Ear training is very important for string players. With no frets, keys or valves to help us know where we are on the fingerboard, we are often almost as dependent on our aural skills as singers are. Being able to sing our cello parts is a very useful fundamental musical skill as well as a help to both our cello-playing and our music-reading. This skill is especially necessary in the higher fingerboard regions, because in the lower (Neck and Intermediate) regions we have more visual, mechanical and kinesthetic references to help us to know where each note is on the fingerboard. This means that often, in those lower regions we don’t actually need to sound the notes in our imagination beforehand in order to know where they are on the fingerboard (see Positional Sense).
Therefore, it is especially in the Thumb Region, and most especially for larger shifts up into this region, that we usually need to have a very clear idea of the pitch of our target note, before the shift, in order to be able to do the shift with security. In other words, we need to be able to hear the arrival note (or the “Intermediate Note” in the case of Assisted Shifts) in our imagination before we start the shift. This requires good aural skills (ear training). For most shifts in (and into) the Thumb Region we must find the notes almost exactly like a singer: “by ear” (with no concrete physical external reference points to help us).
Certain intervals and series of intervals are easy to imagine with our inner ear: octaves and simple scales for example. But others are more difficult, and it is these more complex intervals and patterns that we need to work on, not initially at the cello but rather just with our inner ear: singing aloud, or singing silently in our imagination. Even some very common intervals and interval patterns can actually be quite difficult to imagine. We will look at these below.
In the same way that it helps us to better understand complex numbers if we break them up into their components (758 = [7 x 100] + [5 x 10] +[8 x 1]) we can often understand (and thus hear) complex intervals better if we “construct” them from their basic simple component intervals. For example, the diminished 7th interval is made up of 3 minor thirds piled on top of each other, while the diminished 5th is composed of two of these minor thirds.
Sometimes, especially for large intervals, rather than building an interval up from its components it is easier to find it aurally as a simple subtraction or addition from an easily found aural reference point. In the same way that the number 999 is easiest to understand as 1000 minus 1, a major seventh is usually easiest to hear as an octave minus 1 semitone, and a major 9th as an octave + 1 tone.
In the above example, our imagining of the major 7th interval is made more difficult by the notation. Mixing sharps and flats in the same passage is like mixing up two different languages in the same sentence. It certainly makes the reading of the intervals much more complex and confusing. For more discussion of Reading (Notation) Problems click on the link.
We need to become perfectly accustomed to the different manifestations and fingerings of common intervals and interval patterns. The most difficult intervals for us to hear (imagine) are usually difficult either because of their large size or because of their “strangeness” (the most atonal or harmonically radical ones). Let’s look in more detail at some of these now. Click on the highlighted links for practice material (exercises and repertoire excerpts). We will start with the smallest intervals and work upwards.
SEMITONES: CHROMATIC SCALES
Unless they go quite slowly we will not be able to control (imagine) every note of a chromatic scale (see Control – Overcontrol). We need instead to have just a few reference points during the scale. These reference points will be determined almost certainly by the rhythm, and will probably be the notes that fall on the strong beats. Sometimes this makes our job easy, as in triplet rhythms which divide a chromatic scale into a series of minor thirds, giving us the diminished 7th arpeggio:
When however a chromatic scale comes in binary groupings, then the octave is made up of 3 major thirds (instead of 4 minor thirds). This is much harder for us to hear with our inner ear, especially when the shifts don’t coincide with the strong beats.
Regular chromatic scales do not pose a reading problem, because we know that every interval is a semitone. Irregular chromatic passages do however often pose serious reading problems, because we need to decode each interval separately. Click on the highlighted link for more about this.
We are normally so used to the major and minor scales that they do not present us with any aural difficulties: we can sing them up and down with absolutely no problems. Other more unusual scales (modes) require more work (practice) to feel familiar. We normally practice/sing our major and minor scales starting on the tonic. If we practice starting them on other notes of the scale then we will be effectively accustoming ourselves to all the different modes.
THE MINOR THIRD AND DIMINISHED SEVENTH CHORDS
The minor third is normally an easy interval to imagine even in the most difficult harmonic circumstances, and it is often an extremely useful interval with which to break up (subdivide) larger complex intervals. For example, the minor third is the most tonally-useful common denominator of the octave. Whereas an octave divided in half gives two augmented fourths (or diminished fifths) which can be quite hard to imagine with our inner ear, the octave divided into quarters gives four minor thirds, which are very easy to imagine. So in any series of consecutive minor thirds, the fifth one will be the octave of the first one.
While semitones and tones are the building blocks of all our different scalic progressions, with the minor third we make a quantum leap into the totally new world of harmony. The minor third is a basic harmonic building block, not only of the major and minor chords, but also of the important diminished seventh chord, which is composed of three minor third intervals piled on top of each other. This chord is both very expressive and extremely versatile: by lowering any one of its notes by a semitone, that new note becomes the bass of a dominant seventh chord, permitting a modulation. This makes it a very popular, much-used harmonic and melodic device, so we really need to have its intervals very well ingrained into our ears. On the cello we have two basic standard diminished seventh chord configurations across three strings. These can be moved all over the fingerboard:
Sibelius writes us a little study for these two finger configurations in his Third Symphony:
Here below are links to practice material featuring these useful and important piles of minor thirds:
Diminished Seventh Chords: EXERCISES Diminished Seventh Chords: REPERTOIRE EXCERPTS
AUGMENTED FOURTHS/DIMINISHED FIFTHS
Although these two intervals are exactly the same distance apart, we “hear” them differently, in the sense that the “intermediate notes” (those occurring between the starting and finishing points) are quite different for the two intervals. We will normally hear the diminished 5th as the sum of two minor thirds, whereas to hear the augmented fourth we will probably use the whole tone scale as stepping-stones:
THE DIMINISHED SEVENTH INTERVAL
The diminished seventh interval is a curious one because not only does it sound the same as the major sixth, it is also normally notated identically. So why is it called a diminished seventh? ….. because just like for the above example (the augmented fourth and its identical diminished fifth), we hear the two identical intervals differently. In imagining the major sixth we will use quite different aural stepping-stones to the layered minor thirds that we will use for the diminished seventh.
MINOR SEVENTH INTERVAL (AND DOMINANT SEVENTH ARPEGGIOS)
We can “hear” (find) this interval in two main ways:
- by imagining a note one octave higher, and then going down a tone, or
- by imagining the stepping-stones of the dominant seventh arpeggio (major third + two minor thirds)
FINDING THE BASIC INTERVALS IN A COMPLEX PASSAGE
Often a quite simple passage can be made to seem more complex than it really is due to the presence of chromatic “ornamentations” which produce some strange (hard-to-sing) intervals. It helps a lot in learning these passages if we can see and practice the underlying basic interval structure.
And here is another repertoire example of this procedure, this time with a diminished 7th chord as the basic structure that we need to hear:
A knowledge and awareness of the harmony underneath an awkward interval or passage will usually help us to better hear it with our inner ear (and thus find it on the fingerboard). Very often it is only when we can imagine (or hear) the harmonic accompaniment, that the melodic interval will suddenly make musical sense.