TRIADS

TRIADS

In music, a triad is a set of three notes that can be stacked in thirds.^[1] The term "harmonic triad" was coined by Johannes Lippius in his "Synopsis musicae novae" (1612).
When stacked in thirds, the triad's members, from lowest pitched tone to highest, are called:^[1]

the root
the third – its interval above the root being a minor third (three semitones) or a major third (four semitones)
the fifth – its interval above the third being a minor third or a major third, hence its interval above the root being adiminished fifth (six semitones), perfect fifth (seven semitones), or augmented fifth (eight semitones).
Such chords are referred to as triadic.
Some twentieth-century theorists, notably Howard Hanson^[2] and Carlton Gamer,^[3] expand the term to refer to any combination of three different pitches, regardless of the intervals amongst them. The word used by other theorists for this more general concept is "trichord".^[4] Others, notably Allen Forte, use the term to refer to combinations apparently stacked of other intervals, as in "quartal triad".^[5]
In the late Renaissance, western art music shifted from more "horizontal" contrapuntal approach toward chord-progressions requiring a more "vertical" approach, thus relying more heavily on the triad as the basic building block of functional harmony.
The root tone of a triad, together with the degree of the scale to which it corresponds, primarily determine a given triad's function. Secondarily, a triad's function is determined by its quality: major, minor, diminished or augmented. Three of these four kinds of triads are found in the major (or diatonic) scale.
When we consider musical works we find that the triad is ever-present and that the interpolated dissonances have no other purpose than to effect the continuous variation of the triad.
— Lorenz Mizler (1739), ^[6]

INTERVAL

Music Intervals

Working out music intervals is easy once you know how, and this page tells you how! The key to working out intervals is to learn about them step-by-step. Having some knowledge of scales is essential and if you don't already know how to work out a major scale you need to learn. 

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At the simplest level

an interval is the distance between two notes.

So to begin with, all you need to do is count!

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How to calculate an interval

To find the interval between 2 notes just find the pitch of the lowest note and start counting until you reach the top note. When counting intervals you always start from the bottom noteand count both notes. E.g., to find the interval between C and G, begin on C and count up the scale until you reach G.

E.g. C(1) D(2) E(3) F(4) G(5)

So the interval between C and G is a fifth.

See how easy the first step is? Here is another example

In the example above we count

D(1) E(2) F(3) G(4) A(5) B(6)

So the interval from D to B is a sixth.

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If the interval is an 8th it can be written as an octave. If an interval notes are at the same pitch it is called a unison To start with all intervals will be an octave or less. Compound intervals (bigger than an octave) come later!

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This first step doesn't take any sharps or flats in the scale into account, it merely calculates the distance between the notes, but as one of my piano students often remarks “baby steps”. When studying music theory this is particularly true. Having a clear understanding of the basics is crucial when things become more complicated later on. In fact, a clear understanding of basics means that the “complicated parts” are easy as well! Note the words “clear understanding," for me this is very different from a “good knowledge”. In music theory a “good knowledge” is not as important as a “clear understanding”

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The quality of music intervals

In addition to a number (distance) intervals also have a quality. This distinguishes intervals which are not part of the major scale. The 5 qualities of intervals are major, minor, perfect, augmented and diminished. Double augmented and double diminished intervals are not common. To begin with we will look at 3 of these qualities. Major, Minor and Perfect Intervals.

The quality of a music interval

Each music interval has a quality, depending on whether it is a 2nd, 3rd, 4th, 5th etc.

The three interval qualities explained on this page are: 

Perfect Intervals
Major Intervals
Minor Intervals

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Perfect Intervals

If an interval is a unison (1st), 4th, 5th or Octave (8th) it is called a perfect interval. Both notes in a Perfect interval are in the major scale. The example below shows the interval of a Perfect 5th.

One of the features of perfect intervals is the fact that if you invert them (turn them upside down) they remain perfect. 

