What are the violin note pitches in perfect fifth temperament?

Edited: March 6, 2018, 11:49 AM · Violin is tuned in perfect pitches, which I think I understand, but how are the other notes then played? I know that sometimes some notes are played a bit flat and some a bit sharp, but what is the medium Hz for every pitch against what a pitch is considered to be a bit sharp or a bit flat?

To clarify, if this sounds stupid, I mean that if for example A is 442 and E is 444, D is 440 and G is 438, what is then For example A on E string or G on D string? I mean if it is not equal temperament then how do the notes that are fingered have their pitches?

And please dont shoot me for asking stupid questions, Im a pianist lol, whos child plays violin, but I have just been thinking about it long and cannot figure it out.

Replies (31)

Edited: March 6, 2018, 2:36 PM · It's not a stupid question, but an important question with a long answer, and is still controversial after centuries of practice. I'll skip to the summary: Perfect fifths have a frequency ratio of 3/2. The equal-tempered fifths on your piano are very slightly short: 2/100 of a half-step! As I violinist I think of each note being a cluster of three very close spots; low, middle(equal-tempered), and high. Melodic, Pythagorian,"expressive" tuning uses large whole-steps, small half-steps, large major thirds,small minor thirds. Chordal,-Just, Tartini-style tuning uses a mix of small and large half-steps and whole-steps, short major thirds, and wide minor thirds. Piano-style, equal-tempered, tuning is a compromise that is good enough most of the time, especially needed for modern, non-tonal genres. Knowing when and why to bend notes is a major problem for a string player, a difference between a first class soloist and us ordinary mortals. Fortunately, we have a technical tool that often solves the problem- Vibrato! ~jq
March 6, 2018, 2:43 PM · It's a really complicated technical answer. The short answer is that as a violinist advances in their studies, they are taught to hear pitches in a musical context. The "in a musical context" part is really important. The difficult part about pitch with violin isn't any old C played at an exact frequency, it's actually fitting that C into the musical phrase.

If I recall correctly, your daughter is very young and you are trying to teach her perfect pitch? Worrying about a pitch difference of 20 cents falls in the category of things you don't need to worry about for years. Moreover, the complexity of pitch on a fretless instrument is beyond your daughter's ability at this time. Patience.

Edited: March 6, 2018, 3:18 PM · A short book you might want to read, Maria, is "How Equal Temperament Ruined Harmony (and Why You Should Care)," by Ross W. Duffin goes into this in great detail. It actually is a problem for string players - playing thirds really IN TUNE is a problem ask any professional string quartet. The issue might also be asked of ensembles as "Why is it so hard to play Mozart in tune."

Another book: "Temperament: How Music Became a Battleground for the Great Minds of Western Civilization, by Stuart Isacoff is longer, gets into it more gently and puts it into an historical context.

Edited: March 6, 2018, 3:19 PM · Oh dear.

Notes that are perfect fourths (4/3) fifths (3/2) and octaves (2/1) from the open strings are easy to calculate.

True, "pure" major thirds (5/4), minor thirds (6/5) major sixths (5/3) and minor sixths (8/5) often don't "fit", depending on where they come from.

Thirds derived from fifths (e.g. viola C to violin E) will be 81/64 (major) and 32/27 (minor); sixths will be 27/16 (major) and 128/18 (minor).

Whole tones shoukld usually be 9/8, but 10/9 can sound better.

Semitones are either 16/15, or 256/243

You'll have to calculate the frequencies yourself, my head is spinning!

March 6, 2018, 4:17 PM · Play all Gs Ds As and Es at the same pitch as the open strings. The rest will follow. Everything else is too complicated.
March 6, 2018, 5:42 PM · Hi Maria,

You're asking great questions. Some of your terminologies are confused, you're best off with reading Ross Duffin's How Equal Temperament Ruined Harmony and the Isocoff book suggested by Andrew.

For a kid learning violin, getting the most resonsonance out of the instrument would suffice. One doesn't need to be able to calculate how many cents a just interval is different from an equal temperament interval.

A common demonstration on how intonational depends on context as Julia mentioned:
play first finger B on A string against D string. Once you found a pure major 6th with D string and B, don't move your first finger and play that B against E string — that B won't make a pure major fourth with E string.

Solution: you tune your open strings with tighter fifths (tempering them), or your adjust your first finger.

If you don't understand terms like "just", "temperament", "tuning system", "pure intervals", go read Duffin and come back.

