[Music Theory] chapter 06: intervals

summary how does a minor interval become major?

a minor interval made one chromatic half step larger becomes major.

doubly diminished

a minor or perfect interval that is made one whole step smaller (without changing letter names).

summary how do chromatic half steps affect intervals?

chromatic half steps don't change the letter name of either note.

key concept how do major intervals 3, 6, and 7 differ from their minor counterparts?

major intervals 3, 6, and 7 (built above the tonic of a major scale) are a half step larger than the corresponding minor intervals 3, 6, and 7 (built above the tonic in a minor scale). the interval between 1 and 2 is always a M2.

interval quality

major, minor, perfect, augmented, or diminished.

enharmonic equivalence

the idea that two or more possible names for a single pitch are musically and functionally the same.

unison

the interval size 1, or the distance from a pitch to itself; interval 0 if measured in semitones. sometimes abbreviated U.

doubly augmented

a major or perfect interval that is made one whole step larger (without changing letter names).

diminished interval

an interval one half step smaller than a minor or perfect interval.

perfect unison

an interval that does not span any half steps

perfect octave

an interval that spans 12 half steps

augmented fourth

an interval that spans 6 half steps

perfect fifth

an interval that spans 7 half steps

diminished seventh

an interval that spans 9 half steps

perfect fourth

an interval that spans five half steps

major third

an interval that spans four half steps

minor second

an interval that spans one half step

diminished fifth

an interval that spans six half steps

minor third

an interval that spans three half steps

major second

an interval that spans two half steps

key concept - if a major or perfect interval is made one chromatic half step larger, it becomes __________. - if a minor or perfect interval is made one chromatic half step smaller, it becomes __________. - if a diminished interval is inverted, it becomes __________.

- if a major or perfect interval is made one chromatic half step larger, it becomes augmented. - if a minor or perfect interval is made one chromatic half step smaller, it becomes diminished. - if a diminished interval is inverted, it becomes augmented (and vice versa).

review question name as many enharmonically equivalent intervals to C#-E as you can.

C#-Fb Db-E Db-Fb

summary how does a major interval become minor?

a major interval made one chromatic half step smaller becomes minor.

consonant

a relative term based on acoustic properties of sound and on the norms of compositional practice. a consonant harmonic interval - unison, third, fifth, sixth, or octave - is considered pleasing to hear.

dissonant

a relative term based on acoustic properties of sound and on the norms of compositional practice. a dissonant harmonic interval - second, fourth (in common-practice harmony, as in a 4-3 suspension), tritone, or seventh - is considered unpleasant or jarring to hear.

what is a "courtesy accidental"?

an accidental that is not necessary, but is placed to remind the performer to play the right note (often because it follows an accidental recently placed on the same pitch).

compound interval

an interval larger than an octave

tritone

an interval made up of three whole tones or six semitones: an augmented fourth or diminished fifth. by some definitions, only an augmented fourth is a tritone, since in this spelling the interval spans three whole steps.

simple interval

an interval of an octave or less

augmented interval

an interval one half step larger than a major or perfect interval.

another way what is another way to identify and spell sixths and sevenths?

another way to identify and spell sixths and sevenths is to compare them with the closest perfect interval: P5 or P8. sixths: start with a P5 and make it larger. M6 = P5 + M2 m6 = P5 + m2 sevenths: start with a P8 and make it smaller. M7 = P8 - m2 m7 = P8 - M2

what happens to perfect intervals when they are inverted? major intervals? minor intervals?

as example 6.8 shows, perfect intervals remain perfect when they are inverted. a major interval inverts to a minor interval - for example, a M3 inverts to a m6 (part b). a minor interval inverts to a major interval - for example, m2 inverts to a M7 (part c).

how do major seconds relate to minor seconds?

as seen in example 6.10, major seconds become minor seconds by lowering the top note (part c) or by raising the bottom note (part e).

how do minor thirds relate to major thirds?

as seen in example 6.10, minor thirds become major thirds by raising the top note (part d) or by lowering the bottom note (part f).

what is the relationship between the notes in an interval with matching accidentals?

as shown in example 6.10, an interval with matching accidentals (both sharps or both flats) has the same quality as the white-key intervals (parts a and b).

as shown in example 6.12: - to identify the interval D up to C, think about __________. - since C-D is a M2, D-C is a __________. - this process also works if __________. - follow part b and part c to see the procedure for sixths and fifths.

as shown in example 6.12: - to identify the interval D up to C, think about its inversion, C-D (part a). - since C-D is a M2, D-C is a m7. - this process also works if there are matching accidentals: since C#-D# is a major second, D#-C# is a minor seventh. - follow part b and part c to see the procedure for sixths and fifths.

