## An introduction to music theory

JumpingJackFlash
KVRian

1223 posts since 10 Oct, 2004
This is intended as a simple guide for the beginner, covering the basics of music theory. It also overlaps to cover areas of notation and harmony. If the mods find it worthy, maybe they could make it a sticky?

Tones and Semitones

A semitone is the smallest distance between any two consecutive notes (higher or lower). The octave is divided into 12 semitones. Eg. C to C# is one semitone. Gb to G natural is one semitone. D to Eb is one semitone. E to F is one semitone (because there is no separate note for E#).

A tone is two semitones. Eg. C-D, F#-G#, E-F#.

Sharps and Flats

A sharp (#) raises a note by one semitone.
A flat (b) lowers a note by one semitone.
A double sharp (X) raises a note by two semitones (one tone).
A double flat (bb) lowers a note by two semitones (one tone).
A natural cancels out a sharp or flat.

Scales

The two most common scales now used in Western music are the Major and Minor scales. They are named after the note they start on. This note is referred to as the 'tonic'. Major and Minor scales have 7 different notes before ending up back on the tonic again (an octave higher).

Starting from the tonic and moving upwards, major scales all have the pattern of intervals:
Tone, Tone, Semitone, Tone, Tone, Tone, Semitone.
(Eg. C,D,E,F,G,A,B,C).

Natural minor scales all have the pattern:
Tone, Semitone, Tone, Tone, Semitone, Tone, Tone.
(Eg. A,B,C,D,E,F,G,A).

Note though, that the minor scale comes in different forms. In the harmonic minor (which is perhaps most common), the 7th of the scale is raised by one semitone. Thus the pattern becomes: Tone, Semitone, Tone, Tone, Semitone, Tone+Semitone, Semitone. (Eg. A,B,C,D,E,F,G#,A).

The melodic minor is more tricky. When going up, the 6th and 7th of the scale are both raised by one semitone. (Thus, the pattern becomes Tone, Semitone, Tone, Tone, Tone, Tone, Semitone). When going down however, the 6th and 7th are lowered back to normal, and you play it exactly the same as the natural minor.

The chief difference between major and minor is the third of the scale. In a major key the third is 4 semitones above the root, in a minor key the third is 3 semitones above the root.

The key of a piece indicates the scale around which the piece is written. (For example, a piece in the key of C major typically revolves around the C major scale).

Each note of the scale has a different technical name. In both major and minor scales:
1st of the scale = Tonic
2nd of the scale = Supertonic
3rd of the scale = Mediant
4th of the scale = Subdominant
5th of the scale = Dominant
6th of the scale = Submediant
7th of the scale = Leading Note

These names are also applied to the chords build up from the different notes of the scale, thus for example the 'Subdominant Triad' refers to the triad build up on the 4th degree of the scale.

(A triad is a 3 note chord made up of two superimposed 3rds (root, 3rd and 5th). Triads can be major, minor, diminished or augmented - more on that later.)

Written music

In all music, you will see something like this at the start:

Note, the five horizontal lines like this on which music is written is called the stave or the staff.
At the start of each stave you will see a clef. This indicates the pitch range of the stave (which notes go where).

Today, four different clefs are used: Treble, Alto, Tenor and Bass:

Note, the note shown is middle C in all cases.

The treble and bass clefs are most common, but violas, cellos, trombones and bassoons all make use of some of the others.

The Treble clef is also called a 'G clef', because the end of the squiggle always indicates where the note G is written.
The Bass clef is also called an 'F clef' because the line in-between the 2 dots indicates where the note F is written.
The Alto and Tenor clefs are also called 'C clefs' because the middle of the clef indicates where middle C is written.

Note that when a line is added below or above the stave (such as middle C in Treble and Bass clefs), this extra line is known as a ledger line (sometimes spelt without the d). In times gone by, different clefs were chosen to minimise the number of ledger lines needed (although, these days, ledger lines are quite common).

