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As you have learned, the term interval refers to the distance between any two given pitches. They can be harmonic, meaning that both pitches are sounding at once, or melodic, when one pitch follows the other. Each interval has its own sound and name/number. When counting them, you always start from the bottom note and count the steps between the two notes. counting both notes.
So let's say we wanted to find the number of the interval from C to A. Starting on C (counted as 1), we count up six letters (C D E F G A) to get to A, making C up to A an interval of a 6th.
Sharps and flats are not used when figuring out the number of an interval, only the distance between the letters. So if we wanted to go from Db to G we ignore the flat and count the letters. Starting with D we have D E F G. Four letters, making Db up to G an interval of a 4th (we'll see what kind of 4th later!)
Two notes on the same line or space is called a unison. (That’s latin for “one sound”!) The distance from a note to the next closest note with the same letter name is called an octave. (and that’s latin for “eight”!) We can also keep counting past 8, through 9, 10, 11, 12, and 13, but usually not past 13.
But we can be more specific about any interval. You can also define the PRECISE distance between any two pitches in a couple of ways - one is by determining whether it would fit into a major or a minor scale, with the bottom note being the key. For example, in the following example, the 2 notes are C and E - we know it is a 3rd (C-D-E), but we also can determine that those 2 notes are naturally occurring in the C major scale. Therefore, this a Major 3rd. (The C minor scale would have an Eb.)
A major interval is labeled with a capital "M." So we would label this M3.
You may notice however, that the 2 notes below, C and F, occur in both the F Major and Minor scales. For this reason, it is called "Perfect," labeled with a capital "P." So we would label this P4.
The intervals of unison, a 4th, a 5th and an octave (8th) are all perfect intervals. All of the intervals drawn from a major scale are either major or perfect.
Minor intervals are one half-step smaller than major intervals. Minor intervals should always be worked out from the major scale. Find the major interval and lower the top note by one half-step to give the minor interval. This is because the notes in minor intervals don't always come in minor scales. It is labeled with a small "m." In these examples, the top note is 1 half-step lower than a major 3rd. (e.g. By examining the major scales that begin on the lower note here, C major and D major, you see that a major 3rd on C would be C-E, and a major 3rd on D would be D-F#.)
SO: To change an interval from major to minor, you start with the major interval and then lower it by one half step. C to Db is a minor 2nd, C to Eb is a minor 3rd, C to Ab is a minor 6th, and C to Bb is a minor 7th. Note that although many minor intervals appear in minor scales of the same letter name, this is not always the case, and so is not a reliable check.
There are only 2 intervals that do not occur naturally in one of the scales: a minor 2nd, which is another name for a half step (for example, C to Db), and the tritone which fits in between a 4th and a 5th (for example C to F#), and is also not labeled major or minor, but labeled TT. (This interval contains three whole steps, for this reason it is referred to as the tritone.) More about that later.
Half steps can also help you define intervals in the first place. By counting half steps, you can be absolutely sure that you are defining the interval correctly. (NOTE: when using this method, DO NOT call the first note 1 - you have to move from one note to another in order to have moved a 1/2 step.)
Minor 2nd - 1 half step Perfect 5th - 7 half steps
Minor 2nd - 1 half step Perfect 5th - 7 half steps
Major 2nd - 2 half steps Minor 6th - 8 half steps
Major 2nd - 2 half steps Minor 6th - 8 half steps
Minor 3rd - 3 half steps Major 6th - 9 half steps
Minor 3rd - 3 half steps Major 6th - 9 half steps
Major 3rd - 4 half steps Minor 7th - 10 half steps
Major 3rd - 4 half steps Minor 7th - 10 half steps
Perfect 4th - 5 half steps Major 7th - 11 half steps
Perfect 4th - 5 half steps Major 7th - 11 half steps
Tritone - 6 half steps Perfect Octave (8th) - 12 half steps
Tritone - 6 half steps Perfect Octave (8th) - 12 half steps
You can see that illustrated in different keys here:
IMPORTANT TO NOTE: The interval on the staff MUST BE written to match the letter names that are used. For example, a C to a Bb is considered a minor 7th. That sounds the same as when you play a C to an A# - but that is considered a kind of altered 6th, because it would be counted that way on the staff from bottom to top.
These are enharmonic intervals. Enharmonic intervals are intervals that sound the same but are "spelled" differently. In both cases, the bottom note is C, and the top note is the 3rd of the group of 3 black keys - but in the first case we call it Bb, and in the 2nd we call it A#. A# and Bb are called "enharmonic" pitches.
Consonance and Dissonance
Consonance and Dissonance
Notes that sound good together when played at the same time are called consonant. Chords built only of consonances sound pleasant and "stable"; you can listen to one for a long time without feeling that the music needs to change to a different chord. Notes that are dissonant can sound harsh or unpleasant when played at the same time. Or they may simply feel "unstable"; if you hear a chord with a dissonance in it, you may feel that the music is pulling you towards the chord that resolves the dissonance. Obviously, what seems pleasant or unpleasant is partly a matter of opinion. Of course, if there are problems with tuning, the notes will not sound good together, but this is not what consonance and dissonance are about.
Consonant Intervals
In modern Western Music, all of these intervals are considered to be pleasing to the ear. Chords that contain only these intervals are considered to be "stable", restful chords that don't need to be resolved. When we hear them, we don't feel a need for them to go to other chords.
The intervals that are considered to be dissonant are the minor second, the major second, the minor seventh, the major seventh, and particularly the tritone, which is the interval in between the perfect fourth and perfect fifth.
Dissonant Intervals
These intervals are all considered to be somewhat unpleasant or tension-producing. In tonal music, chords containing dissonances are considered "unstable"; when we hear them, we expect them to move on to a more stable chord. Moving from a dissonance to the consonance that is expected to follow it is called resolution, or resolving the dissonance. The pattern of tension and release created by resolved dissonances is part of what makes a piece of music exciting and interesting. Music that contains no dissonances can tend to seem simplistic or boring. On the other hand, music that contains a lot of dissonances that are never resolved (for example, much of twentieth-century "classical" or "art" music) can be difficult for some people to listen to, because of the unreleased tension.
Why are some note combinations consonant and some dissonant? Preferences for certain sounds is partly cultural; that's one of the reasons why the traditional musics of various cultures can sound so different from each other. Even within the tradition of Western music, opinions about what is unpleasantly dissonant have changed a great deal over the centuries. But consonance and dissonance do also have a strong physical basis in nature.
In simplest terms, the sound waves of consonant notes "fit" together much better than the sound waves of dissonant notes. For example, if two notes are an octave apart, there will be exactly two waves of one note for every one wave of the other note. If there are two and a tenth waves or eleven twelfths of a wave of one note for every wave of another note, they don't fit together as well.
Check yourself - can you identify the intervals played in the online exercises below?
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