Do the violins imitate equal temperament when accompanying the piano?

Question

My previous question about equal temperament was answered with a flourish, so here's the follow-up one:

Because math and harmony don't seem to mix very well, piano tuners have to cheat a little bit, pulling down the fifths, nudging the fourths a bit higher, and so forth (no pun intended).

But there's the string section in the orchestra that is not constrained by anything: no frets, no keys. They can be as "just" as they like.

Question: when accompanying the piano (in Chopin's or Grieg's or Mozart's or Tchaikovsky's piano concerto), do they have to "play along," i.e. do they have to abide by the piano's equal temperament lest the whole structure starts bouncing all over the place, way out of tune?

And what about the woodwinds that have fixed holes - are they made to imitate equal temperament?

Answer 1

Tuning in an ensemble is a skill in relative pitch, not absolute pitch. Players will hear what others are doing, and the group will come to a consensus organically. With instruments that are capable of microtuning adjustments, this will also lead to more just-tuned intervals.

But what's important to note is that these tuning decisions happen on the fly, and subconsciously by an experienced player. It's not as if the orchestra makes an overt declaration about the tuning system they plan to use.

So that means that when playing along with a fixed-pitch instrument, a violinist will simply play in tune with it like they always do. They don't consciously decide to use equal temperament, they simply match pitch.

Woodwind construction is a massively complicated topic. The Fundamental Problem of Woodwinds (as I like to call it) is that you need 12 unique fingerings to cover an octave and bridge the first and second harmonics in order to make a fully chromatic instrument (and the problem is worse for clarinet), yet we only have 10 fingers, and usually at least one is used only for holding the instrument, or else the "nothing pressed" fingering would result in us dropping the instrument. What that means is that some fingers/holes have to do double duty and thus there will always be some notes with imperfect tuning.

I'm not a woodwind maker, but I assume that modern instruments are made with equal temperament as a goal. But these construction issues cause tuning discrepancies that are vastly greater than the difference between tuning systems. While a well-constructed instrument should play as close to 12TET as possible, playing in tune is still the player's responsibility.

Answer 2

The temperament in a professional orchestra tends to vary between just intonation and equal temperament. If they are playing with a piano the strings will tend to adjust to the piano temperament where the difference would be audible and tend towards just intonation when they are playing alone.
Woodwind instruments are built with the aim of playing in tune with equal temperament, but the differences to just intonation are well within the adjustment range of a good player. They will have no problems adjusting to the strings or to the piano.
Amateur orchestras tend be out of tune enough for the difference to be irrelevant.

Answer 3

In general? No, because it feels unnatural, similar to how singing does. However, you'll surely find places in music where the natural pitch against the bass note will not feel like the right thing.

You can test this with your voice if you are a resanable singer: Play the E tone and sing it. Next, play the C major chord without this tone (so C+G) and sing the tone -- your voice will go slightly down. However, if you play C major including the tone (so C+E+G), you'll keep your voice down.

This is even more significant if you sing the major 3rd in C major (C+E+G) vs. the minor 3rd in C# minor (C#+E+G#). The one in C major will be much lower than the one in C# minor.

The difference comes from the tuning obviously (f denotes the frequency of C):

• (major 3rd) If the base note is C with frequency f, the natural frequency of E is f * 5/4 = 1.250 f.
• (pure 1st) The frequency of the E key itself is f * 2^(4/12) = 1.260 f.
• (pure 5th) If the base note is A with frequency f * 2^(-3/12), the natural frequency of E is f * 2^(-3/12) * 3/2 = 1.261 f.
• (minor 3rd) If the base note is C# with frequency f * 2^(1/12), the natural frequency of E is f * 2^(1/12) * 6/5 = 1.271 f.
• (dominant 7th) If the base note is F# with frequency f * 2^(-6/12), the natural frequency of E is f * 2^(-6/12) * 9/5 = 1.273 f.

So the change in pitch is most significant between E in C major chord (that's the flattest) and E in F#7 chord (that's the sharpest) -- there it will be the easiest to try when singing. However, the original exampe with C major vs. C# minor works pretty well too.

Our ears likes to tune purely, so when given a chance, they will force signers (and players equally) to correct the pitch if it's within their technical ability. (On the violin, this comes as a natural, but experienced woodwind and other players will do it as well, possibly without realizing they're doing it. Most signers in choirs probably have no idea they're doing this.)