Perfect Intervals can also be raised or lowered by a semitone to become augmented or diminished, but for the moment all intervals of a Unison, 4th, 5th or octave are perfect intervals. A unison, 4th, 5th or octave can never be major or minor.

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Major intervals and Minor intervals

2nds, 3rds, 6ths and 7ths are either major or minor intervals. Again, it is possible to have other types of these intervals, but at the moment we are focusing on major and minor intervals. As you move on to more complex music theory, you will find that 2nds, 3rds, 6ths and 7ths can also be augmented or diminished, but never perfect. However, for now they are major or minor

Major intervals are those which are part of the major scale. The major scale should always be your starting point when working out an interval. There are 2 example below. The first showing a major 6th interval in the key of C major, the second showing a major 3rd interval in the key of E major.

Minor intervals are one semitone smaller than major intervals. Minor intervals should always be worked out from the major scale. Find the major interval and lower the top note by one semitone to give the minor interval. This is because the notes in minor intervals don't always come in minor scales. E.g. Although the minor 3rd comes in the minor scale, this isn't always the case. The minor second isn't part of the minor scale. This is why it is important to remember to work out intervals from the major scale, not think of them as part of the minor scale. There are 2 examples below. The first shows a minor 7th in the key of G major, the second shows a minor 2nd in the key of D major.

How to remember if a music interval is Major/Minor or Perfect

When you see a list the intervals and their descriptors you can see it is quite easy to remember which intervals are major/minor or perfect.

Perfect 8th (octave)
Major/Minor 7th
Major/Minor 6th
Perfect 5th
Perfect 4th
Major/Minor 3rd
Major/Minor 2nd
Perfect unison (1st)

As you can see above the Perfect intervals are at each side, unison and octave, and in the middle, 4th and 5th. The major/minor intervals come in-between!

Why bother?

Although learning how to find an interval may seem complex to begin with, especially as it relies on your knowledge of scales, as you practice it becomes much easier. It also helps with your sight reading and memorization of music. As with most things in music, the best way to get better at identifying intervals is to practice!

TYPE OF CLEF

KEY SIGNATURE

KEY SIGNATURES

Key signatures are used to facilitate reading and writing of notation in different keys. The key signature applies all the way to the end of the composition, an accidental only as far as the next bar line.Relative keys share the key signatures.During the Baroque period, it was common to include in the key signature only part of the chromatic alterations included in the composition (for example, music written in A sharp would include not more than two sharp signs in the key signature but indicate individual G sharps with an accidental). The reason for this was that melodies were often thought of as representing a church mode instead of a major or minor key.Written in different clefs, key signatures with sharp signs can be perceived as showing a rising tendency whereas key signatures with flat signs show a falling tendency. For keys with sharp signs, the rising tendency can be seen only in the tenor clef since F sharp and G sharp were traditionally written in the upper part of the staff.

Remembering MAJOR Key Signatures

Many musicians have difficulty remembering key signatures and how many sharps and flats there are in different keys. And it is not only for exams that you need to learn the music keys. Knowing which sharps and flats are in different keys will help you with your scales and sight reading as well. There are many different methods to help you remember including mnemonics and various interval based methods, but I have found a good place to start is with my simple technique to remembering music keys 

First here are all the key signatures of the keys that have sharps. I have included the key of C Major (no sharps or flats) at the start, just for the sake of completeness, although clearly there is nothing there!

C Major

G Major

D Major

A Major

E Major

B Major

F Sharp Major

C Sharp Major

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Simple method for remembering
key signatures with sharps

This didn't occur to me until I was writing the number of sharps in the major scales for my students one day. By this point I had been studying music for over twenty years and not spotted this. I could have kicked myself for not noticing it before and, in fact, it can also be used to remember the minor scales as well. You only need to remember two things.

The first things to remember is the order of the sharps which is

F C G D A E B

Some people remember this with the mnemonic 

Father Charles Goes Down And Ends Battle

and others just remember that they need to start on F and keep going up a fifth for each sharp. 

