As I mentioned last week I am writing a series of posts (accompanied by You Tube videos) geared toward musicians who desire to learn the basics of musical notation. In last week's post one of the topics we discussed was the musical distance of a half step and a whole step. In real music, the distance between pitches can extend beyond a whole step. There is a musical unit of measure that we use to measure the distance between pitches. That unit of measure is an interval, and it is the topic of today's discussion.
As we mentioned last week, there are seven letters in the musical alphabet. When measuring distances between these seven letters, we count the starting letter as one and then count our way to the destination letter. So, the distance from A to C would be a third, because we count A as one, B as two and C as three. This graphic helps to demonstrate all of the intervals between the seven letters of the alphabet.
We can count the same way on the musical staff. Every line and space on the staff represents a letter. We count the starting note as one, and then continue to count the lines and spaces up to (and including) the target note to determin the interval. This graphic displays the musical intervals of one cycle of letters from C to C.
If you notice, that last graphic included an interval of an 8th. Remember that the musical alphabet is a seven letter cycle that repeats back to A. Since the letters repeat in a cycle, the interval of an 8th will always be a repeat of the letter you started on. It is not an identical match of the starting pitch (which is called a unison). It is the same letter in a higher or lower register.
When two pitches are sounded at the same time they create harmony. Harmonies that are pure and free from discord are called consonant. There are two types of consonence in music, perfect and imperfect consonence. The perfect consonent intervals in music are the unison, perfect fourth, perfect fifth and octive. The imperfect consonences are thirds and sixths. Harmonies that are discordant or clashing are called dissonant. The dissonant intervals in music are seconds and sevenths.
The pairings of numbers mentioned in the last paragraph have an interesting relationship. Each pair (2&7, 3&6, 4&5) are inversions of each other. An inversion is the flipped version of an interval. If a person plays a C and the E directly above it, this is the interval of a third. If you then change the order of these two pitches by playing the E below the C (instead of the one above) you are playing the interval of a sixth. You are still playing the same two pitches, but you have flipped the order of the pitches. The same is true when flipping a second into a seventh, or a fourth into a fifth.
Consonance and dissonance are used as tools by composers to create tension and release. Any form of good entertainment (a book, a movie, a sporting event, a piece of music, ect.) will contain conflict that builds twoard a climatic moment and then resolves. In music, this is accomplished by having dissonance resolve to consonance. There are other tools used to compose great musical climaxes, but the most basic elements are dissonance and consonance.
Unfortunatly, musical intervals are not always just simple numbers. Remember, there are actually 21 different pitches in music due to the sharps and flats. This means that there are variations on each number when pitches are raised or lowered. The unison and octive cannot be altered at all. Once these distances are changed they are no longer a unison or octive. The other perfect consonent intervals can be shortened (diminished) or lengthened (augmented).
diminished 4th / perfect 4th / augmented 4th
diminished 5th / perfect 5th / augmented 5th
Imperfect consonent intervals and dissonant intervals have two versions, major and minor. In addition, they can also be diminished or augmented.
diminished 2nd / minor 2nd / major 2nd / augmented 2nd
diminished 3rd / minor 3rd / major 3rd / augmented 3rd
diminished 6th / minor 6th / major 6th / augmented 6th
diminished 7th / minor 7th / major 7th / augmented 7th
All of these interval names can get confusing. Remember the principal of enharmonic equavlince from last week's post. Every sharp pitch can also be identified by a corrisponding flat (or in some cases natural) name. This means that many of these interval names overlap each other. A diminished 2nd, for example, is the same thing as a unison. An augmented 4th is the same thing as a diminished 5th. However, if you were measuring the distance from C to F#, you would call it an augmented 4th. If you were measuring the distance from C to Gb (same pitch as F#), you would call it a diminished 5th.
Some of the other examples, like the diminished 2nd mentioned above, occure rarely. For this to take place, you would have to be measuring the distance between a C and a D double flat. The term double flat means that you have lowered the pitch two half steps instead of one. These types of musical concepts are too complex for this basic discussion, so we will leave them for a future date. The most common musical intervals are listed in this figure.
This concludes our discussion on musical intervals. Please refer to the attached video for further understanding. I also provide private music instruction online. Private lessons can be booked from this
Ray Melograne received his BA and ME in music education from Queens College. He is currently teaching music in the NY public schools. He also teaches privately on the Zoen.com network.