Open Music Theory Fundamentals

When all the members of the triad are as close to the bass note as they can be, the chord is in what is called

close position

When ascending, the melodic minor scale uses...

la and ti.

Dots and ties allow for basic durations to be...

lengthened.

minor triad:

m3 and P5 above the root (as in do-me-sol or la-do-mi) lower-case "m"

diminished triad:

m3 and d5 above the root (as in ti-re-fa) lower-case "dim" or a degree sign "°"

minor seventh:

m3, P5, and m7 above the root (or minor triad with a minor seventh) m7 (F♯m7)

diminished seventh:

m3, d5, and d7 above the root (or diminished triad with a diminished seventh) dim7 or °7 (Ddim7 or D°7)

half-diminished seventh:

m3, d5, and m7 above the root (or diminished triad with a minor seventh) ⦰7 (A⦰7)

What are The five possible interval qualities:

- augmented (A) - major (M) - perfect (p) - minor (m) - diminished (d)

If a simple meter is notated such that each eighth note corresponds to a beat, the bottom number of the time signature is

8

if a pitch class other than the chord root is the lowest note in the chord, a slash is added, followed by a capital letter denoting the pitch class in the bass (lowest) voice.

A C-major triad's lead-sheet symbol is simply C. A C-minor triad is Cm. A D-sharp-diminished triad with an F-sharp in the bass is D#dim/F#. And so on.

Solfège can also help to determine the specific interval.

Each pair of solfège syllables will have the same interval, no matter what the key, as long as it is clear which syllable is the lower pitch and which is the upper pitch. Memorizing the intervals between solfège pairs can help speed along your analysis of dyads as they appear in music. For example, knowing that do-mi, fa-la, and sol-ti are always major thirds and knowing that re-fa, mi-sol, la-do, and ti-re are always minor thirds will allow for faster analysis of dyads in major keys.

Mnemonic device for remembering the order of sharps.

Father Charles Goes Down And Ends Battle

similar motion, also called direct motion

In similar motion, also called direct motion, two voices move in the same direction, but by different intervals. For example, the following two voices both move down, but the upper voice moves by step while the lower voice moves by leap. Note also that the two dyads are different generic intervals. This will always be the case with similar or direct motion.

Enharmonic equivalence

Notice that some of the keys have two names. When two pitch classes share a key on the keyboard, they are said to have enharmonic equivalence. Theoretically, each key could have several names (the note C could also be considered D♭♭, for instance), but it's usually not necessary to know more than two enharmonic spellings.

Triad qualities

To find a triad's quality, identify the interval between the root and the other members of the chord. There are four qualities of triads that appear in major and minor scales, each with their own characteristic intervals. - major triad: M3 and P5 above the root (as in do-mi-sol) - minor triad: m3 and P5 above the root (as in do-me-sol or la-do-mi) - diminished triad: m3 and d5 above the root (as in ti-re-fa) - augmented triad: M3 and A5 above the root (as in me-sol-ti)

Identifying and labeling triads

Triads are identified according to their root and quality.

a quarter note with two dots would be equivalent in duration to...

a quarter, eighth, and sixteenth note.

Capital Roman numerals (I, II, III, etc.)

are used for major triads.

Often more specificity is needed than generic intervals can provide. That specificity comes in the form of an interval's...

quality. Combining quality with a generic interval name produces a specific interval.

In a time signature, the top number (and the top number only!) describes the type of meter. Following are the top numbers that always correspond to each type of meter:

simple duple: 2 simple triple: 3 simple quadruple: 4 compound duple: 6 compound triple: 9 compound quadruple: 12

Standard meters in Western music can be classified into..

simple meters and compound meters, as well as duple, triple, and quadruple meters.

In compound meters, the bottom number of the time signature corresponds to the type of note corresponding to a...

single division of the beat.

In major keys, chords with the same Roman numeral are made up of the same scale-degrees (using the same solfège syllables), and they have the same quality. In other words,

triads labeled "I" in any major key will be major triads containing do, mi, and sol. iii triads will be minor triads containing mi, sol, and ti, etc. The same is true for minor keys (though I in minor is different from I in major).

