by Tim Janof

Hans Jørgen Jensen is co-author of CelloMind, a new pedagogy book that was published in November 2017 by Ovation Press. He is Professor of Cello at the Bienen School of Music at Northwestern University. From 1979 to 1987 he was Professor of Cello at the Moore's School of Music at the University of Houston. During the Summer, he is a faculty member at both the Meadowmount School of Music and the Young Artist Program at the National Arts Center in Ottawa Canada, the latter of which is under the direction of Pinchas Zukerman. He has been a guest professor at the Thornton School of Music at the University of Southern California, Oberlin College Conservatory, Eastman School of Music, the Sydney Conservatorium of Music, the Royal Academy of Music in Copenhagen, the Tokyo College of Music and the Musashino Academy of Music in Japan, the Festival de Musica de Santa Catarina in Brazil, the Jerusalem Music Center, and the PyeongChang International festival and School in Korea.

Mr. Jensen has performed as a soloist in the United States, Canada, Europe, and Japan, including solo appearances with the Danish Radio Orchestra, the Basel Symphony Orchestra, the Copenhagen Symphony, and the Irish Radio Orchestra under the baton of conductors such as Simon Rattle, Mstislav Rostropovich and Carlo Zecchi. He has given numerous workshops and master classes across the United States, Canada, Europe, Japan, Brazil, Korea, Australia, and Israel.

His former students have been and are members of major orchestras including the New York Philharmonic, Chicago Symphony, Saint Louis Symphony Orchestra, Cincinnati Symphony, Detroit Symphony, Kansas City Symphony, Colorado Symphony, the Gulbenkian Orchestra in Portugal, the Graz Philharmonic in Austria and the Montreal Symphony. Mr. Jensen's former students are currently the principal cellists in the Toronto Symphony, Detroit Symphony, Kansas City Symphony, the Copenhagen Philharmonic Orchestra, and the Symphony Nova Scotia. His former students hold teaching positions at Northwestern University, the University of California at Berkeley, the Cleveland Institute of Music, the San Francisco Conservatory, Cincinnati College Conservatory, the Royal Academy of Music in Copenhagen, the Desautels Faculty of Music at the University of Manitoba and numerous other music schools.

Hans Jørgen Jensen's students have been first prize winners in competitions such as the 2017 Klein Competition, the 2017 Sphinx Competition, the Cassado International Competition in Japan, the Johansen International Competition, the MTNA National Competition, the ASTA National Competition, the Stulberg International Competition, the Chicago Symphony Young Performers Competition, the WAMSO Young Artist Competition, and numerous other competitions. His students have also been prize winners in the 2017 Queen Elisabeth Inaugural Cello Competition, the Naumburg International Competition, Lutoslawski Cello Competition, and the Klein Competition.

Mr. Jensen was awarded the prestigious 2010 Artist Teacher Award from the American String Teachers Association (ASTA), as well as the Copenhagen Music Critics Prize, the Jacob Gades Prize, the Danish Ministry of Cultural Affairs Grant for Musicians, the Northwestern Charles Deering McCormick Professor of Teaching Excellence award, and the U.S. Presidential Scholar Teacher Recognition Award by the U.S. Department of Education. He was named outstanding studio teacher of the year by Illinois ASTA. He was also the winner of the Artist International Competition that resulted in three New York Recitals. E.C. Shirmer, Boston, published his transcription of the Galamian Scale System for Cello Volume I and II and Shar Products Company published his cello method book, Fun in Thumb Position.

Jensen studied at the Royal Academy of Music in Denmark with Asger Lund Christiansen, at the Juilliard School with Leonard Rose and Channing Robbins, and pursued private studies with Pierre Fournier, also appearing in his master classes.

TJ: You discuss three tuning systems in your book, CelloMind?