The second thing you need to remember is that C major has no sharps and no flats.

Once you know these two things there is a simple method to help work out all the key signatures for any major key. Just watch the short video below to learn how to do it.

Minor Key Signatures

The most important first step in learning about minor key signatures is, strangely enough, to learn the major key signatures! As you will see below, once you have learned these, you already know the minor key signatures.

TIME SIGNATURE

TIME SIGNATURES

Time signatures consist of two numbers: the lower number indicates the note value that represents one beat (the "beat unit"); the upper number indicates how many of these beats there are in a bar.

Note values are traditionally classified as simple (2/4 and 3/4) and other time signatures, including perfect (for example, 4/4=2/4+2/4), triple, complex, and changing time signatures. Note: The Finnish term 'yhdistetty tahtilaji' is not the same as the English 'compound meter'.

Besides providing the time values and their number, a time signature defines the metric structure in a bar. In compound metres, the main beat is divided into parts, which are longer than the beat unit. For example, time signatures 6/8, 9/8 and 12/8 almost always consist of 3/8 units; in other words, the beat unit is not a quaver or an eighth note but a dotted crotchet or fourth note. It is only in slow tempos that a quaver or an eighth note is perceived as a natural beat unit in these time signatures.

LEDGER LINES

Ledger Line

Ledger Lines are short lines which can be written in a musical score for when notes appear above or below the five main lines of the staff. Ledger Line are only used when notes fall outside the 5 main lines, so that notes can be identified.

FOR TREBLE CLEF

If we need more notes above or below the staff we add Ledger Lines, which extend the range of the staff. (Middle C is the first ledger line below the staff in Treble Clef.)

FOR BASS CLEF

Middle C is the first ledger line above the staff in Bass Clef.

SOLFAGE

What is Solfège?

Solfège (or Do-Re-Mi) is like the alphabet for music  - just as the ABC’s provide the building blocks for reading, solfège provides the building blocks for musical education. It is one of the most widely known and popular systems of teaching pitch, which brings together listening, singing and in due course, playing music. Each note of the musical scale is given a different syllable – Do, Re, Mi, Fa, So, La and Ti. With their open vowel endings, the solfège names are much easier to vocalise than traditional 8-note scale names: C-D-E-F-G-A-B-C, which have lots of sounds that strain the voice (eeee sounds). What’s more, singing letter names for a musical scale has the potential to confuse young children who are learning the alphabet in the context of language.

TREBLE CLEF 

The Treble Clef spirals around the second line from the bottom. This spiral tells us that notes on this line are G.From here we can figure out the other note names simply by going forward or backward through the musical alphabet: A,B,C,D,E,F,G

BASS CLEF

The Bass Clef has two dots, above and below the second line from the top. The dots tell us that this line is F.

What is solfège for?

The idea behind the solfège system is to help develop pitch memory, which is the most basic type of musical memory. It does so by requiring the student to hear the note in their mind’s ear, thus honing their listening and aural skills. Because solfège focuses on the use of voice (rather than an instrument) it is the perfect way for young children to learn pitch naturally.

There are two types of pitch – perfect and relative pitch. Perfect pitch (also called absolute pitch) is  the ability to identify or re-create a given musical note without the help of a reference tone. Famous singers with perfect pitch include Michael Jackson, Mariah Carey and Ella Fitzgerald. Relative pitch is the ability to recognize and produce pitches in relation to each other.

There are also two methods of teaching solfège – the ‘fixed do’ system and the ‘movable do’ system. The ‘fixed’ do system is based upon the C major scale and is more in line with building perfect pitch because C is always sung as “Do” and A is always sung as La etc. However, with the Movable-Do solfège system “Do” is sung as the root (first note) of the scale so any scale or key can be used, thus aiding the development of relative pitch.

