All about INTERVALS
Posted 13 August 2006 - 05:30 PM
Part2: Tones and semitones; whole steps and half steps
Part3: Interval number and quality
Part4: Interval classification
Part5: Playing intervals
Part6: Identifying intervals by ear
Posted 13 August 2006 - 07:24 PM
So what exactly is a musical interval?
It has two common meanings which are very closely related.
1. The strict definition is "a measurement of the pitch difference between any two notes". (Just as a "time interval" is a measure of the time difference between two events.)
For example, if we compare a low note such as the low open 6th string of a guitar with the much higher sounding open 1st string, we can hear a big difference in pitch. That's a large (or wide) interval.
If we compare the note on the low open 6th string with the note that we hear from holding that string at the first fret, we can hear both notes sound low, but the note on the first fret sounds just a little higher than the open string note. That's a small (or narrow) interval. The study of intervals involves understanding and learning how to name the pitch differences between all notes, from the very small to the very large.
2. Less strictly, an interval can mean: "any two notes played at the same time or one after the other" - (similar to a chord but consisting of only two notes compared to a chord's minimum of three notes.) These two definitions are so closely related that we can usually ignore the difference between them. They are named in exactly the same way, i.e according to the difference of pitch between them. We often play intervals as two note chords and, just like chords, they all have their own distinct sound and character.
A large part of the vocabulary of many musicians relates directly to intervals. Words such as major, minor, diminished, augmented, semitone, thirds, sixths, thirteenths and many more are frequently used here on the forum by some of the more advanced members, who use them as part of their everyday musical language. Most often, we hear them in the context of chords, which means a complete understanding of chords is impossible without an understanding of intervals.
Posted 13 August 2006 - 07:29 PM
Tones and semitones (Whole steps and half steps)
A common and very useful way of naming small intervals is by the terms tones and semitones, often abbreviated as T & S when used in diagrams. In North America, these are more commonly known as whole steps and half steps, respectively, and often abbreviated as W & H.
A tone, or whole step is the difference in pitch that you hear when two notes are separated by two frets.
A semitone, or half step (as you would expect) is the pitch difference you hear when the notes are just one fret apart.
Play string 3 open. The note is G.
Play string 3 at fret 1. The note is G sharp (G#) (or A flat (Ab)).
The interval between G & G# (or Ab) is ONE SEMITONE (one half step).
Play string 4 open. The note is D.
Play string 4 at fret 2. The note is E.
The interval between D & E is ONE TONE (one whole step) or TWO SEMITONES (two half steps).
In part 3 we'll look at a more systematic way of naming ALL intervals by using numbers and qualifying terms, such as Major thirds and minor sixths, etc.
Posted 13 August 2006 - 08:04 PM
A more complete and systematic way to name intervals 'of any size' is by numbering them according to how many scale degrees (letter names) are covered by the interval. This is easy. To find the number of any interval, you just count UP the letters. (Intervals are always measured from low to high.)
For example, the notes A to B form the interval of a SECOND, because the interval between them spans two letters: A & B. Numbering intervals is as simple as that.
D to G is a FOURTH because there are four letters involved D, E, F, & G.
F to A is a THIRD because there are three letters involved F, G & A.
C to C (both notes exactly the same pitch) is a FIRST because only one letter is involved: C. But we call this interval a UNISON instead of a 'first' (from UNI = 1).
C to the next C higher up is an EIGHTH because there are 8 letters involved (C D E F G A B & C). But we call it an OCTAVE instead of an 'eighth (from OCTA = 8).
Don't worry about sharps or flats when numbering intervals. They make no difference to how an interval is numbered.
The following intervals are ALL thirds because only three letters are involved (A B & C):
A to C
A to C#
Ab to C
Ab to C#.
As we saw in the last section, the intervals A to C and A to C# are both thirds because they both span three letters A B & C. But clearly, they're not the same.
A to C# is larger than A to C, (by one fret or semitone) so it's necessary to qualify them so that we can distinguish between them. That's done by using the words MAJOR to mean the larger one, and MINOR to mean the smaller one.
So, to give those intervals their full name:
A to C is a MINOR THIRD
A to C# is a MAJOR THIRD.
If you want to count the semitones between them, you can see that
MINOR THIRDS are 3 semitones (3 half steps)
MAJOR THIRDS are 4 semitones (4 half steps)
We can add the words MAJOR and MINOR not only to THIRDS but also to SECONDS, SIXTHS and SEVENTHS.
