Music-Intervals

minor second

1 semitone m

minor seventh

A minor seventh is a seventh that contains 10 semitones.

minor sixth

A minor sixth is a sixth that contains 8 semitones

Calculating interval size

By counting every letter name in the interval, including both the bottom and top pitches. By counting every line and space on the staff from the bottom note to the top note of the interval. By looking at the interval on the staff and determining its size based on its visual pattern of lines and spaces.

Things to Remember about Perfect

Avoid the common mistake of simply associating sharps with augmented intervals and flats with diminished intervals. the numeric interval size does not change perfect intervals can never be altered to become major or minor There are only three "states" for perfect intervals: diminished, perfect, and augmented.

enharmonic intervals

Because of these additional possibilities, some intervals with the same number of semitones may have different names

The White Key Method when an accidental is only added to one note

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

Count each letter name (or line/space) only once. Count from bottom to top. Always include the first and last letter names (or lines/spaces) of the interval.

Spelling an interval

Counting semitones is one way to spell an interval or to determine its quality

Odd Numbered Intervals

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

Spelling Compound Intervals

Reduce the compound interval to a simple interval Spell the simple interval Add the octave(s) back in to create the compound interval

Accidentals and Interval Size

accidentals do not affect interval size Accidentals do affect interval quality

Any interval combined with its inversion creates

an ocatave

Simple Interval are

an octave or smaller

Using Inversion to Spell and Identify Larger Intervals

Spell the smaller inversion Invert the result

Interval Size

The size of an interval tells us the number of steps that the interval contains. represent this size by a number (1, 2, 3, 4, etc.) or by a label (unison, second, third, fourth, etc.)

Inversion Patterns

The sum of the sizes of an interval and its inversion always equals 9 Unisons invert into octaves (1 + 8 = 9) Seconds invert into sevenths (2 + 7 = 9) Thirds invert into sixths (3 + 6 = 9) Fourths invert into fifths (4 + 5 = 9) Fifths invert into fourths (5 + 4 = 9) Sixths invert into thirds (6 + 3 = 9) Sevenths invert into seconds (7 + 2 = 9) Octaves invert into unisons (8 + 1 = 9)

The Major Scale Method

Think of the bottom note of the interval as scale degree 1 or the tonic of a major key. Ask yourself the question: Is the top note in the major scale of this key? If the answer is yes, then the interval is either a major interval or a perfect interval (as stated by the rule). If the answer is no, then you will need to determine how it has been altered from major or perfect.

Perfect Intervals

derive their name from the relatively stable and pure quality of their sound is label goes back to the Middle Ages and the Renaissance, when these types of intervals were often used to create points of rest and stability in the music. Only unisons, fourths, fifths, and octaves can be called perfect. The other interval sizes (seconds, thirds, sixths, and sevenths) can never be perfect.

Interval Quality

describes the character or color of an interval

consonance

intervals are pure, relaxed, and stable; they do not sound like they need to resolve. These include most of the perfect intervals (unisons, fifths, and octaves) and all major and minor thirds and sixths

Compound Intervals

intervals that are larger than an octave

minor third

is a third that contains 3 semitones

major third

is a third that contains 4 semitones. (major and minor thirds are building blocks of triads and harmony)

a minor interval increased by a semitone is

major

major sixth

major sixth is a sixth that contains 9 semitones.

two pitches are played consecutively (one after the other)

melodic interval which can occur in an ascending or a descending direction

a major interval decreased by a semitone is

minor

Intervals in the Major Scale

When you calculate all of the types of intervals that occur above the tonic of a major scale, you will see that all of the intervals are either major or perfect. 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.

major

You may have noticed that the minor sixth sounds "sadder" or "darker"

compound intervals are

ntervals that are larger than an octave (ninths, tenths, elevenths, and so on)

minor

tends to sound "brighter" and more "cheerful."

How is the quality of intervals determined?

the quality of an interval is determined by the number of half-steps (or semitones) that it contains. Intervals with the same numeric size may have different qualities, depending on the number of semitones they contain.

harmonic Interval

two pitches are played simultaneously

major second

2 semitones M

major seventh

A major seventh is a seventh that contains 11 semitones.

Simple Interval Size

By size: 1, 2, 3, 4, 5, 6, 7, 8 By label: unison, second, third, fourth, fifth, sixth, seventh, octave

Compound Interval Rule 2 (Quality)

Compound intervals have the same quality as their corresponding simple intervals

Even Numbered Intervals

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

Applying the white key method

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 also that 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.

Example Spelling

For example, if you were asked to spell a perfect eleventh above middle C, you would first reduce it to a simple interval. This gives you a perfect fourth, since 11-7=4 and since the quality of the simple interval will be the same as the compound one. Next, you would spell a perfect fourth above C4, which gives you an F4. Lastly, you would move this F up an octave to F5 to create a perfect eleventh. Click "Show Me" in the example below to see this process illustrated.

