Limit on Intonation

June 3, 2017, 7:48 PM · How many cents would you all say someone could be off a note and still be considered very well in tune?

Replies (78)

June 3, 2017, 7:53 PM · Depends if you're talking melodically or harmonically.
June 3, 2017, 8:55 PM · Less than half a quarter tone, perhaps.
June 3, 2017, 10:59 PM · Important topic. 5-6 cents, 5-6/100 of a half-step is the limit of pitch discernment for most trained musicians. Piano-style, equal temperment is close enough, +/- 10 cents, most of the time. The small interval to be most aware of is the Pythagorian Comma, about 20-25 cents, 1/4 of a half-step. That is the difference between the large and small half-steps, large and small minor and major thirds and sixths, also the difference between harmonic and melodic tuning. jq
June 4, 2017, 3:02 AM · The comma which gets us most into trouble is the syntonic comma: the difference between a true and pythagorean third (e.g. C-E as a pure double-stopped third vs C-E on open string). By chance it is also around 20 cents.

Taking a "tempered" comma (!!), 53 per octave, we may define 3 sizes of semitone, 4 commas for melody, 5 for harmony, and 3 for ornaments.

My 2 cents (haha)

June 4, 2017, 4:31 AM · Ella, less than a quarter?????
That sounds more than horrible!
Edited: June 4, 2017, 7:55 AM · There is an exercise ( called the ear bath) to improve hearing acuity in which you divide a 1/2 step into 8 parts.Play the first note (1), move the finger slightly and hear the difference between note 1 and 2, move the finger again, and again until you get up to 8. On first trying this you will probably reach the next 1/2 step on note 4 or before, which isn't good enough.
June 4, 2017, 8:16 AM · 3-4 cents for a string player. :)
June 4, 2017, 8:28 AM · It was high time I got a raise.
June 4, 2017, 10:26 AM · " It was high time I got a raise."

It's possible you will all get a salary cut once the UK leaves the EU ...

June 4, 2017, 11:06 AM · But I live in Canada... ;)
June 5, 2017, 2:57 AM · That doesn't make cents ...
June 5, 2017, 4:08 AM · Well, while I respect those who know all about cents and commas - not to say common-cents, er comma-sense - uhm, well...I'll leave all that to piano tuners.

Seriously, I think it comes down to training, experience and perception rather than anything prescriptive, though Joel and Adrian's points are very interesting.

June 5, 2017, 4:31 AM · Quite so, Raphael. In string quartets, I find myself doing these adjustments spontaneously, even during a held note, as the harmony changes.

But the approximately-20-cent comma is about 3mm on my viola in first position: wider than my vibrato.

June 5, 2017, 5:13 AM · You use vibrato!? I thought that was forbidden these days ...
June 5, 2017, 5:37 AM · I think its overused but thats another discussion.
June 5, 2017, 7:29 AM · When a violinist has acquired reliable control over their intonation they may (or not!) feel inclined to explore the world of microtone music. As a useful, approachable, and not too difficult, starting point I would suggest Alois Hába's String Quartet No.2 Op. 7 (1/4-tone). Hába was one of the more prominent microtone composers in the last century. I have chosen that particular quartet because it is the only one of Hába's numerous works that is currently available on IMSLP. There is also this recording on YouTube: performed by the Stamitz Quartet.

I have come across quarter tones occasionally in Irish fiddle music, especially from the west coast of Ireland. The one commonly encountered is usually the quarter tone between C-nat and C# on the A-string. It is a definite and unmistakable note, never a result of poor intonation.

Edited: June 5, 2017, 8:13 AM · Has what I call "C-yuk", when my students are lazy about 2nd-finger placing, become an accepted, therefore valid note on the fiddle?
Do the various flutes have the same C's?

Another interesting composer is Harry Partch who consructed many weird and wonderful instruments, including a viola with a very long neck and microtonal frets (played 'cello fashion).

June 5, 2017, 9:08 AM · " I think its overused but thats another discussion."

I was being humorous - English humour that Paul Deck loves! (Maybe it was more sarcasm than humour - who knows ...)

Edited: June 5, 2017, 10:06 AM · Adrian, I too sometimes hear "C-yuk" (and "F-yuk", "G-yuk" and "yuks" attached to other letters of the scale) from some fiddle beginners whose teachers haven't stamped on it from the start. Sadly, this beginner syndrome if left uncorrected can become permanent over the years, along with poor posture, bow and left-hand control, even though the "beginner" has by then often acquired an enviable command and knowledge of the tune repertoire.

