Simply put, an interval is the distance between two notes. We have already been dealing with intervals in a limited way when we built the scales in the previous weeks. We have used intervals of one, two or three half steps to create the scales and thus we have been using three different sized intervals between adjacent notes of the scales.
We use the half step as the smallest unit in our measuring system of musical intervals much the same way that inches or centimeters might be used to measure the length or width of an object. Although an interval is measured in half steps, the name we assign to an interval is related to the context of the notation of the two notes on the staff.
One of the elements we use to name an interval is the line/space distance between the notes on the staff. This distance in line/space positions between two notes is known as the INTERVAL NUMBER. Notes that are on adjacent line/space positions on the staff are said to be a 'second' apart regardless of the amount of half steps between the notes. The notes E and F are a second apart as are the notes F and G. Here are some more seconds, C-D, G-Ab and Db-E. When you measure the intervals in half steps, you will find that some of the seconds are one half step whereas others are two half steps while some are three half steps. Yes, there are different types of seconds each of a different size. This is true of all interval numbers. The interval number alone does not provide all of the information to completely identify an interval. As an analogy, the interval number can be thought of as organizing intervals into catagories or families just as my last name (Sult) identifies my family but doesn't specify which Sult. I have two brothers and two sisters, if you want to distinguish between us, more information is needed such as a first name. When identifying intervals, the 'first name' is called the INTERVAL PREFIX. We use the terms MAJOR, MINOR, AUGMENTED and DIMINISHED for interval prefixes and their meaning will be explained in this lecture. The interval prefix is sometimes referred to as the 'quality' of an interval.
Before dealing with the interval prefix, be sure you are confident in your understanding of the interval number. The interval number is most relevant when looking at music notation. The most obvious characteristic of interval numbers is that odd numbered intervals (unisons, 3rds, 5ths, 7ths) are on similar staff positions, either both notes are on a line or both notes on a space.
Conversely, even numbered intervals (2nds, 4ths, 6ths, octaves) are on different staff positions, if one note is on a line the other is on a space. This is the first step to naming intervals in music notation.
The measuring of half steps is irrelevant at this point and is used only to specify the interval prefix (discussed later).
We return to the major scale for our initial study of intervals. When measuring from the first note (tonic) of the scale, one can create an interval for each scale degree. The interval number of the distance from the first scale degree to the second is a SECOND. The interval number from the tonic to the third scale degree is a THIRD, from the tonic to the fourth scale degree is a FOURTH and so on.
We use the term PERFECT as the interval prefix for four of the intervals measured from the first note of the major scale. If the first note of the scale is used twice (such as two vocalists singing the same note) we call that interval a PERFECT UNISON. There are zero half steps in a PERFECT UNISON. The interval from the first note of the major scale to the fourth note is called a PERFECT FOURTH. There are five half steps in a PERFECT FOURTH. A PERFECT FIFTH is the name of the interval from the first note to the fifth note of the major scale. There are seven half steps in a PERFECT FIFTH. The interval from the first note of the scale to the eighth note (which is the same letter name as the first) is called a PERFECT OCTAVE. There are twelve half steps in a PERFECT OCTAVE.
THE INTERVALS OF 2nds, 3rds, 6ths and 7ths ARE NEVER CALLED PERFECT.
The remaining intervals, measured from the first note of the scale, are called MAJOR intervals The interval from the first note to the second note is called a MAJOR SECOND. There are two half steps in a MAJOR SECOND. The interval from the first note to the third note is called a MAJOR THIRD. There are four half steps in a MAJOR THIRD. From the first note to the sixth note is a MAJOR SIXTH. There are nine half steps in a MAJOR SIXTH. And finally, the first note to the seventh note is a MAJOR SEVENTH. There are eleven half steps in a MAJOR SEVENTH.
THE INTERVALS OF unisons, 4ths, 5ths and octaves ARE NEVER CALLED MAJOR.
It is important to clearly understand that all of these intervals are from the FIRST NOTE of a major scale to the other scale degrees. When starting from other scale degrees you can create additional intervals that might be of a different quality.