Edited: March 7, 2018, 3:15 AM · Right, thanks, ill try to find that book next. Im the kind of person that really likes to know things fully, its hard just too let things be about right, not knowing what is exactly right ;)

Its just that as I dont have perfect pitch, I have to use an app with my daughter to develop her pitch memory. And yes, it is a very good pitch memory that is developing, not absolute pitch, I think so now. It will probably look like a perfect pitch when she is older, but it is not, it is relative pitch with very good pitch memory. And which is probably the best option :)

And when using the app, I can hear myself diferencies of about 15 HZ and it bothers me so much that now I do not know what the exact Hz is for the note that Im aiming to play. I would really want to set my own ear right. Apparently it seams that I have the same latent capacity of good hearing, just not developed (and as Im old it developes so very slowly compared to my daughter)

And thank you for the good answers, it so nice to know, that it isnt an easy question that Im not just stupid not to see the answer lol.

So ill find the book , read it and come back with LOTs of questions lol

Edit. Ordered it, I hope I can understand it :D

Edited: March 7, 2018, 2:18 AM · Do you have a choir in town your daughter could join? One of the best methods to develop a sense of pitch is singing in a group.
March 7, 2018, 7:52 AM · It's a little way off the question but I'm interested to know, does everyone here tune their strings in perfect fifths? This is fine if you're playing alone, but in the context of a string quartet it just doesn't work. If you calculate the frequencies of a circle of perfect fifths starting with the cellist's C string, by the time you get to top C on the violin you'll be sharp relative to the cello's bottom C by a whole semitone!
Edited: March 7, 2018, 8:55 AM · Warning! The study of temperament and tuning is a minefield. If you want to pursue a Master's Dissertation or Doctoral Thesis, then there's your subject.
March 7, 2018, 8:11 AM · I happen to have read both books mentioned above by Andrew Victor, and as a violinist and early music enthusiast I greatly prefer Duffin's book. He gives excellent descriptions and diagrams of how, using for example an E, from a single starting note such as a low C, following the circle of fifths as a series of pythagorean ("perfect") fifths (3:2) brings one to an E that is higher from where it would be if built as a perfect third up from the C 2 octaves higher than the starting C. So if you want better thirds, you have to narrow the fifths...but perfect thirds would ruin your fifths, so was born many different systems of temperament to try to split up the discrepancies (known as commas) by spreading them out among the various intervals in the octave. Ross Duffin explains all this in a historical context that discusses how different composers and performers in different periods and styles had different preferences, and how the special character of different keys was a result of keyboard and fretted instruments yielding slightly different series of intervals depending on which note was "do." Much subtlety of color and emotion was lost when we abandoned that palette of different tunings and the different character of the various keys.

Isacoff's book, on the other hand, mostly seeks to justify the supposed universality and superiority of equal temperament, as if it were a historical inevitability as earlier misunderstandings and ignorances were corrected with the progress of science and reason, culminating in the standard piano tuning system that was codified in the early 20th century. He treats the adherents and defenders of other temperaments as mostly superstitious and closed-minded, and does not seem to appreciate the lost possibilities of harmony and modulation that made non-equal temperaments so rich.

Edited: March 7, 2018, 8:36 AM · Maria, when I was just starting to teach myself to play, I couldn't tell if I was even in tune, and for a while longer, I couldn't tell if I'd moved a whole or half step (especially in cases where both notes were "in tune," such as B and C in the key of C). So as a beginner I played with my tuner on all the time, and played slowly enough that it could register and display the note I was playing. After maybe 2 months I didn't need to play with the tuner on anymore, as my fingers and ears learned how to find the right notes and tell if I was in tune or not. You'll get there too, just keep practicing!
Edited: March 7, 2018, 9:00 AM · Regarding Steve Jones' question about whether we are tuning in perfect fifths or not, when I was using the Snark clip-on tuner I would not even have been able to answer the question, I just let the tuner tell me when the open string was a G, D, A or E. Probably that was NOT perfect fifths because I expect such instrument tuners use equal temperament so everyone else can approach being in tune with the piano.

But because I'm very interested in early music and focus my own playing on baroque violin music, I found a GREAT tuning app called Cleartune which I installed on my phone for just $3.99!!!! It allows me to calibrate the A4 to whatever frequency I want (I use 415) and choose from a variety of historic temperaments --I use sixth comma meantone based on the advice I got from a viola da gamba player of an early music consort, who told me that's what they usually use. It also allows me to select the temperament root, meaning which note starts the series of tempered fifths, basically a way of choosing the "top" of the circle of fifths which means the keys further around in either direction end up with the "wolf" notes that result from the discrepancy between the accumulated differences between the series of perfect octaves against the series of fifths.