In Treble clef, from bottom to top, the notes on the lines are: E,G,B,D,F, and the notes in the spaces are F,A,C,E.
In Bass clef, from bottom to top, the notes on the lines are: G,B,D,F,A, and the notes in the spaces are A,C,E,G.

You can also sometimes get Octave Clefs. These are indicated by a small '8' above or below the clef. - This means the music should be played one octave higher (if above the clef), or one octave lower (if below the clef) than written. (Note though, these are rare and instruments such as Double Bass and Piccolo which naturally sound an octave lower or higher than written do NOT need the use of such clefs).

(Remember one octave is 8 notes (12 semitones); the difference between one note and the same note higher or lower on the keyboard).

Note, the clef at the far right of the above diagram is used for unpitched percussion. For this, pitch is not relevant so any of the other clefs would be inappropriate.

Key signatures
A key signature indicates the number of sharps OR flats in the prevailing key. Every key signature has one major key and one minor key associated with it. With minor keys, the key signature gives you the natural minor. Any raised 6ths or 7ths are NOT part of the key signature (and are instead included as accidentals).

A key signature is generally written on every line of the music. If the music does not have a key signature, it is either in C major, A minor, or it is Atonal (no prevailing key). Note, sharps are always added in the order F,C,G,D,A,E,B. And flats are always added in the order B,E,A,D,G,C,F.

An accidental is a sharp (#), flat (b) or natural sign written just before a note (indicating to raise or lower that note by a semitone). (They could also be a double sharp or double flat sign - see above). Accidentals are usually a temporary thing, and they are not part of the key signature (they may be foreign to the key). An accidental lasts for the entire duration of the bar in which it occurs. For example, once you have played one F# in a bar, every other F in that bar should also be sharpened unless counteracted with a natural sign. In the next bar, any previous accidentals are automatically cancelled out (unless a note with an accidental is tied over from the previous bar, in which case the accidental applies to the tied note also).

Time Signature

The time signature indicates the metre of the music. It usually consists of 2 numbers, the top number represents the number of beats in a bar, and the bottom number represents the 'type' of beat, expressed as a fraction of a semibreve (whole note).
Simple time signatures are where the basic beat is divisible by 2 . The basic beat is a crotchet (quarter note), which is divided into two quavers (eighth notes).
Compound time signatures are where the basic beat is divisible by 3. The basic beat is a dotted crotchet which is divided into three quavers.

1 semibreve = 2 minims = 4 crotchets = 8 quavers = 16 semiquavers etc. (regardless of time signature).
(See herodotus's thread for pictures of these notes, with both the American and British names).

Note though, sometimes you see the letter 'C' as a time signature. This means 'common time' and is essentially 4/4. The letter 'C' with a vertical line through it means 'cut time', 'cut common time', or 'alla breve', and is essentially 2/2.

Triplets are when you have 3 notes in the time of 2. Each note therefore makes up a third of the group (ie, a third of twice the note value).
Thus, crotchet triplets are 3 notes in the time of 2 crotchets (3 notes in the time of one minim - each note is 1/3 of a minim).
Quaver triplets are 3 notes in the time of 2 quavers (3 notes in the time of one crotchet - each note is 1/3 of a crotchet).

Triplet notes are written exactly as normal, except they have a little '3' above (or below) them. (Often the notes of the triplet are enclosed in a bracket or slur).

You can also get 'Quintuplets' which are 5 notes in the time of 4, 'Sextuplets' which are 6 notes in the time of 4, 'Septuplets' which are 7 notes in the time of 4 or 6, 'Nonuplets' which are 9 notes in the time of 8 etc.
Also, 'Duplets' (typically used in compound time) are 2 notes in the time of 3.

Note, any note(s) in the group may be replaced by a rest.

Intervals

An interval is the distance between any two notes (whether the notes are part of a melody or a chord).
Intervals are made up of both a number and a description.

The number is determined by the letters involved. Forget about sharps and flats for this bit, and count up how many notes there are between the two notes. - You count (include) both the starting note and the ending note. Eg. C-G involves 5 notes (C,D,E,F,G). C-G# also involves 5 notes, as does C#-G, and C#-G# (but note, C-Ab involves 6 notes not 5, even though G# and Ab are the same note).
This leaves you with a 1st (unison), 2nd, 3rd, 4th, 5th, 6th, 7th or 8th (octave). For any interval larger than one octave, just pretend it's in the same octave and add the word 'compound' in front of the interval.

