Section 6 - Intervals PDF

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Note for MUS 1005 Theory & Fundamentals Section 6...

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I nt er v al An interval is the distance between two pitches. If two pitches are played simultaneously, the result is a harmonic interval. If two pitches are played consecutively (one after the other), the result is a melodic interval, which can occur in an ascending or a descending direction.

I nt er v alNames An interval name has two components: interval size and interval quality. 

Complete interval name = Quality + Size

I nt er v alSi z e The size of an interval tells us the number of steps that the interval contains.

Rule 1

Odd numbered intervals will always go from space to space or line to line



Rule 2

Even numbered intervals will always go from a line to a space or a space to a

 line

Acci dent al sandI nt er v alSi z e 샵이나 플랫은 numerical interval size 에 영향을 주지 않음

I nt er v alQual i t y Interval quality describes the character or color of an interval. The quality of an interval is determined by the number of half-steps (or semitones) that it contains Quality

Abbreviation

perfect

P

major

M

minor

m

augmented

A, aug, or +

diminished

d, dim, or o

Per f ectI nt er v al s Only unisons, fourths, fifths, and octaves can be called perfect

1. Uni sonsandOct av es When two musicians play very same pitch (in tune), they are in perfect unison. When they play the same pitch an octave apart, we can similarly say that they are performing a perfect octave.

Four t hsandFi f t hs 2. A perfect fourth is a fourth that contains 5 half-step. A perfect fifth is a fifth that contains 7 half-step

Counting the number of semitones from D to A

Augment edandDi mi ni s hedI nt er v al s Diminished fifth because the distance between the two notes has decreased from perfect. Augmented fifth because the distance between the two notes has increased from perfect

Diminished Fifth: C to G♭

Perfect Fifth: C to G

Augmented Fifth: C to G#

Perfect Interval Rule 2

  

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)

Perfect Interval Rule 3



Perfect intervals can never become major or minor

TheTr i t one The intervals of the augmented fourth and the diminished fifth share the same number of semitones (6), dividing the octave (of 12 semitones) neatly in half. In other words, F# is exactly halfway between C and C on the keyboard.

Fourths and fifths involving B and F

TheWhi t eKeyMet hod

White-key fourths and fifths / The "B-F Exception" All of the fourths and fifths in the example below are perfect because both pitches have the same accidental (or both have no accidental) and the two pitches are not B and F.

Perfect Interval Rule 4



Whenever fourths and fifths have the same accidental (or both use no accidental), the interval is perfect, with one exception:

If the two notes of the interval are B and F, then either a B♭ or an F# must be used to make the interval perfect.

I dent i f yi ngPer f ectI nt er v al s For example, if you were given the interval from F to C♭, you would compare it to the white-key interval F to C. We know that F-C is a perfect fifth. Is F-Cb larger or smaller than F-C? It is one-half step smaller, making it a diminished fifth.

Altered unisons and octaves

Spel l i ngPer f ectI nt er v al s The white-key approach will work not only for identifying fourths and fifths, but also for spelling them, if we restate the two steps as follows: 1. 2.

First, write down the corresponding white-key interval and determine its quality. Next, add accidentals to the white-key interval to make it larger or smaller, as needed.

For example, to spell an augmented fourth above the pitch C, first write the white-key interval C to F. Meed to make the interval one semitone larger. Raise the F to an F#, thereby altering the perfect fourth to become augmented



diminished fifth above the pitch G#? first write the white-key interval G to D, which is a perfect fifth. Since we need the bottom note to be G#, we will raise it now



Maj or / Mi norI nt er v al s intervals that can be either major or minor in quality. a major interval decreased by a semitone is minor and a minor interval increased by a semitone is major.

Major Third

Minor Third

Major Second

Minor Second

Major/Minor Intervals

Major/Minor Interval Rule 1



Only seconds, thirds, sixths, and sevenths can be major or minor



Major/minor intervals can never become perfect

1. Mi norandMaj orSeconds A minor second is a second that contains 1 semitone. A major second is a second that contains 2 semitones.

Minor and major seconds

2. Mi norandMaj orThi r ds A minor third is a third that contains 3 semitones. A major third is a third that contains 4 semitones.

Minor and major thirds

Counting the number of semitones from A to C#

3. Mi norandMaj orsi xt hs A minor sixth is a sixth that contains 8 semitones. A major sixth is a sixth that contains 9 semitones.

Minor and major sixths

4. Mi norandMaj orSev ent hs

A minor seventh is a seventh that contains 10 semitones. A major seventh is a seventh that contains 11 semitones.

Minor and major sevenths

Augment edandDi mi ni s hedI nt er v al s The major/minor intervals can also be augmented or diminished. When a major interval is enlarged by a half-step, it becomes augmented. When a minor interval is reduced by a half-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) diminished — minor — Major — augmented (larger)

Count i ngSemi t ones One way to identify a given major/minor interval is to count the number of semitones it contains. The following chart provides a summary of the interval qualities we have discussed, along with the number of semitones they contain. Semitone chart Interval Quality

P1

m2

M2

m3

M3

P4

A4/d5

P5

m6

M6

m7

M7

P8

# of Semitones

0

1

2

3

4

5

6

7

8

9

10

11

12

I. Seconds

Below provides all of the possible seconds using only the white keys on the piano. seconds above E and above B are naturally minor

White-key seconds

II. Thirds Below provides all of the possible thirds using only the white keys on the piano. thirds over C, F, and G are naturally major.

