Muttley - Tuning question

[32-20-Blues]

Hey Muttley, I know you have talked about this before, and I have read all your posts that I could find about it, but can I run some things by you about tuning? I just want to make sure I have some basics straight...

1) The frets on a guitar are placed according to equal temperament. Pianos are also tuned according to equal temperament. Right?

2) People (yourself included) say that a guitar will never play fully in-tune. Does this refer to the fact that equal temperament is, itself, 'out-of-tune', or does it refer to the fact that guitars do not even fully satisfy equal temperament?

Many thanks.

 

[Light]

1) The frets on a guitar are placed according to equal temperament. Pianos are also tuned according to equal temperament. Right?

Guitars are, in theory. Pianos are "stretched", which is to say they tune the lowest octave or two a little flat, and the highest octave or two a little sharp (it's done gradually, of course).

2) People (yourself included) say that a guitar will never play fully in-tune. Does this refer to the fact that equal temperament is, itself, 'out-of-tune', or does it refer to the fact that guitars do not even fully satisfy equal temperament?

Both. There's an in depth answer, but I'm sick, I'm tired, and I need to go clean my basement. I'll let muttley do it when he gets back (apparently he's out on a gig all weekend - or so he said).



Light

"Cowards can never be moral."
M.K. Gandhi

 

[32-20-Blues]

Guitars are, in theory. Pianos are "stretched", which is to say they tune the lowest octave or two a little flat, and the highest octave or two a little sharp (it's done gradually, of course).






Both. There's an in depth answer, but I'm sick, I'm tired, and I need to go clean my basement. I'll let muttley do it when he gets back (apparently he's out on a gig all weekend - or so he said).



Light


"Cowards can never be moral."
M.K. Gandhi

Hey, thanks for the help, I appreciate it.

 

[muttley600]

We have been over and over this. You really must pay attention in class..

1/ Yes the frets are positioned on a standard guitar to achieve equal temperament. 12 note equal temperament specifically commonly abbr. to 12ET.

There are two common methods used to calculate the positions The 12th root of 2, and the rule of 18. The specifics of it are very well described here.

Wikipedia will also give you good explanations.

A piano is also tuned to reflect 12ET. There are many "tricks" a good piano tuner employs to get the thing to sound right. Stretched tuning is one of them, mis-tuned unisons another. An extract from a page this page explains it quite well.

Stretching the tuning

Oh what a world, what a world. A tuning that sounds perfectly tuned is technically not in tune. If a piano were to be tuned to be mathematically perfect, meaning all the octaves were pure and beatless, it would sound out of tune. The treble would sound progressively flat and the bass would sound progressively sharp. Therefore, in order to achieve tuning nirvana, we must use imperfection to achieve perfection.



At the root of the problem is the principle of inharmonicity. The strings on a piano are pulled to incredible tensions, much more so than other stringed instruments. The stiffness of the piano strings cause the overtones/partials to be slightly sharp. Tuning a piano so that it sounds right to our ears means stretching the octaves. How much? Well, that is where tuning gets a bit more relative. How much to stretch the tuning is really a matter of taste. Some people prefer more, some less. I just tune the stretch to what sounds right to me. Probably the most important part of stretching the tuning is to make sure it is an even and consistently linear stretch. After all, the idea is to make the tuning imperfectly perfect.

The bottom line is that everything both on the guitar and piano is trying to get the them to play in 12ET. It can be a challenge because of the nature of the instrument introducing limiting factors.


2/. Any tuning system whether it is the Pythagorean perfect mathematical scale or todays 12ET has benefits and limitations. No system is inherently correct or even better than another. They are simply better suited to some instruments, musical styles or composition.

If I was to agree with this "People (yourself included) say that a guitar will never play fully in-tune" I would qualify it by saying that it is in relation to two things. First what people believe "In Tune" to mean, and second the physical ability of an instrument and it's materials to behave perfectly from a scientific point of view. In the case of guitar strings they don't and you have added complications that are addressed during a good setup.. What I have always said is that you can get a guitar to play as close as makes no odds with a good set up and a reliable instrument.

The link I always start people off with when talking about temperament and intonation (two different things but often lumped into one) is this one

=> => EQUAL TEMPERAMENT AND GUITAR TUNING <= <=. I wish we had signatures back is used to live in mine..