Now for the description. This is either 'Diminished', 'Minor', 'Major', 'Perfect' or 'Augmented'.

The best way of working this out if as follows:

Consider this chart:

Consider the major scale of the lowest note involved (you will have to know its key signature).

For 1sts (unisons), 4ths, 5ths and 8ths (octaves): If the higher note belongs exactly to the lower note's major scale, the interval is said to be 'perfect'.
If the higher note is a semitone higher than the note of the lower note's major scale, the interval is said to be 'augmented' (the interval is greater).
If the higher note is a semitone lower than the note of the lower note's major scale, the interval is said to be 'diminished' (the interval is smaller).

For example, C-G is a 5th of some sort. G fits in with C major exactly, therefore C-G is a 'perfect 5th'.
With C-G#, the G# is NOT contained within C major, it is a semitone greater than a perfect 5th, therefore it is an 'augmented 5th'.
With C-Gb, the Gb is NOT contained within C major, it is a semitone lower than a perfect 5th, therefore it is a 'diminished 5th'.

For 2nds, 3rds, 6ths and 7ths: If the higher note belongs exactly to the lower note's major scale, the interval is said to be 'major'.
If the higher note is a semitone higher than the note of the lower note's major scale, the interval is said to be 'augmented' (the interval is greater).
If the higher note is a semitone lower than the note of the lower note's major scale, the interval is said to be 'minor' (the interval is smaller).
If the higher note is 2 semitones (a tone) lower than the note of the lower note's major scale, the interval is said to be 'diminished' (the interval is even smaller).

For example, C-B is a 7th. B is part of C major, therefore C-B is a 'major 7th'.
C-B#, the B# is a semitone greater than a major 7th, therefore it is an 'augmented 7th'.
C-Bb, the Bb is a semitone lower than a major 7th, therefore is it a 'minor 7th'.
C-Bbb, the Bbb (double flat) is 2 semitones lower than a major 7th, therefore it is a 'diminished 7th'.

Chords

Recall that a triad is a 3-note chord made up of a root, a 3rd above the root, and a 5th above the root.
The root is the 'tonic' of the chord; the basic note from which the other notes are derived. This is the note from which the triad is named. (Eg, in a C major triad, C is the root).

Major triads have a 'Major 3rd', and a 'Perfect 5th' above the root (see 'Intervals' above).
Minor triads have a 'Minor 3rd' and a 'Perfect 5th' above the root.
Diminished triads have a 'Minor 3rd' and a 'Diminished 5th' above the root.
Augmented triads have a 'Major 3rd' and an 'Augmented 5th' above the root.

A chord is a group of (typically 3 or more) notes sounded together. All triads are chords, but not all chords are triads.

In four-part harmony, you will obviously have to double up one note of the triad. The best note to double is the root (typically one octave higher), the next best is the 5th.

A chord in which the top three notes are as close together as possible is known as a chord in 'close position'. A chord in which the notes are more equally spread is known as a chord in 'open position'.

Chord inversions

The inversion of a chord is completely dependant on which note of the triad is the lowest note.

If the root is the lowest note, the chord is said to be in root position
If the 3rd is the lowest note, the chord is said to be in first inversion
If the 5th is the lowest note, the chord is said to be in second inversion.

Chord inversions are sometimes identified with figures representing the intervals within the chord.
Root position chords have the figure 5/3 (known as '5/3 chords') because there is a 3rd and 5th above the bass.
First inversion chords have the figure 6/3 ('6/3 chords') because there is a 3rd and a 6th above the bass.
Second inversion chords have the figure 6/4 ('6/4 chords') because there is a 4th and a 6th above the bass.

Note that the order and position of the other notes of the chord make no difference. E-G-C and E-C-G are both C major triads in first inversion. (It also doesn't matter how many notes are doubled, or how big a gap there is between notes).