Mnemonic device for remembering the order of major key flats in the circle of fifths

Charles Finds Bitches Every Afternoon Def Gettin Coochy

Rhythm refers to

the combination of long and short durations in time.

If a simple meter is notated such that each quarter note corresponds to a beat, the bottom number of the time signature is...

4

triad

A three-note chord whose pitch classes can be arranged as thirds is called a triad.

Harmonic consonance and dissonance

The following harmonic intervals are imperfect consonances, and can be used relatively freely in strict voice-leading (except for beginnings and endings): Major and minor thirds Major and minor sixths The following harmonic intervals are perfect consonances, and must be used with care in limited circumstances in strict voice-leading: All perfect intervals except the perfect fourth (P1, P5, P8) All other harmonic intervals are dissonant, and must be employed in very specific ways in strict voice-leading, including: All diatonic steps (M2, m2) All augmented and diminished intervals (including those that are enharmonically equivalent to consonant intervals, such as A2 and A1) All sevenths Perfect fourths

Minor key signatures

for each major key signature, there is a corresponding minor key that shares its signature. Major and minor keys that share the same key signature are called relative keys. For example, both C major and A minor have zero sharps or flats. A minor is considered the relative minor of C major; likewise, C major is considered the relative major of A minor

Beams are used to...

group any notes at the beat division level or shorter that fall within the same beat.

There are two types of steps:

half steps and whole steps. A half step (H) consists of two adjacent pitches on the keyboard. A whole step (W) consists of two half steps.

Multiple dots can be added to a duration. Subsequent dots add...

half the duration of the previous dot.

If the two pitches of a dyad sound at the same time (a two-note chord), the interval between them is a...

harmonic interval.

A scale is

a succession of pitches ascending or descending in steps.

most composers don't really think about three different "forms" of the minor scale. the melodic minor scale is derived from...

composers' desire to avoid the melodic augmented second interval between le and ti (and some chose not to avoid this!). In reality, there is only one "version" of the minor scale. Context determines when a composer might use la and ti when writing music in a minor key.

most composers don't really think about three different "forms" of the minor scale. The harmonic minor scale simply represents...

composers' tendency to use ti when building harmonies that include the seventh scale degree in the minor mode.

A tie lengthens a duration by...

connecting two adjacent identical pitches.

The major scale

consists of seven whole (W) and half (H) steps in the following succession: W-W-H-W-W-W-H. Here is the D major scale. It is called the "D major scale" because the pitch D is the tonic and is heard at both ends of the scale.

A dot occurs after a pitch or a rest, and it...

increases its duration by half.

interval

An interval is the distance between two pitches, usually measured as a number of steps on a scale. the term interval regularly refers both to the distance between two pitches on a scale and to a dyad whose pitches are separated by that distance.

Simple and compound classifications result from the relationship between the...

counting pulse and the pulses that are faster than the counting pulse. In other words, it is a question of division: does each beat divide into two equal parts, or three equal parts. Meters that divide the beat into two equal parts are simple meters; meters that divide the beat into three equal parts are compound meters.

Three relationships exhibited by these two dyads hold for all interval inversions.

First, the chromatic intervals add up to 12. Second, the two generic interval values add up to nine Lastly, the major interval inverts into a minor, and vice versa.

The first relationship held for all interval inversions.

First, the chromatic intervals add up to 12. (C4-E4 = i4; E4-C5 = i8; i4 + i8 = i12) This is because the two intervals add up to an octave (with an overlap on E4).

Duple, triple, and quadruple classifications result from the relationship between the ...

counting pulse and the pulses that are slower than the counting pulse. In other words, it is a question of grouping: how many beats occur in each bar. If counting-pulse beats group into twos, we have duple meter; groups of three, triple meter; groups of four, quadruple meter. Conducting patterns are determined based on these classifications.

Ties are used to...

either sustain a pitch beyond the length of a single measure, or to make a particular rhythmic grouping in a measure more clear.

