Tuning: What it is and How it Affects Performance

Requisite Knowledge Level for Understanding (* being beginner, ***** being expert): ** - ***

If you have a friend who plays the guitar, you have probably heard him/her mention before he/she begins to play that he/she needs a second to "tune".  You have probably heard of someone "tuning" the piano before.  As well as maybe a singer talking about singing "in tune", their "intonation", or, more likely, complaining about someone being "out of tune".  In these instance, the one speaking is clearly not talking about a "tune" in terms of "that jaunty tune we listened to last week", but rather something more specific having to do with the quality of the music.  Let us talk then about what all that actually means.

Intonation is the basic concept, from which we get ideas like being In Tune, Out Of Tune, Tuning, and so forth.  Intonation, in its most general form, is the relationship of two sounding notes to each other.  Most people who are not musicians think of notes like they are on the piano.  There is a C and a D.  Also one between them that's smaller and black and it is called a C# or a Db.  But that is the smallest interval; there is nothing between a C and a C#.  This is wrong.  In the general tuning system of classical music, each note is separated by 100 Cents (not money, but a very tiny musical interval), and these minute differences are very much utilized.

Imagine, if you will, that you are cooking and you need some of a stick of butter.  The recipe might say "3 tablespoons".  So you cut off three tablespoons and use it, and everything is wonderful.  But no one forced you to cut there, where the printed lines indicate three tablespoons.  You only did that because the recipe requested 3 tablespoons.  You might really like butter and so cut it a little past that line, or might be watching your weight and so cut a little less, but you do not want to mess up the recipe completely because you are not a master chef and are worried that you might mess it all up, so you do not go as far as cutting a full four or down to two tablespoons.

This is the basis for intonation.  In music, we have (mostly) defined each of the notes to be an exact frequency.  The A located above the middle C, often referred to specifically as A440, is defined to occur exactly at a frequency of 440 Hz... in the USA and the UK.  Elsewhere, especially in mainland Europe, 442 Hz and 443 Hz are used.  And that is only for modern intonation.  Classical music (the time/music period) is generally agreed to be tuned to A at 330 Hz, while Baroque music is either generally agreed to be tuned to A at 415 Hz or sometimes A 466 Hz.  Clearly then, there is no "universal A"; the A that, when played, is always the in tune, perfect, correct, the be all end all of As to ever be sounded.

So what is important then becomes the concept of Tuning and being In Tune.  Orchestras tune to the oboe player at the beginning of the concert, the oboe player having already tuned him/herself to A440.  That means that the oboe player has taken his/her instrument played it with some sort of tuning device on hand that has an A 440 preset to match the pitch of the A on his/her instrument with that exactly.  The rest of the orchestra then does the same with their instruments, insuring that every time they strike an A where they consider the A to lie on their instrument, it rings at the exact pitch of the oboe player's A, the A440.  This is Tuning.  Making the minor adjustments on the physical instrument itself, whether that means moving a tuning slide, tightening or loosening a string or readjusting the mouthpiece.

Then we have the concept of being In Tune or Out Of Tune.  This can pertain to two different things:  multiple musicians playing at the same time and making sure that the distances between each notes in the melody that each musician plays are the correct distance apart.  When a musician plays an instrument, with the exception of a piano and other select fixed pitch instruments, the pitch of the "A", for example, on their instrument can vary very easily.  Thus when multiple musicians are playing the same note, they must listen to the exact pitch each one is playing to match it as closely as possible.  This is important because it makes it all sound prettier and results in a finer performance in the same way that a luxury car works better than a generic sedan because the parts are all manufactured with a higher degree of precision and quality.

In order to properly tune, it must then be understood the proper distance between each note.  Harmonically speaking, there are naturally resonating harmonics that sound "good" together.  Things like Thirds, Fourths, and Fifths sound pleasant to the ear.  These are tuned to the main note in the scale, e.g. the C when in C Major.  So the G above the C should be a certain distance away.  This method of tuning each note in the chromatic scale in its natural and perfect relation to the base note is called Just Intonation.  The problem we arrive at with just intonation, is that when all is said and done, and tuned perfectly to the C, we have unequal distances between each successive note.

