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The distance between two pitches is the interval between them. The name of an interval depends both on how the notes are written and the actual distance between the notes as measured in half steps.

The distance between pitches

The interval between two notes is the distance between the two pitches - in other words, how much higher or lower one note is than the other. This concept is so important that it is almost impossible to talk about scales , chords , harmonic progression , cadence , or dissonance without referring to intervals. So if you want to learn music theory, it would be a good idea to spend some time getting comfortable with the concepts below and practicing identifying intervals.

Scientists usually describe the distance between two pitches in terms of the difference between their frequencies . Musicians find it more useful to talk about interval. Intervals can be described using half steps and whole steps . For example, you can say "B natural is a half step below C natural", or "E flat is a step and a half above C natural". But when we talk about larger intervals in the major/minor system , there is a more convenient and descriptive way to name them.

Naming intervals

The first step in naming the interval is to find the distance between the notes as they are written on the staff . Count every line and every space in between the notes, as well as the lines or spaces that the notes are on. This gives you the number for the interval.

Counting intervals

To find the interval, count the lines or spaces that the two notes are on as well as all the lines or spaces in between. The interval between B and D is a third. The interval between A and F is a sixth. Note that, at this stage, key signature , clef , and accidentals do not matter at all.

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The simple intervals are one octave or smaller.

Simple intervals

If you like you can listen to each interval as written in [link] : prime , second , third , fourth , fifth , sixth , seventh , octave .

Compound intervals are larger than an octave.

Compound intervals

Listen to the compound intervals in [link] : ninth , tenth , eleventh .

Write a note that will give the named interval.

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Classifying intervals

So far, the actual distance, in half-steps, between the two notes has not mattered. But a third made up of three half-steps sounds different from a third made up of four half-steps. And a fifth made up of seven half-steps sounds very different from one of only six half-steps. So in the second step of identifying an interval, clef , key signature , and accidentals become important.

A to C natural and A to C sharp are both thirds, but A to C sharp is a larger interval, with a different sound. The difference between the intervals A to E natural and A to E flat is even more noticeable.

Listen to the differences in the thirds and the fifths in [link] .

So the second step to naming an interval is to classify it based on the number of half steps in the interval. Familiarity with the chromatic scale is necessary to do this accurately.

Perfect intervals

Primes, octaves, fourths, and fifths can be perfect intervals.

These intervals are never classified as major or minor , although they can be augmented or diminished (see below ).
What makes these particular intervals perfect? The physics of sound waves ( acoustics ) shows us that the notes of a perfect interval are very closely related to each other. (For more information on this, see Frequency, Wavelength, and Pitch and Harmonic Series .) Because they are so closely related, they sound particularly good together, a fact that has been noticed since at least the times of classical Greece, and probably even longer. (Both the octave and the perfect fifth have prominent positions in most of the world's musical traditions.) Because they sound so closely related to each other, they have been given the name "perfect" intervals.
Actually, modern equal temperament tuning does not give the harmonic-series-based pure perfect fourths and fifths. For the music-theory purpose of identifying intervals, this does not matter. To learn more about how tuning affects intervals as they are actually played, see Tuning Systems .

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Source:  OpenStax, Introduction to music theory. OpenStax CNX. Mar 14, 2005 Download for free at http://cnx.org/content/col10208/1.5
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