Intervals
Introduction
An interval is the distance between two pitches either vertically or horizontally
Intervals are classified by:
Whether pitches are played simultaneously
the numerical distance between those pitches
Their perceived quality
A harmonic interval is when two notes are played simultaneously
A melodic interval is when two pitches are played or sung consecutively (ascending or descending)
Augmented v. Diminished intervals
Augmented- One-half step larger than a perfect or major interval
Diminished- one half step smaller than a perfect or minor interval
Simple and Compound Interval
Simple: Intervals between a union and a octave
Compound: Any interval larger than an octave
Intervallic Inversion: Occurs when two notes are “flipped”. Useful when you do not want to work in the key signature of the note that is the original lower note
Consonant v. Dissonant
Consonant: Intervals that are considered more stable
Dissonant: Intervals are considered less stable as if they need to resolve
Interval Size
Interval Names
Interval has two components: Interval size and interval quality
Complete interval name = Quality + size
Interval size
Size tells us the number of steps that the interval contains
Intervals smaller than an octave are called simple intervals
Intervals larger than an octave are called compound intervals
Calculating Interval Size
Can be calculated in one of three ways:
Counting every letter name in the interval, including both top and bottom pitches
By counting every line and space on staff from bottom note to top note of interval
By looking at the interval on the staff and determining size based on visual pattern of lines and spaces
Accidentals do not affect interval size
Accidentals do not affect interval quality
Interval Quality
Rule: Perfect intervals are never major or minor, and vice versa
When describing or writing an interval, quality comes before size
Interval quality describes the actual sound, character, and color of interval
Semitone content determines interval quality
Perfect Intervals
Only unisons, 4ths, 5ths, and octaves are perfect intervals
2nds, 3rds, 6ths, 7ths, are never perfect
Perfect Fourths and Fifths
see ex 2 and 3 on sec 7 interval ipad ntoes
remember…
Unions, 4ths, 5ths, and octaves are never perfect but never major or minor
2nds, 3rds, 6ths, and 7ths are major or minor but never perfect
Minor intervals are a semitone smaller than major intervals
P4s contain 5 semitones
P5s contain 7 semitones
Perfect intervals are always natural to natural, sharp to sharp, or flat to flat except for fourths and fifths that involve F and B
Augmented and Diminished Intervals
When a perfect interval is enlarged by a half-step, it becomes augmented
When a perfect interval is reduced by a half step, it becomes diminished
(smaller)dim ← p → aug (larger)
Ex.
Diminished fifth: C to Gb
Perfect fifth: C to G
Augmented fifth: C to G#
Only the second interval is a perfect fifth because it has 7 semitones
First interval (C-Gb) contains 6 semitones, so it is smaller than a perfect fifth. Therefore, it is called a diminished fifth because thte distance between the two notes has decreased from perfect
Third interval contains 8 semitones, so it is one step larger than a perfect fifth. Therefore, it is called a augmented fifth because the distance between notes has increased from perfect
remember:
The second step to identifying an interval is to determine its quality
Keep the letter name content and the size of intervals the same when altering them
Perfect intervals can never be altered to become major or minor
Dim4 and Aug5 are rare, but Aug4 and dim5 are common
Augmented intervals are one semitone larger than major intervals
Diminished intervals are also one semitone smaller than minor intervals
The tritone
Contains three whole tones (2+2+2=6 semitones)
Occurs naturally between B and F or F and B
The augmented fourth and the diminished fifth share the same number of semitones (6)
The augmented fourth and the diminished fifth divide the octave (12 semitones) nearly in half
Spelling and Identifying Perfect Intervals
Three methods for identifying intervals: Counting method, white-key method, major scale method
The counting method
Can be tedious and error prone
Must take into account the number of letter names and their staff positions
two intervals may contain the same number of semitones and yet be labeled differently
The interval A4-C#5 contains four semitones, encompasses three letter names (A,B,C), three staff positions, and because of its semitone content, it isa major third
The interval A4-Db5 also contains four semitones, but it encompasses four letter names (abcd), four staff positions, and because of its semitone content it is called a diminished fourth, one semitone smaller than P4
White Key Method
All of the white key fourths and fifths are naturally perfect (except for B-F)
Perfect Rule #4: Whenever fourths and fifths have the same accidental (or both use no accidentals), the interval is perfect
If the two notes are B or F, then either a Bb or an F# must be used to make the interval perfect
Identifying Perfect Intervals
Compare the altered interval to the natural white key interval to determine its quality
Steps
Ignore any accidentals. What is the quality of the underlying white key interval?