So in answer, Equal Temperament is not "out of tune" it is a tuning system that divides the octave into 12 equal harmonic and mathematic intervals. The guitar cannot play any tuning system "perfectly" in tune because of the very materials it is made of and manner in which it produces a fretted note. You can get as close to 12ET that makes no difference. In fact to my ear music that is generated digitally to be perfectly "in tune" often sounds sterile and bland to my ear. That is my opinion though!!

 

[gmhg41]

I agree with everything Mutley says, but I have an interesting anecdote, a personal detail, and some general soapbox!

My cousin learned to tune pianos from his grandfather, who was a piano repair man. My cousin tuned the intervals by ear, so they weren't 12ET, but some kind of just system. His piano always sounded wonderful when he played, but he didn't play music that needed to modulate from any key to any other, which is the strong point of 12ET. As long as he stayed in the range of a few flats to a few sharps it sounded really nice.

When I tune my guitar, I'll usually tune it by ear, with perfect intervals, and try it out in the key I'm going to be playing in, which works pretty well for folk music. It makes some keys really nasty, but I don't play them.

What's really interesting is when you mix instruments with different tuning systems, like violin and piano, or great highland bagpipe and anything

 

[muttley600]

I agree with everything Mutley says, but I have an interesting anecdote, a personal detail, and some general soapbox!

My cousin learned to tune pianos from his grandfather, who was a piano repair man. My cousin tuned the intervals by ear, so they weren't 12ET, but some kind of just system. His piano always sounded wonderful when he played, but he didn't play music that needed to modulate from any key to any other, which is the strong point of 12ET. As long as he stayed in the range of a few flats to a few sharps it sounded really nice.

When I tune my guitar, I'll usually tune it by ear, with perfect intervals, and try it out in the key I'm going to be playing in, which works pretty well for folk music. It makes some keys really nasty, but I don't play them.

What's really interesting is when you mix instruments with different tuning systems, like violin and piano, or great highland bagpipe and anything

His piano must have frustrated the hell out of any one who tried to play along with him as well.

The deal with the violin family and intonation isn't so great as it's primarily set by the players ear and dexterity as practically any interval is possible on a non fretted instrument. Its pretty much a given that the tuning system within an ensemble of any kind should be the same. The results otherwise could be quite challenging.

 

[gmhg41]

His piano must have frustrated the hell out of any one who tried to play along with him as well.

The deal with the violin family and intonation isn't so great as it's primarily set by the players ear and dexterity as practically any interval is possible on a non fretted instrument. Its pretty much a given that the tuning system within an ensemble of any kind should be the same. The results otherwise could be quite challenging.

He used to tune three pianos. One in his home, one in my grandmother's, and one at the church. AFAIK, all three were only ever solo instruments

I know what you're saying about violins, and if you ask violinists, they'll pay lip service to adjusting their intonation, but according to the research, they really only play Pythagorean tuning. Doesn't matter if they play solo, or with a just tuned wind section, or an ET12 piano. They play how they play, and that's it. The key where violin gets furthest from ET12 is Eb. Beethoven wrote a violin sonata in Eb, and if you look at the score, the violin part is never playing the same note as the piano (with perhaps three exceptions). I think Beethoven was giving the violin room to use it's own intonation and not clash with the piano (though I'm thinking ET12 was not used at the time, the same concepts apply).

Brass and winds don't use ET12, and neither do strings. I mentioned bagpipes, which I play. They use a unique tuning system which is mostly just, based on the harmonic series. There are more celtic-rock bands than you can shake a stick at, and the bagpipe sounds great with a guitar behind it.

It's my hypothesis that the reason a horn section sounds sooo good in a rock ensemble is the mixing of intonation systems. Specifically the tight harmony of justly tuned instruments contrasts with the muddy ET of the guitars.

 

[muttley600]

He used to tune three pianos. One in his home, one in my grandmother's, and one at the church. AFAIK, all three were only ever solo instruments

I know what you're saying about violins, and if you ask violinists, they'll pay lip service to adjusting their intonation, but according to the research, they really only play Pythagorean tuning. Doesn't matter if they play solo, or with a just tuned wind section, or an ET12 piano. They play how they play, and that's it. The key where violin gets furthest from ET12 is Eb. Beethoven wrote a violin sonata in Eb, and if you look at the score, the violin part is never playing the same note as the piano (with perhaps three exceptions). I think Beethoven was giving the violin room to use it's own intonation and not clash with the piano (though I'm thinking ET12 was not used at the time, the same concepts apply).

