Intervals
An interval is the distance between pitches. Intervals have a number and a prefix. The number
represents the number of pitch names (A,B,C,D,E,F,G) from the first to the second pitch. For
example, the whole step F to G contains two pitch names, F and G. This interval is called a
second. The interval from F to A contains F, G and A; three pitches. This interval is therefore
called a third. The trend continues through to the interval containing eight pitch names. An
interval containing eight pitch positions (from A to A or from G to G) is called an octave. An
interval from one pitch to the exact same pitch is called a unison. The diagram below shows a C
major scale. The intervals are marked.
The second part of an interval name is based on the quality of the interval. It is referred to as the
prefix.
Perfect intervals include the unison and the octave. Perfect intervals also include fourths and
fifths. Perfect intervals are labeled with a capital "P."
The Major prefix is only used for seconds, thirds, sixths and sevenths. Major intervals are
labeled with a large "M."
Minor intervals occur when a major interval is made one half step smaller. This can be done by
raising the bottom note or lowering the top note. Minor intervals are labeled with a small "m."
Augmented intervals are when a major or perfect interval is made one half step larger, and the
interval number does not change. Augmented intervals are labeled with an "A," the abbreviation
"Aug.," or a "+." For example, above, if the P5 from C to G were changed to a C to G#, it would
become an augmented fifth, or +5.
Diminished intervals are created when a perfect or minor interval is made one half step smaller
and the interval number is not changed. Diminished intervals are labeled with a "d," the
abbreviations "dim" or "deg," or a "°." For example, if the perfect fifth from C to G above were
changed to a C to Gb, the interval would become a diminished fifth, or °5.
Thus unisons, fourths, fifths, and octaves can be diminished, perfect, or augmented. Seconds,
thirds, sixths, and sevenths can be diminished (only if the interval is decreased by two half steps,
such as with a double flat), minor, major, or augmented.
Here are some examples of how this system works:
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P1- This is perfect unison.
M7- This is a major seventh.
m2- This is a minor second.
A6, Aug. 6, +6 - These are all augmented sixths.
d3, deg.5, dim. 5, °5 - These are all diminished fifths.
Consonance and Dissonance
Consonant intervals are intervals that are stable. These intervals require no resolution. The
consonant intervals are P1, m3, M3, P5, M6, and P8. All other intervals within the octave are
said to be dissonant. Dissonant intervals are tense, and require resolution.
Enharmonic Intervals
Enharmonic intervals are intervals that sound the same but are "spelled" differently. These
intervals result from the inclusion of enharmonic equivalents.
The most common enharmonic intervals are the diminished fifth and the augmented fourth,
shown below. These two intervals divide the octave into two equal parts. These intervals contain
three whole steps, for this reason these intervals are referred to as the tritone.
Inverting Intervals
When an interval is inverted, the lower tone is raised one octave. The table below shows some
intervals and their inversions.
Intervals and their inversions.
The Interval When Inverted becomes
Unisons
Octaves
2nds
7ths
3rds
6ths
4ths
5ths
5ths
4ths
6ths
3rds
7ths
2nds
Octaves
Unisons
Perfect
Perfect
Major
Minor
Minor
Major
Diminished Augmented
Augmented Diminished
Compound Intervals
Compound intervals are intervals that span distances greater than an octave. These intervals are
often labeled as their simple equivalents, as if an octave had been removed from the interval. The
actual, or compound, interval name is only used if it is very important to stress the actual interval
size.
Identifying Intervals
The easiest way to find an interval's name is to first, count all the pitch names present, including
the notes themselves (ignore sharps and flats at this point). Then, find out (had it been missing a
flat or sharp) what type of interval it would be, depending on whether it is perfect (a 1,4,5,8) or
major (2,6,7). If there are no sharps or flats, you are done. If there are, figure out if the flat or
sharp decreases or increases the distance between the two pitches. If it increases the distance, the
interval is augmented. If it decreases the distance, and the interval would otherwise be perfect, it
is diminished. If it decreases the distance and the interval would otherwise be major, it is minor.