Every note of every scale has a triad attached to it. These are labelled with Roman Numerals, starting with I for the Tonic Triad, and moving up to VII for the triad on the leading note (7th of the scale). I=1, II=2, III=3, IV=4, V=5, VI=6, VII=7.

In any major key, chords I, IV and V are major chords. (These are known as 'Primary Triads').
In any major key, chords II, III and VI are minor chords. (These are known as 'Secondary Triads').
In any major key, chord VII is diminished.

Chord inversions can also be indicated with a suffix to the Roman Numeral:
Root position chords add the letter 'a', 1st inversions add the letter 'b' and 2nd inversions add the letter 'c'.
Eg. IVb is chord IV in first inversion.

There. That's all for now, hopefully this will benefit someone. If anyone wants any clarifications, examples or has any questions, please let me know and I'll try to help.
Deric
KVRist

492 posts since 16 Oct, 2004
Mega post JumpingJackFlash!

JumpingJackFlash wrote: Simple time signatures are where the basic beat is divisible by 2 . The basic beat is a crotchet (quarter note), which is divided into two quavers (eighth notes).

I don't quite get why you are saying that the crotchet is divided into two quavers.

Cheers,
Deric.
JumpingJackFlash
KVRian

1223 posts since 10 Oct, 2004
Deric wrote:Mega post JumpingJackFlash!

JumpingJackFlash wrote: Simple time signatures are where the basic beat is divisible by 2 . The basic beat is a crotchet (quarter note), which is divided into two quavers (eighth notes).

I don't quite get why you are saying that the crotchet is divided into two quavers.

Cheers,
Deric.

Just as an example of 'Simple Time', where, as I said, the beat is divisible by 2. - So in this case, the crotchet is divided into 2 quavers.
(As opposed to compound time where the beat (dotted crotchet) is divided into 3 quavers).

It's true that a crotchet is still equal to 2 quavers in compound time, but a crotchet is no longer the overriding beat.
vikernes
KVRist

198 posts since 19 Jan, 2006
Small typo "D to Eb is one semitone."
JumpingJackFlash
KVRian

1223 posts since 10 Oct, 2004
vikernes wrote:Small typo "D to Eb is one semitone."

Huh? - No typo. D to Eb is one semitone. (It's also a minor 2nd. I deliberately included this example because it seems weird at first glance).
vikernes
KVRist

198 posts since 19 Jan, 2006
JumpingJackFlash wrote:
vikernes wrote:Small typo "D to Eb is one semitone."

Huh? - No typo. D to Eb is one semitone. (It's also a minor 2nd. I deliberately included this example because it seems weird at first glance).

ROFL. Sorry, I just realized I thought the letter E was before the D.

*stops smoking crack*
JumpingJackFlash
KVRian

1223 posts since 10 Oct, 2004
New Year bump for anyone who missed this over the festive period.
spuddle
KVRian

1226 posts since 10 Aug, 2005
Cyniq
KVRer

25 posts since 20 Jul, 2006, from Melbourne, Australia
Very generous and thorough JJF. What forums are all about.
JumpingJackFlash
KVRian

1223 posts since 10 Oct, 2004

This is meant as an addendum or appendix to my initial post, and I will assume you are familiar with my initial post before you read this.

A cadence is a progression of chords at the end of a musical phrase or section. Cadences provide structure to music. The strongest cadences are always in root position.

(Interesting note: Although today we think of cadences as harmonic formulae, they were originally falling melodic figures which were associated with phrase endings (kind of like the cadenza). The word actually comes from the Latin 'cado' or 'cadere' meaning to fall.)

In the past, cadences have been classified as masculine (where the final chord is on a stronger beat than the preceding chord) or feminine (where the final chord is on a weaker beat than the preceding chord). However, these terms were branded sexist and have now fallen out of general usage.

There are different types of cadence, the most frequently occurring are the perfect and imperfect cadence.

