An Introduction to Chords in Music
This post is a diversion from Bowing Technique 101, which will continue soon. I recently gave an introductory harmony lesson and thought I’d share it here. Although this does not relate specifically to cello playing, I have always found that an understanding of harmony and chords greatly enhances the study of any repertoire, especially when it comes to the interpretive stage of learning the music.
This lesson deals with the triads and seventh chords found in the key of C major. The chord labels (based on the baroque system of figured bass or Basso continuo) are relevant to the triads and seventh chords of all major keys, making it a wonderfully diverse system. As the building blocks of music harmony, chords are best studied in their simplest form in order to understand their use in music. So without further ado, I present to you An Introduction to Chords in Music!
Published by Deryn Cullen
Composer, cellist, cello tutor and writer View all posts by Deryn Cullen
Doublestops and Chords
This article is concerned uniquely with the left hand. For bowing factors in chords and double-stops see the String Crossings (Bow-level Control) section in Bow Technique. To avoid (or postpone) reading this detailed analytical discussion and go straight to some practice material click here:
Doublestops For the Left Hand: Practice Material Chords For the Left Hand: Practice Material 4-String Chord Library
ONE CHORD = TWO (OR THREE) DOUBLESTOPS
We are treating Chords and Double Stops together here because both require the highly developed skill of simultaneously operating different fingers on different strings. This specific branch of lefthand technique is discussed at its most basic level in the article “Left Hand String Crossings” in which we talk about our left hand’s “horizontal” positional sense” (knowing where our fingers are across the different strings). Playing chords and double-stops represents possibly the ultimate level of achievement for this skill.
We can consider double stops as a preparatory step for chords. Whereas doublestops involve only two strings at a time, chords involve three or four strings so, before looking at chords, we will start with a discussion of double-stops. But before jumping into “double-stops” however, we need to take a moment to decide just what is (and isn’t) a double stop.
IS IT A DOUBLESTOP? THE CONCEPT OF “BROKEN” DOUBLESTOPS.
The definition of a “doublestop” is not quite as simple as it may seem, because a doublestop for the left hand is not always a doublestop for the bow (and vice versa). Sometimes something that sounds like a doublestop (sounding two notes at once) is not one, while a passage in which only one note sounds at a time might be constantly in doublestops. This is because the word “doublestop” refers to the left hand’s actions and not to the sounds that we are making. Smoke coming out of your ears? Yes, probably! So let’s use some musical examples, which will make this concept immediately simple and clear:
In the first line of examples there are no “written out” doublestops: in other words, the bow is only ever playing on one string at a time. In spite of this however, our left hand is in fact playing doublestops all the time, because it is working simultaneously (stopping) on two adjacent strings. We will call this situation “Broken Doublestops”. The second line of examples illustrates the opposite situation. Here, although the bow is playing on two strings simultaneously, the left hand is in fact only ever playing on one string at a time, because one of the strings in the “bow doublestop” is always an open string (which obviously doesn’t require the left hand to stop it). Below, we have written out what our left hand is actually doing in each of the above examples:
Here is another repertoire example of a passage in “broken doublestops”, in which we can see very clearly that the left hand is playing constantly double-stops while the right hand is doing its fancy dance across two strings but only ever playing on one string at a time.
To summarise: just because our bow might be playing on two strings simultaneously doesn’t mean that we are playing “doublestops”. And likewise, just because our bow might only be playing on one string at a time doesn’t mean that our lefthand might not be playing doublestops. No matter what the bow is doing, if our lefthand is working on two strings at the same time, then we are playing “doublestops”!!
Using broken doublestops to practice a doublestopped passage is often a very useful idea. Likewise, practicing broken doublestopped passages as “real” doublestops is often a very good idea. These subjects are looked into in more detail below, in the section dedicated to “Practicing Doublestops”.
SHIFTING TO A (BROKEN) DOUBLE-STOP: PLANNING AHEAD
Surprisingly often, it may be convenient to shift to a double-stop with our left hand even though there are no double-stops in the music (yes, this is the definition of a broken double-stop). In this way, we use the shift as an opportunity to get our left hand “in position” on both strings, in order to prepare it for a rapid string crossing that comes after the shift. This technique is especially useful when that rapid string crossing also involves an extension. This is best illustrated with some examples:
BROKEN DOUBLE-STOPS: DO WE MAINTAIN THE FINGER PRESSURE PERMANENTLY ON BOTH STRINGS?
