SOUND PATTERNS

2.1 INTERVALS

The most basic of building blocks in music is the INTERVAL, which is the distance between two pitches. When they occur simultaneously, they are called HARMONIC intervals; when consecutive, they are MELODIC intervals. There is no difference in the way these types of intervals are calculated.

Learn more about intervals

Intervals are given two names. The first name reflects a QUALITY and the second name is a NUMBER. The quality represents the specific number of half-steps between the two notes. The number represents the number of lines and spaces (or more simply, the number of "letter" names) involved in constructing the two notes. For instance, C up to F is a 4th (C-D-E-F) and D# up to Bb is a 6th (D-E-F-G-A-B).

There are three basic types of quality names:

• PERFECT (P)
• IMPERFECT
  • Large variety: MAJOR (M)
  • Small variety: MINOR (m)
• ALTERED
  • Intervals made larger: AUGMENTED (A)
  • Intervals made smaller: DIMINISHED (d)

Note that perfect, major, and augmented intervals are labelled with uppercase letters (P, M, and A) and that minor and diminished intervals are labelled with lowercase letters (m and d).

1. Perfect intervals

   Perfect intervals include 1sts (better known as unisons), 4ths, 5ths, and 8ths (better known as octaves).

   Interval	P1	P4	P5	P8
   # of half-steps	0	5	7	12

   Unisons and octaves are straightforward. Unisons are both exactly the same pitch. Octaves are exactly the same pitch class, but 12 half-steps away.

   

   5ths are best understood through the concept of BASIC INTERVALS first. Basic intervals are all natural notes (or white keys on the piano).

   

   All of the basic 5ths above are perfect (containing 7 half-steps) except the last one (B-F), which contains only 6 half-steps. A 5th that is a half-step smaller than 7 is called a diminished fifth (d5).

   The same basic procedure applies to 4ths. The basic 4ths are

   

   All are P4s (containing 5 half-steps) except the last, F-B, which contains 6 half-steps. A 4th that is a half-step larger than 5 is called an augmented fourth (A4).

   With this information it is possible to calculate any type of 4th or 5th. Some examples:

   Pitches	Basic interval	Effect of accidental(s)	Actual interval
   A up to Eb	A-E: P5	makes smaller	d5
   D up to G#	D-G: P4	makes larger	A4
   F up to Bb	F-B: A4	makes smaller	P4
   C# up to G	C-G: P5	makes smaller	d5
   Bb up to F	B-F, d5	makes larger	P5
   G# up to C#	G-C: P4	none	P4

   Learn more about perfect intervals

2. Imperfect intervals

   Imperfect intervals include 2nds, 3rds, 6ths, and 7ths, and they come in two varieties: major and minor. As with other intervals, the qualities are determined by the number of half-steps between pitches.

   Interval	m2	M2	m3	M3	m6	M6	m7	M7
   # of half-steps	1	2	3	4	8	9	10	11

   Rather than spend time counting half-steps, there are easier ways to learn the imperfect intervals, again using basic intervals.

   The basic 2nds are

   

   Two of them are m2's (E-F and B-C); all the rest are M2's.

   • If a m2 is expanded by a half-step, it becomes a M2
   • If a M2 is contracted by a half-step, it becomes a m2
   • If a m2 is contracted by a half-step, it becomes a d2
   • If a M2 is expanded by a half-step, it becomes an A2

   The basic 3rds are

   

   Three of them are M3's (C-E, F-A, and G-B); all the rest are m3's.

   • If a m3 is expanded by a half-step, it becomes a M3
   • If a M3 is contracted by a half-step, it becomes a m3
   • If a m3 is contracted by a half-step, it becomes a d3
   • If a M3 is expanded by a half-step, it becomes an A3

   You are now prepared to calculate any 2nd or 3rd. Some examples:

   Pitches	Basic interval	Effect of accidental(s)	Actual interval
   E-F#	E-F: m2	make larger	M2
   C-Db	C-D: M2	make smaller	m2
   Bb-C	B-C: m2	make larger	M2
   F-Ab	F-A: M3	make smaller	m3
   A-C#	A-C: m3	make larger	M3
   Eb-Gb	E-G: m3	none	m3

