• It is a description of the pitch interval or difference in frequency, and is nothing to do with an interval of time.
  • This is perhaps confusing, because the most common use of the word interval in English refers to a time interval (particularly the gap between two halves of a show or play).
  • Scientists and mathematicians are probably more used to the more general use of the word interval meaning any sort of gap between two things.
• The most common reason for discussing the interval between two notes is when they sound together or when they follow each other, as in the example above. However, it is valid to ask about the interval between any two notes.
• An interval can be described in pure physical terms as the difference in frequency, which is just a question of subtraction. The more common meaning of the word is the musical description which relates to the way the notes are described in notation rather than to the frequencies of the notes.
• Intervals can be described as diatonic or chromatic.
• Intervals are a useful concept in the discussion of the degrees of a scale, the notes within triads and chords, for transposition and for harmony analysis.
• Intervals are also often used in sight-reading, especially for singing.

• This can either be in the form of the notation, as in the example above, or the note names (in this case, F and B)
• You also need any pitch modifiers for each, again either from the notation or from a description, i.e. the key signature and any accidentals
• So for the example above you need to know that the two notes in question are F and B and, despite the key signature containing a B flat, the B is in fact a natural.

• The gap ordinal is a count of the number of note names between the two notes, but the count is done inclusively. So for example, the gap ordinal between C and E is a third (C, D, E is 3 notes); between A and B is a second; and in the example above, F to B is a fourth (F, G, A, B is 4 notes).
  • This inclusive counting tend to confuse people. It certainly takes some getting used to, because it is not like normal subtraction (you have to add one), but it is consistent with the concepts used in scales.
  • People also get confused that we are talking about the number of note names rather than the number of semitones. Actually, we are talking about the notes of a scale, but in any standard scale, there is only one occurence of each note name, so this is the same thing.
  • This ordinal can be written in words or more commonly as a number, 2nd, 3rd, 4th etc.

• The adjective qualifier can be one of five things: perfect, major, minor, diminished or augmented (theoretically, it is possible to have double-diminished and double-augmented, but these are never used in practise)
  • An interval of a 2nd, 3rd, 6th or 7th must be one of: major, minor, augmented or diminished
  • An interval of a 4th or 5th must be one of: perfect, augmented or diminished
  • A major interval appears in the major scale of which the bottom note of the two is the key-note.
  • A minor interval is one less semitone than its equivalent major interval.
    • Note that a minor interval does not necessarily appear in the minor scale of which the bottom note of the two is the key-note.
  • A perfect interval appears in the major and minor scales of which the bottom note of the two is the key-note.
  • A diminished interval is one semitone less than its equivalent minor or perfect interval.
  • An augmented interval is one semitone more than its equivalent major or perfect interval.
  • The relationship between these is given by the following table:

    -2	-1	0	+1
    	Diminished	Perfect	Augmented
    Diminished	Minor	Major	Augmented

Examples will follow when I have time!

For completeness, we might add a row at the top for zero semitones being a diminished 2nd and a row at the bottom for 12 semitones being an augmented 7th, as well as a perfect octave, but these are not commonly used.

The song or piece given has the specified interval between the first and second notes (unless otherwise stated).

• Minor 2nd (semitone)
  • I'm dreaming of a White Christmas (the whole of this phrase is minor 2nd intervals)
• Major 2nd (tone)
  • Rudolph the red-nosed reindeer - up and down
  • Happy birthday to you - 2nd and 3rd notes on "-py birth" and down again on "day"
• Minor 3rd
  • Greensleeves (Alas! my love)
  • After the ball is over - up and down
  • Star Spangled Banner (Oh! say can you see - USA National Anthem) - down
• Major 3rd
  • Blue Danube - the first ascending interval
  • While Shepherds watched their flocks by night
• Perfect 4th
  • Away in a manger
  • Amazing Grace how sweet the sound
• Augmented 4th/Diminished 5th
  • Mar-i-a, I just met a girl called Maria (from West Side Story)
  • The Simp-sons - main theme of cartoon signature tune
• Perfect 5th
  • Dear Lord and Father of mankind
  • Twinkle, Twinkle little star - between two “twinkles”
• Minor 6th
  • Hearts and Flowers (tear-jerker tune played at silent movies)
  • The Entertainer (otherwise known as the theme from “The Sting”) - the first big jump up between the 3rd and 4th notes
• Major 6th
  • Dashing though the snow (verse from Jingle Bells)
  • Oliver (from the show Oliver) - up and down
  • Chick, chick, chick, chick, chicken (lay a little egg for me) - up and down several times
• Minor 7th
  • The theme from the original Star Trek (actually has the words "Beyond the rim of the starlight")
• Major 7th
  • Climax of the theme from Superman
• Octave
  • Somewhere (over the rainbow - from The Wizard of Oz)