Intonation accuracy

December 14, 2015 at 03:00 PM · The answer to the question is one word - "listen". Listen to the note you're playing in relation to the note you have just played. Listen to the resonances most notes set up in the instrument and be so guided (there are a few notes that don't resonate well, but you'll soon find them).

The second part of the answer is don't use an electronic tuner except for tuning the A-string (a tuning fork is simple and 100% reliable). Tuners make you rely on your eyes and not the ears. And most tuners are tuned to the pianoforte system, which is what you most definitely don't want to use when you're playing the violin.

I don't depart from A-440 tuning - it's too much hassle to retune, and I don't play at 415Hz anyway. My two violins are different sizes - the bridge to nut length on one is 1/4 inch longer than the other, so finger spacings and reaches are different on both. But I adjust naturally because I listen.

December 14, 2015 at 03:03 PM · Steven,

Unless you are a visual type (your preferred sensory input are your eyes), and this is just a temporary phase, looking at tuner is counter-productive.

Why?

Well, you will eventually play with other players in chamber setting, or start playing more complex music on your own, when tuner will simply not be possible to use anymore.

We practice for performance, so the acquired technique (and intonation) can be transferred from practice room to stage or other occasion.

Practice scales. Close your eyes or even switch off the light in the evening. Listen.

Feel the resonance of open strings. Hear when violin sounds at its best.

R

December 14, 2015 at 03:49 PM · I have been playing pieces where the tuner is impossible to use to aid my playing already, which is why I use the tuner only for scale exercises to confirm.

At this point, I can tell when the violin is singing just right, I can tune the violin by ear, and it's almost always right on. I somehow feel this extra "ringing" when the right note is played in tune.

I'm less confident in the higher positions because I'm not so used to it. I've been finger adjacent string to be one octave above or below and listen/look for the sympathetic vibrations if I'm unsure in middle of pieces.

December 14, 2015 at 04:28 PM · Calm. This is a strange word to use for intonation, but I think someone on hear used it to describe when a note is in tune relative to whatever initial frequency you use. Calm as opposed to edgey. I don't know if this helps in higher positions.

December 14, 2015 at 04:43 PM · The basis for improving intonation is the scale. I recommend watching all of the "video tutorials" on the Kurt Sassmannshaus website (www.violinmasterclass.com). He will show you how to understand the origin of the Pythagorean scale, which is the one we use for melodic playing, featuring the large whole steps and narrow half steps.

Another rigorous but user-friendly explanation can be found in either "Basics" or "Scales" by Simon Fischer. Both Fischer and Sassmannshaus are master teachers, their stellar reputations are well deserved. Fischer has those amazing books, Sassmannshaus has really great videos.

It is indeed harder to hear the resonances in the upper register of the violin, where the need for positional accuracy is the greatest because the pitches are closer together (at least it seems that way initially). That's a catch-22. Say you are working on three-octave scales, which are the standard for intermediate players. Listen very carefully during the lower two octaves so that you really grasp how the scale sounds when it's played in tune, how the whole steps and half steps sound. The upper octave needs to match that. The other thing is that you go slow enough so that you CAN hear those upper notes ring. This is also why students often start with G and A major scales -- they don't go too high but they have a lot of ringing pitches. Learning to hear the ringing without taking your bow off the string is not always automatic so don't be too frustrated if you have a hard time with that. It comes.

December 14, 2015 at 05:15 PM · Another difficulty.

Our analysis of pitch is less regular once we go outside the treble and bass clefs: if we us a tuner all the way, the low end seems sharp, and the higher end seems flat.

But.. We won't all agree to the extent of these discrepancies.

For ewample, I find Zukerman's highest notes (on the violin) a bit flat; so does my wife.

Yet another problem: inharmoicity. Strings don't behave like diagrams in physics books; the harmonics are never exact multiples of their fundamentals, because of the stiffness of the strings.

There's more! Both syntonic and pythagorean commas are around 20 cents (1/5 of a tempered semitone) and take 2cm of the string in 1st position (3 cm on my viola).

So Using resnance and harmonics to fine-tune our high notes is a useful starting point, but listening to our fellow musicians is the final arbiter.

December 14, 2015 at 06:26 PM · Adrian, you mean 2mm and 3mm, don't you? 3cm is over an inch in old money! Or you have a humungous viola ;)

December 14, 2015 at 06:56 PM · Sorry, I was wearing my reading glasses!