The good Irish fiddlers who would use the 1/4-tone sharpened C (alias "trick note") when it is part of the music will make a clear distinction between it and C-nat and C# - they generally have the technique and ear to do this.

The Irish keyless wooden flute, which as far as I know is identical or very close to the Baroque flute, is as well capable of being played out of tune as the violin! However, I can't say I have ever heard the trick note C being played on the flute as part of the music, possibly because music using it may be regarded as fiddle rather than flute music.

Returning to Hába's String Quartet No.2, which I mentioned in my previous post, the IMSLP download is of the Universal Edition which in its Preface explains the 1/4-tone notation; and, most usefully, the printed parts have each and every note fingered by the composer. I think this is because Hába, a teacher as well as composer, may have recognized that otherwise experienced players starting out in microtone music need all the help they can get for the fingering.

Hába wrote microtone quartet and other chamber ensemble music not only for 1/4-tones but also for 1/5 and 1/6-tones. I have no idea of what the notation for those two looks like!

June 5, 2017, 10:05 AM · continued~ The limit of pitch discernment. When cellists and violists work with pianists they sometimes, depending on the key, will tune the C string up to the piano C, the difference is 6 cents. I have never heard anyone bother to tune the G string to piano G, 4 cents different. How does the player deal with these math. complexities? The easiest solution is;... Vibrato... For me, I try think of each note being a close cluster of 3 pitches; neutral, tempered pitch, and two others slightly low and high, +/- 10 cents. The trick is to not bend a note in the wrong direction. You tune to the ensemble. Then there is an extra large 1/2 step that sounds awful when used in a melody: tune 1st finger E to the open G, then tune second finger F to the open A. That E-F is extra large, maybe 120 cents? I was fortunate to work with Harry Partch an extremely long time ago at UCSD. His tunings were based on the ancient Greek calcultions and the natural overtone series. Likewise, tunings of Arabic and Turkish traditional music are from Greek music theory. The "tempered quarter tone" of 50 cents is an arbitrary concept, not natural. jq
June 5, 2017, 12:35 PM · Yes, I feel that if the tempered semitone (100 cents) is often an acceptable compromise, the 50-cent quartertone has little musical sense.
Edited: June 5, 2017, 1:01 PM · Thanks Trevor, I will try finding that C trick-note tonight. I bought a book by Harry Partch that says a lot about microtonal composing, but too many other books have kept me from reading much yet.
Edited: June 7, 2017, 9:46 PM · Just reading this now, it seems people are happy with anything between 3 and 25 cents. This makes me feel better about my sloppy intonation, which ranges from 3-15cents depending on which phase the moon is (Not really. I'm just sloppy), but usually land around 6cents on any given note when I bother to check what's up, which frankly is a bit of a pain isn't it?

I've never heard of tuning the C string to match the piano, but that does make a bit of sense. I have however heard of the 'tuning your C string a little sharp to be in tune with the violin's E string'. Is there any validity to that one, from our collective experiences?

Also, out of curiosity, would you rather be '3-25 cents' flat, or sharp? Leaving tonal centers out of it for the moment, which is a whole different can of beans. I know I'd rather be a touch sharp on the viola than flat.

June 7, 2017, 11:05 PM · ~ Michael M --I would not tune the viola or cello C to the violin E. That would only sound right for the C major chord. Play a note slightly flat or sharp? It depends on the context; the key, the position of the note in the chord or the melody. An early violin book (Geminiani?) shows a fingering chart with two spots for each note, high and low. The modern version of that would have three spots for each note, the middle one being equal-tempered. The topic is still controversial. Leopold Mozart says to play major thirds low. Carl Flesch says to play major thirds high. I occasionally judge at auditions. Anyone who consistently plays +/- 6 cents of ideal I would call amazing, perfect. Some orchestra first violins will unintentionally push their high notes sharp with the vibrato so that they can hear themselves. Bottom line; be aware that there are choices, and let your ear (your mind) be your guide. ~jq
June 8, 2017, 1:53 AM · Hi Joel;

Thanks for answering my question RE: C strings, as well as a little extra on sharp/flat.