If you recall from music theory, the distance between a C and a G is the exact same distance as between a D and an A.  However, because of their relationship to the C, while the C and G interval sounds perfect when played together, the D and A interval does not.  It is flattened by about 1/5th of a half step, and as such would not sound as well together.  This is not as much of an issue for instruments like a violin or voice which can make adjustments for intonation on the fly, but for fixed instruments, like a piano, tuning is an ordeal making adjustments for intonation in the middle of a piece impossible.  If the piece is short, and stays in C Major the entire time, it should still sound fine.  But pieces can be quite long, and very regularly employ key changes which take them to any manner of different keys, which, when the piano is tuned to C Major, would make the piece sound worse and worse the further you get from C Major, to the point where a nice melody in F# major would sound horrible and you would want to cover your ears.

In order to solve this issue, musicians came up with the idea of Equal Temperament.  The one used in Western music (most all Classical and Pop music would fall into this category) is the 12 tone system, or 12ET for short.  In this system, each semitone is exactly the same distance from each other.  So the distance between the C and the C# is exactly the same as the distance between the Gb and the G, and holds true over larger intervals as well, such as D to A is equivalent to Bb to F.  The downside to this is that intervals are not as pure as with just intonation; a fifth tuned justly will sound superior to a fifth tuned in equal temperament.  (There was a system using 19 equal tones that was prevalent during the Renaissance period, as well as it has made a very slight resurgence in the last thirty years, which does some things better than the 12 tone system and some things worse.  It is fun to investigate if you are interested, but it is not generally practical at this point in time.)

But equal temperament is VERY CLOSE, which is why it is used.  Just sounds better than equal, but equal is FAR more freeing than just.  In equal temperament, everything is, as it sounds, equal.  You can start in C Major, and change keys dozens of times, getting all the way to F# major, and that key will still sound EXACTLY as good as C Major did, whereas that same piece played on a justly tuned piano would sound horrible, as mentioned above.  This then leads to a second notion of being In Tune.  Tuning not only to the other musicians with whom one is playing, but also making certain that when one plays a G following a C, that that G is of a proper distance above that C and thus each successive note must relate to the ones preceding it.

Given all of that, then, a musician has multiple things to consider when performing music.  Because musicians want the music to sound as good as possible, when playing a non fixed pitch instrument, they will endeavour to make the necessary adjustments, playing the Major 3rd a little flat in Major triad because that is closer to the Just Intonation.  These relationships change constantly though.  Whether a particular note, say an A, is played as part of an A Minor triad in C Major, later in the piece as part of a D Major triad while in the key of A Major, or later still as a suspended 4th tone from the previous triad over an inverted E Major triad before a V - I cadence in the key of E Major, the musician will make the necessary adjustments to make it sound as beautiful as possible, given the circumstances.  As a piano is a fixed pitch instrument, if playing the same melodic line as a piano, the musician would want to tune to the piano, while if the same note is not being played, the musician would want to tune as justly as possible, while not creating awkward intervals for him/herself in their own melodic line.  Add to that the even further thought that musicians can also choose to play a line just slightly a little out of tune in order to further add to the emotion behind the piece, and one can see that "intonation" and the concept of being "in tune" is a very large one.

This has gone on a little longer than I had intended, so I will end by saying that mean tone temperament, while not as perfect as just intonation, was a great achievement, as it finally allowed performers to play pieces in vastly different keys directly after each other and they would all sound good, something that was impossible with just intonation.  For a good example of this, I would suggest listening to Johann Sebastian Bach's "Well-Tempered Klavier" (also spelled Clavier), which, as the name suggests, is written in celebration of this tuning system.  There are any number of performances which are fantastic, though my favourite was recorded by Angela Hewitt.

