celloblog

100 Cello Warm-ups and Exercises Blog 19: Cello Geography -Part 5: Thumb Position and the Upper Registers

100 Cello Warm-ups and Exercises Blog 19: Cello Geography -Part 5: Thumb Position and the Upper Registers – by Robert Jesselson

 

Blogs #15 and #16 discussed the geography of the lower regions of the cello. In sorting out the “latitude” and “longitude” in this part of the instrument the main organizing principle is the knowledge and use of positions. We identify the positions by the location of the first finger on the string up through Seventh position, with “normal” and “extended” variants throughout. When the first finger is playing the A in seventh position on the A string the thumb is still behind the neck – so this is still considered neck position. Seventh position is a significant place on the cello, because it divides the string into two equal parts, and as a result we find the A harmonic there as well.

After seventh position, the thumb is used as a finger up on the fingerboard. (It can also be used on the fingerboard in the lower part of the cello, and is employed there very often for octaves, double stops and special fingerings, even in literature as far back as Boccherini and Haydn.) When the thumb is up on the fingerboard we call it thumb position. I described the basic outline of the thumb in thumb position in Blog #18 (the “inny and the outy”, the C-shape, the Perfect Fourth between the thumb and the third finger, etc.)

The organizing principles of geography in thumb position are different from those of the neck region. We don’t identify positions in the upper part of the cello. Instead, there are three important techniques for understanding location and for navigating around in the cello’s upper regions.

1. Using nodes and other fixed points for reference

2. Measuring distances:

a) understanding and using intervals

b) the “Configuration of the Hand” across string

3. Using the basic thumb position, as described above, and organizing   the finger spacing with tetrachords

1. Using nodes for reference

We use the harmonic nodes on the cello in the upper positions as a fixed reference in our GPS system to locate where we are. Most cellists are aware of the second harmonic, because that is often used to help tune the instrument. For example, on the A string the second harmonic is the A in seventh position, which divides the string in two parts. (The first harmonic is actually the open string; the second harmonic is also called the first overtone – but rather than confusing things further I will just refer to these as harmonics!). The 3rd harmonic on the A string is the E that divides the string into three parts. The 4th harmonic is the A that divides the string into four parts, and the 5th harmonic is the C# that divides the string into five parts.

Below is a simple chart that shows the most important harmonic nodes. The view here is looking down the cello towards the bridge (bottom up). There are many more harmonics on the string than indicated, but these are the most important nodes to use as points of reference. Naturally these harmonics repeat themselves in mirror image going up the string (but we don’t need them right now for this discussion about thumb position). We need to practice finding these nodes using muscle memory with a certain amount of rote practicing, so that we can locate them easily. The 3rd, 4th and 5th harmonics should become as easily accessible as the 2ndharmonic.

untitled

Another piece of information that is useful is to know is what note is right at the end of your fingerboard. Usually it is an F or F#, though depending on the length of your fingerboard it could range from an E to a G.

Once you know where the harmonic nodes are, or knowing what the note is when you put your finger right on the edge of the fingerboard, you can find other notes around by using the second method mentioned above:

2a. Measuring distances – understanding and using intervals

The second important system for understanding the geography of the instrument is to know the distances between notes in different parts of the fingerboard. Basically we measure distances from the node to a note, or from one note to the next. Our unit of measurement is the interval. Unlike the piano, where the distance between half steps remains constant through all 7+ octaves, on the cello a half step (or any interval) gets smaller as you go up the string. This is why it is so important to do scales and arpeggios in all keys in the upper part of the cello – to know and feel the distance of a whole step or a half step, or a minor third or a perfect fourth all over the cello.

Since the basic thumb position involves a perfect fourth between the thumb and third finger, it is important to do exercises for sensitizing this distance all over the cello. A great warmup is to do the Feuillard thumb position scales (#26) and the arpeggios (#27) in every key:

feuillard-thumb-position-scalesfeuillard-thumb-arps

Practicing octaves is important for the same reason, since the octave shape across strings in thumb position is the same as a perfect fourth on one string. Similarly, it is great to practice artificial harmonics to maintain the P4 hand position on one string. So, practicing artificial harmonics is a great way to reinforce octaves, and vice versa. And both are great for maintaining the all-important relationship between the thumb and third finger.