   6ths and 7ths could be done the same way, but there is another way to solve them more easily, through the properties of INTERVAL INVERSION. When the bottom note of an interval is placed above the top, or the top below the bottom, the interval is inverted. The number of an interval and its inversion always adds up to 9:

   • 2nds invert into 7ths [2 + 7 = 9]
   • 3rds invert into 6ths [3 + 6 = 9]
   • 4ths invert into 5ths [4 + 5 = 9]
   • 5ths invert into 4ths [5 + 4 = 9]

   The quality sign reverses in an inversion:

   • Major intervals invert into minor intervals
   • Minor intervals invert into major intervals
   • Diminished intervals invert into augmented intervals
   • Augmented intervals invert into diminished intervals
   • Perfect intervals invert into perfect intervals (which is why they are called "perfect")

   To solve 6ths and 7ths, simply invert and compare to the 3rds and 2nds:

   

   

   Learn more about imperfect intervals

3. Consonance/dissonance

   All intervals fall into two types: CONSONANT and DISSONANT. Consonant intervals are aurally stable; dissonant intervals are aurally unstable and need to move to consonance (RESOLUTION).

   Consonant	Dissonant
   P1, P5, P8, m3, M3, m6, M6	P4, m2, M2, m7, M7, all augmented intervals, all diminished intervals

4. Multiple alterations

   It is possible to diminish an interval more than once, and to augment more than once as well.

   

5. Enharmonic intervals

   The word ENHARMONIC is often misunderstood. It is sometimes defined as "the same pitch spelled two different ways", such as B# and C. A better definition would be "two spellings for the same key on the piano". The truth is, B# and C are NOT actually the same pitch, except on MOST keyboard instruments. This can be proven mathematically if you are dubious of that statement.

   ENHARMONIC INTERVALS are two different spellings for two intervals described by the same two keys on the piano, such as E-A# and E-Bb. They are not, however, the same interval: E-A# is an A4 and E-Bb is a d5 (they have a different number of lines and spaces). An A4 and a d5 are known as TRITONES, since they both contain 6 half-steps (which equals 3 whole-steps). Other common enharmonic intervals are A2 / m3 and A6 / m7.

   

6. Compound intervals

   Any interval can be expanded by an octave. creating a COMPOUND INTERVAL. The number of the expanded interval will be 7 more than the smaller interval, and the quality will remain the same as the smaller interval.

   

DRILLS

Interval Drills

An excellent place to find more interval exercises is at Ricci Adams' music theory.net, an outstanding collection of lessons, trainers, and utilities available at no cost. Make this impressive site a regular part of your studies.

Learn more about identifying intervals

2.2 SCALES AND SCALE DEGREES

SCALES, from the Italian word scala ("staircase" or "ladder"), are a stepwise arrangement of pitches encompassing an octave. There are two traditional scales used in the Common Practice Period: MAJOR and MINOR. In other cultures and time periods, there are also many NON-TRADITIONAL scales.

The pitches used to form a scale are DIATONIC pitches. The remaining ones, those not in the scale, are CHROMATIC pitches.

1. Major scales

   Major scales have a m2 between the third and fourth notes and the seventh and eighth: All the other intervals are M2's.

   

   Regardless of what the first pitch is, this pattern is consistent from one major scale to another.

   

   Each SCALE DEGREE in a major scale has an identity, and there are several ways of labeling each one:

   • Scale degree numbers (^1, ^2, ^3...) which show the order and placement of each step.
     (The caps belong over the number, but due to technical limitations, this text will place them to the left of the number.)
   • Solfege syllables (Do, Re, Mi...), which give a unique syllable to each step.
   • Scale degree names (tonic, supertonic, mediant...), which describe the function of each step.

   

   Learn more about major scales

2. Scale degree names

   The scale degree names are significant since they describe the function of that scale degree within the scale and what it contributes to tonic, thus creating tonality.

   TONIC is obvious; this is the defining note, the center of all activity.

   DOMINANT is the next most important scale degree; it is the furthest from tonic (P5 above) and therefore measures the extent of the scale (higher scale degrees are actually moving closer to the upper tonic), and provides a point of departure that wants to return to tonic.