This is the progression V-I, dominant to tonic. This is sometimes called the authentic cadence, but some people distinguish between them claiming a 'perfect cadence' is only when the root of the final chord is in the highest voice and the chords are in root position, and an 'authentic cadence' is any other V-I. Less fussy people (including myself) use the terms interchangeably. The perfect cadence sounds final, like the end of a piece. It is the musical equivalent of a full stop (or 'period' if you are American) and is sometimes called a 'full close'.

Often the progression will be strengthened by using a dominant seventh: V7-I. This adds a minor 7th above the root of V. (The 7th fits in with the key signature, it is NOT chromatic). For example, in C major, the dominant seventh is G,B,D,F. It is good part-writing to have the 7th fall a step and the leading note (the 3rd of V) rise to the tonic (1st of I).

The 7th is especially good as a passing note, passing between the root of V and the 3rd of I.

The chords preceding the V-I are also important. IV is a common chord used in elementary work (IV-V-I), but the strongest (and most frequently used) approach chord is IIb (Chord II in first inversion). This occurs in almost every kind of tonal music (IIb-V-I).

Chord IIb in this progression can be modified (and/or substituted with other similar chords) extensively. For example, simply sharpen the bass note and you get a secondary dominant. (IIb becomes V of V).
IIb can also be modified to become a Neapolitan Sixth by flattening the root and 5th in a major key (or just flattened root in a minor key).

In 4-part harmony, in the progression IIb-V, double the bass of IIb (so you are doubling the 3rd of the chord, not the root).

Another common trick with IIb in this progression involves adding a seventh to the chord. (In a similar manner to the dominant seventh; the seventh remains in key). This then becomes a secondary seventh. (For example, F,A,C,D in C major).

This makes the progression even stronger. Again, for proper part-writing the seventh should fall by step to the 3rd of V. Also, in times gone by, people would prepare the seventh. - This means, the preceding chord must include the seventh (as a consonance) in the same part. (Exactly the same as with a suspension if you know what they are). Nowadays, the seventh is not always prepared. (In fact, according to some theory, the dominant seventh should also be prepared, although this wasn't even done by Bach and his contemporaries so you certainly don't have to bother doing it now!).

Example of a perfect cadence in C major:

(Note, in the final tonic chord, the 5th is omitted to avoid parallel fifths).

Another very common chord used in cadences is Ic, the cadential 6/4.
Ic is the tonic chord in second inversion. For example, in C major, it is G,C,E. Note that the bass note is the same as with chord V. In fact, Ic functions as a passing chord and is best thought of as an appoggiatura chord to the dominant. Thus, the 3rd of Ic should fall to the 5th of V, and the tonic of Ic should fall to the 3rd of V. V should not be more strongly accented than Ic. The bass of Ic may not be approached by leap from an inversion of another chord (it may only be approached by step, or possibly by leaping from a chord in root position).

If you listen to Bach, you will be able to hear a cadential 6/4 most of the time. - It is extremely common.
Ic-V-I is a good perfect cadence. (Sometimes the bass will leap down an octave from Ic to V).

Because the Ic almost functions to extend the dominant chord, the approach chord to Ic is also relevant. - You can use any of the approach chords to V that were mentioned above. For example, IV-Ic-V-I is very good, as is IIb-Ic-V-I.

As with all second inversions, in 4-part harmony you double the bass of Ic (double the 5th rather than the root).

Also note: Within the progression V7-I, there are stronger and weaker ways of writing the chords, depending on the part-writing.
The strongest progression is where the top part moves from leading note to tonic (3rd of V to tonic of I).
The next strongest is where the top part moves from the 7th of V to the 3rd of I (see example below).
The next strongest after this is where the top part moves from the 5th of V to the tonic of I.
Weaker is where the top part moves from the 5th of V to 3rd of I.
Weakest of all is where the top part remains stationary on the dominant (root of V = 5th of I).

Note though, that in the underneath parts, standard part-writing rules still apply (leading notes rise, 7ths fall).
Obviously, the strongest cadence should occur at the very end of a piece, and weaker cadences could occur at the end of intermediate sections or movements.