I find the 'secret' to getting good intonation is to make sure the finger is contacting the string properly. It's easy to slip to 15+cents off the mark if your figure is even slightly angled too far this way or that way. I think that's one of the most important parts to consistent performance - kind of obvious really - do it the same time each time.

June 8, 2017, 4:47 AM · Michael, from what I understand, you may want to lean to the flat side since vibrato is usually preferred from flat to pitch.
June 8, 2017, 6:04 AM · @Joel: 6 cents is too far off pitch for a seasoned player, they will bear the discrepancy rather obviously. :)

@Michael: 3 cents sharp is preferable to flat on anh string instrument, since the dull sinoroty of being flat is more obvious in most of the more common keys we use.

June 8, 2017, 8:17 AM · no cents! a small part of one cent maybe.
June 8, 2017, 8:45 AM · A.O.-- If you can hear the interval of 3 cents ( 3/100 of a half-step ) as a different pitch and not just a beat or difference tone, I congratulate you; your hearing is better than mine. On several occasions I have done the following experiment in my classes. I bring in my viola, I tune the A to the piano, then tune the strings to perfect fifths (no "beats" or difference tone). Then I compare my viola open strings to the piano, asking the students to raise their hand when they hear a difference. They don't raise their hand until
we get to the C-string, which is 6 cents higher than the piano C. These are music students, not general ed. people. I'll repeat myself; vibrato, typically +/- 25 c, solves the problem for us. thanks, jq
June 8, 2017, 9:51 AM · And... In first position the half-steps are 11 mm apart. My fingers are about 10 mm wide. 3 cents would measure 3/100 x 11mm = 0.33 mm, about the same as the thinnest available mechanical pencil lead. good luck with that.
June 8, 2017, 2:03 PM · @Joel: I can actually tune while tuning and playing to 0.4 cents, down to 0.1 cent if tuning very meticulously. :)

The 3-4 cents is simply the common intune-ness that a pro musician would accept as in tune, so to speak. :D

BTW, thanks for the compliment, I owe it to listening to extremely microtonal Turkish music growing up (octave split into 53 commas, smallest comma being 6 cent intervals-means extremely precise relative pitch).

Try it,and I bet your ear will become rather sharp as well. :)

June 8, 2017, 9:59 PM · Timothy;

Good point! I wasn't thinking in terms of vibrato, more just planting the finger and checking the pitch. Now I'm going to have to take a moment and look at my vibrato and see if I'm going more or up down...!


That's interesting. I've read elsewhere recently that when doing sound editing and they want to mess with pitches, they almost always go down as it's less noticeable. I agree that if I absolutely had to choose to play sharp or flat my entire life my choice would be slightly sharp.

Also interesting on the microtonal stuff!

June 8, 2017, 11:42 PM · @Micheal: The sharp is probably:

1) We hear rather low pitches as sharper than they should be (they sound a bit flat to most people when played spot-on)

2) We hear very high pitches as flat, so we want to sharpen them

In both cases the ear prefers a few cents sharp, not to mention intonation for colour purposes (I will intentionally sharpen cerrain notes/passages to better suit the emotion I'm displaying-true singer intonation). :)

June 9, 2017, 7:56 AM · "We hear rather low pitches as sharper than they should be (they sound a bit flat to most people when played spot-on)" Isn't this a bit self-contradictory?
June 9, 2017, 8:14 AM · No instrument I am familiar with allows you to hear "A PITCH." They all produce overtones that are affected my the nature of the instrument's mechanical properties. For instruments with strings, controlling mechanical properties are mainly the quality and thickness of the strings and the resonances of the instrument. Wind instrument s have different sets of overtone sequences (odd or even) depending upon type. Thick strings of low tones of piano and double bass have overtones that are not "in tune" with the fundamentals and can cause confusion in some contexts. When playing in ensembles "in tune" is strongly dependent on the key and the chords being formed by multiple instruments - string quartets are tough enough for amateurs, string serenades with 13 or more part "harmony" seem devastating - what is "in tune" in that context - who has the deciding vote?

For the past year or two I've been using a clip-on (tempered) tuner when playing with piano to be sure to match a piano, but tune harmonic fifths when playing in string ensembles.

Edited: June 9, 2017, 9:33 PM · @Adrian: Nope!