Answer 4

To supplement on the woodwind perspective: the fixed position of wholes does not nearly fix the pitch. Each instrument has its individual deviations from in-tune (however small), which can/need to be compensated, and there are lots of other variables like

• embouchure,
• modification of volume of mouth/throat
• speed of air
• pressure of air
• angle of air stream to flute head

as well as alternative fingerings, which are continuously chosen or adjusted by the player in a way quite similar to that of a player of e.g. a violin.

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Update: I missed to mention the next step, which is already in MattPutnams answer: All of those variable are used to match, whatever is there: a fixed-pitch instrument (which might even no longer be perfectly tuned) or the most experienced or leading player.

Answer 5

As a violinist and a pianist, I have over 10 years of semi-professional experience in both instruments (currently not a professional), and have previously played in various performance roles in both instruments.

Violins have different sets of temperaments to work with, and change based on skill level and who they play with.

https://www.violinschool.com/knowledgebase/violin-tuners-intonation/

Equal Temperaments will cause the violin to sound bland, because the notes no longer cause harmonic vibrations with the other strings. Expressive Intonation is the opposite, where the violinist plays according to the harmonics of their instrument, but this pushes the intervals of the scale outside of equal temperaments.

A high level violin soloist will play Expressive Intonation when appropriate. The semi-tone between 3rd note and 4th note will be wider than the semi-tone between the 7th note and 8th note, creating harmonics with the other strings and making it sound much richer. If you have a chance to listen to this, a scale sounds noticeably better when done in Expressive Intonation, but by and large very few modern instrument can do this, and it's simply impractical to bring back instruments that are "perfectly" tuned.

With regards to adjusting their pitch, a violinist does this by ear. Given that a violinist would know how to adjust their notes as necessary based on what key the piece in, it is part of a violinist's skill set to adjust his pitch, literally, on the fly.

A violinist will also change the fingering to avoid open strings, since you can't adjust an open string's pitch, and also will shift to higher positions as needed. There are no hard and fast rule, but it generally has to do with making the piece easier to play and to sound better.

A violinist that lacks experience with accompaniment will incorrectly play Expressive Intonation with other instruments, causing rather unpleasant sounds. It is primarily the violinist's job to learn how to play "in tune" with other instruments because very few instruments can adjust their pitch as readily as a string instrument.

So to answer your question, "Yes, the violin will imitate equal temperament", but the process is largely organic and does not follow hard-and-fast rules. The process of the violinist imitating equal temperament should be a subset of the regularly used skill of adjusting their pitch according to the key they are in.

You won't find any violinist sitting with a pitch machine and practicing with that, because that's not how music works.

Answer 6

Of course any instrument that can play 'in the cracks' will do so when not playing alongside a 12tet tuned instrument. At which point, playng with such an instrument, it makes sense that any decent player will try to be more in tune with said instument, rather than pursuing the 'right path'. Why would anything differ from that scenario?

Answer 7

String quartet players - ie strings playing with other strings - have to adapt their intonation the whole time, depending on the ensemble, the piece, the key, the period of the music, the context within the music. Generally in quartet playing - and counter-intuitively - major thirds and sevenths are played flat, minor thirds sharp. In an orchestra with mixed instrumentation it tends to be the opposite. This, as you can imagine, is extremely skilled work but gets easier as ensembles play together over months and years and grow accustomed to each other, developing their own sound as a group.

Answer 8

The question is based on a misconception that singers or players of stringed instruments will naturally play in just intonation, and that therefore if they're playing with a piano they will have to adapt themselves. This just isn't true. For some real-world data, see Deutsch, The psychology of music, 3rd ed., p. 97. Professional musicians generally judge notes to be in tune if they fall within a band of about +-7 cents. The only way the human ear can hear differences in pitch smaller than about 5 cents is when the conditions make it possible to hear beats (which used to be the only technique available to piano tuners), but this isn't normally possible in real-world musical conditions. The difference between an equal-tempered fifth and a just fifth is only 2 cents. Expressive intonation and vibrato are often on the order of 50 to 100 cents.

What equal temperament allows us to do is to modulate between distant keys without a train wreck and have some way of defining what pitches are even intended when we notate a song in a key like F#. This kind of thing becomes an issue only because you can get wildly wrong results if you keep on stacking just fifths on top of just fifths (the Pythagorean comma). That is, the cumulative effect can be large.

Normal practices in composing and arranging don't actually tend to create situations in which it matters whether a violinist exercises freedom in intonation. For example, the difference between a just and an equal-tempered M3 is 14 cents, which is audible under the right musical conditions. But composers usually don't double the third in a chord, so in a piano-violin duet, if the violin has the third, they have freedom to use whatever kind of vibrato, portamento, or expressiveness in pitch they prefer.