Example of a perfect cadence in C major:

Some cadences are decorated with the use of suspensions and other non-harmony notes.

V7d-I is a good intermediate perfect cadence (with the dominant chord in third inversion - with the seventh in the bass). It sounds much less final that V7-I (in root position) and so if useful to denote the end of a section, but not the end of the whole piece.

This is the progression of any chord to V. This ends on the dominant chord and is also called a 'half close'. It is the musical equivalent of a comma, and usually indicates the mid-point of a phrase. It sounds unfinished - the music sounds like it wants to continue.
Commonly, I-V is used, however other possibilities include IV-V, VI-V, IIb-V and Ic-V (see above; the usage of Ic is the same as with perfect cadences).
V7, the dominant seventh, is not often used in imperfect cadences.

In classical music, you often get two phrases of approximately equal length. The first ends with an imperfect cadence, and the second ends with a perfect cadence. This creates a question-answer kind of feel. The first ('question') phrase is called the antecedent, and the second ('answer') phrase is called the consequent.

This is the progression of V to any chord except I. Most often it goes V-VI, and V-IVb is also fairly common. This is also known as a 'deceptive cadence' and occurs when the music seems to be heading for a nice perfect cadence, then suddenly goes elsewhere instead, creating surprise. Sometimes it is used as an alternative to an imperfect cadence, although interrupted cadences should be used sparingly.

This is the progression IV-I, sometimes known as a 'weak close' or 'Amen cadence' since it sounds like the 'Amen' at the end of a Hymn. Although it often occurs at the end of a piece, it is weaker than the perfect cadence and sounds less final.

The progression IVc-I is quite common, using chord IV in second inversion (so it has the same bass as the tonic). Remember to double the bass of IVc.

Sometimes, the minor subdominant is used instead (with flattened 3rd; iv instead of IV) for chromatic colour, although this sounds even less final.

Note
The presence of the chords from any of these cadences does NOT necessarily mean that the progression is a cadence. - For example, it is quite common to have V-I in the middle of a piece without it being a perfect cadence. - Your ears will tell you when there is a cadence; remember they occur at the end of phrases.

There are other cadences too, but these are mostly off-shoots of the above and you don't need to worry about them for now.
exquisiteoath
KVRist

79 posts since 1 Mar, 2005, from Toronto Ontario
Brilliantly useful thread. I know I'll be coming back here again and again as I try to remember things like the chart of intervals and the cadences.

2 Questions about cadences: Is there a firm line that says this V-I is a cadence whereas this other one isn't. Ie Bethoven's 5th begins with a progression that could be considered a Cadence, but it clearly isn't. The other question: if the chords are drawn out into a bar via guitar finger picking, or other forms of arpegiation or rubatto treatment is it still a cadence?

Thank you,
E/O
Accept no substitutes
JumpingJackFlash
KVRian

1223 posts since 10 Oct, 2004

Thanks!

exquisiteoath wrote:2 Questions about cadences: Is there a firm line that says this V-I is a cadence whereas this other one isn't.

Not really, and sometimes there are grey areas. As I said at the bottom of the Cadences post, not every V-I is a cadence. Typically, cadences occur at the end of phrases. So, a V-I at the beginning of a piece (common with anacruses) is probably not a cadence. However, phrases can sometimes be very small units. The 'sentence' is a form which consists of a 2 bar phase, followed by a repeat of these 2 bars, usually on the dominant. It is not uncommon for the first 2 bars to form an imperfect cadence and the second 2 bars to form a perfect cadence.

As with mot things, your ears are the best guide. - Hum a tonal tune in your head, and you should feel when a cadence occurs. Usually it will be on a break in the music, so, finishing on a long note for example.

exquisiteoath wrote:The other question: if the chords are drawn out into a bar via guitar finger picking, or other forms of arpegiation or rubatto treatment is it still a cadence?