It is critical for cellists to know the sound and spacing of the intervals all over the cello, both on one string and across strings. I like to do whole tone scales and chromatic scales to focus on whole steps and half step distances up the cello.

whole-tone-small   chromatic-scale-small   Two other warm-up exercises that I like to do are great to focus on intervals and distances going up a string: an octotonic scale (alternating whole and half steps), and a diminished seventh arpeggio with a replacement fingering to sensitize the distance of the ascending and descending minor thirds.

octatonic-small

dim-7-exercise-smallOnce the intervals are clearly understood, and the hand “knows” the distances in different parts of the cello, we can use this information to find notes related to the nodes.

2b. Configuration of the Hand

Knowing the intervals and distances on one string is vital in understanding the geography of the upper part of the cello. But one still needs to know how notes relate across the strings. For this it is important to understand the intervals that are created when you play two notes on two neighboring strings. I address this with a system that I call the “Configuration of the Hand”, in which we explore all the combinations of the fingers across two strings. Here is a chart with all the combinations of the fingers for playing different intervals. Notice that the fingerings are reversible for fourths and sixths, and for thirds and sevenths (in reading the fingerings, the first number is for the finger is on the lower string, the second number is for the finger on the higher string. For example, 3-1 means 3rd finger on the D string and 1st finger on the A string, producing a P4).

configuration-of-hand-cut    

It is important to know these fingering combinations for playing across strings in the upper part of the cello.

3. Tetrachords

 As discussed previously, it is important that the basic thumb position is stable and consistent. In other words:

  • the octave or P4 relationship between the thumb and 3rd finger must be clear and the intonation solid
  • the “inny and the outy” shape of the thumb must be consistent
  • there should be a C-shape between the thumb and the first finger so that the knuckles are not squashed down
  • the fingers should be round
  • and the fingers should be strong enough so that joints don’t collapse.

The next important step in creating a usable thumb position is figuring out the spacing between the other fingers within the octave (or P4) frame. Since we can play four notes with the four fingers in thumb position (using thumb, 1,2,3) it is useful to identify the various possibilities as tetrachords (four note groupings), giving them names. The most common tetrachords are:

Major:                           W      W      h

Minor:                           W      h       W

Modal (Phrygian):      h       W      W

Octotonic:                     h       W      h

(W=whole step; h=half-step; A=Augmented 2nd)

 Notice the relationship of the first three to the Marys that were discussed in an earlier Blog (#17) – the intervals from the bottom up are the same. All of them are named after the scales that they initiate. The Harmonic Minor Tetrachord is used in minor scales, with an Augmented Second between the 2nd and 3rd fingers:

Harmonic Minor:         h       A       h

We also have Tetrachords in which the interval between the thumb and the 3rdfinger is bigger or smaller than our standard octave or P4. For example the Chromatic Tetrachord, the Lydian Tetrachord (named after scales that begin this way). The Gypsy Tetrachord, and two others are used less often in western music, but they do occur and it is useful to practice them.

Chromatic:                       h       h       h

Lydian (whole tone):   W      W      W

Gypsy:                                W      h       A

                                             W      h       h

                                             h       h       W

I find it helpful to do a variety of different scales in thumb position, recognizing that scales are made up of two tetrachords. In the following chart I present some of the many possibilities of scale systems using thumb position tetrachords. The first three are symmetrical scales, with the same tetrachord on both strings. The others use a variety of combinations of tetrachords. They should be practiced in all keys going up the cello. The ( w ) or (h) in the middle column indicates the interval (whole step or half step) between the third finger and the thumb as we cross strings. In the Locrian, Whole Tone and Octotonic scales the thumb has to move back a half-step during the string crossing. In the Octotonic scale we need to use the 4th finger as well.
thumb-position-scales-p1-cut

Of course sometimes the interval between the thumb and 3rd finger will be much bigger than a P4 (as in the examples of the Locrian, Whole Tone and Octotonic scales above) – often we may need a 5th or a 6th. In playing 10ths across the string, such as in the Haydn D-major concerto, we are playing a distance of a 6th on the top string between the thumb and third fingers, or an octave between the thumb and first finger across the string. Any interval is possible between the thumb and the third finger on the same string, up to (or perhaps more than) an octave. This will be discussed next Blog on the Alexanian exercises.