Another bonus of Cleartune is it displays the frequency in Hz of every note it hears! This is very good for those of us who play with spreadsheets to calculate what the frequencies would be if we change the temperaments and the starting pitch.

March 7, 2018, 8:38 AM · What happens when violin is accompanied by pianowhich is equal temperament. Do they just play in different tune or is the violin tuned in equal temperament?
March 7, 2018, 9:00 AM · Maria, regarding playing with a piano, I highly recommend this great article recently published online by Strings Magazine: "Perfect Fifths: A Few Thoughts on Tuning Your Viola (Violinists & Cellists Invited)" by Atar Arad.
Edited: March 7, 2018, 9:19 AM · In my experience, playing violin, viola, and cello with pianos fairly regularly over the past 50 years. Tuning the violin's A string to the piano and then tuning the E, D and G strings harmonically in perfect 5ths works well enough, although one might want to tune the G string to the piano's (especially since there is no other way to play that note on the violin than with the open G string and that is the only note on violin that can not be adjusted by the player's fingers).

For viola and cello, which have A, D, G and C strings, the C string is distant enough from the A that I have always found it necessary to tune my C strings to the piano's. Actually, I would select to tune to that piano C that will most influence our harmony in what we are playing together.

As far as learning to play the violin in tune, it is accomplished by matching your fingers with your hearing. This is one of the reasons I switched my teaching method after the first 10 years to the basis of the Suzuki books that start with the melody for "Twinkle, Twinkle, Little Star." Actually, almost any musical piece the beginner is familiar with hearing (IN TUNE) and that uses only the E and A strings will serve the same purpose. Actually, my own violin lessons, that began in 1939, while I was 4 years old, started with "Twinkle," and this was long before Suzuki teaching arrived in the USA. I remember very well that my first teacher promised to reward me with a "jeweled" matchbox that was on a table in his music room when I had learned to play that piece in tune and I remember the day I finally earned it!

It is not a mental activity. It's not rocket science - it's probably actually more difficult, but it should be possible for anyone with close-to normal hearing.

(from a retired rocket scientist)

March 7, 2018, 9:11 AM · Maria, the bottom line is, that the music sounds good! Pianos aren't always properly tuned or tuned to the violinist's preferred pitch, but the violin can be adjusted easier to the piano. The player can also adjust each and every note with her/his fingers to match the piano. The world where science and artistry meet is a very gray area.
March 7, 2018, 9:25 AM · Maria,
I think the best answer I can come up with is that 5ths other than the open strings are derived from each string itself, as if that string is the only string on the violin. So for example, on the D string, the best-tuned A is at a place that divides the string into 3 exactly equal parts. This may or may not coincide perfectly with the open A--it depends on how well you tuned the A string.

Another example is the third-finger G on the D string. We're taught to make a good octave against the G string...but that is dependent on where exactly the G is tuned. In fact, that fingered G should be tuned so that it lies one quarter of the way up the string. So there's two issues here: the note with regard to the string it's on, and the resonance it makes with other strings. As Julia says, it's complicated, and we have to rely on context at a given moment.

Though we don't tune in equal temperament, we still have the same problem. For example, if you put a first finger on D and try to tune that a major 6th above the G and a perfect 4th with the A string, you might find it's impossible. You have to slightly roll your finger to adjust the note as you go from one interval to the next. The reason we don't have to worry so much about equal temperament is that we're lucky: we don't have to play more than two notes at a time except in rare occasions. And when we do we learn to compensate very quickly. And vibrate...

I doubt that thinking in terms of HZ will help. If you had precise numbers, what would you do with the information?

It is impossible for the violin to play systematically in equal temperament. Your head would explode, and the wouldn't sound really in tune with itself. An example is that on the piano major 6ths are wide, yet they sound acceptable. There's a beating sound, but it almost sounds vibrato-like. However, wide major 6ths on the violin just sound noisy and ugly. The violin doesn't have the same resonance as the piano.

The violin has to played in tune with itself. Some notes, when played with a piano, can be tweaked, but in general I think most violinists just try to play in tune with themselves and don't worry about it. you can, for example, push an F natural a little one way or another, but probably not a very resonant note like a perfect 4th up on any string. Sure, you'll match the piano, but it will sound out of tune. We all know what a slightly low 3rd finger sounds like, and it's not pretty. I tell my students to imagine the "sound' of sour milk when they play flat.