Brass and winds don't use ET12, and neither do strings. I mentioned bagpipes, which I play. They use a unique tuning system which is mostly just, based on the harmonic series. There are more celtic-rock bands than you can shake a stick at, and the bagpipe sounds great with a guitar behind it.

It's my hypothesis that the reason a horn section sounds sooo good in a rock ensemble is the mixing of intonation systems. Specifically the tight harmony of justly tuned instruments contrasts with the muddy ET of the guitars.

You have me floored on a few things. Can point me in the direction of the research you are quoting, and can you expand the following comments for me, I'm not sure we are talking about the same things?

Doesn't matter if they play solo, or with a just tuned wind section, or an ET12 piano.

As I said the intonation of a non fretted stopped string is dependant entirely on the string length made by the finger on the fingerboard. A good violinist or cellist or double bassist will play according to the temperament of the fixed instruments in that ensemble. The good ones are very good at it and these days thats nearly always 12ET

The key where violin gets furthest from ET12 is Eb.

The violin cannot be closer or farther from any temperament as it can play in any temperament happily. Doesn't matter if its Eb or D#. Beethoven although aware of equal temperament systems had other temperaments at his disposal. 12ET as the norm came later around the time of the Romantics. Exactly when and is hotly debated by musicologists

It's my hypothesis that the reason a horn section sounds sooo good in a rock ensemble is the mixing of intonation systems.

Brass instruments use a combination of overblowing, embrasure and valves to make playing in ET12 easier. A natural end blown tubes series of frequencies do not accurately fit into any common tuning temperament. Physics is the key and the note coming from and end blown tube such as a brass instrument is determined by the length and speed of the column of air in it. Brass sections play in 12ET quite happily. Players can also trim the note by using lip techniques the same way as woodwind players do when they "lip up" or "lip down" a note.

The bagpipe thing. Some bagpipe music I love some I can't listen too. Precisely because of the temperament thing. Thats as an ensemble instrument not solo or with other similarly tempered instruments.

 

[ggunn]

A natural end blown tubes series...

Like the internet?

 

[gmhg41]

You have me floored on a few things. Can point me in the direction of the research you are quoting, and can you expand the following comments for me, I'm not sure we are talking about the same things?

I'll try to find it again. About three years ago I got interested in violinists and intonation, and I went out to see what I could find, and there are quite a few studies, but the one was very interesting, because they specifically wanted to see if a violinist would switch to playing 12ET with an ET accompaniment.

As I said the intonation of a non fretted stopped string is dependent entirely on the string length made by the finger on the fingerboard. A good violinist or cellist or double bassist will play according to the temperament of the fixed instruments in that ensemble. The good ones are very good at it and these days thats nearly always 12ET

Sure, a violinist *could* play 12ET, but they don't. On a violin fingerboard in open position the difference between an ET C# and a Pythogorean C# is about 1/8 of an inch (3mm or so). That's huge. Watch a violinist play sometime. Their fingers come down and land in tune every time. They never land and then adjust for pitch. My wife is a violinist, and she spends a lot of time training her fingers (muscle memory) to land in tune. It's not something they can change on the fly. They're very good at hearing intonation and tuning, too. "Intonation is what we do" is my wife's way of explaining it. Maybe on a sustained note (a half note or longer) if they were out of tune with say a piano they might make an adjustment.

The violin cannot be closer or farther from any temperament as it can play in any temperament happily. Doesn't matter if its Eb or D#. Beethoven although aware of equal temperament systems had other temperaments at his disposal. 12ET as the norm came later around the time of the Romantics. Exactly when and is hotly debated by musicologists

You're talking about the instrument. I'm talking about the violinist. Violinists only use one intonation system for melody notes -- pythagorean, but they do use justly tuned doublestops. Some fiddlers use just intonation. That's why violinists think fiddlers play out of tune. Well -- some fiddlers are really haphazard in their intonation. But even speaking only of the instrument, the open strings of the violin are tuned in pure intervals. This makes the instrument naturally resonate in pythagorean tuning. It will not, and cannot resonate in ET or just systems, but only pythagorean. Interestingly, the bit of the string between the bridge and the tailpiece is a specific length to also resonate in pythagorean tuning.