When descending, the melodic minor scale uses...

the "natural" te and le.

because the beat is divided into three in a compound meter,

the beat is always three times as long as the division note, and the beat is always dotted.

If a compound meter is notated such that each dotted-quarter note corresponds to a beat,

the eighth note is the division of the beat, and thus the bottom number of the time signature is 8.

The third relationship held for all interval inversions.

the major interval inverts into a minor, and vice versa. This always holds for interval inversion. Likewise, an augmented interval's inversion is always diminished, and vice versa. A perfect interval's inversion is always perfect. major ↔ minor augmented ↔ diminished perfect ↔ perfect

If a compound meter is notated such that each dotted-half note corresponds to a beat,

the quarter note is the division of the beat, and thus the bottom number of the time signature is 4.

The first pitch of the scale is called

the tonic, its the pitch upon which the rest of the scale is based. When the scale ascends, the tonic is repeated at the end an octave higher.

take C4-E4 (major third) and E4-C5 (minor sixth). These two dyads have the same two pitch classes, but one has C on bottom and E on top, while the other has E on bottom and C on top. Thus,

they are inversions of each other.

if a quarter note is equivalent in duration to two eighth notes, a dotted quarter note would be equivalent to

three eighth notes.

Generally, undotted notes divide into two notes; dotted notes divide into three. Thus,

undotted notes are typically used to represent the beat level in simple meter, while dotted notes are used to represent the beat in compound meter.

There are five qualities of seventh chords that appear in diatonic music: major seventh, dominant seventh, minor seventh, diminished seventh (also called fully-diminished), and half-diminished seventh. They are comprised of the following intervals above their roots:

- major seventh: M3, P5, and M7 above the root (or major triad with a major seventh) - dominant seventh: M3, P5, and m7 above the root (or major triad with a minor seventh) - minor seventh: m3, P5, and m7 above the root (or minor triad with a minor seventh) - diminished seventh: m3, d5, and d7 above the root (or diminished triad with a diminished seventh) - half-diminished seventh: m3, d5, and m7 above the root (or diminished triad with a minor seventh)

there are six types of standard meter in Western music:

- simple duple (beats group into two, divide into two) - simple triple (beats group into three, divide into two) - simple quadruple (beats group into four, divide into two) - compound duple (beats group into two, divide into three) - compound triple (beats group into three, divide into three) - compound quadruple (beats group into four, divide into three)

seventh chord.

A four-note chord whose pitch classes can be arranged as thirds is called a seventh chord.

Following are the qualities and scale-degrees belonging to each seventh chord in every major key, along with the corresponding Roman numeral reflecting those qualities:

I7: major seventh - do, mi, sol, ti ii7: minor seventh - re, fa, la, do iii7: minor seventh - mi, sol, ti, re IV7: major seventh - fa, la, do, mi V7: dominant seventh - sol, ti, re, fa vi7: minor seventh - la, do, mi, sol vii⦰7: half-diminished seventh - ti, re, fa, la

Following are the qualities and scale-degrees belonging to each triad in every major key:

I: major - do, mi, sol ii: minor - re, fa, la iii: minor - mi, sol, ti IV: major - fa, la, do V: major - sol, ti, re vi: minor - la, do, mi vii°: diminished - ti, re, fa

contrary motion

In contrary motion, two voices move in opposite directions—one up, the other down.

oblique motion

In oblique motion, one voice is stationary, while the other voice moves (in either direction). The stationary tone may or may not be rearticulated.

parallel motion

In parallel motion, two voices move in the same direction by the same generic interval. For example, the following two voices both move up by a step. Note also that both dyads form the same generic interval (sixth). This will always be true when two voices move in parallel motion.

augmented triad:

M3 and A5 above the root (as in me-sol-ti) lower-case "aug" or a plus sign "+"

major triad:

M3 and P5 above the root (as in do-mi-sol) no quality symbol is added

major seventh:

M3, P5, and M7 above the root (or major triad with a major seventh) maj7 or △7 (Gmaj7 or G△7)

dominant seventh:

M3, P5, and m7 above the root (or major triad with a minor seventh) 7 (B7)

Triad roots

To find a triad's root, arrange the pitch classes on a circle of thirds (mentally or on paper). The root is the lowest in the three-pitch-class clump. Expressed another way, if the circle ascends by thirds as it moves clockwise, the root is the "earliest" note (thinking like a literal clock), and the other pitch classes come "later." Once you know the root, you can identify the remaining notes as the third of the chord (a third above the root) and the fifth of the chord (a fifth above the root).