HJJ: Yes, Equal Temperament, Just intonation, and Pythagorean tuning. Equal Temperament refers to the way a piano is tuned, where pitches are equally spaced by a certain distance: 100 cents. This tuning system was developed for keyboards so that they could play in all keys and be reasonably well in tune. Each pitch thus represents a compromise that works well enough for all keys. Just intonation is based on the natural harmonic overtone series and is used for tuning chords and double stops. It can be used both melodically and harmonically for Baroque and early Classical Music, as well as for tuning chordal structures vertically in chamber music ensembles. Pythagorean tuning is based on stacked perfect fifths and is also referred to as "expressive intonation."

How is one supposed to know when to switch between the different tuning systems?

Most of the time we use Pythagorean intonation, but when playing double stops and chords we use Just intonation. Pythagorean intonation works very well when playing with a piano. But when playing in direct unison with the piano we have to match its equal temperament, which might result in slightly larger half steps.

I remember when I played the Brahms E Minor sonata for the first time in my youth. In my own practice, I had found the first E natural by tuning it with the open G string. But at the first rehearsal with piano, I was rather surprised to find that this E natural was in fact very flat. Looking back, it may have been helpful to know that the Pythagorean E natural that matches the 3rd partial on the A string aligns perfectly with the piano. By contrast, the E natural on the C string that tunes with the G string is the fifth partial of the C string and is very flat in the context of equal temperament. Of course, at the end of the day the best method is to use our ears, and simply adjust when playing together with the piano.

Given that there are different tuning systems, what does playing "in tune" even mean? How does one know when one is playing in tune?

The answer to this question has changed throughout history. For instance, what was considered good intonation in the Baroque era is very different from what we are accustomed to now. That being said, it is important to establish a basic framework for what constitutes good intonation, so that one has a solid foundation to build upon, and can then make specific decisions regarding questions of pitch with more confidence and intent. As a cello teacher, I have always spent a great deal of time working on intonation with my students. Being able to explain theories about intonation has made it much easier, but I always try to emphasize that in the end it is all about listening and adjusting.

Does Just intonation sound good when playing with piano?

Just intonation doesn't work when playing with the piano because a lot of the pitches end up sounding flat. Pythagorean intonation works much better. I've noticed that some of my students start playing everything on the flat side after reading the first 6 chapters of CelloMind because those chapters focus on Just intonation. It is important to remember that Just intonation is meant for chords, double stops and Baroque music, but it is not the most ideal option for melodic playing.

When you hear somebody play sour notes, is it possible they are actually playing in tune, but are using the wrong tuning system?

It is very possible they are playing in tune relative to their own concept. Fortunately, perception of intonation is very subjective, and there is often a wide range of acceptable notes, which can vary depending on the performer or context. In any concert, we hear thousands of notes and we select the sounds we want to hear. The brain knows how to sort out information that's not important, so we generally don't focus on intonation when listening to a performance. If you go to a concert with the singular goal of listening for intonation, you will generally hear many more out of tune notes and have a much less enjoyable experience. This is what makes auditions so difficult; the judges are listening more objectively and critically than they would in a concert setting.

Let's say somebody has established a tuning system they are going to follow. Why do they still play out of tune? Could it be posture or form issues?

I separate intonation into two components:
  1. Perception
  2. Implementation
In my experience I have found that when people have problems with intonation the primary issue is usually one of perception. If an individual is hearing the wrong pitch, they won't know where to put their fingers. In fact, they can waste so much time trying to move the fingers around thinking that the issue is a finger problem when in reality it's due to the fact that they aren'pt totally sure what the correct pitch is.

It is therefore necessary to train the student to develop their inner and outer hearing to a higher level. Inner hearing refers to pitches that are heard and visualized within the mind, while outer hearing refers to pitches that are heard by the mind through the ears. Ultimately, theoretical knowledge about intonation should become an intuitive part of a player's vocabulary. One of the goals of our practice should be to reach the autonomous stage where all movements become almost automatic.

You are right to mention posture and form: as we grow as instrumentalists it is so important to spend a lot of time developing great posture and great playing habits. Physically feeling the spacing between the notes and the spacing between the fingers is an integral part of great intonation. In addition, good posture ensures that the line from the sound to the ear remains unhindered.