December 14, 2015 at 10:15 PM ·

December 15, 2015 at 12:22 AM · Trevor and Nate are absolutely right about use of an electronic tuner! There's lots of very good advice here.

December 15, 2015 at 03:49 AM · Thank you everyone for your input. I shall keep at scaling, at a faster rate for the time being. I cannot say that I fully understood some of the advice because musical language isn't my forte. I'm still following Carl Flesch's art of violin playing. I haven't progressed much since the summer, and I probably won't until next summer. I will inquire more as I understand better what's been said, and I've tried them.

December 15, 2015 at 04:07 AM · Greetings,

self deprecation or defeatism?

You know I reviewd Fischers the violin lesson a while back in a blog. The point he akes is that one can take anyone specific aspect of playing and alter it so that it improves, irrespective of age and ability level. He then goes on to show how in in of th

e most informative and common sense guides to the violin ever written. At risk of offending someone I consider that book to be vastly more useful than the Flesch, especially for someoen at your stage. The only reason you are not making progress is you are, frankly speaking doing the wrong things. Stop using e tuner and get Simons book. Put the Flesch on a shelf next to the ashes of your cremate grandmother and leave oth alone. If you dont habe the time or inclination for a teacher (understandable) the emergence of Fischers remarkable volume made the claim that one cannot make progress absolutely redundant.

Cheers,

Burp

The rest is up to ypu

December 15, 2015 at 04:33 AM · I haven't progressed in the past 3 months because I started paying more attention to the quality of the sound I make, in terms of intonation and bowing. I've been learning the same piece for 2 months now. I started recording myself and listening, and I'll admit, while I learned 20 easier pieces since May this year, the quality of the sound was abysmal at best. Not really the intonation, but bowing. Staccato and vibratos sounding like rapid datache or trill almost. It has been improving greatly except ironically I cannot hear my own vibrato while playing.

Also, I'm constrained by time rather than lack of determinism. I am a lot less occupied over the summers because for the rest of the year, I'm stumped with school and research work. I only get to my violin past 9pm. I managed to practice until 2am, and got up to get to class at 8:30 for a month before I started shifting priorities. I'm currently in between exams and thesis writing. Over the winter, I will be teaching 2 courses, and completing one thesis while starting another while taking 4 courses myself. I promised myself that I will learn at least 2 more pieces this year, which I am hopeful to accomplish over the Christmas break. Until May, I doubt I'll be making any progress with violin.

December 15, 2015 at 04:54 AM · Greetings,

actually you can make remarkable improvements on the violin by practicing in two ten minute units twic ea day. It is about doing the right things and knowimg why you are doing them.

I sympathize with the worload though. I squeeE in perhaps forty hours a weke of study on top of full time job.

Its gotta be a labor of love. My advice is pretty good though, if i say so myself.....

Burp

December 15, 2015 at 05:33 AM · 40hrs! That's impressive Buri! Makes me feel like a charlatan.

Steven, if you're time constrained, I agree with Buri, plowing through Flesch is not a good use of your time.

As Buri says, learn what to do and why. Playing through scales does not improve your intonation. It's how you practice them, what you notice and fix, and even then, that doesn't necessarily carry over to repertoire if your scale practice doesn't cover the kind of movement required in that repertoire.

You can dramatically improve your intonation by simply insisting on pure perfect intervals and tuning to open strings and drones. Learning intervals is the basis not only of good intonation, but musical meaning. If you want to plow through something, where the material in and of itself gives you some automatic gains, pick up a copy of Zukovsky's All Interval Scales, for when your mind is too taxed from the rest of your day. (If you can't afford it on top of the Fischer material, just pick a key and play all interval doublestops: 1-4 octaves, 1-3 octaves, 2-4 octaves, fingered octaves, fourths, thirds, fifths, sixths, sevenths, seconds, 1-4 unison, 9ths, 10ths. Don't worry if you can't play most of these. Play each interval melodically, then harmonically. As Trevor said, listen. This is just as much an ear training exercise as anything else. If you're not used to it, take it easy on the stretches--build slowly. Just work on doublestops on a tetrachord (4 notes) at a time at first.)

Fix every instance of an out of tune pitch, especially within perfect intervals, analyzing what caused it (pitch sense, shape of fingers, pattern, inconsistent frame, excess tension, thumb, left arm angle, etc.), then repeat correctly while truly sensing the fix. When you come back to that spot the next session, remember/imagine what the fix felt like before proceeding. That's a daunting task even on a 3 octave scale, not to mention a passage, or complete concerto. The key is time constrained practice. Give yourself a time limit, 10m as Buri suggests, and work on one thing. Use a timer. This will make you focus and you'll accomplish much more in the long run than just doing stuff for the sake of it. This is deliberate practice. People bring up '10,000 hrs to mastery' all the time but neglect this tiny detail, that it's deliberate practice that counts.