Capital Roman numerals followed by a + sign (V+<>/sup>, for example)

are used for augmented triads.

Lower-case Roman numerals followed by a º sign (iiº, viiº, etc.)

are used for diminished triads.

Lower-case Roman numerals (i, ii, iii, etc.)

are used for minor triads.

Following are the qualities and scale-degrees belonging to each seventh chord in every minor key, along with the corresponding Roman numeral reflecting those qualities:

i7: minor seventh - do, me, sol, te ii7: half-diminished seventh - re, fa, le, do III7: major seventh - me, sol, te, re iv7: minor seventh - fa, le, do, me V7: dominant seventh - sol, ti, re, fa VI7: major seventh - le, do, me, sol VII7: dominant seventh - te, re, fa, le vii°7: diminished seventh - ti, re, fa, le

Following are the qualities and scale-degrees belonging to each triad in every minor key:

i: minor - do, me, sol ii°: diminished - re, fa, le III: major - me, sol, te iv: minor - fa, le, do V: major - sol, ti, re VI: major - le, do, me VII: major - te, re, fa vii°: diminished - ti, re, fa

To build a triad on the staff,

identify the root, quality, and bass note from the lead-sheet symbol. The root and quality will tell you what three pitch classes belong to the triad. For example, C+ tells you the root is C, and the quality is augmented. Since the quality is augmented, there is a major third above the root (E) and an augmented fifth above the root (G-sharp). Since there is no bass note appended to the lead-sheet symbol, the bass note is the same as the root: C. Write a C on the staff (in any comfortable register), then write the other chord tones (E and G-sharp) above the C For Cm/E♭, the root is C, and the quality is minor. Since the quality is minor, there is a minor third above the root (E-flat) and a perfect fifth above the root (G). The slash identifies E-flat as the bass note. Write the E-flat on the staff. Then write a C and a G above it to complete the chord

When there are spaces between chord tones, the chord is in

open position

There are four types of contrapuntal motion between two musical lines.

parallel motion similar motion, also called direct motion contrary motion oblique motion Differentiating these four types of motion is essential to generating good voice-leading, both strict and free.

The following melodic intervals are consonant, and can be used in strict voice-leading both for successive pitches and as boundaries of stepwise progressions in a single direction:

- All perfect intervals (P4, P5, P8) - All diatonic steps (M2, m2) - Major and minor thirds - Major and minor sixths All other melodic intervals are dissonant, and must be avoided for successive pitches and as boundaries of stepwise progressions in a single direction, including: - All augmented and diminished intervals (including those that are enharmonically equivalent to consonant intervals, such as A2 and A1) - All sevenths

If a simple meter is notated such that each half note corresponds to a beat, the bottom number of the time signature is..

2

Chord

A chord is any combination of three or more pitch classes that sound simultaneously.

dyad

A dyad is a pair of pitches sounding together (in other words, a two-note chord). Since a dyad is defined by the interval between the two pitches, dyads are often simply called intervals.

the melodic minor scale.

A harmonic minor scale differs from a natural minor scale in that the seventh note is raised one semitone both ascending and descending. Melodic minor scales raise both the sixth and seventh notes one semitone when ascending, and descends like the natural minor scale.