Yes. The 'cadence' as we now understand it is a harmonic thing, so the rhythm of the parts doesn't generally make a difference. (Although the opposite was true in times gone by)
exquisiteoath
KVRist

79 posts since 1 Mar, 2005, from Toronto Ontario
Okay, this makes good sense now. Thank you for the clarification.
Accept no substitutes
cheul
KVRist

499 posts since 9 Oct, 2005
Is there any way to have the mods start making stickies out of all those major theory threads ?
JumpingJackFlash
KVRian

1223 posts since 10 Oct, 2004
Below are answers to a few Frequently Asked Questions by newcomers to music theory. They include theory, harmony and melody related areas. There is overlap with my initial post in this topic, where more information can be found. Even if you think you know all this already, I advise reading it anyway as revision; it can't hurt to make absolutely sure you've got everything right.

Q: What is a 'scale'?
A scale is a progressive sequence of notes moving upwards and/or downwards. The most common scales are The Major Scale, and The Minor Scale. Each has seven different notes spanning one octave, and is named after the note it starts on.

Q: What is an 'octave'?
An octave has 8 steps. An octave is the distance between two notes of the same name, so the note an octave above C is also C (the distance between the two C's is one octave).

Q: What is the difference between major and minor scales?
The difference is in the intervals between notes. In a major key the third note is 4 semitones above the root, in a minor key the third note is 3 semitones above the root. Starting from the 1st note and moving upwards, major scales all have the pattern of intervals: Tone, Tone, Semitone, Tone, Tone, Tone, Semitone. (That is, there is a semitone between the 3rd and 4th notes, as well as between the 7th and 8th notes, everything else is a tone).

Q: What is a 'semitone'?
A semitone is the smallest distance possible between any one note and the note immediately next to it (whether higher or lower). The octave is divided into 12 semitones.

Q: What is a 'tone'?
A tone is two semitones.

Q: What is an 'interval'?
An interval is the distance between two notes. With the Major scale, the pattern of intervals between the tonic and each successive note (starting with the second note and going upwards) is:
major 2nd, major 3rd, perfect 4th, perfect 5th, major 6th, major 7th, perfect octave.
If any of these intervals is increased by one semitone, the interval becomes 'augmented'.
If the intervals of 4ths, 5ths or octaves are decreased by one semitone, the interval becomes 'diminished'.
If the intervals of 2nds, 3rds, 6ths or 7ths are decreased by one semitone, the interval becomes 'minor'.

Q: What is a 'tonic'?
The tonic is the first note of a scale, which is the note that the scale is named after. (In harmony, the tonic can also refer to the triad built from the first degree of the scale).

Q: What is a chord?
A chord is a group of notes sounded together. Usually there must be at least 3 different notes to form a chord. A triad is a particular type of chord. - All triads are chords, but not all chords are triads.

A triad is a three-note chord built from two sets of thirds. That is, there is a third between the 1st and 2nd notes, and another third between the 2nd and 3rd notes (thus there is a fifth between the 1st and 3rd notes). Whether these thirds are major or minor thirds will determine the nature of the triad. A triad can be built from each note of the scale. Triads consist of the 1st, 3rd and 5th notes of a scale.

Q: What is a 'root'?
The root is the primary note of a chord or triad. - It is the note that the chord is named after. It is the lowest note of a triad when the notes are organised so there is a third between each note.

Q: What is the difference between 'tonic' and 'root'?
Sometimes there may be no difference. But 'tonic' generally refers to the first note of the overall key, whereas 'root' refers to the first note of the chord at any given point.

Q: How do I work out which notes go in which scale?
There are several methods. This post contains some information. Remember, each scale (and therefore each key) has one version of each note, and only one. That means, a key must have either A, A#, or Ab, but it cannot have more than one of these.

Q: What is a 'key'?
The key of a piece indicates the scale around which the piece is written. This in turn dictates which chords are available.

Q: How do I know which chords are available in a particular key?
Every note of the scale has a triad attached to it, - that is, every note of the scale can function as the root for a different triad. All notes of every triad must be part of the overall key. Therefore, in any major key, triads built on the 1st, 4th and 5th notes of the scale are major triads. Triads built on the 2nd, 3rd and 6th degrees of the scale are minor triads. A triad built on the 7th note of the scale is a diminished triad. (The overall pattern is thus: Major, minor, minor, Major, Major, minor, diminished).

