Music Theory; Chapters 18 & 19

In a Major Scale

the interval must be either Major (M) or Perfect (P)

Perfect to diminished

One half step down (reduced by one)

Diminished

One half step less than minor (from Major)

P15

A two octave (compound) interval

You do

*not* invert compound intervals - you only reduce them

Chapter Summary (19)

1. A *minor interval* is one half step smaller than a major interval. 2. A *diminished interval* is one half step smaller than a minor or perfect interval. 3. An *augmented interval* is one half step larger than a major or perfect interval. 4. Any type of interval (M, m, P, dim., or aug.) is a modification by one half step of some other type of interval. By using knowledge of major and perfect intervals and modification, we can calculate any type of interval. 5. Intervals above notes that cannot be tonics of major scales can be lowered or raised to simplify the notation or the spelling. When the interval becomes apparent, return the analysis to the original notation. 6. Although intervals may be enharmonic, each must be spelled according to its own designation. C up to A-flat is a m6, and C up to G# is an aug.5. Although enharmonic, one interval cannot be fiver the name of the other. 7. When an interval is rewritten so that the original bottom note becomes the upper, or vise versa, the interval is said to be *inverted*. The constants of interval inversion are shown below. Original Interval - Inversion: P - P M - m m - M dim. - aug. aug. - dim. 1 - 8 2 - 7 3 - 6 4 - 5 5 - 4 6 - 3 7 - 2 8 - 1

Chapter Summary (18)

1. An interval is the difference between two pitches. 2. A *harmonic interval* is the sounding of two pitches simultaneously; a *melodic interval* is the sounding of two pitches consecutively. 3. An interval is named by *quality* and *quantity. Major, perfect, diminished, and augmented* are terms of quality; quantity is determined by the *number* of staff degrees spanned by the interval. 4. Major and perfect intervals occur between tonic and other degrees of the major scale. 5. Because scales are constructed on consecutive staff degrees and intervals are named by number of staff degrees spanned, the scale-step numbers and the quantity number of an interval are the same. 6. *Major* modifies numbers 2, 3, 6, and 7; *perfect* modifies 4, 5, and 8 (and 1). 7. The intervals from tonic up to each of the major scale tones are M2, M3, P4, P5, M6, M7, and P8. 8. In analyzing an interval, assume the *lower note* to be 1^ (tonic) and could the scale degrees to the upper note. 9. *Simple* intervals encompass a perfect octave or less; larger intervals are called *compound* intervals, meaning an octave plus a simple interval. In musical analysis, compound intervals are frequently reduced to simple terminology.

Analyzing an Interval

1. find the quantity (size) 2. ask yourself, 'is the lower note the tonic of a major scale?' [(circle of fifths) tonic=lower note] 3. ask yourself, 'does the upper note belong in the scale?' a. yes=M or P b. no--ask yourself, 'how much has it been altered from M or P

Analyzing an Interval (if the tonic note is the not the tonic of a major scale)

1. find the quantity (size) 2. change the bottom note to the accidental closest that will make it the tonic of a Major scale 3. figure out if adding the accidental back makes the interval bigger or smaller: if it makes it one half step bigger then it is Augmented (from Major or Perfect) - if it makes it one half step smaller it is minor (from Major) - if it makes it one half step smaller it is diminished (from Perfect) - if it makes it two half steps smaller it is diminished (from Major)

Analyzing an Interval (if the tonic note is the tonic of a major scale)

1. find the quantity (size) of the interval 2. ask yourself, 'is the lowest note the tonic pitch of a major scale?' 3. once you have found the tonic pitch, ask yourself, 'does the second pitch of the interval belong in that scale?' 4. figure out if the second pitch (the higher pitch) was altered from the original major scale and how much it was altered ^this process is the same for both ascending, and descending intervals if it was altered to be one half step higher from Major or Perfect then it is Augmented if it was altered to be one half step lower from Major then it is minor if it was altered to be one half step lower from Perfect then it is diminished if it was altered to be two half steps lower from Major then it is diminished

Reducing Intervals

1. lower the upper note/pitch *or* 2. raise the lower note/pitch (do not change quantity)

Augmenting an Interval

1. raise the upper pitch 2. lower the lower pitch

Major Intervals

2nd 3rd 6th 7th

Ordinal Numbers

Put numbers in order

Compound Interval

Bigger than an octave

Cardinal Numbers

Count things

Raising a Pitch with an Accidental

Double Flat - Flat Flat - Natural Natural - Sharp Sharp - Double Sharp

Lowering a Pitch with an Accidental

Double Sharp - Sharp Sharp - Natural Natural - Flat Flat - Double Flat

Five Quality Words

Major - M minor - m Augmented - A diminished - d Perfect - P

Reduced by One Half Step

Major to minor

Intervals flip from

Major to minor minor to Major diminished to Augmented Augmented to diminished *or* Perfect to Perfect

Descending

Modification of Intervals - lower the upper pitch

Ascending

Modification of Intervals - raise the lower pitch

Simple Interval

Octave or less

Quantity

Size Count all the lines/spaces/letter names that the interval encompases

Melodic Interval

Sound at different times (how it is presented; at different times)

Harmonic Interval

Sounding at the same time (how it is presented; at the same time)

Interval

The distance between two pitches measured by its place on the staff example: whole step, half step, octave, fifths

Invert

Turn upside down - flip to the opposite

Major to diminished

Two half steps down (reduced by one)

Quality

Type Distinguishes its special characteristic

Prime

Unisen

Quantity (numbers)

Unisen 2nd 3rd 4th 5th 6th 7th Octave

Perfect Intervals

Unisen 4th 5th Octave

Choral Music

Written for a group of people

Inverted Intervals ALWAYS

add up to nine

Every interval can

be Augmented

Every interval

can be diminished

Perfect

can never be Major or minor

Major

can never be Perfect

The Number of Half Steps and Whole Steps

change the characteristic (quantity) of an interval

Perfect Intervals Can Become

diminished - if the interval is reduced by two half steps (one note is lowered two half steps) Augmented - if the interval is increased by one half step (one note is raised one half step)

To Find the Compound Interval

either lower the top note or raise the lower note (reduce the interval by an octave) then add seven to the quantity of the reduced interval (ALWAYS add seven) the quality stays the same

You cannot

go from Perfect to minor - it goes directly to diminished

Major Intervals Can Become

minor - if the interval is reduced one half step (one note is lowered one half step) diminished - if the interval is reduced by two half steps (one note is lowered two half steps) Augmented - if the interval is increased by one half step (one note is raised one half step)

Major Interval

minus one half step equals minor

To invert

move the lower note up an octave *or* move the upper note down an octave

Perfect has

no opposite

Perfect plus

one half step equals Augmented

Perfect reduced by

one half step goes *directly* to diminished

Only invert

simple intervals

When finding the quantity...

start from the bottom note (the first pitch)

Count

the lines and spaces or the letter names to find an interval

Major or Perfect

to Augmented - add one half step (make the interval bigger)

It does not matter

which note is moved to find an interval either the top note is moved down an octave or the bottom note is moved up an octave

ALWAYS Start

with the lower note

You create an Interval when

you move *one* of the two pitches an octave