Aural Perception Skills (Unit 4): Intervals and Pitches

Pitches and intervals:

Half step is the same as a semitone. A whole step is the same as a tone.
For intervals, I will look at different kinds of intervals: unison, 2nds, 3rds, 4ths, 5ths, 6ths, 7ths and octaves.
An interval is a distance between 2 musical pitches. Both scales and chords are built from intervals. There are two types of intervals:
Harmonic interval- where 2 intervals are played at the same time (Bottom).
Melodic interval- where 2 intervals are played at different times (top).

The identity of an interval is determined by quality and quantity.
Quantity, or number size is based on the number of lines and spaces apart from the first pitch/note. You determine an interval's quantity by simply adding up the lines and spaces included in the interval. Accidentals and sharps do not matter for the quantity.

If an interval spans for more than an octave, it is called a compound interval. For this, you do exactly the same thing and just count the lines. For example, you can have 10ths (octave apart + 2) and 11ths (octave apart +3).

Quality of an interval (half steps)
This is based on the number of half steps from one note to another.Unlike quantity of an interval, accidentals and sharps do matter. This image shows all the harmonic intervals, major, minor, perfect, diminished and augmented.

Major (M): Consists of 2 semitones between notes.
Minor(m): Consists of 1 semitone apart.
Perfect(P): A harmonic quality of unison, 4ths and 5ths.
Diminished(dim): Contains a semitone less than a minor or perfect interval.
Augmented(aug): Contains a semitone less than a major or perfect interval.

Names of intervals

Every interval gets its name from a combination of the quantity and the quality of the interval (e.g. minor third). Here are the combinations:

Perfect (P); used for unisons, fourths, fifths and octaves.
Major (M) and minor (m): can only be used for with seconds, thirds, sixths, and sevenths.
Diminished (dim): can be used with any interval, with the exception of unisons.
Augmented (aug): can be used with any interval.

Unisons, Octaves, Fourths and Fifths:
They are similar in the way that they can all be perfect, augmented, diminished to determine their quality.
Perfect unison's
This is just playing the same note twice. A perfect harmonic unison can also occur when 2 or more people play the same note at the same time on different instruments.

Augmented unison's:
To make a perfect unison augmented, you just add a semitone between the notes. The interval between Ab and A is called an augmented unison. You can't have a diminished unison because it doesn't matter how you change the interval, you still end up with a semitone gap between the 2 pitches.

Octave: is when you have an interval quantity of eight lines and spaces. A perfect octave is like unison as it is the same note being played. The difference is that there is a gap of 12 semitones in between.

To make the octave augmented, you increase the distance by one semitone. For example, if it is C to C octave above, the augmented version would be C to C# or Cb to C 13 semitones apart.

To make an octave diminished, you decrease the distance between the notes by a semitone. E.g. C# to C the octave above or C to Cb.

Fourths:
These are 2 notes, separated by 4 lines and spaces (7 semitones apart). 4ths are always perfect in quality with 5 semitones distance except from F natural to b, which consists of six semitones (augmented 4th).

Fifths: notes separated by 5 lines and spaces. All fifths are perfect 5ths. However, the interval between B to
F is a diminished 5th which sounds the same as a augmented 4th.

Seconds, Thirds, Sixths, and Sevenths:
All share the same characteristic is that they all use the terms minor, major, augmented and diminished to identify their quality.
A major interval made smaller by one semitone makes it a minor interval.
A major interval made larger becomes augmented.
A minor interval made larger by a semitone becomes major.
A minor interval made smaller by one interval becomes diminished.

Here is a table I made to show what interval name is given in relation to the number of semitones:

Seconds

This is when you have an interval quantity of 2 lines and spaces. If it there is 1 semitone difference, this is a minor second. If the gap is 2 semitones, then the interval is a major second. The only place where half steps occur between white-key seconds is from E natural to F natural and B natural to C natural. These are the 2 spots on the keyboard where there are no black keys between 2 white keys.

An augmented second is a half step larger than a major second.

A diminished second is one semitone lower than a minor second therefore there are no steps between each note. They are the same note. It is the enharmonic equivalent to perfect unison its just the notation that is different.

Thirds

This contains 3 lines and spaces. It contains 4 half steps and is called a major third.

Major thirds occur from C to E, F to A, and G to B. If it contains 3 semitones, it is called a minor third, these occur from D to F, E to G, A to C, and B to D.

A major third can be turned into a minor 3rd by decreasing its interval size by one semitone.

A minor 3rd can be turned into a major 3rd by adding a semitone to the interval size.

An augmented 3rd is the enharmonic equivalent to a perfect 4th. Again, they are the same note, just different notation.