Music Theory, the very Basics

Requisite Knowledge Level for Understanding (* being beginner, ***** being expert): *

In the future, I will post articles about classical music's evolution over time.  From Renaissance to Baroque to Classical on through Romantic and Modern and so forth.  To best talk about these changes, you need to be able to understand what I mean when I say something like "sonata form".  These concepts are not hard to follow however, they do require a basic understanding of music theory.  For those of you who know some music theory, this will be review, and I hope you will forgive the time spent.

First off, a definition.  Music Theory is, quite simply, the study of how music works.  It studies how composers achieve their results; why a classical symphony sounds different from a baroque concerto.  This is HEAVILY dependent (though not completely) upon the way music is written.  There are many customs to writing music, but the most predominately used method has been the one passed down in Western music (i.e. European).  This is the basic music staff and notes that you see everywhere.  This is what allows people who play music to play the music that others have written in the way that these words and letters are a way for you to read the words that I have written, or recite a soliloquy from a play that was written by Shakespeare, and so on and so forth.  It sounds basic, but it is absolutely essential, the bare bones and method of communication between people, in this case, musical communication, when not playing the instrument directly.

This is the music staff, a sample from a piece for piano.  This is the grand staff, i.e. the two together form the regular sheet music notation for piano pieces, with generally the top staff being for the right hand and the bottom for the left hand.  The top staff has the Treble Clef symbol at the front, then a flat symbol (looks like a small 'b') and then a 2 on top of a 4, while the bottom staff has the Bass Clef symbol in front of the flat symbol and the 2 on top of a 4.  The music staff is a series of 5 parallel lines.  Each line represents a note, as does each space.  This can be extended past the end of the staff via ledger lines above and below the staff, where each line and space between lines continues to represent a note; an example of this can be seen in the very first measure with the top note on the bottom staff.  The 2 on top of the 4 indicates that there are 2 beats in a measure (in dancing that would be two steps), and that the count of these two beats are delineated by quarter notes (this concept will be left here for the time being, but will all be discussed more in future posts).

The difference between Treble and Bass clefs is the octave in which the notes sound.  If you are not familiar, the first seven main notes in Western music you should learn are:  C D E F G A B, after which comes another C and they continue higher (similarly going in the reverse direction for going downward).  There are also an additional five notes that rest between these notes.  These notes all have two names.  A name reached by adding an Accidental, that would be a Sharp (#, which raises the pitch one half step) in front of one of the main notes, and a name reached by adding a Flat (b, which lowers the pitch one half step) in front of one of the main notes.  These notes are C#/Db  D#/Eb  F#/Gb  G#/Ab  A#/Bb.  The observant person will note that there is no E#/Fb or B#/Cb.  This is because these two notes are naturally one half step apart and thus modifying by a half step achieves the next fully named note, negating the need for the accidental.  These are the complete notes for every scale in Western music (for almost 1500 years).  Modern music can make use of notes between these twelve, but for simplicity's sake, assume that every note that you hear or see written is one of these twelve unless it is specifically mentioned otherwise and you would be right a good 99.9999% of the time (an estimated statistic, though it emphasizes the point).  There is also a symbol for a Natural (♮) which is simply a way of correcting the thought back to the regular note from the accidental, i.e. a B♮ is the same as a B, but might be used in conversation after talking about a bunch of notes that are Bb.

I have started with the letter C here instead of A (the natural beginning of the alphabet) because the C Major Scale is the single most basic building block of music.  A Scale is a series of notes which is essentially the basis for a piece of music.  This would be like saying that I have a pile of oak wood and all those blocks of oak wood is what I am going to be using to build my bookshelf.  I will use things like nails, and maybe some glue to get the job done, which would be other notes defined by accidentals, but in the end, the majority of my new bookshelf will be comprised of that oak wood.  There are many variations of scales, the most common being the Major Scale and the Minor Scale.  The C Major Scale is thus:  C D E F G A B C (it is generally the tradition when writing scales to reiterate the Tonic, i.e. the bottom/top note, though you can see it with the top C left off, in which case, you would always assume that the bottom note is the tonic and the note directly after the last note in the scale would be the tonic again).