When playing “real” double-stops we have no choice: we must maintain the finger pressure permanently on both strings. However, in broken double-stops – fortunately – we can choose what we want to do with the finger(s) which is not sounding. We have three possibilities:
- maintain the pressure
- relax it but maintain the string contact
- release it entirely from the string and then rearticulate when needed again
The following example illustrates these different possibilities:
Maintaining constantly the finger pressure of the non-sounding finger(s) in a broken doublestop adds an enormous amount of unnecessary tension to the hand and is normally not a reccomendable thing to do. Whether we remove the non-sounding finger from the string entirely or just relax it (while its maintaining string contact) is achoice we can make depending on the circumstances. But without a doubt, relaxing the fingers when they are not in use is an absolutely fundamental technical principle that will help keep our hand flexible, alive and responsive even in the fastest repetitive passages. In fact it is the need to maintain constant finger contact that makes passages in “real” doublestops normally so much more difficult than passages in broken doublestops.
PLAYING “REAL” DOUBLE-STOPS
There is a wonderful saying: “doublestops often make one good player sound like two bad players”. How true this is, certainly for the cello !!!
Often, even the very best composers are unaware of the technical difficulties they are creating when they write a passage in doublestops for the cello. If there was a mathematical formula to calculate the level of difficulty, shifting in doublestops would not be the sum of the difficulties of the two simultaneous shifts to the single notes, nor would it be simply twice as difficult as shifting between single notes, but rather it would be the square of all the combined single note shift difficulties! Passages that sound beautiful in the composers imagination – and that would sound beautiful if played by two cellists – can be very awkward (and thus easily sound awful) when played in double stops by only one cellist. Here are some examples:
Brahms loved thick musical textures and was particularly “optimistic” with regard to cello double stops. Even in chamber music pieces, with other instruments available to fill in the harmonies (or play the contrapuntal line), he gives the cello some rather awkward doublestops, guaranteed to make a lovely melody 10 times more difficult
And his “Double Concerto” (for violin and cello) could justifiably be called (and played as) a “Quadruple Concerto” because so much of the solo material is in double-stops!
In particularly difficult orchestral pieces, the solo-french horn players have an assistant who plays certain notes of their part. If each of the two soloists in this Concerto could likewise have an “assistant” to play one of the voices of the doublestops, this piece would probably sound a lot better, and would certainly be a lot more pleasurable to play, especially for a small-handed cellist.
WHY ARE DOUBLESTOPS DIFFICULT?
There are several reasons why doublestops are soooooo much more difficult than just the sum of the two simple single notes:
1. HAND TENSION:
Significant extra tension is normally needed in the left hand to hold down two notes at the same time, especially when the distance between the two fingers is large. This creates problems not only for our vibrato but also for the fine positioning which is needed to both make a beautiful sound and to play in tune. This problem of added tension is much less severe on the violin than on the cello. On the violin, the distances are smaller. The violinist doesn’t need to stretch/strain their hand very much at all in order to place the different fingers at the same time. This is the reason why “normal” double stops are so much easier on the violin than on the cello, and it is for this reason that many (most) of the original double-stops have been removed from the transcriptions of violin music in their version for cello found on this site. If you have a big hand, or are very flexible, then you can play the cello more like a violin …… and you can put the double-stops back in!
There are three exceptions to this principle of doublestops making the hand tense.
- Doublestops in which the two fingers are close together, create very little added tension and can often sound beautiful, even for a small-handed cellist. Sixths (and fourths) are a good example of this. The further apart the fingers are from each other in a double stop however, the greater the tension created. Thirds illustrate this perfectly: the major third stretch necessary to play a “simple” minor third interval across two strings is wide enough to create great tension, especially for a small hand. And even the minor third hand frame can block and rigidify the hand, making vibrato difficult. The discomfort and tension of thirds is made worse by the fact that the higher finger is on the lower string, which is the most unergonomic place for it to be. What a shame it is that passages in doublestopped sevenths don’t sound as nice as passages in thirds!! They are certainly more ergonomic.
