Pianos are tuned to certain temperaments, “Equal” I believe, although there are others. I recognize this has to do with reconciling the difference in, among other things, scales going up versus scales going down. I hope this makes sense.
Unfretted strings can “tune” on the fly, of course, but what about “untuneable” instruments such as the guitar with its frets, xylophones, trumpets (?) and others. Are they tuned to a fixed temperament similarly to the piano?
Standard fixed instruments are tuned to equal temperament, usually with the A above middle C set at around 440Hz.
You can get instruments in other temperaments but they’re not cheap. Some orchestras commission them so they can do accurate reproductions of older compositions.
The short answer for the guitar is yes, of course it is tempered. The long answer for the guitar is somewhat more complicated. There are more compromises in tuning a standard guitar than a piano. In a piano each note is tuned independently, but in a standard guitar the placement of the frets will affect the frequency of multiple notes. Many people have come up with different ways of dealing with this. There are proprietary tuning systems. Guitars have been constructed where the frets are different for each string. Other guitars have the frets arranged in a fan like fashion. None of these variations have really caught on, though each have their adherents.
The piano too is a little different than most in that it can play multiple frequencies on a single “note.” The hammer strikes multiple strings (2 or 3) and each of the stings for the same note can (and should be) tuned to different frequencies.
For valved brass instruments (i.e., all of them except the trombone), each individual valve has a “tuning slide” that can be used to adjust the pitch changes caused by that valve. You can see them in this diagram of the trumpet, labeled as “1st slide”, “2nd slide”, and “3rd slide”. The second slide is not customarily adjusted while the trumpet is being played, but due to temperament issues the first and third slides occasionally needs to be moved in or out to get a note in tune. (The ring on the 3rd slide is there to allow a finger to push/pull the third slide, while the u-shaped bracket allows the thumb to do the same to the first slide.) In principle, they can also be removed and replaced with crooks of other lengths.
All of this is to say that adjusting a standard trumpet to play in a non-equal temperament probably wouldn’t be that tricky, and I suspect it would largely be a matter of adjusting the tuning slides. What would be trickier would be having the trumpeter learn to hear and tune the notes correctly; brass players often use their lips to adjust the pitch of a note as well as the valves/slide, and a brass player playing in a non-standard temperament would have to unlearn some of the tricks that they normally use to play in tune.
If more than one instrument is playing a pitch, any differences between pure tuning and equal temperament are covered up anyway. A violinist is trained to add a vibrato to all sustained pitches, which means that the pitch is constantly being rapidly varied. Add to that the uncertainty of landing exactly on whatever pitch is desired for wind and non-fretted string instruments and you will find that professional musicians are more concerned with playing together than what temperament they are in.
Any instrument that cannot be adjusted on the fly (xylophone, piano, etc.) is normally tuned to an equal temperament scale. I say normally, because there are exceptions for rare, special occasions or pedantic purists who have nothing better to do than argue about it.
Also consider the sitar, which has movable frets. I believe they adjust depending on what scale you’re playing.
It is true that the staggered frets have not caught on (and probably never will) , but fan fretted guitars continue to be made in large (and increasing) numbers by independent luthiers …fan fretting has nothing whatsoever to do with temperament, equal or otherwise…it is all to do with getting the maximum response from the bass strings, while maintaining ease of fretting on the treble strings.
But that causes audible beats. Are you sure?
Multiple strings in a piano won’t resonate independently, they are coupled via the bridge on the frame, which although it is cast iron, does vibrate (otherwise sound would not couple to the sound board) and thus energy couples between the strings. Two strings that are slightly differently tuned won’t simply resonate at separate frequencies and cause beats - they exchange energy and you get a very complex set of interactions that affects the aftersound of the string. The strings move in and out of phase and this affects the apparent admittance of energy into the bridge and hence the soundboard. Even perfect unison tuning of the multiple strings will have energy coupling effects, and since there is no such thing as a perfect hammer, the strings don’t start out in perfect phase anyway.
The seminal paper on the subject. (920kB PDF) suggests that a master tuner will use the manner in which slight offsets in the tuning of the unison strings affect the aftersound to compensate for tiny imperfections in the way the hammer strikes the strings in a multiple set, and thus allows him to create a sound where all the strings have the same aftersound envelope - something that leads to a significant improvement in overall sound.
Good summary. The intonation and, hmm, harmonic resonance of a guitar is a key indicator of its build quality - does it sound in tune and musical up and down the neck, playing in different keys? Tuning a guitar with a digital tuner, then playing a D and a G and checking how in tune they sound is a first-stop on checking out a guitar…
Dante Rosati has created and designed guitars for different tuning/temperament systems–21-tone Just, as well as for his explorations in temperaments never found during the Renaissance efflorescence of temperament research: one using the harmonic series and one using prime numbers.
Fret position is hell, so he spots the different size intervals notes using a color code between positions, resulting in groovy painted fretboards.
His compositions with the alternative tunings, some of which are on his site, are beautiful.
There is an interesting program on temperament on this site. Go down the list of shows available about halfway to show# 423A, “Temper, Temper”.
I can always start out by getting the D and G tuned together well. Then, almost always, the C chord is off, so that the tuning needs further fine adjustments to be completed.
I’ve never bothered with electronic tuners. I use the beats in the harmonics. If, let’s say, these digital tuners can achieve a much finer precision of microhertz than my ears can distinguish in harmonics—what practical difference would it actually make in terms of playing or listening?
That’s actually really cool. I’m just listening to it now, and I like how they show the same song played with different temperaments, especially when they compare something like 1/4 comma meantone vs equal temperament. The ET sounds a bit dull in comparison. Differences are more obvious when you get to stuff like Pythagorean tuning.
True, that’s how I tune a guitar as well (but I’m not a guitarist.) I was just taught the 5th and 7th fret harmonic method, but it never works perfectly if you tune those harmonics completely beatless. I always wondered why that was–it didn’t matter what kind of guitar I was tuning. It worked great as a first pass, but there always needed to be a bit of an adjustment afterwards. Then I found this explanation of guitar tuning, that confirmed I wasn’t going crazy.
That answers my question, and it’s very helpful. That page is so bookmarked for reference. Köszönöm szépen, barát.
Nincs mit! Yeah, it was pretty interesting from a theoretical standpoint. I still tune the same way I always do with a couple of passes, but at least now I know it’s not some intonation problem with the guitar or anything when perfectly tuning harmonics doesn’t work out exactly right.
When I spoke about proprietary tuning systems, I was thinking about the Buzz Feiten method. Here is an interesting video where he talks about what his system does and about temperament in general. His system requires that the guitar be physically modified, but he does not go into that here.
I do not use his system. I occasionally encounter the kind of frustration that he talks about, but if I lie down it usually goes away.