Pluck a low piano atring, and the large amount of bass via the large number of lower partials will make it "seem" a bit on the edit-SHARP side. :)

Conversely, bow a super high note on the violin, and the very high pitch makes the sound seem a bit flat due to the lack of (lower) partials.

Edited: June 9, 2017, 3:23 PM · On my pianos, the opposite is true at the bass end: the notes seem musically higher than they should. The compression of the percieved pitches at each end of the keryboard has nothing whatever to do with fundamental vs harmonics but is a well-documented non-linear property of the human ear.

Another factor is that due to the relation of stiffness vs the length of the strings, the overtones are not truly harmonic (inharmonicity) and the tuner has to allow for this when using thirds to check his fifths.

Not my usual €0.02, just facts! So I have not inserted my usual "I find that.." or "Apparently.." or "I imagine that.." as when I don't like presenting my hunches as facts without verifying them..........

June 9, 2017, 10:17 AM · For my money, the best examples of precise pitch control around are to be found in professional vocal ensembles performing Palestrina, Tallis, et al. a capella, all sans vibrato of course. The "Chapelle du Roi" in London is one such ensemble worth hearing.

I heard a wonderful example some years ago of the effect of combination tones. This was at a Christmas concert in St George's Hall, Bristol (superb acoustic, btw). At one stage, as a carillon of hand bells was playing carols I, and others, noticed the sound of a flute playing a descant above what the hand bells were playing. I looked around; there was no flute to be seen. It then occurred to me that the phantom flautist was in fact a combination tone product of the very pure harmonics that the hand bells were making.

Edited: June 9, 2017, 2:55 PM · Adrian, would that explain the phenomenon of violinists sounding sharp when playing high on the e string (setting aside the ones that are really out of tune)?
June 9, 2017, 3:21 PM · Vocal music stays, as it were, "on the staves", G & F clefs, with ledger-lines to top and bottom C's. In this 4 octave range, our pitch recognition is "linear", and our chests & heads have vibrated at these frequencies as we sing. Also, I believe in this range we have the most hair-cells-per-semitone in the cochlea. The double-bass goes at least an octave lower than this range, and the violin plays 2 extra octaves at the high end, where musicians may not always agree about pitch anyway. We have to really educate our ears in the extreme zones.
Edited: June 9, 2017, 4:00 PM · Interesting topic. So, is the B harmonic up high on the E string a reliable indicator of in-tune-playing when, for example, playing a three-octave scale in F# major
Edited: June 10, 2017, 2:16 AM · @John: No, because that B is B7, whereas vocal range usually ends at C6, which is the first C on the E string. :)

Also, harmonics on are always a slight bit high in finger placement versus the same note fingered due to the slight lengthenening of the string when it is pressed (esp obvious on inflexibility of steel E-barring Amber E of course). :)

Edited: June 10, 2017, 5:08 AM · Ruggiero Ricci, in Book 5 of Applebaum and Roth's "The Way They Play", in the course of a long interview says this about tuning:

" ... if you have the G-string perfectly tuned to the A-string, and you start off on the open G-string, like in the Bruch Concerto No. 1, your open G-string is apt to be flat. In the heat of playing, all of the strings except possibly the steel E-string are in great danger of going flat unless they are tuned 'on the sharp side' to begin with."

In response to a question about how does he tune when playing as a soloist with an orchestra, he says:
"When I am backstage and the orchestra is already performing out front, I take the orchestra's general pitch which is bound to be a bit sharper than the pitch I would receive from the oboe if I were to start tuning onstage. When I play in the open-air I tune backstage - not in my dressing room but somewhere behind the scenery where the temperature is closest to that out front. I listen carefully to the pitch of the orchestra and retune three or four times, which can take from five to ten minutes."

And with reference to the actual process of tuning, this:
"I never tune by screwing the peg up to the note. I tune above the note and then screw the peg down in pitch. ... Then the string pitch is set firmly at the correct pitch."

"When I am a judge in a competition, I start judging the fiddle player by the way he tunes up. I feel that if he's not going to be fussy about tuning, he's not going to be fussy about intonation, either."

Talking about the chords in the Bach 'Chaconne'; "At one time I had the habit of tuning pianissimo like so many violinists do. Then, when I would start to hit the chords [of the Chaconne], my A-string would go flat, and I had to play through the whole piece 'walking on eggs,' pitchwise. Now I tune loud and hit my strings hard in advance so that when I start to play, the strings are already well stretched. It's always a lot safer to tune 'forte,' though I suppose some of my concertizing colleagues might disagree."