Unless there is some egregious discrepancy, I believe that, due to the very different timbres of the instruments, the ear separates them very effectively.

Edited: March 7, 2018, 9:35 AM · Thanks Will (ed. and Scott) - plenty to research and digest there! However 21st century tuning technology hasn't yet reached the orchestra, at least in my neck of the woods. Having obtained an accurate A of 440Hz or whatever from the oboe the violinists tune their other strings purely by ear, in what are hoped to be perfect fifths. Solo violinists when tuning in front of an orchestra also adopt this method; I'm often impressed by the purity of their fifths and wish I could get the same result as easily. Cellists start by ensuring their A string is exactly an octave below the oboe and go down three perfect fifths from there. I calculate this will leave their C string about a quarter tone flat as compared with the soloist's E. No wonder you often find them giving it a tweak in mid-rehearsal.

I think the short answer to Maria's question is that when playing with piano violinists tune (or should tune) each of their strings separately to the piano, and allow the notes in between to take care of themselves. Frankly with my fingers nobody would be able to detect whether I tune one way or another.

March 7, 2018, 9:34 AM · I second Andrew regarding tuning the A-string with the piano and the rest in perfect fifths. The differences in pitch are negligible. Also I wholeheartedly agree that turning violin practice into rocket science is not necessary. Aiming to have the notes sound in tune when playing with the piano is sufficient at the stage your daughter is at. Learning music, especially at an early age, is a very intuitive process. Compare it to the way children learn languages. They rarely, if ever, use computer apps to check whether they pronounce all vowels correctly.
Edited: March 7, 2018, 9:41 AM · Since I added "DaTuner Pro" to my android phone I can tune my strings in any of 40 temperament systems to the closest "cent" (1 cent = 1% of a half tone). However, just varying bow pressure can easily change the pitch of the open string by 5 or more cents. Once you place a finger on the string normal finger or hand unsteadiness can vary the pitch even more.

Intensional vibrato (of much more advanced playing) will vary the instantaneous pitch by much more. However, the human ear seems to hear the resulting colorful sound as a specific pitch.

The actually sound from vibrating strings is very complex and always involves not only the fundamental pitch but many overtone pitches that have harmonic relationships (ratios of integer numbers) to the fundamental. This is further complicated by the way resonant frequencies of the specific instrument emphasize certain harmonics over others.

March 7, 2018, 10:00 AM · @Maria the very short answer is that the violinist plays the instrument in equal temperament to fit in with the piano.

The open strings may not quite be in equal temperament but open strings are reasonably rare in advanced playing, and when they happen tend to be fairly short notes (and it's more difficult to establish the pitch of a short note), so no-one notices or cares.

March 7, 2018, 10:48 AM · We are getting expert info. on this topic, which comes around often.
I read somewhere that the violist W. Primrose, when playing with a piano, would tune the D string to the piano D, then perfect fifths for the other strings. Perhaps Cellists should try that. Good singers working with a piano will naturally synchronize pitch to the piano. String players should also be able to do that. But, I heard one major league violinist, several levels above me, say that the violinist should Not try to match the piano intonation! jq
Edited: March 7, 2018, 11:58 AM · Actually, this can be a fascinating subject.
In the 25th of his 100 on-line "lessonetts," cellist David Finckel (formerly of the Emerson Quartet and now director of the Lincoln Center Chamber Music Society) advocated tuning all 4 strings with a tuner (he used a simple Korg) and said that by tuning all 4 instruments that way, the Emerson Quartet had avoided any arguments about tuning.

That got me started tuning that way (after over 70 years of tuning by ear) and I have not regretted it. I use it for piano trios, orchestra and quartets. Most recently I started using a "D'Addario NS Micro Universal Tuner" that is available from Amazon at a reasonable price. I use the clip-on version and fasten it to my cello bridge to tune and then remove it. It senses the vibrations directly so you can check your strings' intonation even while an entire orchestra is messing around. There are also versions that clip directly to a violin or viola body (at leaf to narrow viola bodies) and can even be kept on while playing.

I have heard from professional cellists who prefer to tune their lowest string (C string) to the piano and tune the rest of their strings in perfect fifths to that.

By the way, Will, I think you did an outstanding job summarizing those 2 books!!

March 7, 2018, 3:33 PM · "I read somewhere that the violist W. Primrose, when playing with a piano, would tune the D string to the piano D, then perfect fifths for the other strings..."

