An Effective Way to Train the Mind’s Ear

By Hans Jørgen Jensen

Why do we need to understand theories about intonation?

People often ask me why, as musicians, do we need to know and understand the theories behind intonation as well as the technical details of intonation such as cent size, numbers of the different intervals and multiple tuning systems? 

Great intonation is controlled by the ear and mind

My answer is always this: Great intonation is 100% controlled by the ear and the mind and the knowledge of the theories about intonation is only useful and helpful if it is used as an ear training tool. If you are a first-rate string player, your musical intuition and technical control are so highly developed that you really don’t need to know more about intonation than you already do. People with great intonation have highly developed intuitive listening skills. Through careful listening and application of intonation theories anyone can develop a more refined control of intonation in both solo and ensemble playing. 

String players with intonation problems

There are several reasons why musicians might have problems playing in tune. We will explore these reasons through two hypothetical performers. 

1. Performer no. 1 does not have a very sensitive ear and is not able to distinguish the fine details of intonation.

2. Performer no. 2 has fine listening skills and, when concentrating, can distinguish where the pitches should be placed on the instrument to play in tune. However other issues are getting in the way.

Use the information as great ear training

For performer no. 1 learning about and gradually integrating intonation theories into practice is a great way to improve their ability to discern fine tuning details.  This is especially true when the intonation is actively incorporated as an ear training tool during practice. A knowledge of intonation theories can additionally expand a teacher’s approach to teaching intonation to students of all levels.

Make sure to concentrate when practicing

Performer no. 2 needs to start using their inner and outer hearing much more when practicing, making sure that they always place their fingers where their intuition tells them that the pitches should be. They also need a higher level of self-critique.

For performer no. 2 the problem can also be that they don’t hear the sound that comes out of the instrument but instead think that what they hear in their mind is the real sound.

Therefore, when they play everything seems ok because they block out the real sound of their instrument by allowing what they hear in their mind to overshadow the real sound from their instrument. When I have students with that problem, I spend time in the lessons having them record themselves and then listen back to the recording.

Blaming the left hand

When students have intonation problems, they very often don’t realize that the problems come from their inability to distinguish the right pitch with their mind’s ear. Having a sense of hand shape and spacing of the fingers is also a factor to a certain degree. When a great player picks up a different size instrument than they are used to, they are immediately able to play in tune. That ability is 100% controlled by the ear and the mind. 

The real reason I decided to write CelloMind and ViolinMind

Over many years of teaching, I have searched for the best way to teach intonation to students that have less than great listening skills. When I work with students that have great inner and outer hearing, I don’t talk to them about intonation theories unless in the context of a pedagogy class. Realizing that teaching students to understand theories about intonation and using that as an ear training tool was the answer to intonation problems has given me an incredible teaching tool and additionally great joy and satisfaction! I have personal observed numerous instances where that knowledge of intonation, when incorporated with the ear, has made a tremendous difference in a student’s playing ability.

The three intonation theories don’t fit under one theory

People often think that understanding the theory behind intonation is difficult, so they use that as an excuse for not learning about it. With some patience and careful study, the theory about intonation is not too difficult to learn. Most importantly, appreciating the inherent value in understanding intonation makes the learning process more effective and enjoyable. One thing that often makes learning about theory difficult is the fact that there are several distinct intonation systems: Just Intonation, Pythagorean intonation and equal temperament are three tuning systems that string players use most often and they don’t fit together under one rule. People with great intonation move between the systems all the time without even being aware of it.  Here is the most basic example: When playing a C major melodic scale, the third (E-natural) is the higher melodic E-natural that has a natural gravitational pull up to the perfect fourth (F-natural). When tuning the E-natural to the G string it is necessary to lower it to tune with the C string. Here is the same example for violin except it is in G major. 

The four fundamental forces of the universe

With this understanding, a parallel can be drawn to the four fundamental forces of the universe: (Gravity, the weak force, electromagnetism, and the strong force). These four forces govern everything that happens in the universe although they don’t fit together under one theory. A theory of everything (TOE) is a hypothetical framework explaining all known physical phenomena in the universe. Researchers have searched for such a model ever since the development of quantum mechanics and Albert Einstein's theory of relativity in the early 20th century.

The incredible importance of the sensitive and discriminating ear

One day when teaching a class at the Meadowmount school of music, a young student Matt Allen (16 years old) gave a comment where he mentioned aspects of another person’s performance that I had not noticed. I asked him more follow-up questions and it was immediately clear to me that Matt’s level of hearing was much more sophisticated and developed than most of the other students’. Matt was also one of the best talents at the school. After that experience it became clear to me that the better we want to play the more do we need to push our ability to perceive and listen at the highest level.

Using theory to train the mind’s ear

When training the mind’s ear it is important to distinguish between what we imagine in our mind’s ear and what we hear from outside sources. A very basic way to train the ear is to play the harmonic E-natural on the cello in the fourth position on the A string (On the violin it is the B-natural a fifth above the open E string) and then press the string down and make sure it is the same note (It is of course one octave lower compared to the harmonic). People with less than great ears have difficulty matching the two pitches. I always point out that the solid note is a bit lower on the fingerboard closer to the nut than the harmonic. The higher the string is above the fingerboard the lower the solid E should be placed on the string to match the harmonic E, because the more we stretch the string the higher does the pitch go. Practicing this exercise is a sample of a very simple exercise that can help train the ear to be extremely precise in telling the difference between two pitches. Happy tuning, and happy practicing!