When working on pitch, go excruciatingly slowly and quietly until you go into a meditative state where you become the pitch--no joke. Do not judge. Be dispassionate. Observe. Fix. Repeat correctly. Check all perfect intervals, especially 4ths. If there are no written 4ths, fill them in and compare written intervals to the 4ths. Play mostly with no rhythm, then play way under tempo a few times. Keep in mind you should still move rhythmically even if you don't play the written rhythm.

When working on something else, bow division, phrasing, flow, tone, dynamics, continuity, don't obsess over intonation. But do make note of it for your next tuning session. Learn to focus on what you're doing. It's difficult but worthwhile.

December 15, 2015 at 03:19 PM · I have honed my intonation with a very simple subroutine. I've made it a point to always know where I am on the fingerboard including the fingers not playing at the moment. This matters to me because where I'm going depends on where I've been and I locate notes by relative position, not pitch.

Perhaps the Guru of finger/hand position was a teacher named Applebaum (easily Googled). His teaching publications include finger/hand management notation. I always avoided his approach until I realized that he was right.

December 15, 2015 at 04:18 PM · That's a good way to put it Darlene. That's also why we need to study double stops and play against drones. And the most important fingers to check are the ones which form a perfect 4th and octave across strings with played fingers. It's also important to sound out those unplayed scale notes in between written notes in passages when we work on intonation (and sound out preparatory notes and guide notes for shifts.)

December 15, 2015 at 08:45 PM · I mentioned this before, from a book by Louis Kievman, chapter 6 on 'note finding'... While it is about finding notes in higher positions after shifting from first position, I applied it to playing notes in tune anywhere. His instruction says to 'THINK THE NEXT NOTE', do not adjust if ( high ) note is missed, go back and try again...NO SLIDING. After doing this exercise I found my self applying this concept to every note I played,(I 'anticipated' the notes). Then some one said...'how do you know what the intonation of the notes are in the first place'....? For that I practised my singing, and double stop etudes, and scale...and modes...At the bottom of the page there is an explanation of this exercise........for the development of the left arm ( left fingers ) in co-ordination with.....ear training.

December 15, 2015 at 09:08 PM · I was getting into the habit of checking my intonation by listening for ringing strings while playing scales. However, my teacher downplays the importance of this, and encourages me to instead listen to how the notes relate to other notes in the scale. This will work even in situation where there are few or no notes that will cause an open string to ring - for example, when playing a D-flat scale, which I've added to my scale exercises. (I play viola - violinists can get the same effect by playing a 3-octave scale in A flat.) This is also good for ensemble work, where you should be listening to the other players and adjusting your intonation to fit in. At my last lesson my teacher had me play a scale, while she played along two notes behind and had me listen to the resulting thirds.

I always thought I had a good sense of pitch - and to an extent, I do. But now I'm moving to another level, where I find I still have a lot more to learn.

December 16, 2015 at 05:17 AM · Jeewon do you play a different C# with and without an A drone?

December 16, 2015 at 06:12 AM · Hi Paul, short answer yes. What's the context without the drone A?

December 17, 2015 at 03:16 PM · I am currently challenging myself with 2 octave scales AND not playing anything in the intoxicating key of "C". Fortunately, most of the church Xmas music I'm tinkering with is in unusual key signatures. Church arrangers seem to love a couple of chromatic key changes!

Anyhow, I must incorporate the Applebaum habits.

I'm finding the violin to be perhaps more mental than physical. Nobody told me I had to think (and play the violin too!)

Jeewon. Interesting.

December 17, 2015 at 07:12 PM · Greetings,

2 octave scales are extremely useful. You can either keep the same relationship between the fingers and play differnet scales by strating on fiorst finger in first position, then second, then third and so on.

Or you can move up one position each time but stay in the same key so that you have to reshuffle your finger patterns. A very powerful exercise indeed.

YOu ddidnt think the violin was mental. Lawks a mussy, what were you thinking, or not...

Everything we do on the violin from the moment we get it out of the case is mental. If thinking doesnt lead what you are doing then it is probably better to quit and just be a brain surgeon.

Cheers,

Buri

December 18, 2015 at 02:09 PM · Just practice without a tuner!