As mentioned previously, there are several types of each interval number. Any perfect interval made larger by one half step becomes AUGMENTED.
Any perfect interval made smaller by one half step becomes DIMINISHED.
When these additional prefixes are included the possibility for enharmonic intervals occurs. Enharmonic intervals are two intervals that have the same number of half steps yet have a different name. A common example is the interval of six half steps which is sometimes called a Diminished Fifth and other times called an Augmented Fourth. This particular interval is known by another name also: the Tritone. The term Tritone refers to the fact that this interval spans 3 whole steps (6 half steps).
    
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| Augmented 4th | Diminished 5th |
To complete the prefix names we must add the term MINOR and expand the use of the terms AUGMENTED and DIMINISHED. Any major interval made smaller by one half step becomes MINOR.
Any major interval made larger by one half step becomes AUGMENTED. This occurs most often in music with Augmented 2nds and Augmented 6ths.
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| Major 2nd | Augmented 2nd | Major 6th | Augmented 6th |
Any minor interval made smaller by one half step becomes DIMINISHED. The most common occurrence in music is the Diminished 7th
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| Minor 7th | Diminished 7th |
A diminished 7th interval can be created in every harmonic minor scale, which harmonic minor scale is this diminished 7th interval from? If you said "D harmonic minor" you are correct and get an A for the day. If you said "How would I know", give it some thought, hmmm, both a C# and a Bb. Go back and look at D harmonic minor.
Here is a table that lists the interval name and the amount of half steps in that interval. The following appreviations are used:
| Num. of half steps | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| Interval Names | P1 | Mi2 | Ma2 | Mi3 | Ma3 | P4 | A4 | P5 | Mi6 | Ma6 | Mi7 | Ma7 | P8 |
| Enharmonic Names | D2* | A1 | D3 | A2 | D4 | A3* | D5 | D6* | A5 | D7 | A6 | D8 | A7* |
* the written intervals marked with the "*" are extremely rare. Composer who use notation that contain these intervals usually end up in a mental institution.
I'm serious.
The following eartraining routine is quite difficult to sing. It contains all of the intervals, ascending and descending, within one octave. The tone center is G and the overall range is two octaves. Try singing along with this exercise. It's a challenge.
Just for a little variety the exercise is written in 7/4. The basic structure is a three note group consisting of 1) the tone center (G), 2) the next note to create the interval then 3) back to the tone center. Each note is a half note with a chance for a quick breath at the end of each measure (tempo of the file is quarter note = 120, but on the internet tempo is kind of 'iffy'). By the way, it would be appropriate to call the tone center the 'tonic' of this exercise. The order of intervals is as follows:
The reason I have included the d5 (instead of the a5) along with the p5 is that the d5 sound is very common and I wanted to relate that sound to both the p4 and p5. You did know that an a4 sounds the same as a d5 didn't you? Good. Do you remember the name we use for two different named intervals that have the same sound? Yes, enharmonic is used again this time as in "an augmented 4th and a diminished fifth are enharmonic equivalents" or if you are in a hurry just say "they're enharmonics", we musicians know what that means.
Although this exercise uses all of the intervals, ascending and descending, within an octave, the notation does not have all of the possible ways of writing those sounds. Many of the intervals could be written as enharmonics. For instance, the interval of an augmented 2nd is not written. An augmented 2nd has the same amount of half steps as a minor third. The augmented second, although not common, is not a rare interval either as it occurs in every harmonic minor scale. I've decided to limit the enharmonic combinations in the notation to only one: augmented 4th / diminished 5th.
Here is a partial list of enharmonic intervals, they have the same amount of half steps but often their context makes them sound different. strange.
The augmented 2nd and minor 3rd are enharmonics.
The augmented 5th and minor 6th are enharmonics.
The diminished 7th and major 6th are enharmonics.
The augmented 6th and minor 7th are enharmonics.
The other enharmonics are too rare to mention at this time.