   SUBDOMINANT is a P5 below tonic, and measures the lower extent of the scale ("sub" means "below"), and wants to move towards dominant.

   MEDIANT lies halfway between tonic and dominant, and becomes closely associated with tonic.

   SUBMEDIANT lies halfway between tonic and subdominant, and becomes closely associated with tonic in a secondary way.

   SUPERTONIC lies a step above tonic ("super" means "above'), and tends to resolve down to tonic.

   Following this logic, the scale degree below tonic should be called the SUBTONIC, and it sometimes is. But this scale degree (^7) has a greater purpose: it propels the ear towards tonic in a powerful way. Sing a major scale and stop on the seventh scale degree and you will hear it immediately. Therefore, the name LEADING TONE is much more descriptive of what it actually does. Leading tone always is a m2 below tonic.

   The cartoon below, by John Bogenschutz, from Tone Deaf Comics is a humorous, yet amazingly accurate, view of scale degree functions:

   

   Used by permission of the author. Go to Tone Deaf Store online for more.

3. Chromatic syllables

   The SOLFEGE syllables mentioned above are well-known to anyone who knows The Sound of Music. Less known is that each syllable can be altered chromatically; the vowel is changed to reflect that alteration. Raised syllables end with the letter "i", and lowered syllables end with the letter "e" (except for "Re" which already does, so it will be labeled "Ra").

   

   

   Solfege syllables can be classified two ways: "fixed Do" and "moveable Do". "Fixed Do" is simply another way of naming pitches: Do is always "C", Re is always "D", and so on. "Moveable Do" is more useful, since Do changes with each key, always expressing the tonic of that key.

4. Natural minor scales

   NATURAL MINOR SCALES have a m2 between the second and third notes and the fifth and sixth: All the other intervals are M2's.

   

   No matter what the first pitch is, this pattern is consistent from one minor scale to another.

   

   Each note in this scale has a unique identity, just like a major scale:

   

   Of special interest is ^7, which is no longer a leading tone; it is now called a SUBTONIC, which is always located a M2 below tonic. Subtonic does not lead to tonic; in fact, it does quite the opposite, moving the ear away from tonic.

5. Harmonic minor scales

   The natural minor scale is the most basic form of minor, but the absence of the leading tone is problematic. Therefore, composers of the Common Practice Period appropriated the leading tone from the major scale, and created what is known as a HARMONIC MINOR SCALE:

   

   There is no music in a minor key from the Common Practice Period that does not utilize the leading tone significantly. Leading tone should be considered an automatic part of music composed in minor. It is regrettable that the symbol for the leading tone in minor is called an "accidental"...it is no accident.

6. Melodic minor scales

   The harmonic minor scale is good at establishing tonic since it has a leading tone, but it has an awkward gap (an A2) between ^6 and ^7. To avoid this, composers would also appropriate ^6 from the major scale to smooth the motion to ^7, creating a MELODIC MINOR SCALE:

   

   However, this scale is now almost identical with the major scale; only ^3 is different. To solve this problem, composers return ^6 and ^7 back to where they were in the natural minor as they move away from tonic.

   

   Learn more about minor scales

DRILLS

Scale Drills

Scale Degree Drills

More scale and scale degree information at Ricci Adams' music theory.net.

2.3 KEY AND KEY SIGNATURES

The key of a piece is described by the name of the tonic note plus the quality of the scale, for example, Bb major (tonic of Bb and vocabulary of a major scale) or G# minor (tonic of G# and vocabulary of a minor scale). The specific type of minor scale is not traditionally stated; no one speaks of a piece of music written in the key of C melodic minor.

Constructing major and minor scales on different pitch levels create a great number of accidentals. It is customary to collect these accidentals into key signatures.

Key signatures consist of sharps (#) or flats (b), with the well-known exception of C major which has no sharps and no flats. The sharps always occur in the same order when placed into a key signature. The following mnemonic device will help you to memorize the order of sharps (there are several other devices if you like).

F#	C#	G#	D#	A#	E#	B#
Father	Charles	Goes	Down	And	Ends	Battle

The flats also always occur in the same order, which is the reverse of the sharps. The proper order of flats uses the same mnemonic backwards.

