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Intervals Explained
Distance Between Notes
Related Worksheets
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A musical interval is the distance in pitch between two notes. Intervals are one of the basic building blocks of melody, harmony, and chord structure. When you hear a tune move up or down, or when two notes sound together, you are hearing intervals in action. Understanding intervals helps students connect music theory to the physics of sound.
Intervals can be described in two linked ways: by note names in music theory and by frequency relationships in acoustics. On a piano, an interval is often measured by counting letter names or semitone steps between keys. In sound science, the same interval changes the ratio between frequencies, such as 2:1 for an octave. These patterns explain why some note pairs sound stable and consonant while others sound tense or dissonant.
Key Facts
- An interval is the difference in pitch between two notes, heard either successively or simultaneously.
- A semitone is the smallest standard step in Western equal temperament, and 12 semitones = 1 octave.
- Frequency ratio for an octave: f2/f1 = 2/1.
- Frequency ratio for a perfect fifth: f2/f1 = 3/2.
- In equal temperament, f2 = f1 x 2^(n/12), where n is the number of semitones.
- Interval names combine a number and a quality, such as major 3rd, minor 6th, or perfect 4th.
Vocabulary
- Interval
- An interval is the distance in pitch between two musical notes.
- Semitone
- A semitone is one step between adjacent notes in the standard Western tuning system.
- Octave
- An octave is an interval where the higher note has twice the frequency of the lower note.
- Frequency ratio
- A frequency ratio compares the frequencies of two notes to describe their interval.
- Consonance
- Consonance is the sense of stability or smoothness produced by certain note combinations.
Common Mistakes to Avoid
- Counting keys instead of semitone steps, which gives the wrong interval size because intervals are measured by the number of pitch steps between notes, not just by how many notes are touched.
- Ignoring the starting note when naming an interval, which is wrong because interval numbers count both the first and last note names.
- Assuming all thirds or fifths are the same, which is incorrect because interval quality matters, so a major 3rd and a minor 3rd have different semitone counts.
- Confusing frequency difference with frequency ratio, which is wrong because musical intervals are tied to multiplicative ratios, not simple subtraction.
Practice Questions
- 1 A note has frequency 220 Hz. What is the frequency one octave above it?
- 2 Using f2 = f1 x 2^(n/12), find the frequency of a note 7 semitones above 440 Hz. Round to the nearest hertz.
- 3 Two note pairs are played: one has frequency ratio 2:1 and the other has frequency ratio 45:32. Explain which pair will usually sound more stable and why.