What is a Musical Intervals?
Beyond the numerical names (size) (αριθμητικό μέγεθος ή γένος) of musical intervals, which show the distance between two notes, we can see that a C-E sounds different from a C-Eb. (You can find these in Chapter 1). This happens because they have a different number of tones and semitones. This difference in the relationship between the top and bottom notes is called the quality (modifier, είδος) of the interval.
To put it simply, the size is the numerical distance between the first and the last note, based in the diatonic scale. However, the quality is determined by the total number of tones and semitones found within that distance.
Interval Classification: Simple vs. Compound
When discussing the size of an interval, we seperate them into two main categories.
First, Simple Intervals (απλά διαστήματα) are those that do not exceed the distance of eight notes (octave): 1st, 2nd, 3rd, 4th, 5th, 6th, 7th and 8th
On the other hand, Compound Intervals (σύνθετα διαστήματα) are formed by an octave plus a simple interval. Theυ include the 9th, 10th, 11th, 12th, 13th, and so on.
The Five Qualities of Intervals
The quality of an intervals is determined by the specific number of tones and semitones they contain. These qualities are categorized as follows:
- Perfect Intervals (Καθαρά)
- Minor Intervals (Μικρά)
- Major Intervals (Μεγάλα)
- Diminished Intervals (Ελαττωμένα)
- Augmented Intervals (Αυξημένα)
It is important to note that while all intervals can become augmented or diminished, they cannot belong to both Perfect and the Major/Minor groups simultaneously. For instance, if an interval is classified as Perfect, it cannot be Major or Minor.
Furthermore, an augmented interval is formed when a Major or Perfect interval is increased by one semitone. Converselt, a diminished interval is created when a minor or Perfect interval is decreased one semitone.
First (Unison), Second, and Third Intervals
The Unison (or first) interval is essentially the repetition of the same note. A Perfect Unison is described as two notes with the exact same pitch, meaning there is zero distance between them. However, when the top is raised by a sharp, it is considered an augmented unison. Conversely, if the top note is lowered by a flat, it is called a diminished unison. The opposite rule applies when the bottom (bass) note is altered.
PS: In some music theory books, the unison (1st) is not categorised as a diminished interval. It is only classified as Perfect or Augmented.
Furthermore, second and third intervals can have four different qualities. For natural diatonic (notes), these intervals are categorised as minor if they contain a natural semitone, E-F and B-C. If no natural semitone is present, they are characterised as major. It should be noted that this specific rule applies only to natural and changes when accidentals (sharps or flats) are used.
Fourth and Fifth Intervals
In music theory, all fourth and fifth intervals are categorised as perfect, meaning cannot be classified as major or minor. However, two notable exceptions exist: the augmented fourth (F-B) and diminished fifth (B-F).
This occurs because most fourths and fifths contain exaclty one natural semitone. In contrast, the F-B interval consusts only the whole notes, making it larger (augmented), Conversely, the B-F interval contains two natural semitons, which makes it smaller (diminished_ than a standard perfect fifth.
(Caution: It must be noted that these rules apply specifically to natural notes. When accidentals (sharps or flats) are added, the quality of the intervals is altered accordingly.
Furthermore, if you are interrested in music hostory, you can read about the “Devil’s Tritone” (Diabolous in Musica). This specific interval contains three whole tones and was historicalle avoided or “forbidden” due to its intense and dissonant sound.
More info:
Sixth and Seventh Intervals
When discussing sixth and seventh intervals, we return to the categories of major and minor, as these intervals cannot be classified as perfect.
Similar to seconds and thirds, their quality is determined by the number of natural semitones the contain. For natural (diatonic( notes, a sixth or seventh is considered minor if it contains two natural semitones. Conversely, if the interval contains only natural semitone, it is characterized as major.
As previously mentioned, it must be noted that these rules apply to natural notes. If accidentals are added, the number of tones and semitones changes, and the interval quality is altered accordingly.
The Octave (8th Interval)
Finally, we reach the octave, which is the distance between two notes with the same name, such as C to the next C above it. Similar to the unison, fourth, and fifth, the octave is classified as a Perfect Interval.
In its natural state, a Perfect Octave consists of exactly twelve semitones (six whole tones). It is characterized by its clear and stable sound, as the two notes vibrate in a 2:1 ratio.
However, if the top note is raised by a sharp (#), an augmented octave is created. Conversely, if the top note is lowered by a flat (b), it is considered a diminished octave. As previously mentioned, these qualities are altered whenever accidentals are applied to either the top or the bottom note.”
Intervals in the Melody: Steps, Skips and Leaps
When intervals are used within a melody, they are categorises as steps, skips, or leaps based on their size. This classification describes the specific melodic motion of the music.