Why is it that one can hear every sour note when others play but not one's own?

One hears more objectively when one is further away from the instrument. I've even noticed when I teach; I hear much better when I am at a distance. Objectivity can be lost as a player because it is easy to get caught up with the mechanics of playing and become more emotionally involved in the music.

Is it common to hear notes sharp when nervous?

Yes, very common. I remember listening to recordings after my performances and I was often much sharper than I had anticipated. It must have something to do with the heart beating at a faster rate due to the adrenaline surge. I've only known one person who played flat when he was nervous. He would slow everything down and lower the pitches. We have to learn how to compensate for this by being more aware in the moment.

How does one learn this?

By performing a lot. There is no other way to simulate the high pressure situation of a performance. Even a performance class is not the same. The only way to learn how to perform is to perform.

Whenever I hear a singer practice, they do so with piano. Given that equal temperament is out of tune, does this mean that singers are doing themselves a disservice by using a piano?

Due to the fact that singers have to depend completely on their inner and outer hearing and do not have a physical instrument to relate to, using the piano can help give them a solid tonal center that grounds their sense of pitch. Even with piano accompaniment, however, there is still plenty of room for the singer to use expressive intonation. Of course, in acapella groups and choirs in general, Just tuning is often used in order to line up pitches vertically.

How does one find notes when using Just intonation?

Just intonation is based on the harmonic overtone series and is always relative to a specific key or pitch. When playing on a string instrument the open strings play a very dominating role. Because of this, keys for Just intonation in CelloMind have been organized in such a way that all the keys are related to the open strings.

It is important to understand that in Just intonation the pitches always have to be tuned in relation to the tonic. The most difficult key is F major because the F can be tuned either to the C or the A string.

Doesn't the location of a note depend on which key you are playing, and therefore there are multiple pitches for the same note name?

Yes, in Just intonation the pitches change according to the keys. Baroque musicians didn't need to modulate that much, so they didn't have to contend with the intonation minefield that comes with complicated modulations.

The great thing about intonation is the fact that we use the Pythagorean system most of the time, which means that all 24 pitches are always the same, making it rather simple and not so complicated.

The following three examples can be used to show how Just intonation works.

Example 1 – Prelude no. 1 in G major, mm. 1-4

Click here for video: Cellist Brannon Cho

The opening chords – although written as separate notes – have a strong vertical chordal function and require the use of Just intonation. The tonic open G pedal point is the dominating pitch and the four subsequent chords must tune against the G.

  1. Measure 1: Use the B that matches the 5th partial of the G string

  2. Measure 2: Use the E that matches the 5th partial of the C string and the C on the A string that matches the open C string.

  3. Measure 3: Use a slightly lower C to accommodate its role as the seventh in the dominant seventh chord with the G pedal point. (The seventh in a dominant seventh chord is usually lowered 31 cents compared with equal temperament, but due to the G pedal point the C sounds better staying the same or only being lowered ever so slightly)

  4. Measure 4: Return to the same B as in measure 1.

Couldn't one just tune the B with the open D string in the Bach Prelude?

Yes, the B that tunes with the open D string is the same as the 5th partial of the G string.

Example 2 – Menuet no. 2 in D minor, mm. 1-7
Click here for video: Cellist Emily Yoshimoto

  1. Use Just intonation for all the double stops. Use a higher F and higher B-flat that tunes as a small Just major third with the A string and the D string respectively.

Example 3 – Sarabande no 1 in G major, mm. 13-16
Click here for video: Cellist Riana Anthony

  1. For the B natural and E natural, match with the 5th partial B from the G string and the 5th partial E from the C string.

  2. Note: For the chord in m. 14, use a lower A that is a perfect fifth under the just E (5th partial E of the C string). However, it is fine to use an open A in the melodic descent into m. 15. In the first beat of m. 15, use the A that matches the A string, which also tunes as a perfect fourth to the open D string.

Would you say Pablo Casals played with Pythagorean intonation?

