Tuning With Harmonics Options

[Violinia]

The perfect fifth is an interval fixed in nature - this is why there is no vibration when the interval is true.

This is almost universally believed by musicians, but experimental acousticians, starting with Helmholtz in about 1852, have demonstrated that it is not true on all instruments. For a brief description of this work, with references to some of its documentation, see my essay on Schenker, particularly chapters 2 and 3.

The most familiar example of consonance resulting from coincidence of the frequencies of partials, rather than from frequencies in small integer ratios, is the sharpness of the high register and the flatness of the low register of a well-tuned piano, when every octave is adjusted to eliminate beats. This is discussed in chapter 4 of the essay.

I would suggest, as a replacement for your sentence: "The frequency ratio of the correctly tuned perfect fifth on bowed strings, blown wind and the human voice is indistinguishable from 3/2; on struck instruments it may differ widely from this value."

You may well be right, kenm, and I'll take your word for it as I'm sure you know a lot more about the finer points of acoustics than I do. But for the purposes of this thread, the fact that there is no vibration when two strings are sounded together exactly a fifth apart is what a (bowing) string player needs to know.

Out of interest, are you saying the intervals of the strings of a violin will sound different pitchwise if they're struck with a hammer rather than bowed?

[fayewolf]

Can you explain the harmonic method in more detail? (beginner here).

with the disclaimer that i'm no more than a beginner myself, so you should take this with a large grain of salt... finger the lower string (G) like this, and the higher string (D) like this. according to my tuner, these are both a slightly sharp D. you can finger them both at once like this (apologies for the poor image quality - photographing your hand with a phone camera while holding a fiddle is harder than you might think ;-)

i'd suggest listening to the more experienced people here who recommend learning to tune in fifths - i'll probably have another look at that myself. (violinia, thanks for the explanation - i think that's the best description of how to tune in fifths i've found yet...)

rosfrog - i'm curious to know more about why an electronic tuner shouldn't be used. is there a difference between the frequency the tuner looks for and the 'real' note that's actually played on the fiddle?

Thank you so much for the pics, but it's kina difficult to judge where it is from the pic (they are great pic!! But its hard for me to tell) can you tell me what note they are if you fingered them normally on the strings (not their harmonic note), what about A and E string?

[river]

Thank you so much for the pics, but it's kina difficult to judge where it is from the pic (they are great pic!! But its hard for me to tell) can you tell me what note they are if you fingered them normally on the strings (not their harmonic note), what about A and E string?

i'm afraid i couldn't name the notes - i only play in first position (according to my tuner, they're both roughly a D). for me, if i hold the neck in the crevice between my thumb and index finger (all the way down, not the normal playing position), then slide my hand up until the edge of my palm is against the body of the fiddle, the harmonics for G/D are about the same place my finger fall naturally (using my index and pinky finger).

the harmonic will only sound if your finger is in the right place, so if you can get roughly the right position, you can shift around a bit until you find it. make sure your fiddle is already in tune so you can check you have the right harmonics.

for D/A and A/E, the fingering is the same, just shifted up a string.

[kenm]

But for the purposes of this thread, the fact that there is no vibration when two strings are sounded together exactly a fifth apart is what a (bowing) string player needs to know.

I agree with that. I'm worried when people (e.g. Heinrich Schenker) call it a law of nature.

Out of interest, are you saying the intervals of the strings of a violin will sound different pitchwise if they're struck with a hammer rather than bowed?

The frequencies of the partials will be slightly different, which does affect the perceived pitch, but modern violin strings are so flexible that very few people, if any (Boulez?), will hear any difference. The main "presenting symptom", as it were, of string stiffness is "harmonics" (in the conventional string instrument sense) that are not at the usual intervals of octave, 12th, 15th, 17th etc. I can't hear any difference in these intervals on my rather thicker bass strings, on which the higher harmonics come nicely into the register where the ear is reasonably sensitive to pitch differences. Piano strings, especially at the top end, are much stiffer, which is why an electronic tuner can measure the effect on a well-tuned piano. On church bells and on the principal instruments of the gamelan (metallophones rather like a marimbas with bronze bars), the deviation of the partials from harmonic frequencies is large. Composers for carillon know that the major triad is very discordant on conventional bells; the minor triad sounds much smoother. The gamelan scales, markedly different from European ones, are constructed so as to accommodate the partials of the principal instruments.