On the music staff, each non-modified note, C D E ... B C, takes its place as is, with no accidentals.  Notes that are sharp or flat share the same line or space with another note, e.g. a B Flat appears on the same line as the B, thus the need for the flat symbol illustrating that a different note is to be played.  Given this, there are clearly multiples of each notes as well, two notes that are C that do not sound exactly the same.  These notes are separated by an Octave, that would be, they sound almost exactly the same except that one is higher in pitch than the other, but when you play them together, they still sound very good together and become almost indistinguishable from each other when done well.  The basis for keeping track of all these different notes then is determined by where on the staff they are.  The note C higher on the staff than another C will obviously sound higher and vice versa.  In the image above, as I mentioned, there are two staves (plural of staff), one with a Treble Clef and one with a Bass Clef.

As the words imply (in Italian), the Treble Clef is higher while the Bass Clef is lower.  The middle line in the Treble Clef is a B, while the middle line in the Bass Clef is a D.  Each successive line and space above and below those then are the next notes in either direction.  Thus the Treble Clef lines, from bottom to top are E G B D F, while the spaces are F A C E, and the Bass Clef lines from bottom to top are G B D F A, while its spaces are A C E G.  The two are related exactly by the note directly in the middle of them, the Middle C or C4 (not the explosive).  It is called this because, on the piano, it is the middle of the 7 Cs, or the 4th one from the bottom, with C1 then being the first note on the left hand side and C7 being the last one on the right hand side.  This Middle C (most refer to it that way, though I prefer C4) is located one the very next ledger line below the bottom of the Treble Clef staff and on the very next ledger line above the Bass Clef staff.  The observant person will note then that the very first note on top of the Bass Clef in the first measure of that example above is the D located in the space directly below the Treble Clef, thus being the exact same note as the D located there in the beginning of the 3rd measure, this time on the upper staff (a Measure simply delineates one section of written music from another for ease of reading, and is indicated by a solid line stretching from the bottom line of the staff to the top line of the staff, in this case, since the grand staff is used, it stretches from the bottom of the bottom staff to the top of the top staff, thus clearly indicating a total of four measures, separated by three different measure lines).

The quality of the Scale is determined by the relationship between each note in the scale.  Remember there are a total of twelve notes in western music, in order from C, bottom to top:  C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B C, each of which is then the very next direct note, there are no regular notes that can be found between these (this is called the Chromatic Scale).  Given that then, the distance between any two of those successive notes in the chromatic scale is called a Half Step (e.g. C to Db or F to F#) while the distance between two notes in the situation of *note, skip one, note* from the chromatic scale is a Whole Step (e.g. G to A, skipping G#, or Bb to C, skipping B).  The two main scales that are regularly used as the basis for most music are the Major and Minor Scales.  These are called by their tonic note, i.e. the C Major Scale begins on a C.  This is also then called the Key, as in the piece is in the key of C, or C Major (when not stated, the assumption is major, minor or otherwise will always be stated).  From that note then, the Major Scale is constructed by then going up the following distances:  whole step (C - D), whole step (D - E), half step (E - F), whole step (F - G), whole step (G - A), whole step (A - B), half step (B - C), thus completing the scale.  The Minor Scale is constructed similarly, only starting on the 6th note of the major scale, e.g. the A Minor Scale:  whole step (A - B), half step (B - C), whole step (C - D), whole step (D - E), half step (E - F), whole step (F - G), whole step (G - A).  The observant person notices that in the major scale, the last note before the tonic again is separated by a half step, while in the minor scale it is a whole step.  This quirk of scales and other scales not listed here are a topics for further articles, as well as anything else you see on the example above not mentioned in this post such as those big curvy lines or the 'f' that appears in the middle of the two staves.

This is a lot of information for someone who has never seen it before or is not familiar with it.  To try and familiarize yourself with it if you do not play an instrument, my best recommendation would be to listen to music while watching the sheet music to the same piece.  Easy examples to start with would be some Mozart piano sonatas, as you can find a lot of them on youtube edited so that the sheet music on the image corresponds exactly to the music being played, as in this example:  Mozart, Piano Sonata No. 16 in C Major