I'm new relatively to violin, but not to music. I'm a very analytical type. I try to think of the fastest, most efficient ways of achieving technically what I want to do in music.

The reason I tell you this is because I played with a tuner almost exclusively for the first three months of my playing this year. The whole time, the tuner would tell me I was basically in tune, but my ears would tell me something was not quite right. One day I put the tuner down, put some music on, and played along to whatever song come up on my Spotify playlist, just for fun. That was the first time I ever felt a grasp of intonation. I wasn't visually aiming for something on a tuner, I was aurally aiming to match pitch with the music, just like any other instrument.

When I returned to practicing without my music, I found myself hitting the notes in tune much more accurately. So, I went from having a roughly 20% pitch accuracy, to a now 80% - 90% accuracy. Trusting yourself and checking harmonics and open strings to the notes you're playing really helps, though not constantly.

Of course, just like you, I started finding myself getting satisfactory intonation results and those results revealed my weaknesses in the right hand. It's easy to think that the left hand is the harder hand to master, and that pouring all your efforts into intonation and scale work would be the fastest way to get good at the violin, but it's actually the right hand that's harder. And just like you, I'm working very much so to improve my bow arm. I was playing very crooked to the bridge, and as well my bow started to dip when I would play the G or E strings, hitting the sides of the instrument.

What should you take from this? Everyone is right. There's no clear-cut way to get good intonation results. There are many things you can do, but relying on a crutch for any aspect of playing will only serve to waste your time. From what it seems you're so busy you only get two, three, four hours of practice. That's A LOT of time. If you're as committed to learning this instrument as you say you are, then you have to accept these facts. It's hard work. You're required to trust yourself. You may not sound quite as pleasant for the first couple of times practicing without a tuner. You just have to dig in and stick it out for the long haul, and eventually you'll find what you want.

To practice both your intonation and bowing skills, you should try scales with different bowings/bow distributions. I can also say after practicing more with the right hand, my left hand skills have improved as well. I'm producing a better tone and the good intonation is easier to hear. Working on and isolating just the one aspect of playing won't just benefit that one area. When you practice properly and efficiently, no matter what instrument, you find the benefits bleed into other aspects of playing.

December 18, 2015 at 02:40 PM · "Everyone is right. There's no clear-cut way to get good intonation results."

Wesley, you are not right. The only way to good intonation on an instrument tuned in pure fifths is to train yourself to hear and play pure perfect intervals (unison, octave, fifth, fourth) and temper imperfect intervals according to context. Sometimes you even have to temper perfect intervals but that's a bit more advanced.

December 18, 2015 at 03:02 PM · Jeewon, what I said means that there's no short cut. And it also implies that there are many applications for everything you said. You and I are in complete agreement.

December 18, 2015 at 03:34 PM · I found that playing with a tuner was not productive because a lot of the music I was using as backup was not exactly in tune.

December 18, 2015 at 03:36 PM · Wesley, actually, I'm not in agreement with your statement I quoted... but ok. If you'd written 'there's no shortcut to good intonation' then maybe. But wait a sec, learning pure perfect intervals is the shortcut, so no.

Darlene, If you want to go even more mental(!) think in keys, rather than reading through scales. You can keep a chart of all 24 keys in front of you if you want, with key signature, name of tonic and dominant, and raised intervals for minor keys.

Pick a key, pick a position. Identify the degree of the scale you'll start on. Sing the scale in solfege if it helps. Think the interval patterns and finger patterns, and then and only then play, using all four fingers across all four strings, ascending and descending, rhythmically without retries. If you goof, stop, think the key, interval pattern, finger pattern, go back a couple of notes and resume. I have made many a student go mental in this manner.

December 18, 2015 at 07:03 PM · Position scales are perfect for developing a good frame. But go through all the keys in succession, chromatically, starting with G maj, A-flat maj, A maj, etc., to map the frame to the shrinking fingerboard. To clearly feel the shrinking frame, it's useful to do all similar patterns, all major keys, then all minor keys, etc., similarly for arpeggios. Another great position exercise is Dounis' Daily Dozen First Exercise, C (after reviewing A and B, the easy and difficult settings of the hand.) Sustain first finger as a double stop to tune the other fingers.

December 18, 2015 at 09:35 PM · I have already performed wonders with scales but not necessarily by intent.

While I have the attention of many veterans here, I have a final question that won't go away. My intonation is simply better if I address the strings using perpendicular fingers. Why? Worth cultivating?

