Music Theory – part 3

Intervals

The interval between two notes is their distance apart as tabulated below:

Same octave (less than 8 notes apart One octave (8 notes) above
C – C (same note) unison C – C’ octave
C – D 2nd C – D’ 9th
C – E 3rd C – E’ 10th
C – F 4th C – F’ 11th
C – G 5th C – G’ 12th
C – A 6th C – A’ 13th
C – B 7th C – B’ 14th

The notes at both ends are counted when calculating intervals so as can be seen above C to E is a third, C plus D plus E = 3 notes.

When adding 2 intervals together to make a compound interval, remember, the note in the middle has already counted and shouldn’t be counted twice. Two octaves make a 15th (if we added 8 + 8 we would be counting the middle note twice and would get a 16th which is not correct). An octave and a 2nd is a 9th (not a 10th as in 8 + 2 because again the middle note would then be counted twice).

Intervals greater than an octave are compound intervals.  For the most part we’ll concentrate on simple intervals here – much of what is said of them applies equally to the corresponding compound intervals.

The numerical value of an interval can always be found simply from the counting the letters in the note names e.g. C, D, E, F, G = 5 letters to make an interval of a 5th. The following intervals are all 5ths, but they are different kinds of 5ths.

 

 Diminished 5th C – G flat
 Perfect 5th C – G
 Augmented 5th C – G sharp

 

There are two classes of intervals: perfect and imperfect.

Perfect intervals are the set of intervals, which were historically determined to be consonant (pure and sounding good) up though the 17th century. This set of intervals includes unisons (1), fourths (4), fifths (5), and the octave (8) plus their compound (more than one octave apart) counterparts.

Imperfect intervals are intervals which are not as pure as the perfect intervals. They fall into two groups depending on their accepted consonance (sounding good)/dissonance (Ouch! My ears!):

consonant imperfect intervals: Major/minor third, Major/minor sixth.

dissonant imperfect intervals: Major/minor second, Major/minor seventh.

Try playing them and hear the difference

To distinguish different intervals with the same letter names, they are classified as perfect, major, minor, augmented and diminished.

The intervals from the tonic (first and last note of the scale and note after which the scale/key is named) to other notes on a major scale are all either perfect or major.  Again taking the scale of C major as a prototype we have:

C – C perfect Unison (same note
C – D major 2nd
C – E major 3rd
C – F perfect 4th
C – G perfect 5th
C – A major 6th
C – B major 7th
C – C’ perfect octave

For each major interval there is a corresponding minor interval (not used in the major keys), which can be found by flattening the upper note by a semitone but preserving the letter names of the notes.  Thus the minor intervals from C are

C – D flat minor 2nd
C – E flat minor 3rd
C – A  flat minor 6th
C – B flat minor 7th

If the upper note of a perfect or major interval is sharpened then the interval is said to be augmented. If the upper note of a perfect or minor interval is flattened then the interval is said to be diminished.

Thus the names of intervals from the note C can be tabulated as:

C – C flat diminished unison
C – C perfect unison
C – C sharp augmented unison
C – D flat diminished 2nd
C – D minor 2nd
C – D sharp major 2nd
C – E flat minor 3rd
C – E major 3rd
C – E sharp augmented 3rd
C – F flat diminished 4th
C – F perfect 4th
C – F sharp augmented 4th
C – G flat diminished 5th
C – G perfect 5th
C – G sharp augmented 5th
C – A flat minor 6th
C – A major 6th
C – A sharp augmented 6th
C – B flat minor 7th
C – B major 7th
C – B sharp augmented 7th
C – C flat diminished octave
C – C perfect octave
C – C sharp augmented octave

 

Doubly diminished and doubly augmented intervals also exist

(eg C-G Double Flat (double flat),  C-G Double Sharp (double sharp)) but are rare.

Note that some intervals are enharmonically (notes at the same pitch with a different name) equivalent to each other – for example an augmented 4th and a diminished 5th are both 6 semitones apart, just as the names F sharp and G flat are both the same note (dear purists – we are talking equal temperament here) .

How to recognise intervals by ear

If you memorise the first 2 notes of these melodies you will be able to identify intervals when you hear them.

Rising Falling
Minor 2nd -“Something’s Coming” (Bernstein, West Side Story) -Joy To The World
Major 2nd -“I’ve Got You Under My Skin” (C. Porter)-Happy Birthday -Yesterday (Beatles)
Minor 3rd -Greensleeves -“I’m Leaving on a Jet Plane”
-Hey Jude-Frosty The Snowman
Major 3rd -“Michael Row the Boat Ashore”-Oh When The Saints (Go Marching In) -“Summertime”
Perfect 4th -“Here Comes the Bride” (Wagner)
-“Auld Lang Syne”
-Hallelujah (Handel)
Augmented 4th / Diminished 5th -“Maria” (Bernstein)
-“The Simpsons”  (1st and 3rd)
Perfect 5th -Twinkle Twinkle Little Star-“God Rest Ye Merry Gentlemen” -Theme from Swan Lake (Tchaikovsky)
-“Flintstones”
Minor 6th -Theme from Love Story (Mancini?)
Major 6th -“My Bonnie Lies over the Ocean”
Minor 7th -“Somewhere” (West Side Story)
Major 7th -“Somewhere Over the Rainbow” –(1st and 3rd)
Octave -“Somewhere Over the Rainbow”

 

I think that’s enough for now. More advanced theory for the brave will follow in future posts. 😉

 

 

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