review question which interval sizes are considered consonant? dissonant?

consonant intervals: unison, 3, 5, 6, 8 dissonant intervals: 2, 7, any augmented or diminished interval special case: P4 (usually treated as a consonance melodically and a dissonance harmonically)

summary what are the consonant intervals? what are the dissonant intervals? are there any special cases?

consonant intervals: unison, 3, 5, 6, 8 dissonant intervals: 2, 7, any augmented or diminished interval special case: P4 (usually treated as a consonance melodically and a dissonance harmonically)

true or false if you are writing an interval down, you should adjust the given note as necessary.

false if asked to write an interval up or down from a given note, never change the given note; make the adjustment for quality on the other note.

true or false labelling compound intervals exactly is only an ornamental skill; labelling intervals with their simple equivalent is always more useful and generally preferred.

false often, you will want to label an interval without regard for the "extra" octaves between pitches - writing 3 instead of 10, or 5 instead of 12. however, there are times when it is important to label the span of an interval exactly.

true or false when you write harmonic intervals, the note heads should be staggered to ensure that they are easier to read.

false when you write harmonic intervals (part b), align the two note heads with one directly above the other; for unisons and seconds, though, you must write the note heads side by side with the lower notes on the left, unless each note gets a separate stem (part c).

summary for a diminished 2, 3, 6, or 7, start with __________ and add an accidental to make it __________.

for a diminished 2, 3, 6, or 7, start with minor 2, 3, 6, or 7 and add an accidental to make it one chromatic half step smaller.

summary for a diminished 4, 5, or 8, start with __________ and add an accidental to make it __________.

for a diminished 4, 5, or 8, start with perfect 4, 5, or 8 and add an accidental to make it one chromatic half step smaller.

summary for an augmented 2, 3, 6, or 7, start with __________ and add an accidental to make it __________.

for an augmented 2, 3, 6, or 7, start with major 2, 3, 6, or 7 and add an accidental to make it one chromatic half step larger.

summary for an augmented U, 4, 5, or 8, start with __________ and add an accidental to make it __________.

for an augmented U, 4, 5, or 8, start with perfect U, 4, 5, or 8 and add an accidental to make it one chromatic half step larger.

key concept an interval measures the musical space between two pitches. what two ways are intervals identified?

intervals are identified by their size (typically a number between 1 and 8) and quality (such as major or minor).

summary intervals are labelled by their size and quality. 1. size measures __________. 2. intervals 2, 3, 6, and 7 may be __________, but not __________. 3. intervals U, 4, 5, and 8 may be __________, but not __________.

intervals are labelled by their size and quality. 1. size measures the number of letter names spanned: U, 2, 3, 4, 5, 6, 7, 8. 2. intervals 2, 3, 6, and 7 may be major or minor, but not perfect. (e.g., m2, M3, and m6) 3. intervals U, 4, 5, and 8 may be perfect, but not major or minor (PU, P4, P5, and P8)

summary intervals may be 1. 2. 3. 4.

intervals may be

enharmonically related interval

intervals that span the same number of half steps but have different names.

did you know? who is often credited for characterising "perfect intervals"?

many writers from the Middle Ages and Renaissance attribute the characterisation of "perfect intervals" to the famous Greek mathematician Pythagoras, who was said to have discovered mathematical ratios by listening to smiths striking anvils with hammers in a blacksmith's shop and making observations about the sounds it produced.

key concept how are melodic intervals formed? how are harmonic intervals formed?

melodic intervals are formed between to successive pitches in a melodic line. harmonic intervals are formed between two pitches sounding at the same time.

review question what is the different between a major and a minor interval of the same size (for example, M6 and m6)?

one half step.

summary what is special about perfect intervals?

perfect intervals can't be made major or minor.

key concept can the intervals of unison, octave, fourth, and fifth be major or minor?

perfect intervals, which share identical pitches in parallel major and minor keys, are never major or minor. memorise these labels: PU, P4, P5, P8.

what is one method for identifying and spelling intervals?

some musicians find it easiest to memorise the size (major or minor) of the white-key intervals on a keyboard, beginning with seconds, thirds, and fourths (example 6.9).

review question what is the interval called that is one chromatic half step smaller than a minor interval? one chromatic half step larger than a major interval?

the interval that is one chromatic half step smaller than a minor interval is diminished. the interval that is one chromatic half step larger than a major interval is augmented.