Analyzing passages in the repertoire using Tetrachords can be very useful. For example, in this passage from the 3rd movement of the Saint-Saens Concerto we can see that there are groupings of Major Tetrachords, Minor Tetrachords, Octotonic Tetrachords and Modal (Phrygian) Tetrachords. The numbers in this example show the fingering patterns; the colored lines show the tetrachords (not the bowings).

saint-saens-example

In the second half of this passage the thumb works like a percussive finger, lifting each time it moves back. More about this in the next blog (#20) with exercises by Alexanian for the moveable thumb.

About the Author:

Robert Jesselson

Robert Jesselson is a Carolina Distinguished Professor at the University of South Carolina, where he teaches cello and plays in the American Arts Trio and the Jesselson/Fugo Duo. In 2013 he was named as the Governor’s Professor of the Year by Governor Haley and the SC Commission on Higher Education.

Dr. Jesselson has performed in recital and with orchestras in Europe, Asia, South America, and the United States, and has participated in the Music Festivals at Nice (France), Granada (Spain), Santiago (Spain), Aspen (CO), Spoleto (SC), the Grand Tetons (WY), and the Festival Inverno (Brazil). His performance degrees are from the Staatliche Hochschule fuer Musik in Freiburg, West Germany, from the Eastman School of Music, where he studied with Paul Katz, and the DMA from Rutgers where he studied with cellist Bernard Greenhouse. He has been principal cello of the South Carolina Philharmonic Orchestra, and the Orquesta-Sinfonica de Las Palmas, Spain. In 1983 Dr. Jesselson was in China for a six-month residency, one of the first Western cellists to visit that country. During that time he performed as soloist, gave master classes, and taught at several conservatories (including Beijing, Shanghai, and Canton). In December, 2001 he led a delegation of string players and teachers to Cuba to begin professional contact with Cuban musicians. He has also taught at Sookmyung University in Korea, Sun Yat Sen University in Taiwan, University of Auckland in New Zealand, at the Royal College of Music in London and recently in St. Lucia in the Caribbean. His recent CD of new music for cello and piano is called “Carolina Cellobration” and is available on CD Baby and Cellos2Go.

Dr. Jesselson was the national President of ASTA, the American String Teachers Association, from 2000-2002. During his tenure as president he initiated the National Studio Teachers Forums (2000 and 2002), started the National String Project Consortium (with sites now at 44 universities and grants of $3.1 million), and began the planning for the first stand-alone ASTA national convention in 2003. He was the founding Executive Director of the National String Project Consortium, and is currently on the NSPC Board.

Dr. Jesselson is former conductor of the USC University Orchestra and the Columbia Youth Orchestra, and he was the cello teacher at the S.C. Governor’s School for the Arts for 17 years. For 15 years he was the director of the USC String Project, building the program into one of the largest and most prominent string education programs in the country. His pioneering work on this program was recognized in an article in the New York Times in December, 2003. ASTA awarded him the “Marvin Rabin Community Service” Award in 2009 for his work with the NSPC and teacher training. He is the recipient of the 2015 USC Trustees Professorship and the 2010 Mungo Distinguished Professor of the Year, the highest teaching awards given by USC. He has also been awarded the 2002 Cantey Award for Outstanding Faculty, the 1992 Verner Award, the 1989 S.C. Arts Commission Artist Fellowship, the 1995 Mungo Teaching Award, and the first SC ASTA Studio Teacher Award in 2005. Next summer Dr. Jesselson will be teaching cello at the Green Mountain Music Festival in Vermont and at the Cellospeak Festival. He plays a 1716 Jacques Boquay cello.

Robert Jesselson website: http://in.music.sc.edu/fs/jesselson/index.html
Articles by Jesselson: http://in.music.sc.edu/fs/jesselson/articles.html