Which one of us did not feel the sorrow and tragedy in Chopin's first Piano Concerto? How about the energy and shadow felt at Beethoven's mighty 5th Symphony? When it comes to anxiety and mysticism, who can beat the 4th movement of Mahler's 1st Symphony? Mozart, a man of sheer joy and happiness may present you his cheerful Rondo (K.485) or his upsetting Adagio (K. 540) full of despair.
So what exactly makes us to feel those emotions? Is it only the dynamics of playing, either soft or loud, or the keys they were composed, major or minor? Welcome to the world of intervals.
What is an Interval in Music?
An interval in music is defined as a distance in pitch between any two notes. The larger the interval between two notes, then the greater the difference in pitch between the notes. Semitones and tones or half steps and whole steps, are the building blocks of intervals.
The smallest possible interval is a semitone, or in the US it's called a half step. A semitone is the very next higher or lower note. For example, from E to F or from C to C sharp (C#) on a piano keyboard. (Exhibit-1)
A tone or 'whole step', therefore, is an interval of two semitones. (Exhibit-2)
When measuring vertically, we refer to harmonic intervals because the two notes sound simultaneously. When measuring horizontally, we refer to melodic intervals because the notes occur one after the other. (Exhibit -3)
Names of the Intervals
Leaving interval quality (major/minor) aside, we will focus on the numerical size of intervals. In simple terms, we count the semitones between the two notes for numeric identification. Here are some examples for better understanding:
Exhibit-4 shows us the distance between note C and E. We count as C(1), D(2) and E(3). So this is a 3rd with 4 semitones in between. This makes our interval a Major 3rd (Minor needs to have 3 semitones). Exhibit-5 demonstrates the intervals with examples for your use. For those who are unfamiliar with piano, C4 shows the middle C on piano keyboard. Rest of this article will analyze the mood of every melodic interval with examples from repertoir.
Intervals of Joy
In line with above mini course in harmony, let us try to analyze the opening of Mozart's Rondo in D major and try to reveal cheerful intervals hidden in the score. (Exhibit-6)
Starting immediately from the downbeat (1st note) of the first measure, this piece is full of energy and childish joy. Let us start with breaking down the D major key into a scale and a chord: (Exhibit-7)
Now we can start our basic harmonic analysis of the piece and notate major intervals: (Exhibit-8)
Mozart's Rondo starts with the D Major chord (harmonic interval) and each member of the chord circled in red: D-Tonic, F#-Mediant, A-Dominant
Melody in the first measure leaps from A to D, summing into 7 semitones likewise another 7 semitone leap from G to C as noted in the second measure. This gives us the Perfect 5th (P5) interval which sounds stable and cheerful. As per Willems (1977) the sensorial value of P5 is balance, affective value is calm and intellective one is certainty.
Intervals of Doubt and Fracture
Let's continue with Mozart and review his Adagio in B minor (Exhibit-9)
As usual, first we should break down the B minor key: (Exhibit-10)
Now we can start our basic harmonic analysis of the piece and notate major intervals: (Exhibit-11)
The first three notes of the first measure is composed of B minor chord elements: BDF# as you notice. Mozart starts with a B and leaps to note F# which makes 5 semitones. Therefor our first interval is a Perfect Fourth (P4) which express hardness and cold. From F# to D we count 8, a minor sixth (m6) interval famous for its upsetting and worrying attributes. Chords highlighted with rectangles have 6 semitones, namely diminished fifths (d5). They resemble instability, anxiety and uncertainty. Mozart's Adagio is what you can get from P4+m6+d5 equation. Take a listen.
Intervals of Tragedy and Sorrow
E minor Concerto of Chopin is a tailor made example for this interval type. Exhibit-12 shows the mournful opening of the piece:
E minor chord consists of notes E, G and B. (Exhibit-13)
Now we can start our analysis of the opening passages as shown in Exhibit-14:
The notes of E minor chord was distributed to the strings at the opening first two measures as seen. The melody line (first staff) starts with a B and then leaps to E by taking 5 semitones which forms a perfect 4th (P4). This interval is mild dissonant and evokes vague, somehow cold sensation. Then comes D# and we climb 8 semitones to stop in B again. 8 semitones corresponds to minor 6th interval, known as upsetting, melancholic or worrisome. At the last measure with diminuendo, we descend 3 semitones from G to E, namely a minor 3rd which is full of lament and sorrow.
Another E minor beauty?
Well, how one can forget about beautiful opening of Brahms's first cello sonata in E minor. He did not write something very special but just broke down the E minor triad itself (Exhibit-15)
Now you should be able to analyze your favorite music and try to match the intervals with relevant emotions. There is an interesting research done in Florida International University by Julian Zuluaga and Cengiz Kaygusuz related with “Impact of Intervals on the Emotional Effect in Western Music”.
360 passages were analyzed by 12 experts and 116 university students. Below find the results: (Exhibit-15 & 16)