Brass instruments use a combination of overblowing, embrasure and valves to make playing in ET12 easier. A natural end blown tubes series of frequencies do not accurately fit into any common tuning temperament. Physics is the key and the note coming from and end blown tube such as a brass instrument is determined by the length and speed of the column of air in it. Brass sections play in 12ET quite happily. Players can also trim the note by using lip techniques the same way as woodwind players do when they "lip up" or "lip down" a note.

I've heard that brass players use 12ET, but after seeing the other research I doubt it more than ever. People can't hear 12ET easily (my evidence is that piano tuners (other than guys like my cousin) don't tune strictly by ear). I don't believe a brass player, on his own with no outside reference would play 12ET. Even if one would on his own, I'm absolutely certain that a brass trio would not play ET intervals, especially not when it comes to thirds. When I see video of brass musicians recording tracks in a recording studio (like on the new Real Big Fish CD/DVD), the intervals are always pure, which means they can't be ET. Maybe they don't even have the guitar in the headphones when they record?

The bagpipe thing. Some bagpipe music I love some I can't listen too. Precisely because of the temperament thing. Thats as an ensemble instrument not solo or with other similarly tempered instruments.

As an interesting side note, pipers have been changing their tuning over the last 100 years. Particularly over the last 40. The C and the F used to be midway between C and C# (or f/f#), but now they are decidedly C# and F#. Our tuning is becoming very harmonically just. In part, this trend is probably due to pipers listening to other kinds of music. It may also have something to do with the rise of the pipe band, and in particular the playing of harmony parts.

 

[muttley600]

I'll try to find it again. About three years ago I got interested in violinists and intonation, and I went out to see what I could find, and there are quite a few studies, but the one was very interesting, because they specifically wanted to see if a violinist would switch to playing 12ET with an ET accompaniment.

About thirty years ago I began studying musical acoustics. I went out and got fancy letters after my name in the subject. I'd be interested to read the study in question.

Violinists play in 12ET quite happily with orchestras throughout the world either as part of a string section or as a soloist. In fact they are required to. They play in 12ET when they are accompanied by a pianist playing in 12ET. There are occasions when violinists will adjust intervals within the scale especially when they are playing with other non fixed pitch instruments, a string quartet for example. If the piece involves much in the way of modulation they have to do this with care. The fact that a violinist is capable of tempering certain intervals does not mean he or she is playing in a just or mean temperament. It means they are adjusting intervals to be either in tune with the fixed pitch accompaniment or to make the intervals more pleasing to their ears where the situation allows. Vocal and choral singers do exactly the same.

Sure, a violinist *could* play 12ET, but they don't.

They do. It is required whenever they are playing with an ensemble that is based on 12ET. So do brass and woodwind. They do so or they would be out of tune with fixed pitch instruments in those ensembles. Good intonation is the mark of a good musician across genres.

On a violin fingerboard in open position the difference between an ET C# and a Pythogorean C# is about 1/8 of an inch (3mm or so). That's huge. Watch a violinist play sometime. Their fingers come down and land in tune every time. They never land and then adjust for pitch. My wife is a violinist, and she spends a lot of time training her fingers (muscle memory) to land in tune. It's not something they can change on the fly. They're very good at hearing intonation and tuning, too. "Intonation is what we do" is my wife's way of explaining it. Maybe on a sustained note (a half note or longer) if they were out of tune with say a piano they might make an adjustment.

You cannot describe the difference between two notes that way it depends on string length, action, string gauge and where on the fingerboard. Open position fine, but the rest still apply. You describe the difference between intervals in cents. I have watched violinists play, I have worked on acoustic research papers with some of the finest, I have handled nearly a dozen Stradivari's over the last twenty years. I now teach this very subject to others. In other words I have seen good violinists of all traditions effortlessly match pitch and temperament. 3mm is a huge degree for error.