Yes, Casals used very high major thirds and leading tones when playing concertos and sonatas with piano. One of his ideas was to tune the cello a little higher than the piano or orchestra, allowing it to project effortlessly in a large hall. In his Bach recordings, however, he also used Just intonation in most of the double stops.

One modern performer, Jean-Guihen Queyras, uses Just intonation in his wonderful recording of all the Bach Suites. His intonation is simply stunning, and the whole recording is very creative and stylistically beautiful.

I once asked Nathaniel Rosen about expressive intonation. He said:

"I don't believe in it. I think it's a false concept. I think the whole idea that there are different ideas of intonation is a minefield. Casals dominated every chamber music situation that he was in. What would he have done if somebody had said, "I don't agree with you. I don't hear it that high?" And then what if another musician says, "I hear it lower." Who's going to decide who's right? The fact is that, if people practice their scales in an orderly manner, they will all come to the same idea of where the note is supposed to go. That decision is predicated not only on practicing the scales, but on practicing arpeggios, thirds, etc. You can't do all those things and have a different ideal of intonation. All the tones, if they're based on a harmonic framework, will gradually come to their center, to their proper place, and everyone will play together. I never have trouble playing in tune with my colleagues who deal with the fundamentals such as scale practice, arpeggio practice, and double stops, particularly thirds. I only have difficulty playing in tune with people that make an ideology out of expressive intonation. Piatigorsky didn't talk about that stuff. He wanted things to be in tune. Period."

Do you agree with him?

First of all, it is important to note that great performers don't necessarily need to know the theories about intonation, and will intuitively play in tune together. So with that in mind, Nathaniel Rosen is 100% correct as far as he is concerned. I have heard Mr. Rosen in numerous concerts and was always so impressed with the level of his control and expression. In particular, I remember a performance from a number of years ago when he played the Rococo Variations with the Houston Symphony. It was a stunning performance, one I will never forget.

Over the years, however, I have had a number of students with whom I was not as successful when it came to teaching them permanent great intonation. Because of this, I kept searching for better ways. I wanted to find a system that would allow the students to perfect their understanding of intonation and would last them into the future.

To take a case in point, cellist Allan Steele, one of my former students who is now the Principal cellist in the Fort Worth Symphony, told me a few months ago that he still goes through the advanced overtones series on the instrument every day. In his words, "It sets my ear and then I'm set for the day." He still uses the ideas and concepts that are in CelloMind Chapter 16 (Advanced Sympathetic Vibrations).

I remember the day many years ago when Allan came to a lesson as a teenager and told me excitedly, "I have found the F …the F that makes the 7th partial on the G string vibrate… I know the 7th partial F is 31 cents lower than the piano pitch, so when using it as a tonic, I place it higher than the 7th partial on the G string." That was a proud day for both of us.

I tell my students never to discuss intonation theories when playing chamber music. If, for example, you play with a talented first violinist who has great ears and naturally plays in tune, it is important to listen to him or her and adjust accordingly. Theoretical understanding of intonation can never replace or compete with great hearing, but it is nonetheless a good way to improve one's own perception and understanding of pitch.

Nathaniel Rosen emphasized the need to play scales. Is this not helpful?

Yes, but it is important to understand that we can tune the scales in different ways. In melodic tuning this means higher thirds and leading tones, and in Just tuning, lower thirds and leading tones.

The pitches that are the same in Just and Pythagorean scales are the first step (the tonic), the second step (the super tonic), the 4th step (the perfect fourth) and the 5th step (the Perfect fifths). The third, sixth and seventh scale degrees are higher in the melodic Pythagorean system and lower in the Just tuning system. Making sure people are aware of these two possibilities totally changes the way they perceive and implement intonation.

Does the speed of the notes change how music is played, from an intonation perspective?

The slower one goes, the more one perceives the music vertically. The faster the music flows the more it is perceived melodically. In fast technical passages, using small half steps can often make the music sound more brilliant. In whole tone trills it sounds more in tune if the whole step is slightly sharp.

How does one practice intonation?