Ear Training
Go to the Big Ears interval ear training Java applet to help learn what different intervals sound
like, and quiz your recognition of different intervals.
Scales and Key Signatures
Here is a list of all the topic on this page:
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Scales
Transposition
Key Signatures
Modes
Solfeggio
Scales
A scale is a group of pitches (scale degrees) arranged in ascending order. These pitches span an
octave. Diatonic scales are scales that include half and whole steps. The first and last note is the
tonic. It is the most 'stable' note, or rather the easiest to find. Because of this, diatonic melodies
often end on the diatonic note. The other notes in the scale also have names. The second note is
the supertonic. The third is the mediant, halfway between the tonic and dominant. The fourth
note is the subdominant. The fifth note is the dominant. The submediant is the sixth note. The
subtonic is the seventh note in the natural minor scale. The seventh tone of the major, harmonic
and melodic minor scales is called the leading tone if it is one half step lower than the tonic.
The Major Scale
The major scale consists of seven different pitches. There are half steps between the third and
fourth and seventh and eighth scale degrees; whole steps exist between all other steps. Below is a
the C major scale. The pattern of whole and half steps is the same for all major scales. By
changing the first note, then using the pattern as a guide, you can construct any major scale.
Likewise, if you know the pattern for any other scale, you can create them, too.
The Natural Minor Scales
These scales have seven different scale degrees. There are half steps between the second and
third and the fifth and sixth degrees; whole steps exist between all other steps. Shown below is
the A minor scale.
The Harmonic Minor Scale
This scale is the same as the natural minor scale, except the seventh step is raised a half step.
There is now an interval of one half step between the seventh and eighth notes, and one and a
half steps between the sixth and seventh notes. This is a harmonic A minor.
The Melodic Minor Scale
This is another minor scale variation. In this scale, the sixth and seventh notes are each raised
one half step. All the patterns to this point have been the same as one climbs and descends the
scales. The melodic minor scale, however, ascends with the modifications noted above, but
descends in the natural minor scale. This is a melodic A minor.
Pentatonic Scales
Pentatonic scales, as their name suggests, have only five notes. To get from one end of the scale
to the other, they require gaps of more than a half step.
Scales that do not follow the interval patterns of the diatonic or pentatonic scales are called
nondiatonic scales. Many nondiatonic scales have no identifiable tonic.
The chromatic scale is a nondiatonic scale that consists of half steps only. Because each pitch is
equidistant, there is no tonic. A whole tone scale is comprised of whole steps. Like the chromatic
scale, it too has no tonic. The blues scale is a chromatic variant of the major scale. This scale
contains flat thirds and sevenths which alternate with normal thirds and sevenths. This
alternating creates the blues inflection.
Transposition
Scale patterns can be duplicated at any pitch. Rewriting the same scale pattern at a different pitch
is called transposition. Thus, if you used the major scale pattern, but started at G, you would
just have to count up according to the major scale pattern to transpose it. All the notes of a piece
can be modified in this way, by finding a note's counterpart in the modified scale.
Since some notes will always be sharp once transposed or in certain scales, it is sometimes
helpful to place accidentals at the very beginning of a piece in order to modify all the notes of a
certain pitch. Placing accidentals at the beginning of the music (as opposed to right beside a
note) allows the accidentals to affect every note in the entire piece. So, placing a sharp on line F
makes every F sharp. The arrangement of sharps and flats at the beginning of a piece of music is
called a key signature.
Key Signatures
To help understand and remember key signatures, a chart called the circle of fifths can be used.
On the outside are the major key names, separated by fifths. On the inside are the corresponding
minor key names. In the middle is the number and position of the sharps or flats.
There is a little trick to figuring out a key signature's name. When confronted with a key
signature that consists of flats, look at the flat second from the far right. This flat is on the line or
space the key signature is named after. One flat is F, since you can't go to the next -to-last flat.