You're talking about the instrument. I'm talking about the violinist. Violinists only use one intonation system for melody notes -- pythagorean, but they do use justly tuned doublestops. Some fiddlers use just intonation. That's why violinists think fiddlers play out of tune. Well -- some fiddlers are really haphazard in their intonation. But even speaking only of the instrument, the open strings of the violin are tuned in pure intervals. This makes the instrument naturally resonate in pythagorean tuning. It will not, and cannot resonate in ET or just systems, but only pythagorean. Interestingly, the bit of the string between the bridge and the tailpiece is a specific length to also resonate in pythagorean tuning.

You are talking rubbish. If a violinist used a Pythagorean scale built of perfect fifths when playing with fixed pitch instruments the results would be appalling. Period. If the Pythagorean scale worked that way we wouldn't have a need for Just, Mean, or equal temperament tunings. Just because the open strings of the violin are tuned in perfect fifths does not mean that the instrument is played in Pythagorean tuning or that it is more resonant as a result. That is just absolute nonsense from both a scientific and musical view point and to me as a luthier.. I'm calling you out on this one. You need to produce some evidence that this is the case and then I'll blow it away with a mountain of violin acoustic papers I have written and read.

Sorry, but if your going to say things like "but according to the research, they really only play Pythagorean tuning." and "This makes the instrument naturally resonate in pythagorean tuning. It will not, and cannot resonate in ET or just systems, but only pythagorean. Interestingly, the bit of the string between the bridge and the tailpiece is a specific length to also resonate in pythagorean tuning." you are going to have to prove it to me. Interestingly the distance between the bridge and tailpiece on a violin has long been set at 1/16 of the mensur or two octaves and a fifth because it was thought this would help avoid wolf tones and not vibrate sympathetically with any other note. This view is changing.


As I said above a decent violinist will temper the intervals to suit the music being played. In modern western music that is nearly always 12ET because of the fixed pitch instruments that are played alongside and the need to modulate through keys frequently.

I've heard that brass players use 12ET, but after seeing the other research I doubt it more than ever. People can't hear 12ET easily (my evidence is that piano tuners (other than guys like my cousin) don't tune strictly by ear). I don't believe a brass player, on his own with no outside reference would play 12ET. Even if one would on his own, I'm absolutely certain that a brass trio would not play ET intervals, especially not when it comes to thirds. When I see video of brass musicians recording tracks in a recording studio (like on the new Real Big Fish CD/DVD), the intervals are always pure, which means they can't be ET. Maybe they don't even have the guitar in the headphones when they record?

There you go again with the third party statements and such. Back them up then we can talk seriously about temperaments and tunings and the intonation issues they present.

Bottom line. Any none fixed fixed interval instrument can temper any interval it likes but when it has to play with a fixed interval instrument it has to follow that. These days thats 12ET. Has been for over a century or more..

 

[gmhg41]

Start here:
http://www.violinmasterclass.com/intonation_qt.php?video=int_def1&sctn=Definition
["This site provides information that was until now available only to those able to audition into the world's foremost violin studios, such as the classes of Dorothy DeLay, Ivan Galamian, and Carl Flesch." -- I think those are the three biggest names in violin pedagogy.]

Then go get "Violin Intonation" The Journal of the Acoustical Society of America -- January 1937 -- Volume 8, Issue 3, p. 207. The bottom line, "The average extent of each of the five intervals approximated its theoretical magnitude in Pythagorean intonation"

Here's a more recent study, "Comparison of Solo and Ensemble Performances with Reference to Pythagorean, Just, and Equi-Tempered Intonations" Journal of Research in Music Education, Vol. 8, No. 1 (Spring, 1960), pp. 31-38. This is the one I mentioned previously.

If you read any of the literature on teaching or learning violin, there is absolutely no mention *anywhere* of methods to learn to play ET, but there are loads of references to "ringing tones"; that is, playing so that the open strings resonate (which, as I mentioned, is the definition of pythagorean).

You question my method of specifying the distance between an ET C# and a pythagorean C# -- It was a violin, so that specifies the string length. I could have mentioned it was the A string (there are only two C#'s in first position), and that it was a perlon string (the difference is probably greater on the G string). You can convert the cents between an ET and a pythagorean C# if you like, but I don't see the point; I choose to measure the distance between the two notes on the string. There's just no way any violinist who spend literally thousands of hours learning where that C# goes would suddenly play the other one. A violinist with small hands will have the C# finger literally touching the D. A violinist with large hands will need to move the C# finger out of the way to play the D in tune. ANY violin student who plays ET at a lesson will be told that their C# is FLAT.