[plonkee]

rosfrog - i'm curious to know more about why an electronic tuner shouldn't be used. is there a difference between the frequency the tuner looks for and the 'real' note that's actually played on the fiddle?

A tuner shows you tempered intervals, rather than perfect ones. If you tune each string so it shows up green on the tuner, your fiddle will be slightly out of tune.

To get it right, thet A should be spot on, the e slightly sharp, the D slightly flat and the G slightly flatter again.

I'm guessing that electronic tuners are set up so that only the 'A's are perfectly in tune (with the other 11 chromatically being equidistant).

What about when you play with a piano? Normally, I tune my A to the piano A (or D minor chord), and then tune my other strings directly from that. Is it likely that if the D minor chord is played I'll subconsciously adjust my tuning to the piano's perfect fifth?

[kenm]

I'm guessing that electronic tuners are set up so that only the 'A's are perfectly in tune (with the other 11 chromatically being equidistant).

That's my understanding too, with the proviso that I suspect the frequencies are approximated by dividing integers into a high frequency string of pulses from a quartz time base.

What about when you play with a piano? Normally, I tune my A to the piano A (or D minor chord), and then tune my other strings directly from that. Is it likely that if the D minor chord is played I'll subconsciously adjust my tuning to the piano's perfect fifth?

If you are playing with the piano, that's exactly what you should do, so as to play in tune with it (your pianist can't play in tune with you (IMG:style_emoticons/default/sad.gif) ).

If you are playing in a string ensemble, you should make your A strings sound the same (or an octave lower, if you are the 'cellist) and, ideally, tune the other strings by Violinia's method. You then have the opportunity to vary the tuning of each note to fit the context in which it occurs. Good professional quartets spend quite a bit of time sorting out the appropriate tuning for particular pieces of music.

[AmandaL]

It really isn't difficult to tune in fifths if you're prepared to give it time and really listen.

I agree. too many people give up after no time at all (a few weeks, a couple of months) using the excuse that they 'just can't hear' 5ths. It can take a couple of years, sometimes longer to be able to learn how to tune bowed strings in 5ths. The art to it is not to give up at all, just plug on at it and the penny will eventually drop.

I'm horribly afaid that too many years of listening to and playing equal-tempered pianos and keyboards is actually ruining our ability to hear these perfect intervals. If we go the other way and give up on them altogether we'll lose our ability to hear these natural intervals and with it we'll lose the ability to play fretless stringed instruments in tune altogether.

Makes me really glad I don't listen to piano music too often, or indeed play the piano. Being tuned in to the natural intervals is probably the reason all pianos sound horribly out of tune to me.

To re-iterate - all we need to do is slow down and listen hard for those vibrations. They're there, and discernable to anybody and everybody - you just need the patience to listen out for them. The more you listen out for them the more you'll develop your musical sensitivity and aural awareness, an ability that all musicians should be only too happy to cultivate and nurture.

(IMG:style_emoticons/default/agree.gif) says it all really

[Gorf]

(apologies for the poor image quality - photographing your hand with a phone camera while holding a fiddle is harder than you might think ;-)

I am not so sure about the black nail varnish? <joke> (IMG:style_emoticons/default/blush.gif)

[maya3]

It really isn't difficult to tune in fifths if you're prepared to give it time and really listen.

I agree. too many people give up after no time at all (a few weeks, a couple of months) using the excuse that they 'just can't hear' 5ths. It can take a couple of years, sometimes longer to be able to learn how to tune bowed strings in 5ths. The art to it is not to give up at all, just plug on at it and the penny will eventually drop.