He identifies the general faults of string players as: "Sloppy execution; not taking sufficient care. Too much willingness to 'settle for less.' Intonation, intonation and intonation! Get a violin teacher who is critical [of intonation]."

There is much, much more in the 20-page interview on most aspects of violin playing that I obviously cannot reproduce here; indeed, it reads almost like an advanced workshop on the art of playing the violin.

Edited: June 10, 2017, 2:10 AM · Dear A.O, more facts, sorry! So €0.00.

- We place our finger a little further up for harmonics because the contact is the lowest point of the finger pad instead of nearer the nail.
- When the finger presses down, the string lengthens, not shortens, and the tension increases slighly.

Please be accurate, many folks count on us for precise information... (Or add "I imagine" etc.)

John, indeed we often find the highest natural harmonics sound flat. (A.O, note the "we often find"!!)

Trevor a possible problem of tuning forte under the ear is tha our pitch perception is partly affected by loudness (another well-documented fact at €0.00!) But the degree and direction of this effect depends on the individual. Noisy arguments assured!

June 10, 2017, 2:17 AM · @Adrian: Corrected, my bad. Always get the direction mixed up for some reason... :D
June 10, 2017, 4:39 AM · Very interesting post Trevor.
June 11, 2017, 8:22 AM · "Another factor is that due to the relation of stiffness vs the length of the strings, the overtones are not truly harmonic (inharmonicity) and the tuner has to allow for this when using thirds to check his fifths."

Adrian, as a piano tuner, I'm not sure what you mean. Using thirds (if I'm guessing your intent correctly) is a very general test to determine if the 5th is tuned slightly narrow, but it is not very precise. We use the a similar test to expand the 4th as well, and hopefully the 4th and 5th are expanded/contracted by the same amount. Inharmonicity does affect all the intervals, but it is not what makes the 5ths narrow--that is simply the demands of equal temperament. We tune the octaves according to the inharmonicity, but we don't directly test other intervals this way--we just space them out accordingly once a given octave size is determined.

June 11, 2017, 8:28 AM · "Michael, from what I understand, you may want to lean to the flat side since vibrato is usually preferred from flat to pitch."

No one should EVER lean to the flat side of a pitch. And (in my opinion), an effective vibrato should not sound like a change in pitch. It should be perceived as a change in intensity. The only pitch noticed should be the highest one, and that should be in tune.

June 12, 2017, 3:20 AM · Scott, I have read that counting beats in thirds (and tenths etc) is a check during the piano tuning cycle. I do understand that inharmonicity only concerns octaves (in equal temperament). But does it not affect the countong of beats in other intervals?
June 12, 2017, 3:32 AM · To come back to the violin, one can now buy the solo sonata by Bartok as he intended it, with 1/4-tone "scurrying" in the finale. Menuhin (the dedicatee) aske Bartok to replace these passages with semitones, which is how we usually hear the work. The great difficulty of the successive slurred 1/4- tones is in the fingering: they are too close for adjacent fingers, and too fast to articulate clearly wth sliding fingers (at least for lesser mortals!)
Edited: June 12, 2017, 11:58 PM · @Adrian: Quartertones are child's play in non-Western music, surely it is not that difficult? ;D

Turkish music has-edit, 1/16ish tones (not 1/32!) in the form of 5-6 commas and multiple sharps/flats in the same key signature, but you don't them complaining or playing out of tune! :)

June 12, 2017, 1:32 PM · Quarter-tones are not difficult to hear; I was pointing out the practical problem of playing them sequentially in slurred runs of sixteenths!
June 12, 2017, 1:56 PM · Adrian,
Yes, 3rds and 10ths are used to tune the octave to a specific set of partials--the 4th of the lower note and the 2nd of the higher. Hence we call that octave a "4:2". However, that just works in the middle of the piano. As we tune into the bass, we use different partial pairs, such as the 6:3, 8:4, 10:5, 12:6, and in the upper treble we use 4:1 and 2:1. Each has their own test note to verify. For 5ths and 4ths, we want to know only if we have tuned them on the narrow or wide side, so we use another test to verify this.

