that each semitone increases the frequency by about 5.9%.
A semitone (half step) is the smallest interval in Western music, while a tone (whole step) equals two semitones. On a piano keyboard, a semitone is the distance between any two adjacent keys (white to black or black to white), while a tone skips one key. For example, C to C# is a semitone, while C to D is a tone. In terms of frequency ratios, a semitone represents a ratio of approximately 1.059 (2^(1/12)), while a tone represents a ratio of about 1.122 (2^(2/12)).
Equal temperament is the tuning system that divides an octave into 12 equal semitones. In this system, the frequency ratio between any adjacent semitones is exactly the same: 2^(1/12) or approximately 1.059. This standardization allows musicians to play in any key with acceptable intonation, as the intervals retain the same frequency relationships regardless of the starting note. Before equal temperament became standard, various other tuning systems were used where not all semitones had the same size, which limited the ability to modulate between different keys.
To count semitones between two notes:
1. Start from the lower note and count each key (white or black) on a piano until you reach the higher note
2. Include the starting note but not the ending note in your count
3. Alternatively, you can use the chromatic scale (C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab, A, A#/Bb, B) and count the steps between your notes
For example, from C to E, the semitones are: C to C# (1), C# to D (2), D to D# (3), D# to E (4). So there are 4 semitones between C and E.
Semitones are the building blocks for scales and chords in Western music:
Major scale follows a pattern of whole and half steps: W-W-H-W-W-W-H (or in semitones: 2-2-1-2-2-2-1)
Natural minor scale follows the pattern: W-H-W-W-H-W-W (or 2-1-2-2-1-2-2)
Chords are built using specific semitone patterns:
- Major triad: root, 4 semitones up, 3 more semitones up (e.g., C-E-G)
- Minor triad: root, 3 semitones up, 4 more semitones up (e.g., C-Eb-G)
- Diminished triad: root, 3 semitones up, 3 more semitones up (e.g., C-Eb-Gb)
- Augmented triad: root, 4 semitones up, 4 more semitones up (e.g., C-E-G#)
By understanding these patterns of semitones, musicians can construct any scale or chord in any key.
The frequency ratio for any interval in equal temperament can be calculated using the formula:
frequency ratio = 2^(n/12)
Where n is the number of semitones in the interval. For example:
- 1 semitone: 2^(1/12) ≈ 1.059 (minor second)
- 4 semitones: 2^(4/12) ≈ 1.260 (major third)
- 7 semitones: 2^(7/12) ≈ 1.498 (perfect fifth)
- 12 semitones: 2^(12/12) = 2.000 (octave)
These ratios are important in instrument design, tuning, and audio engineering. For instance, to raise a note's pitch by a perfect fifth (7 semitones), you multiply its frequency by approximately 1.498.
Enharmonic notes are notes that sound the same (have the same pitch) but are written differently in musical notation. In equal temperament, C# and Db represent the same physical pitch—they're one semitone above C and one semitone below D. Other examples include F# and Gb, or A# and Bb.
The choice between enharmonic equivalents depends on the musical context, particularly the key signature and harmonic function. For example, in the key of D major (with F# and C#), you would use C# rather than Db for clarity and consistency, even though they represent the same pitch separated by zero semitones.
Transposition using semitones is straightforward:
1. Determine how many semitones you need to transpose (up or down)
2. For each note in your original piece, move it by that exact number of semitones
For example, to transpose from C major to E major (up 4 semitones):
- C becomes E (up 4 semitones)
- D becomes F# (up 4 semitones)
- E becomes G# (up 4 semitones)
- F becomes A (up 4 semitones)
- G becomes B (up 4 semitones)
- A becomes C# (up 4 semitones)
- B becomes D# (up 4 semitones)
This process works for any melodic or harmonic material and ensures that all the interval relationships are preserved in the new key.
Share This Calculator
Found this calculator helpful? Share it with your friends and colleagues!