To find the name of a key signature with sharps, look at the sharp farthest to the right. The key
signature is the note a half step above that last sharp.
Key signatures can specify major or minor keys. To determine the name of a minor key, find the
name of the key in major and then count backwards three half steps. Remember that sharps and
flats affect names.
Modes
In the middle ages, modes were used to organize the melodic and harmonic parts of music. From
the 17th century until the 19th century, modes were not used as widely. Modes in this time were
replaced by the major and minor scales. Modes, however, are still heard in contemporary music.
Modes, created mainly by the churches, were the basis for most of western music. Curiously, in
modes, the beginning tone is called the final, as opposed to the tonic as in other diatonic scales.
Name
Dorian
Phrygian
Table of Modes
Half Steps Are
Range Final
Similar Scale
Between
D to D D
2-3, 6-7
Natural minor scale with raised sixth degree
E to E E
1-2, 5-6
Natural minor scale with lowered second
Lydian
F to F F
Mixolydian G to G G
Aeolian
A to A A
Ionian
C to C C
4-5, 7-8
3-4, 6-7
2-3, 5-6
3-4, 7-8
Locrian
1-2, 4-5
B to B B
degree
Major scale with raised fourth degree
Major scale with lowered seventh degree
Same as natural minor scale
Same as major scale
Natural minor with a lowered second and fifth
degree.
Modes may begin on any tone as long as the arrangements of half and whole steps remain the
same. The identity of a transposed mode can be quickly determined since the final of each mode
lies in the same relationship to the tonic of the major with the same key signature.
1.
2.
3.
4.
5.
6.
7.
The final of the Dorian mode is always the second degree of the major scale.
The final of the Phrygian mode is always the third degree of a major scale.
The final of the Lydian mode is always the fourth degree of a major scale.
The final of the Mixolydian mode is always the fifth degree of a major scale.
The final of the Aeolian mode is always the sixth degree of a major scale.
The final of the Ionian mode is always the first degree of a major scale.
Locrian modes are rarely used.
Solfeggio
Often, solfeggio is used to help with practicing. The solfeggio syllables are associated with the
notes in a given scale. The syllable Do (pronounced dough, or doe), corresponds to the tonic.
The next syllable (in ascending order) is Re (say 'ray'). Re corresponds to the supertonic. Mi (say
'me') is the next syllable. Mi corresponds to the mediant. Fa (long a) comes next, corresponding
to the subdominant. Sol (say 'so') is the syllable that corresponds to the dominant. La (long a) is
the syllable that corresponds to the submediant. Ti (say 'tea') corresponds to the leading tone.
This table shows the solfeggio syllables and corresponding hand signs in descending order.
Do - a fist that is held straight.
Ti is index finger pointing up and the thumb and middle ring finger and pinkie are all touching
(the same as for sign language T).
La is all four fingers and thumb facing the ground and the wrist is bent down as well.
Sol is the thumb facing the ceiling the rest of the hand is out straight.
Fa is a thumbs down.
Mi is the hand held flat.
Re is a flat hand help up straight out and then raised to about a 30 degree angle. Both Mi and Re
have palm side down.
Do is the fist sign again.
The table above shows the hand signs that correspond to the solfeggio syllables. The hand signs
start with the lower tonic at about waist level. Each successive hand sign is a little higher than
the last. The second tonic ends a little above eye level.
Solfeggio is a good practice tool. Since it is fairly generic, it can be used with a variety of scales.
Pentatonic scales consists of five tones, and therefore Fa and Ti aren't used.
There are also solfeggio accidentals. These accidentals are shown and listed in the chart below.
Di is the accidental above Do. To make Di, make the fist for Do and lift the wrist up.
Ri is the accidental between Re and Mi. Ri looks just like Re, but the pointer finger in Ri is lifted
away from the other fingers.
Fi is between Fa and Sol. Fi is a thumbs up.
Si is an open hand, palm towards the chest and the wrist tilted up. Si is between Sol and La
Ta is like Ti, but the finger is pointed down. Ta is between La and Ti.