Open MIDI file
Open mp3 file
Play file
Often it is helpful to have a song that you can associate with a specific interval. This section contains some MIDI files that demonstrate some interval in the context of some songs.
Open MIDI file
Open mp3 file
Play file
Open MIDI file
Open mp3 file
Play file
Open MIDI file
Open mp3 file
Play file
Open MIDI file
Open mp3 file
Play file
The major scale has only perfect and major intervals when measured from the tonic of the scale. The minor scale has perfect, major and minor intervals when measured from the tonic of the scale. When starting from scale degrees other than the tonic, one can create intervals of perfect, major, minor, augmented, and diminished quality. I don't mean to imply that one can create any of these intervals at any scale degree, what I mean is that when using all of the possible combinations of scales and intervals you can find at least one of each prefix although not all prefixes at each interval number.
For a complete listing of all possible intervals within the context of the four scale forms we have studied in this course, see the second part of the chapter on intervals from the text. If you haven't already looked at it, please check all of the intervals within the scales, from the text.
The composition 'Birdland' by Joe Zawinul is an interesting example of how context can determine the perception of consonance and dissonance. The synth bassline that opens the piece has the notes B,C,D then B,C,D,G. The melody played on top of the bassline starts on the note Bb. One might expect (well I would expect) the B bass against the Bb melody to have a clashing discordant sound but it sounds very natural to me. In fact this type of combination of tones is commonly used in jazz, blues and rock & roll. It is not very common in classical music until you get near this century and harmony began using upper extensions of 9th, 11th and 13ths. In other words Mozart and Beethoven didn't get this funky (maybe at the after hours party, who knows), although I think that J.S.Bach was so far ahead of his time he might have come up with this combination of notes. Chopin implied this on occasion, especially the little phrase in the middle of his E minor prelude.
This MIDI file doesn't do the tune justice. If you want to hear the definitive version, you can't beat the original by Weather Report on the 'Heavy Weather' CD. Jaco Pastorius plays a beautiful fretless bass passage that knocks me out every time I hear it. Manhattan Transfer also did a vocal arrangement that is pretty fun.
Open MIDI file
Open mp3 file
Play file
Other Reading:
Required Test10 and Test 11 are in the 'Quizzes''.
Below are some samples from the tests for this week. These ARE NOT the actual tests but instead a short example from the tests so that you can get an explanation of how to take them and the "look and feel". To take the real test you must go to the Quizzes area.
Below are several intervals. Examine the locations of the notes on the staff and determine the interval number for each one. It is not important to analyze the half step distances on this test, only the interval number. Click on the button next to the correct interval number for each interval.
Measure the line/space difference between the two notes. In the first example shown below the first note is on the space above the staff. Count the line/space difference between the space above the staff and the fourth line. Counting down from the space above the staff (1), to the top line (2), to the fourth space (3) to the fourth line (4). The interval is a fourth.
In the second example the first note is on the first space and the second note is on the space below the first ledger line below the staff. Counting from the first space (1), to the first line (2), to the space below the staff (3), to the first ledger line below the staff (4) to the space below the first ledger line below the staff (5). The interval is a fifth.
In the third example the first note is on the first line and the second note is on the third space. Counting from the first line (1), to the first space (2), to the second line (3), to the second space (4) to the third line (5) to the third space (6). The interval is a sixth. The third menu is set to the correct answer.
  
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What is the number of the above interval? |
What is the number of the above interval? |
This menu is set to the correct answer |
Below are several intervals. Examine the locations of the notes on the staff and taking into account the distance between the notes, determine the interval name for each one. Click on the button next to the correct interval name for each interval.
In the 2nd example shown below the interval from Gb to Ab is a 2nd with a total distance of 2 half steps. The correct answer is Major 2nd.
In the 3rd example shown below the interval from F# to A# is a 3rd with a total distance of 4 half steps. The correct answer is Major 3rd. The third menu is set to the correct answer.
 
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What is the name of the above interval? |
What is the name of the above interval? |
This menu is set to the correct answer |