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Consider following excerpt of the first movement of Mendelssohn's Violin concerto:

enter image description here

It contains a series of arpeggios.

What are the rules to write such arpeggios?

  • Are the four notes always played on the four separate strings?
  • Which jumps are possible?
  • Does the fingering change inside a group of four notes?
  • Are the rules different for violin/cello?
  • Is is mandatory to combine an upwards figure with a downwards figure (same notes or different ones), or is it possible to play a series of upwards (downwards) figures?
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    Whatever you write needs to be playable. Consult a violinist (or cellist) about specific ideas. The Mendelssohn extract is a good model because it works.
    – Peter
    Aug 15 at 2:40
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Arpeggios are an incredibly common figure in violin music. Most of the limitations you seem worried about simply don't exist. Arpeggios are just notes to us; there are no special rules about which strings or fingerings are expected.

If you want to be extra nice to the players and make everything easy (or if you have very fast arpeggios that need to be easy):

  • Avoid perfect fifths that aren't on open strings. The same finger has to jump, which makes it hard to play smoothly and in tune.

  • Avoid jumping over strings (e.g. from the G string to the A string). Self-explanatory.

  • Keep your repeated figures within a range of about two octaves or less, which is what the hand can reach without shifting along the neck.

  • Don't pick a key with more than like, four sharps or flats. No one wants that.

None of these are rules; in fact a whole piece that observed all of them would be a dream. But they should give you a basic concept of what is and isn't easy.

As for cellos, I don't play one. Most of the above would still apply, but if there are further intricacies, I can't tell you.

As Peter said, when in doubt, ask someone who plays the instrument to test what you've written.

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    Cellos are tuned in fifths, double basses in fourths.
    – Peter
    Aug 15 at 7:08
  • @Peter Ah, my mistake! I'll edit. Aug 15 at 7:09
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    You can have perfect fifths which are not open strings. And you do not jump with a finger, you place one finger on two strings. Look at the Mendelssohn example provided in the first post at the lower notes in the two first bars. But avoid perfect fifths with the 4th finger. Aug 15 at 9:17
  • @LarsPeterSchultz I didn't say it couldn't be done, just that it's something to be aware of. Aug 15 at 18:07
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    Well, you said that the same finger had to jump. So I just corrected that since you do not jump with the finger in that situation. Aug 15 at 21:53
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I have played this particular section in the Mendelssohn before, so I have some knowledge about it.

Mostly, the fingering depends on the speed at which you are going to perform the arpeggio and the bow stroke. For example, most violinists (including me) would play this section of the Mendelssohn with a ricochet or a brush stroke. For those types of bow strokes, it is recommended to have the notes go across the string. An example of a piece with arpeggios that don't go across the string for every note is Wieniawski's Scherzo Tarantelle. Arpeggios in that piece have one note on the E string and two notes on the A string. It is not mandatory for the arpeggio to stay in one position and go across strings; if the arpeggio isn't supposed to be fast, shifts can be made while playing it. However, consider the tempo when choosing to put a shift. Jumps, again, are based on the tempo, but as most arpeggios are played quickly, try to put most of the fingers within reach and without too much stretching.

I saw in a different answer that perfect fifths without open strings should be avoided. This is not necessarily true, and Scherzo Tarantelle contains multiple perfect fifths with the same finger without jumps. Also, avoiding keys with a lot of sharps or flats isn't necessary either; as long as the arpeggio can be played without too much finger movement or awkward hand placement, the accidentals shouldn't matter much.

Finally, it is not mandatory to combine an upwards arpeggio with a downwards one. For example, in the first movement of the Tchaikovsky Violin Concerto, the solo violinist ends the exposition into the first major tutti with a series of ascending arpeggios.

As I am a violinist, I don't have much perspective for the cellos so I will leave my advice at that.

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There's an important semantic distinction here. I think the OP understands this, but it should be highlighted for references: This passage isn't just about arpeggiation; it's about a specific cross-string bowing technique. For instance, Paganini's fifth caprice for solo violin starts with some big A-minor arpeggios; as Flesch's fingerings here show, there's no doubt that fingering changes during the arpeggio: enter image description here

This passage from the end of the Mendelssohn cadenza, though, are an example of a technique that I don't have a good name for. I've seen it referred to as bariolage and ondeggiando, but technically "bariolage" applies to passages that use different strings primarily to highlight their differences in timber, and "ondeggiando" can apply to two-string patterns.

Whatever you call it, the point is that you voice chords in ways that put a note on each of the four strings, and then rapidly roll the bow across all four strings. The effect can be very arresting, since one can roll the bow much more quickly than one can change left-hand fingers, so you can spray out scintillating showers of 16th notes while only moving your left hand perhaps once per beat or per bar. Another prominent example is in Bach's "Chaconne" from the D minor solo violin partita. In this case, Bach starts out by notating all the pitches, then starts just writing stacked chords with the indication "arpeggio," assuming that you can see from the example how to break them apart. enter image description here

This passage presents challenges to interpretation. For one thing, he starts with a "zig-zag" pattern (arguably "double ondeggiando" juxtaposing two overlapping pairs of strings) rather than arpeggiating straight up and then down, but later chords don't accommodate that (and are traditionally done in the same style as the Mendelssohn example), and some chords have three members and some four (do you play triplets? 16ths? Do you double a chord member, or "hop" the bow over a non-adjacent string?).

For a composer, you could take the same approach and leave fingering and voicing up to the performer, or you could spell it out. In any case Peter's comment is important: get the input of an instrumentalist. This cross-string technique is highly idiomatic to bowed string instruments, and while we can "cheat" in a number of ways (yes, you can change fingering within the chord, but you don't want to; yes, you can put two notes on one string or skip a string, but it seriously challenges the bow articulation), you are choosing a technique in which the physicality of the instrument dictates the voicing, and might as well write idiomatically. Mendelssohn worked closely with the violinist for whom he was writing the concerto, Ferdinand David. The fact that Mendelssohn notated a cadenza at all was a bit of a break with precedence. A Mozart concerto would expect the performer to improvise a cadenza. I'm having trouble finding the citation for this, but if I recall, Mendelssohn was reluctant to provide a cadenza himself and David encouraged him to, but the result was the product of a lot of correspondence between both, and just as much David's work as Mendelssohn's. (This autograph score shows an early version; it does contain the arpeggiation, though like Bach he notates it as stacked chords, but David eventually stretched it to a much longer cadenza. enter image description here

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  • I am not sure what you mean by zig-zag pattern in the Bach example. The first note F is played on the G string in fifth position, the second note D is the open D string and the third note is A in fifth position on the A string. Thus the bow is arpeggiating from the lower string, the middle string, upper string and back again, a basic arpeggio pattern. Aug 17 at 0:11
  • Oh, just that the first few chords actually have their "voices crossed." Sure, the bow pattern is "normal," but since the middle note comes first, the pitch pattern is "mid-low-high-low." A great example of how this technique is instrument-predicated; that's "obvious" to performers but not to anyone simply analysing the score without taking the instrument into context (or worse, composing without doing so). (Which is all the more striking in Bach, who was fairly instrument-agnostic and transcribed his own works for different instruments regularly.) Aug 17 at 12:35
  • Well, Bach certainly knew how to write something that is especially designed for violin. The violin solo pieces are very difficult but appeals to the violin player. The arppegio quote in question above is from the Chaconne. It is a fantastic piece. Aug 17 at 17:45

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