That's great if the piece is so simple that it stays in D. What if it's in D-flat? Or is starts in D and modulates all over the place as a Romantic or 20th century piece might?

That's why I say to tune to the piano's A, then just play in tune with yourself. Let's face it--most of us have a hard enough time doing that alone.

Edited: March 8, 2018, 12:50 PM · I came to an epiphany one day. Just like wine, it doesn’t hurt to read a lot about intonation but you have to hear it (or taste it) to really get it.

So, we take our 7 yo to a lot of live performances to develop her ears. She has a razor-sharp perfect pitch but that is different from understanding what beautiful intonation is.

Below is similar to what Scott above and I found it really useful to put into context:

These questions about tuning and scales are interesting in a theoretical sense, but IMHO they are of only marginal real-world importance.

Consider. While it is nice to think about adjusting the tuning of chords in a string quartet for expressive effect, only the finest groups can manage that, and even they cannot do it consistently. And it is nice to try to do the same thing with solo violin music, but if the chordal writing moves at any pace (e.g., the ascending staccato thirds in the Sibelius concerto, or the chordal writing in the violin part in the last movement of the Brahms double), the player is holding on for dear life, with no time to think about anything other than "major, minor," or "wide, close."

Finally, you simply adjust, subtly and automatically, when playing with the piano. All it takes is open ears and a relaxed left hand.


March 8, 2018, 1:40 AM · Andrew - I'm sure David Finckel and the Emerson Quartet know what they're about, but do you remember what they tuned their strings TO as well as WITH?! If they used a similar method as some other quartets it was a holy mixture of perfect fifths for the violins E, A and D and the viola A and D, "close" fifths between the viola G, D and C, and perfect octaves between the viola and cello.

I'm perseverating here but I did some arithmetic - if you were to tune to perfect fifths over a range of 4 octaves (7 intervals of a fifth) the top octave would finish up sharp by +6.79% as compared with the bottom, when a semitone of course is 5.95%. Yikes! Of course if the cello simply reflects the viola an octave lower you only need to consider 4 intervals of a fifth, but that would still be a highly noticeable 3.88%. So our cellist and violist were always encouraged to check their C strings against the violins' E. This particularly matters in flat keys and those with one or no sharps, where an open C from the viola or cello might otherwise be embarrassing.

March 8, 2018, 7:55 AM · I got the impression that the Emerson Quartet just used the tuner to avoid any arguments about "perfect fifths" when tuning their strings. Finckel was not clear about that (it is easy enough to "Youtube" his lessonetts and find the 25th one). As Kiki said, for the rest of it "all it takes is open ears and a relaxed hand."
March 8, 2018, 8:33 AM · Just remember yet one more reason a violinist can't get too caught up in playing in equal temperament with a piano:

Pianos are not all tuned the same. There is a varying amount of stretch at either end, depending on the size of piano, and the ear, software, and training of the tuner. I've heard that Steinway technicians were trained to stretch the octaves, perhaps more than most tuners. And there can be discontinuities as you descend into the wrapped wire strings, somewhere around C3. Bigger pianos tend to have more stretch, and small pianos less. So you could be practicing for a recital in a tiny practice room with your accompanist, then in your teacher's studio with a Steinway B, then have the concert on stage with a 9' D. Are you really going to make those tiny adjustments to match the tunings in all of those pianos? What about playing at a retirement home with a terrible donated vertical from the Edwardian age?

I think a quartet should tune its open strings carefully, and I think professional quartets do spend a lot of time perfecting their intonation to the extent that they can (especially considering the vast number of very fine quartets and the high standards out there these days...). But I still maintain--don't drive yourself nuts trying to match every pitch on a piano.

March 8, 2018, 11:54 AM · I talked to a piano tuner recently. He told me that he indeed uses more stretch on Steinway than on Börsendorfer grand pianos in order to emphasize their respective characteristics.

Here's another reason why you shouldn't worry, at least about the lower strings being too low...

March 8, 2018, 12:46 PM · If you want to hear what perfect intonation really sounds like you can do no better than listen to a good a capella choir singing Palestrina, Tallis, Byrd, Victoria, Lassus (and others), and not forgetting the extraordinary harmonic structures of Gesualdo.

For myself, I can listen for hours to Alistair Dixon's Chapelle du Roi singing the works of Thomas Tallis, one notable example being his mighty 40-part motet "Spem in alium", "40-part" in this instance meaning eight five-voice choirs.

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