Add the accidentals back to determine how they affect the quality of the white key interval. Do they makle the interval larger or smaller?
More complicated example: Interval from Bb to F#
Compare Bb-F# to white key interval B-F, Ignoring accidentals. We know that B-F is a diminished fifth
Is Bb larger or smaller than B-F? It is two semitones larger, with a raised upper note and a lowered bottom note. Enlarging the diminished fifth B-F by one semitone makes it perfect. Enlarging it by two semitones makes it augmented.
Spelling Perfect Intervals
White key approach works to spell fourths and fifths
write down the corresponding white key interval and determine its quality
Add accidentals to they white key interval to make it larger or smaller as needed
Augmented fourth above C
Write down the white key interval c-f ; its a perfect interval
make c-f one semitone larger (augmented). Because C was given, you should not change it
Raise the F to an F#, to change the interval from perfect to augmented
Diminished fifth above the pitch G#
Write the white key interval G-D, which is perfect fifth
Raise the G to G#, which will atomically make the white key interval G-D a half step smaller than the perfect
Now we have a diminished fifth
Major/ Minor Intervals
If a major interval decreases by a semitone, it becomes minor
If a minor interval increases by a semitone, it becomes major
Major Minor rule 1: Only seconds, thirds, sixths, and sevenths can be major or minor
Major Minor rule 2: Major/minor intervals can never become perfect
Minor and Major seconds
Minor seconds contain 1 semitone
Major seconds contain 2 semitones
Major and minor thirds
Minor thirds contain 3 semitones
Major thirds contain 4 semitones
Building blocks of triads and harmony
Minor and Major Sixths
A minor sixth contains 8 semitones
A major sixth contains 9 semitones
Minor or major sevenths
A minor seventh contains 10 semitones
A major seventh contains 11 semitones
Augmented and Dimimnished Intervals
when a major interval is enlarged by half a step, it becomes augmented
When a minor interval is reduced by half a step, it becomes diminished
Major/ Minor Interval Rule 3:
When a major interval is enlarged by a half-step, it becomes augmented
When a major interval is reduced by a half-step, it becomes minor
When a minor interval is enlarged by a half-step, it becomes major
When a minor interval is reduced by a half-step, it becomes diminished
(smaller)dim ←→ m ←→ M ←→ aug (larger)
Keep the same letter names if you want to change the quality of the intervals but keep their size
The only augmented and diminished intercals that occur with only regularity are the augmented second, the tritone, the augmented sixth, and the diminished seventh
Spelling and Identifying Major/Minor Intervals
Counting Semitones
A way to identify a given major/ minor interval is to count the number of semitones it contains
Only works best for smaller intervals
Interval Quality; number of semitones
P1; 0
m2; 1
M2; 2
m3; 3
M3; 4
P4; 5
A4/d5; 6
P5; 7
m6; 8
M6; 9
m7; 10
M7; 11
P8; 12
There is not a one-to-one correspondence between number of semitones and interval name
White key method
Seconds
There are two seconds that are naturally minor: The minor seconds above E and above B
Two locations on piano where there are no intervening black keys between white keys
All other seconds are naturally minor
Thirds
Three of the thirds- those formed over C, F and G are naturally major and the rest are naturally minor (important for triads)
Sixths
Three of the sixths (those formed over E, A, and B) are naturally minor adn the rest are naturally major
Sevenths
Only two sevenths are naturally major: the major sevenths above C and F
All other sevenths are naturally minor
The sevenths above C and F are only one half smaller than a perfect octave
Remember:
Knowing the location of the half-steps above E and above B will make identifying and spelling seconds easier
There is not a one-to-one correspondence between the number of semitones and the interval names
When identifying an interval, consider the numeric size of the interval and the number of semitones it contains
Applying the White Key method
Two basic steps in this approach:
Ignore the accidentals if any- and ask, “what is the quality of the underlying white-key interval?”
Add the accidentals back in to determine how they affect the quality of the white key interval. Do they make the interval larger or smaller?
Seconds
Given the interval from B to C# → compare to white key interval B to C (Naturally occurring minor second)
B to C# would be one semitone larger than this, making the interval a major second
Thirds
Consider the interval from F to Ab → evaluate white key interval from F to A (Natural minor third)
F to Ab is one semitone smaller than this major third, making the intercal a minor third
Sixths
Consider the interval from Ab to Fb → evaluate white key interval from A to F (natural minor sixth)
Since both pitches are altered similarly, these accidentals will not alter the size or quality of the interval, so Ab to Fb is also a minor sixth
Sevenths
Consider interval from F# to E → Evaluate white key interval F to E
Does the F# make the interval smaller or larger?
