Limit on Intonation
How many cents would you all say someone could be off a note and still be considered very well in tune?
Depends if you're talking melodically or harmonically.
Less than half a quarter tone, perhaps.
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
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.
Ella, less than a quarter?????
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.
3-4 cents for a string player. :)
It was high time I got a raise.
" It was high time I got a raise."
But I live in Canada... ;)
That doesn't make cents ...
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.
Quite so, Raphael. In string quartets, I find myself doing these adjustments spontaneously, even during a held note, as the harmony changes.
You use vibrato!? I thought that was forbidden these days ...
I think its overused but thats another discussion.
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:
Has what I call "C-yuk", when my students are lazy about 2nd-finger placing, become an accepted, therefore valid note on the fiddle?
" I think its overused but thats another discussion."
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.
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
Yes, I feel that if the tempered semitone (100 cents) is often an acceptable compromise, the 50-cent quartertone has little musical sense.
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.
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?
~ 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
Michael, from what I understand, you may want to lean to the flat side since vibrato is usually preferred from flat to pitch.
@Joel: 6 cents is too far off pitch for a seasoned player, they will bear the discrepancy rather obviously. :)
no cents! a small part of one cent maybe.
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
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.
@Joel: I can actually tune while tuning and playing to 0.4 cents, down to 0.1 cent if tuning very meticulously. :)
@Micheal: The sharp is probably:
"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?
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?
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.
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.
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)?
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.
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
@John: No, because that B is B7, whereas vocal range usually ends at C6, which is the first C on the E string. :)
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:
Dear A.O, more facts, sorry! So €0.00.
@Adrian: Corrected, my bad. Always get the direction mixed up for some reason... :D
Very interesting post Trevor.
"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."
"Michael, from what I understand, you may want to lean to the flat side since vibrato is usually preferred from flat to pitch."
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?
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!)
@Adrian: Quartertones are child's play in non-Western music, surely it is not that difficult? ;D
Quarter-tones are not difficult to hear; I was pointing out the practical problem of playing them sequentially in slurred runs of sixteenths!
@Adrian: That's why you play the runs a la Paganini/Indian/Middle Eastern using 1 finger. :D
Scott, thanks for the info..
I have a healthy interest in tunings and temperaments, and the imperfections of strings, which don't seem to have read the physics manuals!
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.
The beautiful complexity of the violin--"in tune" isn't a frequency, it's a state of mind=)
I just got paid to play Vivaldis Gloria. 2 violins, 1 viola, cello, trumpet, oboe and chembalo.
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 usually go a bit higher from the beginning before giving the a around. Altough a oboist should be able to compensate...
Marc, I do the same stretching thing with my strings, but I can't say I see many others do this.
@Jason: Join a baroque orchestra or jam with me, where everybody tunes sharp, plucks after. :D
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.
I enjoy trying microtones, with or without a drone, but in a ensemble, or with piano, we have to "let go" a little!
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;-(
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)"
Han, that is very interesting; I've never heard that before.
Hans, many thanks for that most informative link.
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.
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.
Thanks again Han! We would all do well to copy your posts, and those of Carmen Tanzio.
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.
Might not much of the energy for the harmonics come from the fundamental?
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.
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