My wife is a professional violinist. In a concert she listens first to her stand partner, second to the people behind her, third to the 2nd violin section, and then to the other strings (counterclockwise around the circle). Ask any violinist -- if they're honest with you they'll tell you they don't really listen to the other sections. As I previously alluded to, she sits and plays scales. They are pythagorean scales. Up and down three octave scales in three seconds. Drives a sane man batty. She only has two ways to play any given note: The right way, and out of tune. I've heard discussions she's had with her friends. They're not even aware in the slightest of any of this stuff. They've just been taught what "in tune" is, and that's how they play.

Violinists mostly play with other string players. There are exceptions, of course, but probably 90% of the world's violinists only really play with other strings, and they all play pythagorean, because it's what makes the instruments sound best.

Yeah, I know all the theory too, but then there's reality. Take an FFT sample of any modern violinist playing anything. Rachel Barton Pine is a good choice, or Hilary Hahn. They don't play 12ET. Ms. Pine has a lot of youtube video that's easy to analyze. Watch the DVD of "The Devil's Instrument." Izhack Perlman discusses intonation. He affirms that there is only one way to play a violin in tune. He goes on to explain that in the past (i.e. in the early 1900s) that violinists sometimes played things with different tuning, but that no violinist today would dare to play "out of tune like that."

Your turn: cite any published peer reviewed study that supports your claim that string sections or solo violinists routinely play 12ET. Or find some violin literature that supports your claim, something that teaches a student how to play ET.

 

[muttley600]

Jeez man that first site is what?? It won't load for me anyway.

I have the last 20 years of The Journal of the Acoustical Society of America. They have kindly published some of my research in the past. I can't go back as far as 1937 though.

This "The average extent of each of the five intervals approximated its theoretical magnitude in Pythagorean intonation" means nothing. Precisely nothing. Nada..

I can get hold of this next week. "Comparison of Solo and Ensemble Performances with Reference to Pythagorean, Just, and Equi-Tempered Intonations" Journal of Research in Music Education, Vol. 8, No. 1 (Spring, 1960), pp. 31-38. I look forward to reading it. As the Abstract doesn't give much away and thats all I can get access to online right now.

If you read any of the literature on teaching or learning violin, there is absolutely no mention *anywhere* of methods to learn to play ET, but there are loads of references to "ringing tones"; that is, playing so that the open strings resonate (which, as I mentioned, is the definition of pythagorean).

I've read it and teach the importance of temperaments to both musicologists and young aspiring string players who are studying for a degree in music.

Just as an appetizer here is an extract from "any of the literature on teaching or learning violin," as you put it.

Intonation is a vexing problem for string players. In fact it is so much so, that often one of the distinctions between the most sought-after string performers and ensembles from their professional colleagues less in demand, is the quality and consistency of their intonation. The notion of “in tune” as a goal, however laudable is simplistic. In order to achieve satisfying and consistent sounding intonation, it is critical to have a concept for tuning, based on certain acoustical realities, and based on the context in which you are working.

Any discussion of intonation in the modern era begins with an understanding of the system of equal temperament. With equal temperament, by adjusting every interval to the same degree in the scale, two problems of tuning chords are dealt with via compromise: octave displacement, and the effect of the qualities of different intervals of the triad in different keys. In the equal-tempered system, music sounds relatively in tune (or out of tune) to the same degree in every key. A keyboard tuned to equal temperament frees a composer to write pieces containing any and every possible modulation. Because of this advantage, equal temperament has become the most universally used tuning system for keyboard instruments. J. S. Bach was one of the first musicians and composers to fully exploit the virtues of the system of equal temperament. The great keyboard sonatas of the classical and romantic eras, and most of the repertoire written in the years since would have been impossible without the equal-tempered system. In the modern era, the equal tempered system also provides a convenient base line for tuning all non-keyboard instruments in a manner that requires no specific knowledge of the harmonic context of a situation. Modern orchestras typically conceive of tuning in equal temperament. Electronic tuning machines generally use equal temperament as their default setting partly for this reason.