But yes, inharmonicity must affect everything, not just the octaves. Just think: if the octave is wide, then mustn't all the intervals within that octave? So theoretically, F3-A3 beats at something like 6.93 beats per second. But that major third could be a little narrower or wider depending on the piano.

Ps I don't think anyone really counts beats, which is practically impossible. It's mostly just comparing the rates and seeing if one set of beats is faster, matching, or slower than another. For example, we can check an overall tuning to see if the major thirds and 6ths very gradually speed up we ascend. If they slowly speed up from pair to pair, then the next pair is equal or slower, then that tells us we did something wrong (or the notes slipped).

June 12, 2017, 2:18 PM · @Adrian: That's why you play the runs a la Paganini/Indian/Middle Eastern using 1 finger. :D
June 12, 2017, 11:49 PM · Scott, thanks for the info..

I just meant that the octaves are the only intervals that "pretend" to be pure in Equal Temperament.

June 13, 2017, 10:04 AM · Adrian,
Octaves are simultaneously sharp, flat, and pure. It depends on the partial pair they are tuned to. and often they are tuned between the partial pairs if a compromise is needed. Often, especially in the bass of small pianos, if one partial pair is tuned purely, then other partial pairs will beat quickly and sound terrible. So you have to place it somewhere in between to a "least worst" tuning. Thus nothing is in tune.

4ths and 5ths should sound as if they pure. Anything less would bother a musician. The amount by which the 4ths are wide and 5ths narrow is so subtle that very few people will notice. In fact, it's taken me much practice to discern that very slow beat (about 1/second) and control it. So technically, it's the 4th and 5ths that are the pretenders.

Probably more than you, or any normal person, would want to know about pianos....

June 13, 2017, 2:21 PM · I have a healthy interest in tunings and temperaments, and the imperfections of strings, which don't seem to have read the physics manuals!
And never mind organs....
June 15, 2017, 9:10 AM · Re: Fussy tuning before the performance. My experience has been the opposite. When I hear that I frequently think; "too much tuning, not enough playing in tune." I was in two fully professional non-classical bands that I won't name, and don't remember ever doing a formal tuning session. Everyone just knew how to play in tune.
Harmonics-- they can sound flat. Our brain does a marvelous job of converting the exponential frequency curve to a linear pitch scale. But it is not perfect, it drops off a little in the upper octaves. Compare your double high E harmonic with the same note on a well-tuned piano. That high E harmonic at the end of Scherezahde; you need to push it higher somehow. The last time I did it I tuned the open E a little sharp, right before the 4th movement.
June 15, 2017, 9:51 AM · The beautiful complexity of the violin--"in tune" isn't a frequency, it's a state of mind=)
June 16, 2017, 12:21 AM · I just got paid to play Vivaldis Gloria. 2 violins, 1 viola, cello, trumpet, oboe and chembalo.
Freezingly cold church and the other violin playing Eudoxa, no time to acclimatate the instruments. It was the pure horror in intonation! We retuned in the middle of the whole thing (my d string dropped close to a 1/4 tone, the other violinist sounded like that instrument did not get tuned once. Just want to say, tuning can help, it was the hell to play before the retuning, it was ok after.
I usually tune a bit higher then stretch the string with my finger like a strong pizz. This usually assures to me that the string does not drop during playing without making heavy forte tuning noise.
June 16, 2017, 2:27 AM · Our leader asks the oboe for an A. I know perfectly well that this A will go up as the wind instruments warm up (the air comumn, not the ambient temperament), so we sort of allow for it.
I'm reluctant forgo the Wittner tailpiece, as I can make minute (guessed) adjustments between phrases.
June 16, 2017, 7:01 AM · I usually go a bit higher from the beginning before giving the a around. Altough a oboist should be able to compensate...
June 16, 2017, 10:11 AM · Marc, I do the same stretching thing with my strings, but I can't say I see many others do this.
June 16, 2017, 11:36 AM · @Jason: Join a baroque orchestra or jam with me, where everybody tunes sharp, plucks after. :D
Edited: June 19, 2017, 10:30 AM · Plucking brings a fraction of string over the nut and bridge, lowering the tension, but raising it in the after length and pegbox. If one has lubricated the grooves with graphite, the string may tend to revert to its former condition fairly quickly.
June 20, 2017, 3:22 AM · I enjoy trying microtones, with or without a drone, but in a ensemble, or with piano, we have to "let go" a little!
June 20, 2017, 4:19 AM · Hopefully you are not playing them microtones on a major or minor third in an ensemble. Bottom line- depending on whether you're playing with singers, a piano, organ, strings, or anything else, you have to treat tuning as fluid- temperament means (get it?) that you always are adjusting. The natural (get it?) tendency is to play sharper -unless you play bass, in which case all bets are off;-(
You have to listen and blend- period.
That's why I originally wrote no-cents ( no sense !)
Edited: June 29, 2017, 12:07 AM · Adrian wrote: "Another factor is that due to the relation of stiffness vs the length of the strings, the overtones are not truly harmonic (inharmonicity)"