December 18, 2015 at 11:55 PM · If you're paying attention to using perpendicular fingers, it means you have a consistent hand frame / positioning relative to the string across strings and positions, so intonation gets more accurate because instead of trying to hit the right place from hundreds of different angles, you're trying to hit the right place from the same consistent angle.

December 19, 2015 at 01:37 AM · @Jenny: It means that as you climb up the instrument, your hand works its way around but the fingers stay in more or less the same position as in 1st position (except for the required flexing that the fingers have to do as the spaces become tiny and the ribs get in the way). :D

December 19, 2015 at 02:09 AM · A perpendicular finger points straight at the fingerboard. A YouTube of Perlman will show a good example of hand/finger form.

I would adopt the style but I then must play more to the right with my elbow to position the fingers.

Simple but feels much different than "lazy" fingers.

December 19, 2015 at 02:46 AM · Greetings,

im confused too. Does this mean flat fingers as opposed to curved? If so, Not a good idea. The relationship of the left elbow to the violin changes according to what string you are on for most but not all people. The important thing is to return to the natural position of perpendicalr ( i do understand this in rleation to the elbow) as ,uch a spossible. Deviate as little as possible.

Cheers

Buri

December 19, 2015 at 09:08 AM · Perpendicular fingers sounds like a square cello left hand (like a square German bow hold, where each finger is perpendicular to the stick.) If so, Perlman does not have perpendicular fingers (nobody does.)

December 19, 2015 at 09:10 AM · except Spock.....

December 19, 2015 at 09:22 AM · Yes... the Vulcan school of violin is so illogical!

Darlene, what point of view are you using? Players pov looking down the fingerboard, birdseye, profile as seen from the audience or from behind the players shoulder?

The best way to describe the left hand shape is skewed, kind of twisted about the ring finger. How uniform the curl in each finger looks relative to each other depends on the uniformity of their lengths. I.e. the longer the pinky relative to middle finger, the more uniform are their curls; the greater the difference in lengths, the more extended the ring and pinky fingers, and the more curled are the middle and fore fingers, with the first base knuckle being extended straight for most average and smaller hands.

A common mistake is to hold all the base knuckles open straight, and supinate the forearm and twist the palm so the base knuckles are near parallel to the strings, thereby greatly impairing left hand function and adding unnecessary tension. The base knuckles should form an oblique line to the strings in the lower positions.

December 19, 2015 at 02:47 PM · Violinfromscratch.com

Then find. Playing violin with all the fingers (title of lesson)

See happy vertical 1,2,3 and compromised pinkie. I submit that less than vertical discourages intonation.

December 19, 2015 at 03:47 PM · Darlene I don't see "happy vertical 1,2,3 and compromised pinkie" on http://violinfromscratch.com/learn-violin/playing-violin-with-all-the-fingers. Do you need paid access to see it?

In any case judging by her photo it's not what I pictured when I described "common mistake" above.

If by vertical you mean the angle of the tip joint of the middle finger as seen from the player's pov looking down the fingerboard, I concur it is perpendicular to the tangent intersecting each string. But, depending on the relative lengths of the ring and pinky fingers, they will be more or less oblique.

December 20, 2015 at 02:31 PM · ---"I've been ear training by very long and slow scales and with an electric tuner attached to my violin." --

This doesn't do anything, but it is an okay bow exercise.

---"Everyone is right. There's no clear-cut way to get good intonation results."---

Not necessarily.

There are 3 qualities required for good intonation:

1. Strong music memory

2. Strong proprioception sense

3. Great Focus

3 extra qualities that help

1. Good technique

2. Good diet

3. Teacher

I want to focus on the first three qualities.

1. To develop a strong music memory you listen to 3-4 notes; repeat the notes in your mind a few times, do something else that is not musical for 30 seconds and then repeat the notes( on piano, violin, voice etc...).

This is the fastest way, or "short cut", to good intonation.

Overtime you can increase the number of notes and wait time. If you practice this 2-3 times a day with 15-30 min. practice sessions you will develop a strong music memory in a few months. With a strong music memory you will understand the melodies quickly, have better focus, better intonation and be able to memorize music quickly.

Here's an example:

https://www.youtube.com/watch?v=ybO1ck-7lWo

2. A strong proprioception.

Students with a weak proprioception sense will struggle with intonation. They can hear "in tune", but they have very poor consistency in finger placement. The only way, that I know of, to strengthen this sense is to play with your eye close or don't look at your fingers when playing.

https://www.youtube.com/watch?v=b2iOliN3fAE

3. Focus.

When your mind is over stimulated or tired you will struggle with focus. Diet, meditation and good sleeping habits help a lot with focus. A good habit when practicing is to have a quick 30-60 second meditation. This quick meditation slows the hyper, over stimulated mind down and "resets" it.

