In teaching any students, but especially beginners or when teaching music by ear, it is very useful to be familiar with scales and arpeggios. These patterns help us group notes so that we don’t have to think about each note individually.
For beginners, scales help confirm what it means to play “up” and “down” from one note to another. It’s amazing sometimes how long it takes for some beginners to feel comfortable with “up” and “down”, especially adults who sometimes second-guess themselves.
But there are more scales out there than we usually think about, and they can be useful for students of all levels. For example, beginners can easily work with pentatonic scales, which limit the number of notes they have to work with while still yielding beautiful melodies. Advanced players can certainly benefit from a familiarity with pentatonic scales as they create moods from major pentatonic with a country sound, to the minor pentatonic with its bluesy feel.
The major pentatonic is generally notes 1,2,3,5,6 of the major scale, while the minor pentatonic uses the same notes starting on relative minor, resulting in notes 1,3,4,5,7 of the minor scale.
But that’s only a beginning. Classical major scales, and the melodic and harmonic minor scales are essential learning because they are so commonly used.
Then there are the modes, which may seem to arbitrarily start on different notes of the scale, but also happen to represent common scales from different cultures. They can sometimes be best understood in this cultural context rather than as musicological theory. For example, what musicologists may call a mixolydian mode (major with flat seventh) is what Scottish musicians simple consider their major scale. Their minor scales is what theorists call the phrygian mode.
Other patterns are harder for musicologists to label. For example there is the Celtic pattern of switching regularly between one key and the key directly below, or above, which I call a double-tonic key. One of the common modes in klezmer music can be recreated by playing a melodic minor scale, but using the 5th note as the root–in other words, starting out with a half step followed by a step and a half.
I was once roped into being a subject in a music experiment while I was working in an office at MIT. They wanted to know the reactions of western musicians to hearing various modes used in music of India. I was astonished at how many combinations of scales they make use of, none of which were typical major or minor patterns.
Jazz certainly expands one’s vocabulary, regardless of one’s instrument. Pentatonics are often used, and other scales such as whole tone scales. I find it an adventure for ears and fingers to play diminished scales, which alternate whole and half steps, and figure out how to finger them. Some day I’ll learn how to use them!
Maqams are decorated scale patterns used in middle Eastern and north African music, which I don’t know enough about to describe, but hope to learn more about some day.
Regardless of the type of music being taught, opening students (and yourself as teacher) up to the possibilities of new scales patterns, and their associated arpeggios, can stretch a musician’s vocabulary, provide valuable finger training, and help train ears to listen more intelligently to a broader range of music.