C to D is a MAJOR SECOND (2 semitones)
C to Db is a MINOR SECOND (1 semitone)
C to A is a MAJOR SIXTH (9 semitones)
C to Ab is a MINOR SIXTH (8 semitones)
C to B is a MAJOR SEVENTH (11 semitones)
C to Bb is a MINOR SEVENTH (10 semitones)
Some intervals are called perfect. They sound so pure when we hear them that it's tempting to think that that's why they're called 'perfect'. In fact, they're called perfect for historical reasons that we needn't bother with in this lesson.
The perfect intervals are the unison, octave, fifth and fourth.
Augmented and diminished intervals
If we stretch a major or a perfect interval by one semitone (but keeping the same letters), the interval number stays the same but we call it augmented instead of major or perfect.
C to F is a PERFECT FOURTH (5 semitones)
C to F# is an AUGMENTED FOURTH (6 semitones)
C to D is a MAJOR SECOND (2 semitones)
C to D# is an AUGMENTED SECOND (3 semitones)
If we shrink a minor or perfect interval by one semitone, it becomes DIMINISHED.
B to A is a MINOR SEVENTH (10 semitones)
B to Ab is a DIMINISHED SEVENTH (9 semitones)
B to F# is a PERFECT FIFTH (7 semitones)
B to F is a DIMINISHED FIFTH (6 semitones)
Posted 14 August 2006 - 01:58 PM
This lesson focuses on the various ways intervals are classified. It's not as important as the previous sections, but is included for completeness. It will be more useful as a reference rather than as information to be studied and memorised.
SIMPLE AND COMPOUND INTERVALS.
If an interval is smaller than an octave, it is a simple interval.
If it is an octave or greater, then it's classed as a compound interval.
So far, the highest interval number that we've mentioned is 8 (the OCTAVE) but you will often come across three more interval numbers, namely: 9, 11 and 13, mostly in chord names. They are known as compound intervals and are just simple intervals which have been expanded by an octave. There is little difference in effect between a simple and compound interval. Mostly it's a naming convention used with chords.
For example, C to D is a SECOND, (2 letters, C & D); but C to the next higher D is a ninth (9 letters, C D E F G A B C & D).
To convert a compound interval back to its simple form, subtract SEVEN.
A NINTH is really a SECOND.
An ELEVENTH is really a FOURTH.
A THIRTEENTH is really a SIXTH.
If we reverse (or invert) the order of notes of a simple interval, the interval changes number and quality.
For example C to E can be inverted as E to C.
C to E is a THIRD (3 letters - C, D & E).
E to C is a SIXTH (6 letters - E F G A B & C).
To invert an interval, just subtract its number from 9.
SECONDS become SEVENTHS.
THIRDS become SIXTHS.
FOURTHS become FIFTHS.
The interval quality also changes, as follows:
MAJOR intervals become MINOR.
MINOR intervals become MAJOR.
AUGMENTED intervals become DIMINISHED.
DIMINISHED intervals become AUGMENTED.
PERFECT intervals remain PERFECT.
A to C is a MINOR THIRD.
C to A is a MAJOR SIXTH.
E to F is a MINOR SECOND.
F to E is a MAJOR SEVENTH.
A to E is a PERFECT FIFTH.
E to A is a PERFECT FOURTH.
C to F# is an AUGMENTED FOURTH.
F# to C is a DIMINISHED FIFTH.
In many cases two intervals will sound exactly the same yet they have different names.
For example C to D# is an augmented second but C to Eb is a minor third. D# and Eb are the same sound so the intervals containing them will sound the same, but will have different names. Such intervals are known as ENHARMONIC EQUIVALENTS of each other.
C to F# (augmented fourth) sounds the same as C to Gb (diminished fifth).
D to A# (augmented fifth) sounds the same as D to Bb (minor sixth).
HARMONIC AND MELODIC INTERVALS
When the two notes of an interval are heard at the same time, the interval is said to be HARMONIC.
When the two notes are heard one after the other, the interval is said to be MELODIC.
Melodic intervals (apart from unisons) may be further described as ascending or descending, depending on the pitch order of the notes. Remember, though, that intervals are always measured from the lower note to the higher note, regardless of whether the notes are ascending or descending.
CONSONANT AND DISSONANT INTERVALS
Consonance and dissonance are terms used to describe how well the notes of an interval blend together.
Consonance is the quality we hear when the two notes combine well and produce a sound which, at best, is pleasant and agreeable and, at worst, bland and colourless. consonant intervals include all the perfect intervals, i.e.unisons, octaves, fourths and fifths. Those are classed as perfect consonances.