White-key thirds

III. Sixths below provides all of the possible sixths using only the white keys on the piano. sixths over E, A, and B are naturally minor.

White-key sixths

IV. Sevenths below provides all of the possible sevenths using only the white keys on the piano. major sevenths above C and above F are naturally major

White-key sevenths

Appl yi ngt heWhi t eKeyMet hod 1. 2.

First, ignore the accidentals (if any). What is the quality of the underlying white-key interval? Now 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?

Remember if the same accidental is added to both pitches of an interval, it does not change the size or quality of the interval, so we can ignore both accidentals when determining the quality of that interval. I. Seconds If you were given the interval from B to C#, you would compare it to the white-key interval B to C. This is one of the two naturally occuring minor seconds. B to C# would be one semitone larger than this, making the interval a major second.

II. Thirds Consider the interval from F to A♭. First, we ignore the A♭ and evaluate the whitekey interval F to A. F is one of the three pitches over which we naturally get major thirds. F to A♭ is one semitone smaller than this major third, making the interval a minor third.

III. Sixths Now consider the interval from A♭ to F♭. Since there are flats on both pitches, we can safely ignore both accidentals and evaluate the white-key interval from A to

F. A is one of the three pitches over which we naturally get minor sixths. Since both pitches are altered similarly, these accidentals will not alter the size or quality of the interval, so A♭ to F♭ is also a minor sixth.

IV. Sevenths If you were given the interval from F# to E, you would compare it to the white-key interval F to E. This is one of the two naturally occuring major sevenths. F# makes the interval one semitone smaller, making the interval a minor seventh.

Spel l i ngMaj or / Mi norI nt er v al s The white-key approach will also work for spelling major/minor intervals, if we restate the two steps as follows: 1. 2.

First, write down the corresponding white-key interval and determine its quality. Next, add accidentals to the white-key interval to make it larger or smaller, as needed.

For example, if you were asked to spell a major third above the pitch E, you would first write the white-key interval E to G. What is its quality? Only thirds above C, F, and G are major, so the third above E would be minor. Since you were asked to spell a major third, you need to make the interval one semitone larger. The pitch E was given, so you should not change it. Instead, you should raise the G to a G# to create a major third.

Now what if you were asked to spell a diminished seventh above the pitch C#? Using this method, you would first write the white-key interval C to B, which is

one of the two major sevenths. Since we need the bottom note to be C#, we will raise it now. What effect does this have on the underlying white-key interval? It makes the interval a half-step smaller than major, so we have a minor seventh. We are not done yet; we still need to make the interval one semitone smaller. Lower the B to Bb and we now have a diminished seventh over C#.

ConsonanceandDi ssonance Consonant intervals are pure, relaxed, and stable; they do not sound like they need to resolve. Dissonant intervals, on the other hand, sound harsh, unrelaxed, and unstable Consonant intervals: These include most of the perfect intervals (unisons, fifths, and octaves) and all major and minor thirds and sixths. Dissonant intervals: These include the major and minor seconds and sevenths as well as augmented and diminished intervals. 

Perfect fourth is not included in the two categories above

I nt er v alI nv er si on To invert an interval means to reverse the order of the two pitches in the interval. For example, the inversion of the interval from F to A (a major third) is A to F (a minor sixth). When you invert an interval, you essentially move one of the pitches by an octave so that it "flips over" the other note.

when inverting intervals is that the letter names of the two pitches involved do not change. So F-A becomes A-F, C-Eb becomes Eb-C, F#-D becomes D-F#, and so on.

An interval and its inversion create a perfect octave

Remember



The sum of the sizes of an interval and its inversion always equals 9

Unisons invert into octaves Seconds invert into sevenths Thirds invert into sixths Fourths invert into fifths Fifths invert into fourths Sixths invert into thirds Sevenths invert into seconds Octaves invert into unisons

(1 + 8 = 9) (2 + 7 = 9) (3 + 6 = 9) (4 + 5 = 9) (5 + 4 = 9) (6 + 3 = 9) (7 + 2 = 9) (8 + 1 = 9)

Remember 

When you invert intervals, the qualities change consistently:

Perfect always inverts to perfect Major always inverts to minor Minor always inverts to major Augmented always inverts to diminished Diminished always inverts to augmented

(Ex: P5 to P4) (Ex: M3 to m6) (Ex: m2 to M7) (Ex: A4 to d5) (Ex: d7 to A2)

CompoundI nt er v al s Up to this point, we have only dealt with intervals that are an octave or smaller (these are called simple intervals). Intervals that are larger than an octave (ninths, tenths, elevenths, and so on) are called compound intervals.

Compound intervals

I dent i f yi ngCompoundI nt er v al s The simplest way to identify a compound interval is to reduce it to a simple interval by removing any extra octaves. For example, if you had the interval from C4 to E5 (as shown in the example below), you can remove one octave, resulting in the simple interval C4 to E4

Compound Interval Rule 1



To find 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

2+7=9 3 + 7 = 10 4 + 7 = 11

Compound Interval Rule 2



Compound intervals have the same quality as their corresponding simple intervals

Rule



Measured from the tonic note of a major scale:

The intervals of the unison, fourth, fifth, and octave are always perfect. The intervals of the second, third, sixth, and seventh are always major....