December 20, 2015 at 04:03 PM · Focus, diet, good sleeping habits, meditation! No wonder I'm having problems. I was afraid it might be lack of talent! I can easily give up Devil Dogs for the sake of the art.

For intonation, the mystery question is "What is the ideal foot print for the finger prints" ?

(Mister Cook, your grasp of the topic is impressive and may even be right.)

December 20, 2015 at 07:23 PM · Many times I find that although precision tuning is extremely necessary, the actual placement and pitch of the note varies depending on the key of the piece and the scale degree the note is on. For example, in A Minor, a G# (leading note) would have to be placed much higher than a G# in, say, B Major. Just a thought, maybe lose the electronic tuner?

December 20, 2015 at 09:56 PM · "Focus, diet, good sleeping habits, meditation!"

This just shortens the learning curve.

---"For intonation, the mystery question is "What is the ideal foot print for the finger prints"---

There isn't any, that I know of, and Bach drove himself crazy trying to figure this out. From my experience, intonation needs to "FLOAT" or to adapt to sound correct. There is some play with notes also. Thirds and sevenths can have some bend to them, whereas fourths, fifths and root notes need to be almost perfect.

To show you how well our mind's music memory and proprioception work in tandem, and there isn't a PERFECT spot, we can try this: Play a two octave scale in tune- easy right. Then play a two octave scale with one string slightly out of tune. You should notice that it is still easy to play the scale in tune, and the only note that would be out is the open, out of tune string; the other notes will still be in tune. Why? Because we are use to, or trained at adapting intonation. We are subconsciously adapting intonation to sound in tune all the time.

Technically, there is no such thing as Muscle Memory in violin or singing; or perfect spot. If there was such a thing as Muscle Memory then when we get to the out of tune string we would play all the notes on that string out off tune, but this doesn't happen.

December 21, 2015 at 02:08 PM · Vibrato is basically a change in pitch accomplished by small changes in finger contact.

Therefore, the best stationary notes are achieved in just the opposite way. Minimal contact. Less confusion for the ears.

December 22, 2015 at 09:24 AM · So many excellent things said here ... just adding one comment I believe came from Niekrug: Intonation is a matter of the mind.

I find this to be very true on many levels.

December 23, 2015 at 01:55 PM · It definitely comes from the mind, but it still has to reach everyone's ears as sound!

December 26, 2015 at 02:10 PM · I think that Buri said that the violin needed a lot of attention every time out of the case. That (intonation) is true for me. The violin never gives me a break but how else can 4 strings and a box produce such wonderful music?

December 26, 2015 at 04:57 PM · Earlier in this thread I mentioned "vertical" fingers in connection with intonation. This caused some confusion but I just happened to find an example of finger position. See Fiddlerman LEARN TWINKLE TWINKLE LITTLE STAR ON THE VIOLIN in LESSONS section. Nice pictures of left hand (fingers).

December 29, 2015 at 08:43 AM · Good technique is important, and helps with consistency and speed, but arguably, not necessary to learn intonation.

Intonation is a procedural memory technique, or you can say a sequence of events that must be followed to achieve fluency of play. In the first weeks of learning the violin it very important that this sequence is taught. If it wasn't taught at the beginning, the person will not HEAR IN TUNE. So playing in tune or playing out of tune will sound the same to them, or they have this constant question, "doesn't sound right" when they play out of tune notes. People who don't learn the sequence will not be able to pitch match at all. For instance, if I played a note on the piano, and then asked them to repeat it; it would be IMPOSSIBLE for them to match the pitch, even with my help. It would take several weeks or months of retraining the mind, or getting the sequence right, for them to pitch match the note.

I've learned about intonation from the Eric Kandels of the world not the Heifetz of the world. Eric Kandel is a neuroscientist, and he teaches us how we learn: how we process information.

December 29, 2015 at 01:53 PM · Charles, I find that intonation needs muscle memory to play near the right spot, and audialization-guided proprioception for quasi-instant adjustments. And at highest speeds, there will be no time for adjustments. I agree with your analyses, even if I have sometimes wished for more individualized strategies.