I can 'hear' 5ths between the G, D and A strings. However, I find it very difficult to tell if my E string is too sharp or flat, I only know if its in tune or isn't.
My teacher told me to turn my fine tuner one way so its excessively sharp/flat and then work backwards to get around this problem and it works fine for me, but I was wondering is there ny hope that one day, I will be able to tell if it is sharp or flat?
x

[Violinia]

I can 'hear' 5ths between the G, D and A strings. However, I find it very difficult to tell if my E string is too sharp or flat, I only know if its in tune or isn't.
My teacher told me to turn my fine tuner one way so its excessively sharp/flat and then work backwards to get around this problem and it works fine for me, but I was wondering is there ny hope that one day, I will be able to tell if it is sharp or flat?
x

This is a difficult one and it's very hard to explain how to tell whether a note is too high or too low. I think the best thing for you is practice. Get someone to help by playing two notes on a violin, one higher, one lower. You have to pick out which is the higher one. Get them to make it harder and harder by bringing the notes closer and closer; you'll soon find out at which distance your ear begins to find it difficult to work out which is which. This is the point you have to work on, and I'm afraid it's just practice, practice, practice. The ear can definitely be trained, so just do it!

You'll get there, I promise.

[maya3]

thanks. Like I said, it's only on the E string that I can't tell and then only because its either slightly sharp or slightly sharp, but even then i just *know* when its in tune. Hopefully one day my ear will be trained properly, I'm only 17 so there's plenty of time!
x

[Cath]

Interesting thread!

Violinia, Kemn, do you think then it is okay to use an electronic tuner when playing with a piano so that you are tuned with equal temperament? What about when playing with an orchestra? Are other families of instruments natural tempered in the same way as string instruments? I would assume it would be the case with brass but what about woodwind?

Thanks!

[kenm]

Violinia, Kemn, do you think then it is okay to use an electronic tuner when playing with a piano so that you are tuned with equal temperament? What about when playing with an orchestra? Are other families of instruments natural tempered in the same way as string instruments? I would assume it would be the case with brass but what about woodwind?

There's not one answer to this, and what is best for a particular person depends upon their own ear for tuning; also their ability to avoid open strings. |In some circumstances, even a very good piano tuner might use an electronic tuner, e.g. if the piano was to be used with a rock group whose bass player tuned with one; in that case you might as well do the same. Pianos to be used in "art" music will not be tuned to an electronic tuner. As I explained above, on a well tuned piano, the tuner will eliminate beats when tuning the octaves; their frequency ratio will be slightly larger than 2; and the electronic tuner will show the bottom register as flat and the top as sharp. Also, although the notes within these octaves will be close to equal tempered, they may not be exactly so, inter alia because of the adjustments that the tuner's ear will suggest to make crossing the mechanical break points (chaged numbers of strings per note, string windings) sound as uniform as possible.

If you don't trust your ear, I suggest that for each string you adjust your tuner until it thinks the corresponding piano note is in tune (in the middle register the adjustment may be small), and then tune your string to that. However, this is a complicated subject; at the highest level some string players find piano tuning very unsatisfactory and try to stay with their string quartet or trio.

Most modern wind instruments are nominally equal tempered, but good players know how to tune them dynamically for the musical circumstance and good orchestras play in equal temperament only when fixed pitch instruments (piano, harp, tuned percussion etc.) are an important component of the work. It is standard practice for a second horn to play just intervals with the first, and the horn has three possibilities to achieve this: the lip, the hand in the bell and (except for the very lowest register) alternative fingerings. A professional quality trumpet will have levers to adjust the length of the tubing that is added by depressing the first and third valves. Slide trombones have similar freedom to that of the strings. Tubas are perhaps the most dependant for tuning upon their players lip, though they have some alternative fingerings also. I know less about modern woodwind, though most have alternative fingerings from their second octave upwards and closing holes well below the lowest open one is a standard way of flattening the note slightly. My understanding is that on most of the woodwind, the player learns how to make tuning adjustments with the embouchure.

In the 18th C, at least one flute method gave fingerings for 17 notes per octave: seven naturals and five each of flats and sharps; I don't know whether this was possible throughout the lowest octave. Of course, in those days nothing was tuned in 12-note equal temperament.