2. Most doublestops involving the thumb are exceptions to the “doublestops = tension” rule. This is because the distance between the finger (any finger) and thumb can be opened out widely and easily without creating tension. For this reason, even in the neck and intermediate regions (where we would not normally need to use it) we may prefer to use the thumb instead of a lower finger in some doublestopped passages. The reduction in hand strain that comes from the use of the thumb can significantly help our sound quality as well as facilitating our vibrato. This use of the thumb is especially useful for playing double-stopped minor third intervals across two strings (requiring the major third stretch). Here the use of the thumb eliminates the need for the extended-back first finger on the higher string (which is a real vibrato-killer).
2. AURAL CONTROL: THINKING, HEARING AND TUNING DOUBLESTOPPED PASSAGES.
HEARING/DISTINGUISHING THE SEPARATE VOICES
Keyboard players and guitarists are used to playing several notes at the same time. They thus learn, almost automatically, to hear, think, play and memorise music both harmonically (vertically) and melodically (horizontally. We string players, on the other hand, are principally horizontal, melodic thinkers because we spend such a large majority of our playing time just playing one voice (one note at a time). Because of this, we can be quite weak at thinking and hearing harmonically. When we finally have one of our rare passages in doublestops, our ears can get a little lost amongst the two voices. Trying to distinguish between them and work out what to listen to can appear difficult but in fact is largely a question of practice and training.
Surprisingly, even for cellists, used to playing the lower voices, our ears are normally attracted to the higher voice, especially in passages where the two voices move in parallel. We can confirm (or disprove this) by playing different scales in thirds and sixths in which we sing one of the voices and play the other. Usually it is easier to sing the top voice than the bottom voice.
The following link opens up two pages of material (exercises) for working on this aural skill of voice separation:
Exercises For Better Hearing of Doublestopped Sequences
The fact that keyboard players and guitarists don’t need to correct the intonation of each note makes multi-voice playing so much easier for them. But for a string player the situation is very different: playing and correcting two notes at the same time is much more than twice as difficult as playing one note. Hearing and tuning two notes at the same time – even in the same position (without any shifting) – is comparable to doing two different mathematical calculations, not one after the other, but at exactly the same time! And if we incorporate shifting into a double-stopped passage, the aural (brain, computing) difficulties increase exponentially.
3. FINGER PLACEMENT, INDEPENDENCE AND COORDINATION.
When our left hand is playing on different strings at the same time we not only have the problem of “horizontal geography” (placing several fingers simultaneously on different strings – see Left Hand String Crossings) but also of finger independence and coordination. When playing on only one string, we need to remove all the higher fingers in order to play a lower finger, but when playing on two strings at the same time, this is no longer the case. Suddenly, the possibilities of operating (lifting on and off the string) different fingers at the same time are multiplied exponentially and thus a whole new world of problems of finger coordination, independence and simultaneous finger placement opens up. Sometimes we might choose to shift more in a doublestop passage in order to avoid the need for the fingers to jump between strings. This “trick” can often allows us to maintain a true legato.
The Cossmann Doubletrill Finger Independence exercises (see links below) are undoubtedly the best practice material for acquiring the skills of finger coordination and independence on two strings simultaneously. They are also excellent for developing strength and aural skills (hearing and tuning two notes at the same time). We can do these exercises in both the Neck Region and in Thumbposition.
Cossmann Doubletrill Exercises: Neck Region
Cossmann Doubletrill Exercises: Thumbposition
THE DIFFICULTY OF MEMORISING DOUBLESTOPPED PASSAGES
The complexities of both hearing and playing our doublestops means that they – as well as any large intervals which need to be heard harmonically rather than melodically – are also often particularly difficult to memorise. The Bach Cello Suites offer some good examples of this: the Prelude of Suite IV with all its leaps and harmonic writing, along with Gavotte I of Suite V and the Sarabande of Suite VI with their high frequency of chords and double-stops (see Chords and Double-Stops in the Bach Suites), are perhaps the most difficult movements in the Bach Suites to memorise. The cadenza from the Rococo Variations is another good example of the added difficulty of memorising chordal passages.