- Steps (Βήματα) (Conjunct Motion-Συνεχής)
Intervals of a second are defines as steps. This type of movement is called conjuct motion (or stepwise motion) because the notes follow each other consecutively, sucj as C-D-E. Alhtough some music theoet textbooks classify diminished/doubly diminishes thirds as conjuct due to their sound (1 tone or 1 semitone), they are traditionally viwed as skips in formal theory.
- 2. Skips and Leaps(Πηδήματα) (Disjunct Motion-Αφεστώτα)
When an interval is a third ot larger, the movement is called disjunct motion. This occurs bacause at least one note in the scale is “skipped” over.
- Skips: An interval of a third is typically called a skip because exactly one note is left out. For example, C to E skips note D.
- Leaps: Ant inteval larger that a third (such as a fourth, firth etc.) is classifief as a leap. In a leap, multiple notes are skipped between the base and the top note. For example, C to G.
- 3. Chromatic Motion (Xρωματική Κίνηση)
Finally, chromatic motion is ebserved when a melody moves by chromatic semitones (notes with the same name but dufferent accidentals, like G to G#). This type of movemtn is used to form the chromatic scale and adds a unique color to the melody.
Conclusion: Summary of Melodic Motion
Steps (Conjunct Motion): These are intervals of a second (2nd). They are described as consecutive notes, such as G to A.
Skips (Disjunct Motion): This term is used for interval of a third (3rd). A skip occurs when one note is bypassed, such as G to B (skipping A).
Leaps (Disjunct Motion): Any interval larger that a third is classified as a leap. This motion is created when multiple notes are skipped between the base and the top note, such as G to D.
Interval Inversion
Interval inversion (αναστροφή διαστημάτων) is a process in music theory where the lower note (base) is moved an octave higher to become the top note, or the top note is moved an octave lower to become the base.
The Rule of Nine
When an interval is inverted, a specific mathematical relationship is observed: the sum of the original interval and its intersion always equals 9. This occurs because the shared note between the two ontervals is counted twice.
The numerical changes are categorized as follows:
- A 1st (Unison) becomes an 8th (Octave) (1+8=9)
- A 2nd becomes a 7th (2+7=9)
- A 3rd becomes a 6th (3+6=9)
- A 4th becomes a 5th (4+5=9)
- A 5th becomes a 4th (5+4=9)
- A 6th becomes a 3rd (6+3=9)
- A 7th becomes a 2nd (7+2=9)
- An 8th (Octave) becomes a 1st (Unison) (8+1=9)
Changes in Interval Quality
Furthermore, the quality of the interval is also transformed during inversion, with in a notable exception: Perfect intervals always remain perfect. For all other qualities, the opposite is applied.
| perfect intervals | remain | Perfect |
| Minor intervals | become | Major |
| major intervals | become | Minor |
| Augmented intervals | become | Diminished |
| Diminished intervals | become | Augmented |
Compound Intervals
Compound intervals (σύνθετα διαστήματα) are defined as intervals that are larger that a single octave. Special attention should be paid to their naming, as that can be described in two different ways.
For instance, a 9th is formed by an octave plus a 2nd. This can also be referrd to as a compound second. Furthermorem. 10 th is created by an octave plus a 3rd and its often called a compound third.. Essentially, the term “compopund” is added to the name od the simple interval that exists beyond the octave.
How to Identify Compound Intervals
A compound interval is easily found by moving the loiwer note uo an octave and identifying the remaing simple interval.
For example, if a note is moved and the remaining distance is a perfect fourth, the otginal compoind interval is identified as a perfect 11th (8+4=12, BUT we substract one because the overlapping note is countd once.)
| Name | Degrees | Composition |
| 9th | 9 | Octave+Second |
| 10th | 10 | Octave+third |
| 11th | 11 | Octave+fourth |
| 12th | 12 | Octave+fifth |
| 13th | 13 | Octave+sixth |
| 14th | 14 | Octave+seventh |
| 15th | 15 | Octave+octave |
Enharmonic Intervals
Ehnarmonics Intervals
To inderstand enharmonic intervals, it is helpful to first review the basic definition of enharmonics. In music theory, ehnarmonic notes are fenined as two consequetives notes that have differnent names but ptodice the exact same sound (e.g. C# and Db)
Similarlt, ehnarmonic intervals are intervals that share the nymber of tones and semitones. Ehule they sund identical when played on an instrument like. thepiano, they are written with a different notation and given differnet names.
For example, an augmented fourth (F-B) and a diminished fifth (F-Cb) are considered enharmonic. Although the physical distance on the keyboard remains the same, the musical context and the way they are identified in a score are distinct. By recognizing these variations, the complex structure of a musical piece can be more accurately analyzed.