December 29, 2015 at 02:54 PM · Intonation describes accuracy of pitch. But accurate compared to what? Since it refers to pitch, we discuss tuning systems, not memory or learning theory. Tuning has to do with the physics of sound, but more importantly is determined by the cultural and historical context in which it's developed, including the logical layout of the instruments devised in that culture. A culture without an instrument which covers 7 octaves, or even 3, would never develop equal temperament. And since we're talking about intonation on the violin, we discuss violin technique as related to the logic peculiar to the instrument. Of course general ear training is important for intonation, but again we're learning Western, as opposed to Indian, or Chinese classical systems, and so we refer to tuning systems developed in our tradition. But no matter how well trained the ears (ear-brain, if you want,) learning good intonation, i.e. learning to match finger placement, or embouchure or vocal chord/palette 'placement' to a particular tuning system, has equally to do with mastering the necessary technique specific to that instrument (ear-fingers-hand-arm-brain for us.)

December 29, 2015 at 05:30 PM · "Accurate to what."

My first impulse was to respond "in tune to the open strings and their partials."

But I'm not sure I agree with your overall premise that intonation is entirely cultural. We have many centuries of experience to suggest that people do in fact want to hear intervals according to the Pythagorean ratios. And many cultures base their music on the octave, even if they split them up differently. I don't know enough about other divisions of the octave, but I wouldn't be surprised if Pythagorean intervals still existed as some part of those systems and were thus tuned accordingly. Perhaps someone familiar with Indian scales could comment.

Anyway, the whole battle for the last thousand years has the fact that that the ear WANTS to hear pure intervals, but our music is too complex to make it work, thus equal temperament.

The Chinese did realize the value of equal temperament way before we did, but it was for reasons other than the need to play complex harmony.

On the violin, if you hit an octave of an open string, you get a open, ringing sound, and if you're flat it sounds choked off. I don't think that's due to cultural reasons. The same with 5ths and 3rds. These are due to partials. Someone mentioned inharmonicity, but I'm not sure how prominent it is on the violin or how it affects our finger placement.

Someone also mentioned feeling that Zukerman's intonation sounded flat. This is not Zukerman's problem but rather the listener and is a common issue, especially among older ears. Many a piano tuner are asked to tune the high treble very sharp. As a participant in an interval study in a psych lab once, I was surprised at how flat pure electronic octaves actually sound.

"There's more! Both syntonic and pythagorean commas are around 20 cents (1/5 of a tempered semitone) and take 2cm of the string in 1st position (3 cm on my viola)."

I'm not exactly sure what this means for a string player, and I doubt many are familiar with the terminology unless they are prepping for a piano tuning exam. The Pythagorean comma is the discrepancy

between 12 5ths and 7 octaves. It would be mighty convenient if they converged at the same exact pitch, but they don't (we force them to on the piano, though, hence equal temperament).

String players don't need to think in cents or commas--we just naturally fudge things in very tiny ways to try and get our pure intervals when we can.

December 29, 2015 at 05:52 PM · Never said "entirley." I don't pretend to know anything about tuning systems of other cultures either (heck, I don't know that much about my own.) Just going by what I hear. And I don't hear Pythagorean, or any variety of Just tuning upon cursory listening. There are microtonal adjustments going on all over the place that we'd consider out of tune, as I'm sure other tuning systems would say of Western tuning.

To answer my own rhetorical question, accurate to a given tuning system. No Western trained musician tunes to the overtone series, as all the upper partials are flat.

December 29, 2015 at 06:17 PM · On the piano, the partials are sharp. This is because the strings are struck. To make the piano sound "in tune" with itself, piano tuners often employ stretched tuning, thus making the high notes sharp.

December 29, 2015 at 06:25 PM · Kevin, are you talking about overtones in a single vibrating string or across 88 pitches, outside a few octaves? In practice even equal temperament must be tempered. And underscores how tuning is passed down from master to student, not learned through theory alone.

December 29, 2015 at 07:40 PM · https://en.wikipedia.org/wiki/Stretched_tuning

December 29, 2015 at 07:54 PM · Did not know that! Learn something new everyday... I guess I was referring to natural harmonics on bowed strings. I knew pianos were tweaked at both extremes but never knew why.

Edit: inspired by Kevin's link to stretched tuning, I did a search for equal temperament in China. Even if equal temperament was devised mathematically in 1584 by Prince Zhu Zaiyu, the question remains, was it adopted widely in practice as a result?

December 29, 2015 at 10:10 PM · 1) My "2mm comma" was in answer to a question on commas and cents. BTW it is wider than my usual vibrato.

2) Zukerman playing flat in the higher octaves? Of course it's the listener's problem, not his! But he is the only great soloist who gives me this impression.