I have seen statements like this before (have been lurking for a while). However, I think it only applies to free vibration of a string, such as in a piano or during pizzicato.

When a string is bowed, the slip-stick process at the bow forces all harmonics to stay in sync. At least, that's how I understand the Helmholtz wave on a violin string (I am a physicist).

June 29, 2017, 12:33 AM · Han, that is very interesting; I've never heard that before.
June 29, 2017, 3:07 AM · This fiddle physics page shows the slip-stick effect for an ideal (no rigidity) string. If the harmonics were not at integer multiples due to string rigidity, then after a few 100 oscillations, the wave contribution of the harmonics would be out of phase with the fundamental, which would cause the transversal string motion to be at non-constant speed during the stick phase. Since the constant speed of the bow forces the transversal string speed to be constant during the stick phase, this cannot happen.
June 29, 2017, 3:30 AM · Hans, many thanks for that most informative link.
Edited: June 30, 2017, 4:51 AM · Han, I must bow to your superior comprehension, but I would have thought that in our stiff string, the segments producing the inharmonic overtones can be stable (and in phase?), even if their frequencies are not integer multiples of the fundamental.

I am thinking of a string in good condition, not a worn one with uneven distribution of mass.

Edited: July 3, 2017, 10:54 PM · Adrian, I'm not sure what you mean. If the fundamental is at 440 Hz and the first overtone is at 881 Hz (rather than 880), it means that the string motion due to these two harmonics, at the bridge, is in phase at the start and gets fully out of phase after 0.5 seconds. When they get out of phase near the bridge, the stick-slip motion of the bow would need to become stick-slip-slip-stick or something.

It's like a pendulum that has a natural frequency of 1 Hz. If you hold it near the suspension point and shake it at 0.9 Hz, the pendulum will swing at 0.9 Hz even if that is not it's natural frequency. The amplitude will of course be smaller if you excite it off-resonance.

Example: sawtooth wave, 3 harmonics, with and without anharmonicity. The bow stick phase would be the downward stretches; the quick upward stretches are the slip phases. You see that after 4 periods, the down phase gets faster than the actual bow motion, which would require the string to slip in the opposite direction. I suppose that it could happen if you bow very lightly.

Late reply; I hadn't noticed that there was a question for me.

Edited: July 4, 2017, 4:37 AM · Thanks again Han! We would all do well to copy your posts, and those of Carmen Tanzio.

I see the difference between forced and free vibrations, and between a bowed and plucked string (never mind bells or timpani!) I think your last sentence about bowing lightly corresponds to what I meant. In practice we have to maintain string motion (forced vibration) without hampering it (free vibration). When we produce a "rich" tone, I might imagine that we "force" the fundamental, and let the overtones develop "freely" under the bow-hair. A sort of "accompanied" vibration?

I shall have to record my open strings with different bow pressures etc to analyse the harmonic content. And re-read the incredibly detailed findings of Norman Pickering

July 4, 2017, 7:22 AM · I'd think that bowing so lightly that the harmonics can go out of phase will not be good for the sound quality; once string goes from stick into slip, the bow can no longer provide energy to keep the sound going.
July 4, 2017, 9:26 AM · Might not much of the energy for the harmonics come from the fundamental?
And surely, even without inharmonicity, after the initial attack, the various segments of the string proucing overtones are not all moving in the same direction all of the time (except very near the bridge).
Edited: July 4, 2017, 10:11 AM · First question: No, they get energy from the bow or finger. If you excite a string with a pure sine wave (tuning fork), the overtones will have and keep zero amplitude.

Q2 what does that matter? Near the bridge is where they receive energy from the bow and where they transmit energy to the violin body.

July 4, 2017, 2:47 PM · Fair enough!

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