However practical it may be as a compromise, for non fixed-pitch instruments equal temperament is not a means to the most beautiful or satisfying intonation in either harmonic or melodic contexts. There are situations where equal temperament makes sense for non fixed-pitch instruments. In the modern orchestra for instance, any large deviance from equal temperament can leave a player sounding less unified with the group. There are situations in chamber music settings as well, where equal temperament is the most exigent solution to a conflict of acoustical and technical realities.

In certain repertoire, even with fixed-pitch (keyboard and fretted)
instruments, there are tuning choices to consider besides equal temperament, depending on the degree to which a piece modulates, and depending on the actual keys to which the piece modulates. Early music practitioners, especially keyboard players, must incorporate an understanding of temperament as essential among the tools they bring to the problems of performance. There are thousands of possible temperaments for tuning, and at various points in history, prior to the widespread adoption of equal temperament as a universal tuning system, various temperaments have informed composers and vice-versa.

The best non fixed-pitch instrumental performers invariably employ intonation based on the harmonic, melodic, and instrumental contexts in which they are playing, even if they don’t always know they are doing so. When playing with piano, string players are most often relegated to a modified version of equal temperament. In some instances we can cheat and deviate from the temperament of the piano, but many times such deviance will leave a string player sounding out of tune with the piano. Other than the instrumental context of playing with piano, there are two other common contexts that present tuning problems: octave displacement and harmonic-versus-melodic. String players need to consider these problems, both intellectually and intuitively in order to develop satisfying and consistent style of intonation.

Violinists don't play 90% of the time with violinists. They play all sorts of gigs. Seriously I know tons of professionals string players. They take whatever gigs they get.

I questioned your assessment that you assume that if the difference of 3mm in string length is to small for a violinist to bother with. That is nonsense.

If you create a scale in Pythagorean fifths you end up with a pthagorean comma at the octave that sounds horrid. I still don't think we are talking about the same things here. Your understanding of the Pythagorean scale seems to allow you to play a circle of fifths and remain in tune at the octave. Can't be done.


I've done more Fourier tests than I care to recall, mostly on violin plates and their modes of vibration not for a few years admittedly but I don't think the physics has changed.. Doesn't mean that modern composition is not done in 12ET and that violins don't have to respect that.

I'm going to do you a favour and chuck a shit load of of reading your way next week when I'm back at Uni you'll be able to study exactly what 12ET is and how it works. In the meantime you have failed to explain to me about the resonant properties of the violin body and how it only works if you play in Pythagorean tuning and not in ET or just systems. I was looking forward to that.

Anyway I'm off to my bed now that the weekends jet lag is creeping in.

 

[gmhg41]

Just as an appetizer here is an extract from "any of the literature on teaching or learning violin," as you put it.

Um, I was hoping for something written by someone besides yourself.

Violinists don't play 90% of the time with violinists. They play all sorts of gigs. Seriously I know tons of professionals string players. They take whatever gigs they get.

OK. But talk to them about what they listen to. The ones I've talked to listen, (as I said) to their stand partners more than anything.

I questioned your assessment that you assume that if the difference of 3mm in string length is to small for a violinist to bother with. That is nonsense.

Duh. First, you completely misunderstood. I'm saying that the 3mm is the difference in *finger position*. String length is standardized for violins.

If you create a scale in Pythagorean fifths you end up with a pthagorean comma at the octave that sounds horrid. I still don't think we are talking about the same things here.

You totally don't understand pytahgorean tuning if you think there's a comma at the octave!!!!

Octaves are pure in pythagorean, as are 5ths. If you cycle all the way through 12 octaves you hit the comma, but you'd have to be a dog to hear it. MMmmm. Muttley, eh?

But name any piece of music commonly played that cycles through 12 key signatures. Most of them stick to a range of maybe 4 1/2 steps (example 1 flat to two sharps). Yeah, if you were Bach and you could write a piece to show off the wolf, and you could catch up a violinist. But why would you? The literature leaves open the possibility that violinists will move the wolf to the other side of the circle of fifths on the fly. That's my theory, but no evidence supports (or denies) it.

but I don't think the physics has changed.. Doesn't mean that modern composition is not done in 12ET and that violins don't have to respect that.

I listen to the radio, and I go to a lot of concerts. Where do you go to hear modern composition???