Q: What is the difference between the different sorts of triad?
'Major' triads have a Major 3rd, and a Perfect 5th above the root.
'Minor' triads have a Minor 3rd and a Perfect 5th above the root.
'Diminished' triads have a Minor 3rd and a Diminished 5th above the root.
'Augmented' triads have a Major 3rd and an Augmented 5th above the root.

Q: What are 'inversions'?
An inversion of a chord (or triad) refers exclusively to which note is lowest:
If the root is the lowest note, the chord is said to be in 'root position'.
If the 3rd is the lowest note, the chord is said to be in 'first inversion'.
If the 5th is the lowest note, the chord is said to be in 'second inversion'.

Triads can be extended to include other notes as well. The most obvious is adding yet another 3rd to the top of the chord (when in root position). This note is a seventh above the root, and the triad then becomes a 'seventh chord'. But I advise becoming fluent with triads before you get too adventurous.

Minor keys are more complex, because there are several types of minor scale.

Q: What are the different types of minor scale?
In theory, the 'natural minor' is purely according to key signature. The 'harmonic minor' goes according to key signature but with the seventh note raised by one semitone. The 'melodic minor' goes according to key signature, but with the 6th and 7th notes both raised by one semitone when ascending, but lowered back to normal when descending.

In practise, music in minor keys may treat the 6ths and 7ths differently for different situations. Sometimes the 6th will be raised a semitone, sometimes the 7th will be raised a semitone, sometimes both, and sometimes neither. - In your own compositions, I would advice sticking to the harmonic minor as a sort-of default, but modifying the 6ths and 7ths according to context; as always, go with what sounds best at any given time.

Q: Is there a relationship between minor scales and major scales?
Yes, each minor scale shares the same key signature as the major scale a 'minor 3rd' higher. (And thus, each major scale shares the same key signature as the minor scale a 'minor 3rd' lower).

Q: What is a 'key signature'?
A key signature is written at the start of a every line of a piece of music. It indicates what sharps or what flats there are in the key.

Q: What are chord progressions?
A chord progression is a series of chords, one after the other.

Q: Which chord progressions sound good?
Chords whose roots are a 4th or 5th apart generally sound good. - Experiment and see what you like.

Generally, diminished triads and augmented triads sound bad, and should be treated with care (or even avoided in elementary work).

Q: Do I have to play block chords all the time?
No. You can spread the notes of the chord around each instrument that is playing. Sometimes you will need to double one or more notes of the chord. The best note to double is the root, the next best is the fifth.

Q: Am I limited to using only notes of the chord?
No. You can experiment with other notes too. Notes that do not belong to the chord are called 'non-harmony notes'. Generally these occur either off-the beat, and/or on a weak-beat of the bar. They usually move by step to the next note (either up or down). Usually these extra notes belong to the key, even if not to the chord at that point, however, it is possible to use notes which do not belong to the key, these are called 'chromatic' notes. More information on non-harmony notes can be found here.

Q: What does 'off-the beat' mean?
The beat is given by the bottom number of the time signature. When the bottom number is 4 for example (e.g. 2/4, 3/4 or 4/4), the beat is every crotchet (quarter-note). Notes that start exactly on any of the crotchets are said to be on-the beat. Notes that start after or before the crotchets are said to be off-the beat.

Q: Which beats are strong and which are weak?
The first beat is always strong, the next is usually weak, and it generally alternates. In 4/4, beats 1 and 3 are strong, beats 2 and 4 are weak.

Q: What is a 'step'?
A step is the interval of a second; either major, minor, diminished or augmented. Thus it can be either a tone or a semitone (or, rarely, it can even be 3 semitones, as for example with the 6th to sharpened 7th notes of the harmonic minor). Usually we mean a 'diatonic step', which means it moves to the adjacent note in the scale/key (either up or down). A leap is any interval of a third or more.

Q: How do I write good melodies?
This is up to you. Generally, a good melody should have a mixture of steps and leaps.
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