The White Key Method for non accidentals and when same accidentals is added to both notes

If we keep in mind this "B-F exception," we can conclude that all other white-key fourths and fifths are perfect. Well, if the same accidental is added to both pitches, then the quality of the interval would remain the same, since the distance between the pitches has not changed; the interval is only shifted higher or lower. 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.

major and minor

Only seconds, thirds, sixths, and sevenths can be major or minor Major/minor intervals can never become perfect

When you invert intervals, the qualities change consistently:

Perfect always inverts to perfect (Ex: P5 to P4) Major always inverts to minor (Ex: M3 to m6) Minor always inverts to major (Ex: m2 to M7) Augmented always inverts to diminished (Ex: A4 to d5) Diminished always inverts to augmented (Ex: d7 to A2)

Complete interval name

Quality + Size

the white key interval seconds

The example below provides all of the possible seconds using only the white keys on the piano. Here we see that there are only two seconds that are naturally minor: the minor seconds above E and above B. These are the two locations on the piano where there are no intervening black keys. All other seconds are naturally major. Although it is not difficult to count the number of semitones in seconds, just remembering the location of these two half-steps will make identifying and spelling seconds easier.

sevenths

The example below provides all of the possible sevenths using only the white keys on the piano. Here we see that there are only two sevenths that are naturally major: the major sevenths above C and above F. All other sevenths are naturally minor. Another way to think of this is to ask yourself "How close is this seventh to a perfect octave?" The sevenths above C and F are only one half-step smaller than a perfect octave, making them major. The minor sevenths are a whole-step smaller than a perfect octave.

sixths

The example below provides all of the possible sixths using only the white keys on the piano. Here we see that three of the sixths (those formed over E, A, and B) are naturally minor and the rest are naturally major. In other words, sixths over E, A, and B are naturally minor.

The white key intervals thirds

The example below provides all of the possible thirds using only the white keys on the piano. Here we see that three of the thirds (those formed over C, F, and G) are naturally major and the rest are naturally minor. This is an important observation that we will use later when we learn about triads: thirds over C, F, and G are naturally major.

Tritone

The name tritone comes from the fact that the interval contains three whole tones (2 + 2 + 2 = 6 semitones) Both the augmented fourth and the diminished fifth can be called tritones, which is sometimes abbreviated Tt. The tritone occurs natually between the white keys of B and F (or F and B). You cannot see this clearly on the staff, but you can verify that it is true by counting the half steps on a keyboard. Either a B♭ or an F# (not both) must be used to alter this natural tritone so that it is perfect, as illustrated below. the tritone is highly dissonant and unstable, leading early musicians to call it the diabolus in musica or "the devil in music."

Spelling Major/Minor Intervals

The white-key approach will also work for spelling major/minor intervals, if we restate the two steps as follows: 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.

Compound Interval Rule 1 (Numeric Size)

To determine the numeric size of a compound interval, add 7 for each octave larger than the simple interval second ⇒ compound ninth 2 + 7 = 9 third ⇒ compound tenth 3 + 7 = 10 fourth ⇒ compound eleventh 4 + 7 = 11

Invert

To invert an interval means to reverse the order of the two pitches in the interval. When inverting an interval, the note on the bottom becomes the note on top, and vice versa. To invert, you can move the top note below the bottom note or you can move the bottom note above the top note The most important thing to remember when inverting intervals is that the letter names of the two pitches involved do not change, , although their order will be switched.

augmented and diminished major scale

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)

augmented

When a perfect interval is enlarged by a half-step, it becomes augmented (smaller) dim — P — aug (larger)

diminished

When a perfect interval is reduced by a half-step, it becomes diminished (smaller) dim — P — aug (larger)

Perfect Octave

When they play the same pitch an octave apart, we can similarly say that they are performing a perfect octave. 12 semitones in a perfect octave.

Perfect Unison

When two musicians play or sing the very same pitch (in tune), we say that they are in perfect unison. Note that there are always 0 semitones in a perfect unison

Perfect fourth

a fourth that contains 5 semitones.

Perfect Four

he perfect fourth can be either consonant or dissonant, depending on the context. Since it is a perfect interval, its sound is not particularly dissonant. But in some contexts, it sounds like it should resolve to a third, making it less consonant than the third it resolves to

Interval Qualities and Abbreviation

perfect P major M minor m augmented A, aug, or + diminished d, dim, or little o

Perfect fifth

perfect fifth is a fifth that contains 7 semitones. Note that both of the pitches in each of these intervals use the same accidental (or have no accidental). This is almost always the case with perfect fourths and fifths (with one exception to be discussed later). You can also determine whether fourths and fifths are perfect by counting the number of semitones between the two pitches on a piano keyboard.

dissonance

sound harsh, unrelaxed, and unstable; they sound like they need to resolve to a more consonant, stable interval. Composers use dissonant intervals to propel the music forward to a more consonant resolution. These include the major and minor seconds and sevenths as well as all augmented and diminished intervals.

Interval

the distance between two pitches