I'm going to do you a favour and chuck a shit load of of reading your way next week when I'm back at Uni you'll be able to study exactly what 12ET is and how it works.

Don't bother. Not interested. Been there, done that.

Like I said though, please cite any peer-reviewed study that supports your contention of violinists playing 12ET -- let me add -- in common practice!

Yeah, sure, there's some funky modern stuff. But no one's really playing or recording it, so what difference does it make? Going back to bagpipes, Maxwell Davies wrote a piece for bagpipe in a=440. All modern bagpipes are a=475 or higher. So what does Davies' piece prove? Bozo composers can write anything, even if musicians don't normally play it. My bagpipe teacher recently performed the piece. She pointed out some of the bizarre ornaments, and her teacher said, "well, but you'll play it however you want, right?" That's the theory vs. reality that I brought up before. It doesn't really matter what the theory says if real musicians aren't doing it.

On the violin resonance (since you asked): The strings are tuned in perfect intervals E A D G. If you play an in tune E on the A string, it will (by definition) resonate with the E string. If you play an E on the G string, or a G on the E string, or any other note on any string that has the same name as any open string note, it will, by definition, resonate with the open string.

This "fact" is known by all violinists. Ask any of them. Now name which scale has E, A, D, and G all in perfect fifths. Since violinists play by muscle memory (ask one), it follows that the fingered note B on the E string will be in the same position as the fingered 5th on the other three strings, so you can add B to the circle of perfect fifths. Once you've got that much of the scale locked down you start looking at the intervals. G to A, or D to E -- a whole step -- is proscribed by the open strings. So now you've got whole steps and 5ths built in. You've also got 4ths, 7ths, and 3rds, if you count the B on the E string. G to E gives you the 6th. The only interval lacking is the 1/2 step. To get the 1/2 step, you've got to take that E up two more fifths past B. But you can get there, and it works.

I'm sorry you couldn't open the violinmasterclass website. It's a robust server, so there's a problem on your end. Try a different browser. The information will be worthwhile. They explain how to derive a violin scale on the instrument, and further, how to derive double-stop notes. The violinists who created the website are top notch. They teach reality. Alter your theory as necessary.


OK, now forget about all the theory. Use your ears and go find me any recording with brass in a rock setting that is ET.

 

[gmhg41]

Listen to "The New Version of You" on RBF Monkeys for Nothing.

The horns are nowhere close to ET. Play em on your piano and see. Don't work, do it?

 

[gmhg41]

Dude. Listen to any RBF track with horns (I'm in the process of listening to them all!). They're not freaking ET intervals.

 

[gmhg41]

I've done more Fourier tests than I care to recall, mostly on violin plates and their modes of vibration

On the wood? WTF? Give me the name of any recording of a violinist playing ET that I can verify for myself!

 

[gmhg41]

So forget about all that technical stuff.

Cite me any recording I can find on I-tunes that has Et strings or brass.

In the mean time, listen to RBF.

 

[Paraglider]

I've read the whole thread and have to say that Muttley is on the money all the way through. He knows what he's talking about, and not just because he regularly cites my ET for Guitarists article!

Just a couple of things to add. Piano tuning is ET in the mid range. The stretching of the upper and lower ends of the range are for slightly different reasons. The bass stretch is needed because the harmonics of a correctly tuned bass string would clash with the mid range fundamentals. This is the inharmonicity effect - the harmonics are not quite in tune. The reason for the treble stretch is partly psycho-acoustic - very high in-tune notes just sound a bit flat.

It's maybe also worth mentioning that if a player or singer employs vibrato it becomes almost meaningless to discuss temperament. The pitch range of typical vibrato is wider than the difference between, say, a perfect and a tempered fifth. Most opera singers have a vibrato you could drive a bus through!

 

[muttley600]

Hey Paraglider, I did look over those articles you sent me. I've been snowed under recently so haven't had a chance to add comments. They look good to me I was just going to add a few interesting technical bits that may shed some light on the subject material. I'll get round to it soon. I'm solid in the workshop for the next few weeks but when I've cleared my back log I'll get on it. The general info in all of them is sound and well presented. It's refreshing to see info from someone who has a solid grounding in the subject and it's wider applications and implications. Keep up the good work.