ORCHESTRAL (AND ENSEMBLE) DOUBLESTOPS: AN ERROR OF ORCHESTRATION
Because of all these difficulties associated with doublestops, in orchestral playing, no matter what the composer specifies with respect to the doublestops that they write, the end result will almost always be better if we play them “divisi” (divided up) with our stand partner. The common wisdom of “united we stand, divided we fall” could not be more wrong when applied to double stops. When we divide them up (by playing them “divisi”) the section will sound good, but when we play them “united” we can easily bomb!! Even in chamber music it may be possible to redistribute the notes among the different players to improve or eliminate awkward double-stops – certainly pianists usually have a spare finger available to lighten our load and this can make the difference between pleasure and suffering ….. for both player and listener.
A good example of the use of divisi for orchestral doublestops can be found at the beginning of the final movement of Beethoven’s Sixth Symphony. In a totally transparent texture, where every tiny bit of out-of-tune playing can be heard immediately, Beethoven writes a series of low sustained doublestopped fifths (F and C) for the cellos. Fifths are the hardest doublestop to play in-tune and the lower register is the hardest one in which to hear and tune our doublestops. This is absolutely nothing to be gained for a cello section by trying to play these as doublestops. In fact this passage is almost an IQ test for a section principal (or conductor). Anybody who suggests that “because Beethoven didn’t write divisi we must play them as doublestops” should change jobs!
THE GOOD SIDE OF DOUBLE STOPS
They may be difficult to play and very ungrateful in performance, but double-stops are a wonderful tool for practicing. They develop, in an accelerated, concentrated and highly efficient way, many extremely useful skills, such as:
- strength in the left hand (practicing double-stops is like doing weightlifting)
- awareness of the different finger positions within any one hand position (because now we can hear the finger spacings simultaneously rather than consecutively)
- awareness of the different hand positions on the fingerboard (positional sense)
- intonation (ear training and aural control)
- finger independence and coordination
- horizontal (across the strings) positional sense
- bow level control.
If we can play (and shift on) two notes quite well at the same time, then when we only have one note to play (or shift on), it will feel fantastically easy. Imagine a dancer who practices with weights attached to their arms and legs and a blindfold over one eye: when the weights and the blindfold are removed, everything feels easy. It’s the same for us cellists: double-stops are an excellent training tool for both hands and for our ears/brain. For example, compare the following two shifting exercises, one in double-stops and the other with single notes. The exercise in double stops is incomparably more efficient and useful.
Even if there are not many double-stops (or none at all) in a piece we are playing, much of that same music is often made up of “broken double-stops”, for which practicing in “real double-stops” is the best preparation. Consider the following example:
DOUBLESTOPS IN ONE POSITION (NO SHIFTING)
When we work (practice) with double stops, we are not just learning “how to do double stops” but are actually using double stops as a turbo-powered practice tool through which we can establish and develop our fundamental left-hand cello technique in the most intense, concentrated, and efficient way. Doublestopped exercises in any one position (with no shifts) are magnificent for building strength, finger independance, finger coordination and for establishing perfect finger spacings. Some of the best exercises are “doubletrill” patterns in which different possible finger combinations and alternations on any two adjacent strings are used. One of these many possibilities is shown here below. Although this example uses “closed” (non-extended) position, these exercises can also be done in extended position.
Bernard Cossmann “discovered” and published some of these in his “Studies for Developing Agility, Strength of Fingers, and Purity of Intonation for Cello” in the late 19th century. On the cellofun.eu website these exercises are developed, elaborated, and extended, forming the basis for our left-hand technical foundations not just in the Neck Region but in all the fingerboard regions. Here below is an example of how these exercises are perfectly transposable into the Thumb Position.
In Thumb Position, we can do these exercises also using the flattened second finger (F natural in the above example) as well as with both the first and second fingers flattened (Bb and F natural in the above example).