It is one semitone smaller, making the interval a minor seventh
Remember
All of the seconds are major except for two: E-F and B-C
All of the thirds are minor except for three: C-E, F-A, and G-B which are major
All of the fourths are perfect except for one: F-B which is an augmented fourth (a tritone)
All of the sevenths are minor except for C-B and F-E, which are major
Spelling Major/ Minor Intervals
White key method will also work for spelling major/minor intervals if we restate the two steps as follows
Write down the corresponding white key interval and determine its quality
Add the accidentals to the white key interval to make it larger or smaller as needed
ex) Spell a major third above the pitch E
Write the white key interval E to G
Only thirds above C, F, and G are minor, so the third above E would be minor
Make interval one semitone larger (per directions)
The pitch E was given, so you should not change it
Raise G to G# to create a major third
ex) Spell diminished seventh above the pitch C#
Write the white key interval C to B, which is one of two major sevenths
Because we need bottom note to be C#, we will raise it now
Makes the interval a half step smaller than major, so now we have a minor seventh
Lower the B to Bb and now we have a diminished seventh over C#
Hearing Intervals
Consonance and Dissonance
categories determined by sociocultural, geographic, and historical circumstances
Consonant intervals are perceived as pure, relaxed and stable; they don’t sound like they need to resolve
Dissonant intervals may sound harsh, unrelaxed and unstable
Consonant intervals
Consonant intervals are the unison, 8ve, P5, and all major and minor thirds and sixths, including their inversions
Perfect consonances- most stable consonances
unison, 8ve, and p5
Imperfect consonances- Might be less stable depending on the context
3rds and 6ths
Dissonant Intervals
Include major and minor seconds and sevenths, and all augmented and diminished intervals
The perfect fourth can be dissonant or consonant depending on the musical texture
remember:
Consonance and dissonance are not absolute categories
Consonant intervals include: unison, 8ve, P5, M3, m3, m6, and their inversions
Dissonant intervals include: m2, M2, m7, M7, and all augmented and diminished intervals
The perfect fourth can be considered consonant or dissonant depending on context
Interval Inversions
To invert an interval is to reverse the order of two pitches
Simple inversions my be inverted by raising the lower pitch an octave or lowering the upper pitch an octave
Ex)
F-A (M3) is A-F (m6)
C-F (p4) is F-C (p5)
The letter names of an inverted interval do not change even though their positions have changed
Any interval combined with its inversion creates an octave
Inversion patterns
Seconds always invert into sevenths
Thirds always invert into sixths
Fourths always invert into fifths
The sum of two interval sizes always equals nine
Qualities of inverted intervals:
Perfect intervals remain perfect
Major intervals become minor
Minor intervals become major
Augmented intervals become diminished
Diminished intervals become augmented
Using inversion to spell and identify larger intervals
Spelling large intervals by means of inversion
Invert the interval
Identify and spell the inversion
Invert the result
ex) Minor seventh above F#
invert- m7 inverts to M2
Spell: What is an M2 below F#? E
Invert result: Move E up an octave- Flipping it over F#. Answer = E
Compound Intervals
Compound Intervals are intervals that span more than an octave
Identifying Compound Intervals
Simplest way to identify a compound interval is to reduce it to a simple interval by removing any extra octaves
Ex.
In interval C4 to E5, removing one octave results in the simple C4 to E4
The smaller major third interval is easier to identify
Compound interval rule 1:
To determine the numeric size of a compound interval, add 7 for each octave larger than the simple interval
Second → Compound ninth
Third→ Compound tenth
Fourth→ compound eleventh
Compound inverval rule 2:
Compound intervals have the same quality as their corresponding simple intervals
Octaves, 11ths, and 12ths are perfect like their counterparts
9ths, 10ths, 13ths are major/minor like their simple counterparts
Spelling Compound Intervals
Spelling Compound Intervals
Reduce the compound interval to a simple interval
Spell the name interval
Add the octave(s) back to create the compound interval
Ex) Spell a P11 above middle C
Reduce the 11th to a simple interval
11-7=4. This gives you a fourth
Spell the simple interval: A P4 above C4 is F4
Add the octave back to create the compound interval: Move F4 up an octave to F5 to create a P11