review question what is the interval called that is one chromatic half step smaller than a perfect interval? one chromatic half step larger than a perfect interval?

the interval that is one chromatic half step smaller than a perfect interval is diminished. the interval that is one chromatic half step larger than a perfect interval is augmented.

review question what information is missing when only an interval's size is given?

the interval's quality.

look at example 6.7 to compare the intervals between the F major scale and its parallel minor, F minor. what intervals change?

the intervals between 1 and 3, 1 and 6, and 1 and 7 change. in the major scale (part a), these form a major third (M3), major sixth (M6), and major seventh (M7), respectively. in the minor scale (part b), they are a minor third (m3), minor sixth (m6), and minor seventh (m7).

imperfect consonance

the intervals of a third and sixth.

perfect consonance

the intervals of a unison, fourth, fifth, and octave. the harmonic interval of a fourth is treated as a dissonance in common-practice style.

interval

the musical space between two pitches or pitch classes.

inversion

the musical space between two pitches or pitch classes.

interval size

the number of steps an interval contains.

what is one method you can use to identify larger intervals?

the smaller intervals (2, 3, and 4) can help you identify and spell their inversions (7, 6, and 5).

melodic interval

the span between two notes played one after another.

harmonic interval

the span between two pitches played simultaneously.

key concept learn these visual landmarks to identify interval sizes quickly. thirds, fifths, and sevenths always have __________. - for thirds, the lines or spaces are __________. - for fifths, skip __________. - for sevenths, skip __________. seconds, fourths, sixths, and octaves always have __________.

thirds, fifths, and sevenths always have both pitches on lines or both on spaces. - for thirds, the lines or spaces are adjacent. - for fifths, skip one line or space. - for sevenths, skip two spaces or lines. seconds, fourths, sixths, and octaves always have one pitch on a line and one on a space.

what is the procedure for naming compound intervals?

to name compound intervals, add 7 to the simple interval, as in example 6.3. for example, a second plus an octave equals a ninth, and a fourth plus an octave equals an eleventh. add 7 rather than 8, because we number the unison as 1 rather than 0.

how can you write an interval?

to write an interval (example 6.11): - write the note heads for the correct interval size on the staff without accidentals (part a) or with matching accidentals (part b). - if the quality of the interval is not correct, adjust by adding a flat, sharp, or natural to raise or lower the upper note. - either note of the interval can be adjusted (part c).

true or false the intervals 4, 5, 8, and unison have long been considered special/more pure intervals.

true from the time of the earliest writings about music, around the fifth century BCE, these intervals (4, 5, 8, and unison) were considered the purest, hence the term "perfect."

inversionally related intervals (tonal)

two intervals that, when combined, span an octave (e.g., E3-G#3, a major third; plus G#3-E4, a minor sixth). when inverted, major intervals become minor (and vice versa), diminished become augmented (and vice versa), and perfect stay perfect. the interval numbers of inversionally related intervals sum to 9 (third and sixth, second and seventh, etc.).

when naming compound intervals, why is it important to add 7 instead of 8?

we add 7 rather than 8 because we number the unison as 1 rather than 0.

key concept when intervals are inverted, - perfect intervals __________. - major intervals __________. - minor intervals __________. - the two interval sizes always __________.

when intervals are inverted, - perfect intervals remain perfect. - major intervals invert to minor. - minor intervals invert to major. - the two interval sizes always sum to 9 (e.g., 1 inverts to 8, 3 inverts to 6, 4 inverts to 5).

key concept which letter names should you count when naming intervals?

when naming intervals, always count the first and last letter names. for example, from A up to D is a fourth (A-B-C-D); any A up to any D is some kind of fourth, no matter what the accidental. similarly, from A down to D is a fifth (A-G-F-E-D).

key concept how are two intervals different when they share the same size but not the same number of half steps?

when two intervals share the same interval size but not the same number of half steps, they differ in quality. to find the quality of small intervals, count half steps: minor intervals are a half step smaller than major intervals.

what is one basic way to spell intervals, despite it being slow?

you can also spell intervals by counting the scale steps from the first pitch to the second, then counting the half steps (semitones) between them, as shown in figure 6.1.

the F major scale and its parallel minor, F minor, are given in example 6.6. which scale degrees are exactly the same in the two scales?

you'll see that scale degrees 1, 4, 5, and 8 in the two scales are exactly the same. the interval from 1 to 4 is a perfect fourth (abbreviated P4), from 1 to 5 is a perfect fifth (P5), and from 1 to 8 is a perfect octave (P8). the interval from 1 to itself is a perfect unison (PU).