More on Intervals

More on Intervals

Chapter 6

Enharmonically Equivalent Intervals

Enharmonic intervals are the same number of half steps apart, or the same distance, but have different names. They will always sound the same to the human ear. F to Ab is a m3, while F to G# is an A2.  Despite being written differently on the staff, both sound the same.

"The Musician's Guide to Theory and Analysis" (Clendinning and Marvin)

“…any interval can be spelled in several ways, all of them enharmonic.  (Think of enharmonic intervals as similar to homonyms in language:  ‘here’ and ‘hear’ sound the same but have completely different meanings in a sentence.)  The correct spelling is important: it reveals how the interval functions in the music” (page 130)

Multiple Choice

What interval is enharmonically equivalent to a A5?

• m6

• M6

• PU

• d5

Multiple Choice

What interval is enharmonically equivalent to a d7?

• m6

• M6

• A5

• A6

Multiple Choice

What interval is enharmonically equivalent to a P4?

• A4

• P5

• A3

• d5

Special Cases for Augmented and Diminished

As we know, if perfect intervals are raised or lowered by a half step, we consider them to be augmented or diminished. However, if perfect intervals are raised or lowered by a whole step, we consider them to be doubly augmented or doubly diminished.

Enharmonic Intervals

Each interval can be rewritten so that it looks different on the staff but sounds the same when played or sung. What are all of the ways we can write the notes C to E?

​

1) as is (M3)

2) C to Fb (doubly diminished 4th)

3) C to Dx (doubly augmented 2nd)

​​

Remember, although these look different on the staff, they would sound the same when played or sung.

Fill in the Blank

What is a doubly augmented 4th above C?

Fill in the Blank

What is a doubly diminished 5th above G?

Fill in the Blank

What is a doubly augmented 5th above Db?

Tritones

A diminished fifth or augmented fourth is known as a tritone. Augmented fifths and diminished fourths sound the same even though they are spelled differently.​

​

The difference between the two intervals is how they resolve. An augmented fourth typically resolves outward to a sixth. A diminished fifth typically resolves inward to a third.​

​

The tritone is so harsh sounding, it was known as the "devil in music" during the Middle Ages.

Fill in the Blank

An A4 and a d5 are also known as...

Consonant and Dissonant Intervals

Western music is built on the idea of tension and release, and intervals can be divided into two groups based on this idea. Consonant intervals sound pleasing to the ear and are considered tonally stable. Dissonant intervals sound harsher to the ear and are in search of stability.​

​

How we interpret intervals (i.e. consonant vs. dissonant) depends on what historical period we are in as well as our own musical template.

Consonant Intervals

That being said, perfect consonances typically include the unison, fifth, and octave.​

​

Imperfect consonances typically include the third and sixth.​

​

Dissonances typically include the second, seventh, and augmented/diminished intervals.

Multiple Choice

A P5 is a(n) ______ interval.

• perfect consonance

• imperfect consonance

• dissonance

Multiple Choice

A M3 is a(n) ______ interval.

• perfect consonance

• imperfect consonance

• dissonance

Multiple Choice

A m6 is a(n) ______ interval.

• perfect consonance

• imperfect consonance

• dissonance

Multiple Choice

A M2 is a(n) ______ interval.

• perfect consonance

• imperfect consonance

• dissonance

Multiple Choice

A d5 is a(n) ______ interval.

• perfect consonance

• imperfect consonance

• dissonance

But what about the fourth?

The interval of a perfect fourth is both consonant and dissonant. If it is used harmonically, it is considered dissonant. If it is used melodically, it is considered consonant.​

​

We will talk more about this when we discuss the rules and history of counterpoint.

Multiple Choice

The pictured interval is considered...

• consonant

• dissonant

Multiple Choice

The pictured interval is considered...

• consonant

• dissonant