In the Intermediate Region we only really have three fingers (instead of the four that we have in the Neck and Thumb positions), so we cannot do the “doubletrill” exercises (which require two fingers on each string). Nevertheless, we still use doublestopped exercises involving all the different possible two-string finger configurations as the basis for our left-hand technique in this region.
Here then are our complete compilations of the many different doublestop possibilities in any one position, for all three of the cello’s fingerboard regions. In these exercises we have preferred to be complete rather than concise: some of the finger permutations are extremely awkward (if not totally impossible) and some are horribly dissonant. Others however are both very harmonious and easy to play.
Doublestopped Exercises in One Position: NECK REGION
Doublestopped Exercises in One Position: INTERMEDIATE REGION
Doublestopped Exercises in One Position: IN THUMBPOSITION
This large, complex and fascinating subject has its own dedicated page here:
HOW TO PRACTICE DOUBLE STOPS
Double stops can and should be practiced in the same way that pianists practice their two hands: separately. But while pianists practice each hand individually, we will practice each string individually. We can use three different graded preparatory levels of separation to work up progressively to the finished double stop passage.
1. At the first and easiest level we practice each string separately without even bothering to finger the notes on the “other” string. Here, not only is our ear/brain freed from the difficulty of controlling both musical lines simultaneously, but also our hand is freed from the physical complication of playing on two strings simultaneously.
2. The next level of difficulty is to play (bow) each string separately while also simultaneously (but silently) fingering the notes on the other string. In this way, our left hand is doing everything it will ever have to do in the passage, but our ear/brain is still free to focus on one line at a time.
3. Next, we can play them as broken double-stops, starting on both the top and bottom string successively, as in the following illustration which usess a simple scale in thirds. Broken double stops are undoubtedly the best, most painless, way to learn and work on double stopped passages. With broken double stops, there are also almost unlimited possibilities to create exercises for Bow Level Control (string crossings) on two strings.
4. The final step is to play both strings together.
SEPARATION OF THE TIMING OF THE FINGER ARTICULATIONS IN DOUBLE STOPS
Sometimes in double-stops we will place both the fingers simultaneously. This is especially common when we have plenty of time to do so comfortably:
At other times however it may be helpful to place the two fingers at different times. Normally this means that we will place the finger on the “new” (silent) string slightly before we actually need to sound it with the bow. By doing this we don’t need to coordinate its articulation (placement) with the bow’s arrival on the new string: the finger is already there. It also means that we don’t need to coordinate the simultaneous articulation of both fingers of the double-stop, once again because one of the fingers is already prepared. This means that even though we are playing a double-stop with the bow, for the left hand we are converting the beginning of the double-stop into a broken double-stop. This can make double-stops much easier, as in the following examples. In the “practice” version of this example we deliberately sound this anticipated finger placement with the bow. This is a good way to practice this little trick as it makes the anticipatory placement of the finger audible and thus much more deliberate.
More discussion about this can be found in the article on Anticipation.
BREAKING THE ENDS OF DOUBLE STOPS (NOT MAINTAINING BOTH NOTES FOR THEIR FULL VALUE)
We have seen that we can convert any double stop passage into “broken” double stops as both an aid to learning the required left hand skills and also to make exercises for bow level control (string crossings) on two strings. But even in a performance situation, we very often break double stops that are written out as non-broken. In other words, we will often cut short one of the notes of a double stop (i.e. stop bowing on that string) in which, according to the score, each note should have the same rhythmic value. This “break” is however usually imperceptible as it is at the end of the stop, and it is almost impossible to notice that one note of the pair lasts less than the other, because the note that we have stopped bowing continues sounding both in our imagination and in the room’s (and resonance). There are several reasons why we might want to do this.
Many Classical and Baroque composers systematically write the double stop for as long as it is harmonically valid, even if playing it for its full written duration is technically or musically impossible. In the following example from the C major Fugue of the third violin partita for example, the only way to maintain the long note for its full length would be to slur the upper notes. This is “musically impossible” as it would change the character of the fugue theme completely. Obviously Bach never meant for the long bottom notes to be actually played by the bow for their full written value. Bach does this always, and we can usefully apply the lessons of this example to most of the double stopped passages of the Baroque and Classical eras.