Whether you use the ‘fixed do’ or ‘‘movable do’, both systems are tools for helping to develop the muscle memory for pitch, especially if you add the Curwen/Glover hand signs.

Solfège chart showing the hand signs

During the 1840’s, John Spencer Curwen developed hand signs to go with the solfège syllables (do re mi, etc.) based on Sarah Glover’s Manual of the Norwich Sol-fa System. Later, Hungarian pioneer of children’s music education Zoltán Kodály, adapted the hand signs slightly and integrated them into his teaching methods.

This solfège chart show the hand signs. Hand signs allow children to actually see the height or depth of the pitch. The low “do” begins at your midsection. Each hand sign (pitch) is then made above the previous one. Thus, you have the hand signs going up when the pitch goes up. The upper “do” is at eye level. The reverse is done on the way back down and that’s a little trickier.

NOTE VALUE

Each music note written on the stave has a duration (length) as well as pitch. It is the design of the note that tells you its duration, in the same way as the position on the staff tells you the pitch. So each music note on a stave gives you two pieces of information, pitch and duration. This page focuses on the duration of each note.

Whole Note (Semibreve)

The Whole note is the longest music note in general use today. It is an open note with no stem.  The duration of the whole note is 4 quarter notes.

Half Note (Minim)

The Half note duration is 2 quarter notes. It differs from the whole note in that it has a stem, although it is still open. For students I liken this stem to the line in the middle of the ½. This also helps them remember that 1 half note is worth 2 beats (in 4/4 timing, which is what they are usually working in when learning this).

Quarter Note (Crotchet)

The quarter note has become the de facto standard 1 beat music note. This has happened as the 4/4 time signature is the most popular (with 3/4 and 2/4 following close behind) and quarter notes have a duration of 1 in these time signatures. It is also roughly in the middle of the most used notes in the Rhythm Tree, making the quarter note the ideal candidate for ensuring whole notes don't become too long to count, and shorter, popular notes such as eighth and sixteenth notes aren't impossible to count in terms of them being fractions of a note. The quarter note changes from the half note as it is filled in, as opposed to empty. 

Eighth Note (Quaver)

The eighth note is worth ½ of a Quarter note. It may also be considered as a one beat note in 3/8 and similar timings, the 8 on the bottom of the time signature giving the clue that you are counting in eighth notes. This is the first note in the rhythm tree to have a flag. The flag is the name for the 'tail' added to the eighth note. Eighth notes may be a               single as shown on the left, or joined together with beams.

It is common to see eighth notes joined into sets of 2 to make one beat. Eighth notes may also be grouped in 3s, 4s, 5s, or even 6s depending on the time signature. Remember, however, that no matter how many eighth notes are joined, each one is                       worth half a quarter note.

Sixteenth note (Semiquaver)

The Sixteenth note is worth ¼ of a Quarter note. It may be beamed together in the same way as the eighth note. It changes from the eighth note by having an additional flag. Look at the picture and you see a double flag at the top of the stem. This is how you tell a note is a sixteenth note.

Sixteenth notes may be beamed together in the same way as Eighth notes. When you see sixteenth notes beamed together each note has a double flag. Here is an example of 4 Sixteenth notes beamed together, they are also                                           common in groups of 2.

Mix and match different music note values

Eighth and sixteenth notes (and other music notes with flags) may be joined together. The key to knowing which note you are dealing with is very simple look at the number of beams joined to the stem of the note. By counting the beams joined to the stem of the note you will always know what type of note you are looking at. In the examples below you can clearly see how this works.

In this example there are 2 Sixteenth notes (2 beams touching the stem) joined ot an Eighth note (1 beam touching the stem)

In this example there is 1 Eighth note (one beam touching the stem) joined to 2 Sixteenth notes (2 beams touching the stem)

This is a note grouping that often confuses people, but it needn't! It is simply 1 Sixteenth note (2 beams on the stem) joined to an Eighth note (1 beam on the stem) joined to another Sixteenth note (2 beams on the stem!)