They also include major and minor thirds as well as major and minor sixths. These are classed as imperfect consonances. They still combine well but not as well as the perfect intervals. This slight mismatch gives them an edge that makes them sound far more interesting than than the pure consonances. This is the reason that chords are built from thirds.
Dissonance is the opposite of consonance. An interval is dissonant if its notes seem to clash when they combine. If played without care the effect will usually be harsh and unpleasant. If played with care in a well composed setting, the effect may be a thrilling build up of psychological tension in the listener that seeks to find emotional release in well-chosen consonant intervals. This is basically how most western harmony works.
Dissonant intervals include major and minor seconds, major and minor sevenths and the augmented fourth or its enharmonic equivalent, the diminished fifth.
There are also certain circumstances in which the perfect fourth (officially a perfect consonance) can sound dissonant, (e.g. when heard within a suspended fourth chord)
C to G is a perfect fifth and highly consonant. Being so consonant means it has very little harmonic effect when heard within chords.
C to Gb is a diminished fifth and is highly dissonant. This interval is also called a tritone because it consists of three whole tones or whole steps. When first discovered in early medieval times, its pungent dissonance led to its avoidance by many composers. It gradually became, and remains, the most important dissonant interval in western music.
Posted 15 August 2006 - 04:57 PM
The final section of the intervals lessons deals with how they can be played on guitar. Harmonic intervals are always present within chords, of course, but there are some distinct musical effects that are obtained by playing the same types of (usually consonant) harmonic intervals in succession.
FIFTHS AND FOURTHS
Perfect fifths and fourths were being used long before the first chords made an appearance. They were the first attempts at harmony in western music, and began to be used as standard in the middle ages by monks singing Gregorian chant. The haunting, hollow sound that we associate with this type of singing (called organum) is purely as a result of using only perfect fifths and fourths.
Nowadays, fifths and fourths are most commonly heard in rock music as power chords, played on electric guitars usually with overdrive. Despite the name, power chords aren't really chords, they're intervals consisting of perfect fifths or fourths (with or without octave doubling). Power chords are unique because their perfect consonance means they can withstand high levels of distortion. Full chords or other intervals can sound unacceptably discordant when distorted at high amplification levels. Well-known examples of power chord sequences in songs are:
Smoke on the water - Deep Purple
Smells like teen spirit - Nirvana
My Generation - The Who
Thirds generally add a pleasing harmony to a melody.
Depending on the key and melody notes, the thirds will vary between major and minor forms in accordance with the key. Some guitarists practise thirds in scale form. That means playing a scale but accompanying every note with another scale note a third above, For example:
The scale of C major harmonised by major and minor thirds above.
E F G A B C D E
C D E F G A B C
They are often heard in fingerstyle and classical guitar playing as compound intervals, i.e. a third plus an octave. In this form, they can make a very effective bass and melody, as in the example below. Playing intervals is sometimes preferred to using chords because of their lighter sound. This also means they can change on every note. Chords, by contrast, don't sound so good if they are constantly being changed on every note.
Sequences of sixths are very common in blues and blues-influenced music. They are really inverted thirds as was explained in the previous lesson (inverted intervals) and the above scale can also be practised with the same notes but inverted. so that the harmony notes lie below the main scale notes, rather than above (as thirds). As with thirds, the key will determine whether any sixth in the sequence will be major or minor. As the notes of sixths aren't played on adjacent strings, they are mostly played fingerstyle. They can't be played with a pick unless a finger is brought in to pick the upper notes while the pick is used on the lower notes, in the technique known as 'hybrid picking'.
The scale of C major harmonised by major and minor sixths below.
C D E F G A B C
E F G A B C D E
In conclusion, we've seen that intervals are highly varied and very useful in both the theory and practice of music. Once you understand them completely, many doors to a more advanced understanding of the complex structures of music will be opened to you.
1. Compound thirds as bass and melody in a typical simple classical style. Notice how the lightness of intervals means they can change on every note to good effect - unlike chords, which usually need to sustain longer.
2. Sixths in a typical blues intro. At first the notes are played separately, then together as true harmonic intervals.
Posted 25 July 2007 - 05:01 PM
IDENTIFYING INTERVALS BY EAR
Improve your ability to recognise intervals by their distinctive sound with this interval ear trainer/ tester. Try to identify each interval as you hear it. Start with the default options, then try the more advanced options.
Pointing your mouse cursor over most of the settings buttons displays some information on their use.
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