Now that CelloMind has been written, I recommend that my students spend 15 to 30 min every day working their way through the book. It is important, from the outset, that they understand the two ways of tuning and that they work on both systems simultaneously. Since we mostly use Pythagorean intonation and it is a system where the pitches are always the same, it is really not so difficult. As stated before, Pythagorean intonation has 24 pitches that never change. When using Just intonation for chords and double stops the important thing is to decide which note is the dominant pitch that the other note or notes have to tune to. If there is an open string in the chord or double stop, the other note or notes of course have to adjust.

In chords without open strings the tonic is the foundational pitch that the other notes have to adjust to. In thirds, the low note is the melodic note and the higher note needs to adjust. In sixths, the higher note is the melodic note and the lower note has to adjust.

It is important to develop this skill over time by practicing scales, arpeggios and double stops on a daily basis. In the end it becomes an intuitive skill, and an individual that might have had intonation problems in the past can really learn to play in tune.

There are thousands of notes in any piece. How does one check so many notes?

It's not as daunting as it may seem. How many different notes are there in the Bach G Major Prelude, for instance? Not that many. The important thing is to use horizontal pitch memory so that corresponding pitches in different octave registers remain identical.

Does one play each note and compare it to the overtone?

No, you tune the chords. In the first chord of the Bach G Major Prelude, for example, the B should match the fifth partial on the G string. If one plays the Pythagorean B, which cellists often do, it will sound too sharp. Fortunately, the average listener's ear will tolerate the sharpness.

When practicing in a slow tempo it is possible to tune each pitch individually, but when speeding the tempo up it is important to listen in a more global, harmonic way, even if it is a melodic section with higher leading tones. As an example, I try to teach the students to practice arpeggios going through all the keys with low Just thirds in a slow tempo. Then I have them switch to a faster tempo using higher Pythagorean thirds. The lower Just thirds make the arpeggios sound more round and relaxed, while the higher melodic thirds sound brighter and more brilliant.

Developing this skill over a number of months helps students increase their level of awareness and perception, so that they have full control over their intonation. I am sure that great string players intuitively visualize music like this even if they are not aware of it.

One can become de-sensitized to intonation problems after practicing a piece for a long time. How does one prevent this? Go back to the overtone series?

Yes, it is very important to always go back to the basics. I like to compare practicing to building a card house: if you want to make it taller you have to make a broader foundation.

Let's take the opening of the Saint-Saens Concerto as an example. The first note starts on the E, which is the same as the harmonic E on the A string. The second note is a D, which should match the open D string, the third note is a C, which should match the C string, the fourth note is a Pythagorean B natural, which should match the 9th partial on the A string. Going back and checking every note like this in a very slow tempo for 10 to 15 minutes can really help bring one's sense of pitch perception back into focus.

Do you consider certain notes as being fixed, like C, G, A, E?

In Pythagorean tuning all the pitches are fixed including the pitches that match the open strings but in Just intonation the pitches move around according to the keys and their functions.

As an example, the A that tunes as a double stop with the open C string is lower than the pitch that matches the open A string, and the C on the D string that tunes with the open A string as a double stop is higher than the C that matches the C string. The important thing to remember is that, with Pythagorean intonation, only the octaves, fourths and fifths can be checked as double stops. The thirds, sixths and sevenths, on the other hand, are out of tune as double stops.

Do you recommend practicing with drones?

When people practice scales with a drone they are practicing Just intonation and will end up playing everything quite flat when playing together with the piano.

On the one hand, you say thirds and leading tones should be raised in Pythagorean intonation.  On the other hand, you say that notes corresponding with open strings or their octaves are fixed.  Take the keys of E-flat and A-flat.  G is the third and the leading tone in these keys, respectively.  What is the correct way to play G, raised or matching the open G string?

In Pythagorean tuning, the flats are lower so that open strings can serve as leading tones or as major thirds. Before I understood the theories about intonation I simply told students to make the tonic low in the flat keys so that the open string can serve as a high leading tone.

