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The Wiki article lists a 27 note range for the violin, viola, 'cello, and double bass. The first three are listed as conservative estimates, and less so for the double bass. Am I correctly inferring then, that the range of a double bass is typically smaller than the other three? I assume this estimate is for simply fingered notes, not for harmonics or notes played behind the bridge.

As a casual observer, I always assumed the four instruments would have the same size range. Are the violin and 'cello the same, but the double bass and viola not? I am not quite sure what this article is getting at by saying the "ideal ratio of string length to pitch is compromised somewhat" for the viola, but I assumed it would be a factor here.

Bonus points for use of scientific pitch notation instead of Helmholtz.

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    Please note that the Double Bass is a transposing instrument what they play and what you here is not the same. – Neil Meyer May 8 '15 at 18:13
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    @NeilMeyer is that similar to guitar, where the concert pitch differs by an octave, or is it a different note altogether? and then is e1-c5 the double bass range in notation or concert pitch? – aeroNotAuto May 8 '15 at 18:22
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    Yes the sound it produces is an octave lower than notated. – Neil Meyer May 8 '15 at 18:23
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    @NeilMeyer: I consider that a needlessly complicated perspective. Guitar and double bass aren't transposing instruments, they simply use a different clef, which happens to be an octave lower than treble / bass clef, respectively. In guitar scores, this is generally written as such (with an 8 below the clef); for double bass it somehow hasn't caught on. – leftaroundabout May 8 '15 at 19:04
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    @leftaroundabout - nevertheless it's a relevant fact. It effectively gives the double bass an extra octave to what it seems looking at the dots. Just what the OP ordered. Transposing or not? I feel a question coming... – Tim May 9 '15 at 7:58
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I would say that those ranges are a good guideline. Of course, their range upwards is theoretically infinite (or at least until you run out of fingerboard, for fingered notes), but it's somewhere around there that they start getting screechy and it takes a professional quality section to play in tune. You can expand those ranges a bit for soloists (especially for cello, modern repertoire has really pushed the range of the instrument). Bass has less range because its strings are tuned in fourths, and also because it's rarely asked to play high so players don't tend to have much experience up there.

As a casual observer, I always assumed the four instruments would have the same size range.

Usually the larger the instrument, the greater the range. As you make an instrument larger, you gain notes at the bottom faster than you lose them at the top. This is because small instruments are finicky and difficult to control due to how close together everything is--a cello is going to more easily play way up its fingerboard than a violin because there's more space to work with.

"ideal ratio of string length to pitch is compromised somewhat" for the viola

The viola is only slightly larger than the violin, but plays a fifth lower. To maintain the same ratio, it really should be 1.5x larger than the violin.

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The upright bass has four strings tuned in fourths, whereas the cello, viola and violin have four strings tuned in fifths. Therefore, the practical range of the cello, viola and violin are about a fifth wider than that of the upright bass.

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    i guess in hindsight, that should have been obvious, despite the fact that it didn't occur to me. – aeroNotAuto May 8 '15 at 17:11
  • Don't forget that there are also 5 string double basses (as well as 5 string electric basses) that give another 4th to the range. – Tim May 8 '15 at 17:52
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    Actually what is more common with modern orchestral upright basses is for a 4-string instrument with a low C extension mechanism on the low E string, enabling playing two whole steps lower. But this is not yet considered a standard part of the bass' range. – user1044 May 8 '15 at 18:18
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    @WheatWilliams: in Europe, five-strings are rather more common than extensions. – leftaroundabout May 8 '15 at 18:26
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    @WheatWilliams the notion of the "standard" lowest note on the bass is not very well defined. For example in the 18th century the "standard" bass had 3 strings tuned in 5ths C-G-D. Most orchestral scores of that period assume the lowest note was C, as with the current "extension", not E. – user19146 May 8 '15 at 20:23
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There is one important way how the small and big instruments differ, with regard to this issue: on cello and double bass, there are two very different fingering techniques used, namely, the positions above 5th are normally played as thumb position. Thumb position gives a very stable basis to notes almost arbitrarily high on the fretboard, which is why some cellists can play virtually anything that would normally be played on violin.

The downside of thumb position is that the hand is not as flexible as in neck positions, which makes smooth vibrato a bit tricky. Also you can't use the thumb as a force-balance on the other side of the neck, which I suppose makes playing bass even more physically demanding than usually. Therefore, I'd reckon, thumb position is rather more commonly and more extremely used on cello than on double bass. Add to this that bass sounds a bit weird-raspy in high registers, whereas cello can be exceptionally sweet and expressive here, and of course that the fourths-tuning is intrinsically narrower1, then I'd sum up that, yes2, cello has a substantially vaster characteristic range than double bass.

Now, with violin and viola, you don't switch to something like thumb position – ar least I've never seen it. The higher notes have to be reached while the thumb is still more or less on the neck. That seems to work pretty well on violin (though it must be really difficult to hit the notes!), but probably not so easy on viola, which – so I've heard – is a pretty arm-twisting instrument to begin with. So again, you can probably say that violin has a wider range than viola.

If I were to specify the ranges of the instruments (as in: what I'd consider reasonable to use in any score, not just as a special effect), I'd probably go with

  • Violin: G3 - E7
  • Viola: C3 - D5

    ! Ok ok, joking, violists... I know, some of you can play fourth or even fifth position!
  • Cello: C2 - C6
  • Bass: E1 - C4

1OTOH, 5-string basses (or low-C extensions of 4-string basses) are quite common, that of course immediately extents the range by a fourth (however, it makes particularly thumb position more tricky to bow, because you have less angle between the strings). There are also 5-string violins, violas and cellos, but these are somewhat exotic – more used by e.g. bluegrass fiddlers (or, amplified, in rock music) than by classical players.

2Since I play cello myself (and electric bass, but not double bass), I might be a bit biased here.

  • The upward range of the violin and viola is limited by the fact that the body of the instrument limits how far the left hand can reach along the strings. This is more significant on the viola because it is bigger than the violin. On cello and bass the left hand and arm can reach over the body to any position, including playing on the short sections of the strings below the bridge as a special effect. – user19146 May 8 '15 at 20:34
  • @alephzero: well, violinists and violists could probably reach over the body too, but they couldn't establish a stable thumb position there as on the cello and bass – and without that, intonation is just a bit too much of a roulette. — As for special techniques, sure you mean below the bridge? That's normally a bow-only thing, there's not really much interesting the left hand could do there. What is occasionally done is, playing (flageolett) notes higher than the fingerboard reaches, but still above the bridge. – leftaroundabout May 8 '15 at 21:06
  • An octopus could probably reach over a violin/viola body that way, but not a normal human. As for fingering below the bridge on cello/bass, it depends how avant-garde you get. If it's physically possible, somebody will want to do it one day, if they haven't already! – user19146 May 8 '15 at 23:16
  • I've experimented (cello) and found that, with care, one can open-string finger notes below the fingerboard. These are not harmonics; my suspicion is that the pitch is so high that the energy propagating towards the scroll is dissipated in the string & thus never reflects off the nut. – Carl Witthoft May 9 '15 at 12:55
  • @CarlWitthoft: yeah, that's also possible. I've always interpreteted it that the fingers act like a bottleneck slide up there (the high frequency means you need very little inert mass to stop the string). But IMO these notes sound rather harried; artificial harmonics tend to come out smoother. – leftaroundabout May 9 '15 at 13:39

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