Bb	Eb	Ab	Db	Gb	Cb	Fb
Battle	Ends	And	Down	Goes	Charles'	Father

1. Sharp key signatures

   The name of the major key associated with sharps can be determined from the last sharp in the signature, which is always the leading tone (Ti).

   

2. Flat key signatures

   The name of the major key associated with flats can be determined from the last flat in the signature, which is always the subdominant (Fa). Tonic can also be viewed as the penultimate flat (shown with slurs below).

   

3. Minor key signatures

   Minor key signatures collect the pitches found in the natural minor scale, and do not include the alterations made on ^6 and ^7. Although major and minor keys have a fundamental difference, there are some special relationships between them that are important.

   PARALLEL KEYS share the same tonic (such as G major and G minor). This is a close relationship. RELATIVE KEYS share a key signature (such as C major and A minor), which on the surface makes them appear to be similar, but they are, in fact, quite different since they do not share a tonic. Also, the relative minor will always have a leading tone, which is a pitch not found in the major key.

   The relative minor key is always located a m3 below the major key. Please note that if a key is referred to by letter name only, major keys are written UPPERCASE and minor keys lowercase.

   Sharp keys	1#	2 #	3 #	4 #	5 #	6 #	7 #
   Major	G	D	A	E	B	F#	C#
   Minor	e	b	f#	c#	g#	d#	a#

   Flat keys	1 b	2 b	3 b	4 b	5 b	6 b	7b
   Major	F	Bb	Eb	Ab	Db	Gb	Cb
   Minor	d	g	c	f	bb	eb	ab

   Learn more about key signatures

4. Circle of fifths

   Learn about the circle of fifths

DRILLS

Key Signature Drills

More key signature drills at Ricci Adams' music theory.net.

2.4 MODES

Major and minor scales were not the primary vocabulary prior to the Common Practice Period. The "scales" then are called MODES. Like scales, they are stepwise collections of pitches encompassing an octave. Musicians of the Middle Ages attempted to draw parallels in the sound of them with classical Greece, and named their patterns after locations in Greece. The modes used in this text are

• DORIAN
• PHRYGIAN
• LYDIAN
• MIXOLYDIAN
• IONIAN (the same pattern as a major scale)
• AEOLIAN (the same pattern as the natural minor scale)

There are four ways that modes can be identified, and each has its own merits. It would be a good idea to know all four ways for accuracy.

1. Indicate where the half-steps are located

   

   This is an accurate way to indentify the mode, but it can be cumbersome.

2. Compare the modes to major and minor scales

   Two of the modes (Dorian and Phrygian) have only one different note compared to the natural minor scale (also known as the Aeolian mode):

   

   The other two (Lydian and Mixolydian) have only one different note compared to the major scale (also known as the Ionian mode):

   

   This is a good method to learn how to sing the mode or to identify it by ear.

3. Compare each mode to its scale degree within a major scale

   The basic modes (all natural notes) correspond to the key of C major, and each mode begins on a different scale degree:

   

   This can be projected to any major key, for instance E major:

   

   This is a quick way to figure out the content of any mode starting on a given pitch.

4. Compare key signatures to major and minor scales

   With the minor-like modes (Dorian and Phrygian), the key signatures vary by one accidental of the natural minor:

   • In flat key signatures
     • Dorian subtracts one accidental
     • Phrygian adds one accidental

     

   • In sharp key signatures
     • Dorian adds one accidental
     • Phrygian subtracts one accidental

     

   • In the key signature with no accidentals
     • Dorian adds one sharp
     • Phrygian adds one flat

     

   With the major-like modes (Lydian and Mixolydian), the key signatures vary by one accidental of the major:

   • In flat key signatures
     • Lydian subtracts one accidental
     • Mixolydian adds one accidental

     

   • In sharp key signatures
     • Lydian adds one accidental
     • Mixolydian subtracts one accidental

     

   • In the key signature with no accidentals
     • Lydian adds one sharp
     • Mixolydian adds one flat

     

     Learn more about modes

   This is a quick way to figure out the key signature for any mode on a given pitch.

DRILLS

Mode Drills

More mode drills at Ricci Adams' music theory.net.