Mnemonic device for remembering the order of Minor key sharps in the circle of fifths

Absolutely Everything But F***in Cheap God Dam Appetizers a e b f# c# g# d# a#

Mnemonic device for remembering the order of Minor key flats in the circle of fifths

All Dicks Get Chafed From Bouncing Extra Ass a d g c f bb eb ab

All other harmonic intervals are dissonant, and must be employed in very specific ways in strict voice-leading, including:

All diatonic steps (M2, m2) All augmented and diminished intervals (including those that are enharmonically equivalent to consonant intervals, such as A2 and A1) All sevenths Perfect fourths

The following harmonic intervals are perfect consonances, and must be used with care in limited circumstances in strict voice-leading:

All perfect intervals except the perfect fourth (P1, P5, P8)

Mnemonic device for remembering the order of flats.

Battle Ends And Down Goes Charles Father

Mnemonic device for remembering the order of major key sharps in the circle of fifths.

Charles Goes Down And Ends Battle For Child

To obtain an interval's quality, find both the generic interval and the chromatic interval. Then consult the following table to find the specific interval.

For example, C4-E4 is a generic third, and has a chromatic interval of i4. A third that encompasses four semitones is a major third (M3). Note that both generic interval and chromatic interval are necessary to find the specific interval, since there are multiple specific diatonic intervals for each generic interval and for each chromatic interval. Note that some generic intervals can be augmented, perfect, or diminished, and other intervals can be augmented, major, minor, or diminished. There is no generic interval that can be both major/minor and perfect; if it can be major or minor, it cannot be perfect, and if it can be perfect, it cannot be major or minor. An augmented version of an interval is always one semitone wider than major or perfect; diminished is always one semitone smaller than minor or perfect.

Consonance and dissonance

Intervals are categorized as consonant or dissonant based on their sound (how stable, sweet, or harsh they sound), how easy they are to sing, and how they best function in a passage (beginning, middle, end; between certain other intervals; etc.). Different standards apply to melody and harmony.

The following categories will be essential for your work in strict voice-leading, and they will be a helpful guide for free composition and arranging work, as well.

Melodic consonance and dissonance Harmonic consonance and dissonance

The following harmonic intervals are imperfect consonances, and can be used relatively freely in strict voice-leading (except for beginnings and endings):

Major and minor thirds Major and minor sixths

Rests

Rests represent silence in musical notation. For each durational symbol there exists a corresponding rest.

Scale degrees and solfège

Scale degrees are labeled with Arabic numerals and carets (^). The illustration below shows a D-major scale and corresponding ISO notation, scale degrees, and solfège syllables.

The second relationship held for all interval inversions.

Second, the two generic interval values add up to nine (a third plus a sixth, or 3 + 6). This is because the two intervals add up to an octave (8), and one of the notes is counted twice when you add them together. (Remember the counterintuitive way of counting off diatonic intervals, where the number includes the starting and ending pitches, and when combining inverted intervals, there is always one note that gets counted twice—in this case, E4.)

In simple meters, the bottom number of the time signature corresponds to the type of note corresponding to a...

Single Beat

the harmonic minor scale.

The A harmonic minor scale. Its seventh note is raised by a semitone. The notes of the harmonic minor scale are the same as the natural minor except that the seventh degree is raised by one semitone, making an augmented second between the sixth and seventh degrees.

The Chromatic Scale

The chromatic scale consists entirely of half steps, and uses every pitch on the keyboard within a single octave. Here is the chromatic scale that spans the pitches C4 through C5.

Compound intervals

The intervals discussed above, from unison to octave, are called simple intervals. Any interval larger than an octave is considered a compound interval. Take the interval C4 to E5. The generic interval is a tenth. However, it functions the same as C4 to E4 in almost all musical circumstances. Thus, the tenth C4-E5 is also called a compound third. A compound interval takes the same quality as the corresponding simple interval. If C4-E4 is a major third, then C4-E5 is a major tenth.

Melodic and harmonic intervals

The last distinction between interval types to note is melodic v. harmonic intervals. This distinction is simple. If the two pitches of a dyad sound at the same time (a two-note chord), the interval between them is a harmonic interval. If the two pitches in question are sounded back-to-back (as in a melody), the interval between them is a melodic interval. This distinction is important in voice-leading, where different intervals are preferred or forbidden in harmonic contexts than in melodic contexts. The difference is also important for listening, as hearing melodic and harmonic intervals of the same quality requires different techniques.