3) "Stretched" tuning on pianos is not just to satisfy our "compressd" hearing; in the higher octaves, the partials are sharp not only because they are struck but because the strings are short and stiff.

December 29, 2015 at 10:39 PM · So does that mean upper partials are sharp on all piano strings because of their inharmonicity, or just on upper, shorter strings? Also, do the sharpened harmonics come close to generating an acceptable diatonic scale?

The point of my post above is that we should learn tuning from musicians (like Adrian,) not psychoanalysts, not even physicists or mathematicians.

December 30, 2015 at 02:24 AM · All of the piano strings exhibit some amount of inharmonicity, and the variables include string lengths, tension (IH decreases with tension), whether wound or plain steel, and overall scale design. We don't hear IH so much in the higher strings because they generate very few partials to begin with. The issue is very noticeable in here bass because they generate so many partials. The higher the partial on any given string, the sharper it is (simply put, IH grows with the square of the partial number). That's why octaves in the high treble can sound pure, but bass octaves are impossible to cleanly tune with anything more than one specific partial. I do not think IH is responsible for our desire to hear wider intervals in the high treble--theres some other psychoacoustic going on. The phenomena exists even with few or no higher-order partials. But obviously, We DO get perfectly acceptable diatonic scales. The bigger the piano, the better the tuning, though. Small vertical pianos are basically impossible to tune acceptably.

Jeewon, you say you don't hear Pythagorean tuning, but if you can play in tune, I'm betting you actually do, but haven't thought about it or realized it. Because when we hear intervals that don't conform to the simple whole-numbers of Pythagorean tuning, they sound noisy, dirty, or beaty. The "microtonal adjustments" you're talking about are our attempts to bring things back into Pythagorean tuning.

For example, try to play the chord G (open string), E (on the D) and open A. Any violinist knows it's impossible to put the first finger in the same place and get a good interval against both the open G and the open A. You have to make a tiny adjustment. Alternately, you can tune a good perfect 4th with the open A, thus letting the 6th below be very wide. It may be acceptable, though if the bottom interval is played quickly enough--the ear will pick out and judge the 4th. I think that's the type of "comma" Adrian is referring to that we need to be aware of and adjust for automatically with experience.

December 30, 2015 at 03:37 AM · Thanks for that explanation of piano tuning, Scott.

Re.: "Jeewon, you say you don't hear Pythagorean tuning...", I was talking about in non-Western tuning systems. Not that I've listened to much Indian or Chinese (or even Korean) music, but from my recollection they didn't sound very Pythagorean to me. The microtonal adjustments I'm talking about are exactly what I meant. Unequal wholetones and semitones, if you can even call them that (you can't) which change according to contexts I don't really know, which often change ascending and descending. They may share our taste for pure unison, octave and fifths. But there's no way they hear Pythagorean diatonic tuning (not even Pythagorus did.)

Re. Diatonic scales, I'm referring to deriving scale tones from overtones. I don't buy this kind of backwards, naturalistic rationalization.

I actually don't like Pythagorean thirds. I can hear them fine, but they sound high to me even when played melodically, or as you put it, 'dirty.' Though I can understand why some soloists would want to play 'dirty.' Pythagorean tuning is dirty, harmonically. I guess sometimes you want dirty, especially when tight minor seconds give you wide augmented seconds. Ooh, salacious. Just thirds don't sound flat to me played melodically, they sound just, as do just 7ths. I like Sevcik's approach of tuning to upper open strings when tuning melodically (dominant and the upper open string to dominant, or octave to second degree,) what he terms 'tempered,' and go expressive when called for, which, to me means leaning on tendency tones (outside of geometry, do we actually need Pythagorus ever?) Some people (notably several colleagues with absolute pitch) seem to prefer equal temperament. People hear differently. Just to make life more... interesting.

So your assertion that Pythagorean tuning is somehow natural, that we gravitate towards it, doesn't ring true for me. It's a mathematical construct. It's a cultural construct, as are all tuning systems. I can see a case being made for just tuning being 'natural' but harmony too is a cultural construct, so no.

Another option for your out of tune chord, is to temper both intervals. Also you could temper the open G (and D--I think Adrian brought this up somewhere,) as most performers I've met, who care to talk about such things, do. Not that we know by how much. We just tune 'tight.' There are some string players who just like to tune equal tempered, to an electronic tuner. Blasphemy? Perhaps... but practical, especially in orchestral contexts, where everything is often approximate anyways.