As an example: to find the Pythagorean flats, match the C natural on the A string with the C string and go down by perfect fifths from F to B flat to E flat to find the Pythagorean flat pitches. Now match the E flat on the D string with the Pythagorean E flat on the C string and you can see how the open D string serves as a high leading tone in E flat major.

Understanding the intonation theories was incredibly eye-opening for me. To experience how these theories actually fit together and interact with one another was simply magical. Of course, all of this goes back to Mother Nature and the overtone series.

I love this quote by Leonard Bernstein:

"I believe that from the earth emerges a musical poetry, which is by nature of its sources tonal. I believe that these sources cause to exist a phonology of music, which evolves from the universal known as the harmonic series"

Do you consider any note that activates a natural harmonic to be fixed?

Again, the important thing to understand is that Pythagorean pitches are fixed and don't move; in Just tuning, however, the pitches move. Let's take the F natural on the D string as an example (see excerpt below). There are three F's on the D string that can activate natural harmonics:

Notice that the distance from the A string becomes increasingly large as the F is lowered.
  • The F that tunes with the A string is a Just major third and is 386 cents.

  • The F that tunes with the C string is the Pythagorean major third and is 408 cents

  • The F that tunes with the G string is 431 cents under the open A string. That is the F that is used in a G dominant 7th chord.
  • Click here for video: Cellist Zhihao Wu

    The F that tunes with the C string is the Pythagorean F and is the F we should use when playing melodically. When playing together with the piano it can be very helpful to tune the A string to the piano's A , the C string to the piano's C and then tune the G string to the C string and the D string to the A string. This is particularly important when playing works such as the Prokofiev Sonata in C major or the Brahms F major sonata, both of which feature many instances where the C string is played together with the piano's low C.

    I recently played the Adagio from the Brahms F Major Sonata, which is in F# Major. This is a difficult key to play in tune.

    Yes, the tendency is to get sharper and sharper as one goes up the A string in this melody. Chromaticism is often difficult to control. The trick is to listen to the piano and adjust accordingly. It can also be helpful to pick specific chords or pitches to use as a point of reference. In this wonderful opening melodic line use the A natural in measures 6 and 7 that matches the harmonic A and the C sharp in measure 8 that matches the piano's C sharp in the left hand. Whenever you return to that C sharp make sure it is the same C sharp. Keeping that C sharp in your mind ensures that the passage does not modulate upwards and become too sharp. Another way to train the ear is to sing the cello line while playing the piano part. If you are not able to play the whole piano part, pick out the important line or chords. I find that students are less tolerant of their intonation problems when they sing.

    There are a lot of musicians who play with beautiful intonation and they've probably never heard of the concepts in your book. How do they do it?

    They are the elite players who have a special gift. My father once told me jokingly that the string players who are experts on the theories of intonation are usually the ones who can't or don't play in tune. He would always make fun of this topic. However, as I was working on the book during the last week of his life, I explained to him that all the things that he had taught me about intonation were now going to be laid out in a book, explained from a theoretical point of view. He responded, "I trust that in writing this book you will allow cellists to achieve a higher listening ability." He was delighted to know that the information that he had taught me about vertical and horizontal intonation would now be passed on to other string players, despite being explained in a different way.

    I've seen students suddenly start playing in tune, as if by magic. How does this happen?

    It isn't magic, they must have worked on it. But over the years I have taught a number of students who played out of tune but actually had perfect pitch and a great sense of intonation. For some reason, however, they did not care enough to use their listening abilities. With these students, simply making them more aware of listening often brought fast results. The ability to listen is one thing, but it is also of the utmost importance to spend time actually doing it and cultivating it as a specific skill.

    Do players have a more ringing, resonant sound when they play in tune?

    Yes, absolutely. I remember hearing Henryk Szeryng play the Prelude from the E Major Partita in Carnegie Hall. The entire hall was filled with a sparkling, vibrant sound. All the overtones lined up and it sounded like the sound was coming from everywhere in the hall.