The natural minor scale

The natural minor scale consists of seven whole (W) and half (H) steps in the following succession: W-H-W-W-H-W-W. Note the changes in solfège syllables.

Chromatic intervals

The simplest way to measure intervals, particularly at the keyboard, is to count the number of half-steps, or semitones, between two pitches. To determine the chromatic interval between C4 and E4, for example, start at C4 and ascend the chromatic scale to E4, counting steps along the way: C#4, D4, D#4, E4. E4 is four semitones higher than C4. Chromatic intervals are notated with a lower-case i followed by an Arabic numeral for the number of semitones. C4-E4 is four semitones, or i4.

The minor scale

There are several scales that one might describe as minor, all of which have a characteristic third scale degree that is lower than the one found in the major scale. The minor scale most frequently used in tonal music from the Common Practice period is based on the aeolian mode, which is sometimes referred to as the natural minor scale. The natural minor scale consists of seven whole (W) and half (H) steps in the following succession: W-H-W-W-H-W-W.

If you sing through the natural minor scale, you'll notice that the ending lacks the same sense of closure you heard in the major scale. Why is that?

This closure is created in the major scale, in part, by the ascending semitone between ti and do. Composers often want to have this sense of closure when using the minor mode, too. They're able to achieve this by applying an accidental to the seventh scale degree, raising it by a semitone. If you do this within the context of the natural minor scale, you get something called the harmonic minor scale.

Borrowed divisions

Typically, a meter is defined by the presence of a consistent beat division: division by two in simple meter, and by three in compound meter. Occasionally, composers will use a triple division of the beat in a simple meter, or a duple division of the beat in a compound meter.

Diatonic intervals

When identifying a diatonic interval, begin with the letter names only. That is, treat C, C-sharp, and C-flat all as C for the time being. Next, count the number of steps (different letters) between the two pitches in question, including both pitches in your count. This gives you the generic interval. For example, from C4 to E4, counting both C and E, there are three diatonic steps (three letter names): C, D, E. Thus, the generic interval for C4-E4 is a third. The same is true for any C to any E: C#4 to E4, Cb4 to E#4, etc. They are all diatonic thirds.

Octave Designation

When specifying a particular pitch precisely, we also need to know the register. In fact, if all you have is C-sharp or B-flat, you do not have a pitch, you have a pitch-class. A pitch-class plus a register together designate a specific pitch. We will follow the International Standards Organization (ISO) system for register designations. In that system, middle C (the first ledger line above the bass staff or the first ledger line below the treble staff) is C4. An octave higher than middle C is C5, and an octave lower than middle C is C3. The tricky bit about this system is that the octave starts on C and ends on B.

When comparing the natural minor to the harmonic minor the last two notes of the scale sound much more conclusive, but you might have found it difficult to sing le to ti. How can this be corrected?

When writing melodies in a minor key, composers often "corrected" this by raising le by a semitone to become la when approaching the note ti. When the melody descended from do, the closure from ti to do isn't needed; likewise, it is no longer necessary to "correct" le, so the natural form of the minor scale is used again. Together, these different ascending and descending versions are called the melodic minor scale.

Scale degrees and solfège

While ISO notation allows us to label a pitch in its specific register, it is often useful to know where that pitch fits within a given scale. For example, the pitch class D is the first (and last) note of the D-major scale. The pitch class A is the fifth note of the D-major scale. When described in this way, we call the notes scale degrees, because they're placed in context of a specific scale. Solfège syllables, a centuries-old method of teaching pitch and sight singing, can also be used to represent scale degrees (when used in this way, this system is specifically called movable-do solfège).

Dyads formed by the same two pitch classes, but with different pitch classes on bottom and on top, are said to be...

inversions of each other, because the pitch classes are inverted. Likewise, the intervals marked off by those inverted dyads are said to be inversions of each other.

If the two pitches in question are sounded back-to-back (as in a melody), the interval between them is a...

melodic interval.