This shortening of one of the notes of the double stop is not only important musically but is also technically useful. It allows us to reduce left hand tension, and is often a big help in our preparation for the next note, both for the bow and for the left hand. The shortening doesn’t necessarily have to be always on the lower note of the pair.
- TO FACILITATE SHIFTS OR STRING CROSSINGS
“UPSIDE DOWN” DOUBLE STOPS
Very often we can make use of double stop fingerings in which the the higher open string is used as the lower note of the double stop as in the following examples:
There are several reasons why we might want to use these fingerings instead of the “normal” fingerings:
- The use of the open string gives greater resonance to the note, and gives absolute intonation security
- It may remove the need for an extension, thus reducing hand tension
- We may be able to avoid a shift
Upside down double-stop fingerings can be quite confusing for our brain and hands because we are so accustomed to having the lower notes always on the lower strings. In the above examples we have chosen to use “upside down” double-stop fingerings but often, we have no choice, and are quite simply obliged to finger up and down on a lower string while using the higher string as a “pedal” or “drone”. Bach was an expert in creating special effects of this type. For more practice and repertoire material for working on this skill, click on this link.
VIBRATO IN DOUBLE STOPS
Vibrato can “muddy” the intonation of our doublestops so we need to be careful not to try too hard to vibrate wildly (and widely) on them. This is actually fortunate, becauses many doublestops create great tension for the left hand ……. and we know that forcing our vibrato onto a tense hand usually gives the opposite effect to the musical warmth that our vibrato is supposed to create!!
One way we can add vibrato without muddying the doublestop is to shorten one of the notes (usually the bottom note) and then add vibrato to the note that is being played alone. That way we get the best of both worlds: the note that has been shortened stays in our ear like a sustained doublestop, but we can also add a beautiful melodic vibrato to the passage. Try this especially in the last bar of the above example.
This phenomenon of an excessively wide vibrato muddying the harmonies is often heard in its most extreme form with operatic singers. A capella (unaccompanied) vocal quartet passages (such as in the last movement of Beethoven’s 9th Symphony and various moments of Verdi’s Requiem) are often sung with such wide operatic vibratos that the sense of harmony, tonality and tuning is completely lost. Rather than music, the end result sounds more like a wild animal bellowing competition in the jungle!
Chords can be considered as a slightly more complicated version of double-stops. The same ambiguity with respect to their definition applies to both chords and double-stops. Just because the bow may be playing a 3 or 4-string chord doesn’t mean that the left hand is also necessarily playing on the same number of strings:
Likewise, the opposite situation – that of “broken chords” – is often true. Here, even though the bow might be playing only single notes (one string at a time), the string crossings occur so quickly that the left hand must maintain fingers stopped on more than two strings at the same time. It is as if we were playing chords on the guitar. Broken chords are exactly like broken double-stops, just with the fingers on more strings at the same time:
Even though we can never really play with the bow on more than two strings at once, this situation in which the left hand is playing on three or four strings simultaneously is quite common. And of course in pizzicato chords we can – unlike with the bow – actually play on three or four strings at once, either with a four-finger-pluck or with a guitar strum.
The following link opens a library of as many of the possible 4-string chords that I could find on the cello. Only the most basic harmonic chords have been included. This means only major, minor and dominant seventh chords, in all their possible inversions, together with diminished sevenths. Certainly some have been missed, which is why gaps have been left for the additions.
4-String Chord Library
Chords and Double-Stops in the Bach Suites
That wiggly line is a standard notation for arpeggio. You can meet it on other instruments too (like piano). It means to play the notes not all at once, but in a quick succession, from lowest to highest, without muting them, so that the whole chord is eventually sounding.
A chord without the wiggly line should (strictly technically) be played all at once.
I don't play the cello, but this is the meaning on the piano and on the guitar. When, on the guitar, you're rolling all the fingers down one by one, you actually make a sort of rasgueado, which is somewhat different sound, used mainly in flamenco guitar (most often denoted either by a word "rasgueado" or explicitly with written-out quintuplets with lots of arrows and right-hand finger designations all over the place :--)). Chances are that it works this way on the cello as well.
answered Dec 17 '17 at 16:22
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