    I've noticed that a lot of cellists look at their fingers when they play, even soloists. Does this help us play in tune? There's nothing to see, actually, since there are no frets.

    We all do it, but I encourage my students not to. The goal is to hear the notes in our mind, separate from the instrument. Look how Pinchas Zuckerman can switch between violin and viola and play perfectly in tune. This doesn't happen by sight.

    I once had a very young student try my cello. Her own cello was a half size. She took my cello and played in tune immediately. The more I teach, the more I realize that intonation is in the ear and the fingers just have to follow. We spend too much time thinking about the fingers and not enough time thinking about how we visualize and perceive the music in our mind.

    I've heard that Pablo Casals used intonation to toy with audiences. For instance, at the end of the Adagio of the Brahms F Major Sonata, he would intentionally play the E-sharp, which is the leading tone, painfully high so that the audience would feel an increased sense of relief with the resolution in the next bar.

    There is no question that intonation can be an incredibly expressive tool. I once heard Nadia Salerno-Sonnenberg in a concert do the same thing with the leading tones over and over again to the point that it was almost annoying. She took certain pitches way over the edge. It was clear that she did it on purpose and the result was actually very expressive and powerful.

    Is this something you teach?

    Absolutely. Just like we discuss vibrato, it is important to talk about the expressive effects of intonation. This often comes up in chamber music; I encourage groups to experiment with intonation and tuning strategies depending on the key of the piece, or in order to create tension and different colors in the harmonies.

    Why does it seem to be harder to play in tune up high on the D, G. and C strings?

    Probably because you don't spend as much time up high on these strings. It is common to go up the A string, but other fingering solutions tend to be neglected. It can also be difficult to hear intonation down low on the C string because we are close to the limit of human hearing: the C string vibrates at roughly 65 hertz and the lowest we can hear is approximately 20 hertz.

    I read that Pablo Casals once said the hardest note to find on the cello is the first B on the A string. How do you teach your students to find that B?

    We have two B naturals on the A string that we use a lot. The first one is the B natural that tunes as a double stop with the D string (Just intonation), which is the one we use when tuning a G major chord with the open G and D string. The second one is the Pythagorean B natural that is the 9th partial of the A string. The 9th partial can be found by going up to the A string to the harmonic A three octaves above the open string. The harmonic right after that A is the 9th partial Pythagorean B natural. That B natural works perfectly when played together with the piano. It is 4 cents sharper than the equal tempered B natural but that is such a small amount that nobody will notice. Also, when vibrating the pitch of a note it is distorted anyway. We use this B natural for the opening of the Dvorak concerto and the opening of the second movement of the Arpeggione Sonata.

    Click here for video: Cellist Brannon Cho and Lydia Rhee

    Should we be using Pythagorean intonation when playing a concerto?

    Absolutely. Pythagorean intonation can allow for more expressive intonation. The brightness of this tuning system helps the string instrument project better out in the hall.

    A challenge with chamber music is that each musician may have a different concept of intonation.

    That's why professional chamber groups rehearse so much, and why they can get on each other's nerves when they don't agree. Even with people who have great ears, they may still have different tastes regarding what they think is correct.

    Intonation at the highest level is a very expressive tool that can add a lot of color to the music. In some ways it can be compared to using spices in food. It is my hope that cellists using CelloMind will have a tool that can help them on their journey towards developing more sophisticated inner and outer hearing. Do people need to know and understand all this? No of course not but for me to write a book about this topic I felt I needed to 100% understand these concepts. For some students just telling them a few small facts can help them a lot. With students that have fantastic intonation I still want them to understand these concepts because it can help them in the future when they have to teach or give master classes. As stated before, having some understanding about intonation can help train the ear. Even after having written this book the knowledge and information I have keeps expanding and I constantly find and see things that I did not realise before. Almost every day there is a new discovery.

    To learn more about intonation and other topics go to CelloMind.com


    Direct correspondence to the appropriate ICS Staff
    Webmaster: Tim Janof
    Director: Tim Janof
    Copyright © 1995- Internet Cello Society