Harmony for Dummies : Intervals

As usual, I strongly suggest you take notes, try to re-calculate the intervals I will speak about, organize all this on a piece of paper in various ways, in short, get used to handle all this in the same way you get used to learn to make additions: keep training, again and over again.

Basics to understand the intervals

(especially the vocabulary to understand the rest):

• An interval is the distance in tone and half tone between two notes
• The full name of an interval is composed of the name of the interval AND an adjective. Example: major third, the name is "third" and the adjective is "major". There are other types of thirds, which therefore vary only in their adjective.
• We can speak of harmonic, ascending melodic and descending melodic intervals. A harmonic interval is when two notes are played simultaneously, a melodic interval is when two notes are played successively, ascending when we go from lower to higher notes, and descending when we go from higher to lower notes. It is not that much useful, I have to agree with those who say that the theory is useless
• Just as there exists enharmonic notes (two notes of different names but the same height), there are enharmonic intervals: one interval may have many names.

Intervals : how they are built

To learn about intervals, it would be easy to get a complete list and memorize them by heart. But I find it more interesting to learn how they are built to be able to find them if you can't remember them. Therefore, I do not give you a complete list of intervals, I let you do it yourself (I would correct you on request if you have any doubt).

So we start from the C major scale, which contains the following notes: C-D-E-F-G-A-B-C

We name each note according to its degree. It is quite simple, the first note is the degree I (Roman figure), the second note the degree II etc. So the degree IV of the C major scale is F.

Then we define all intervals in the scale compared to the level I, i.e. the interval between level I and II, between level I and III, between I and IV, I and V etc ...

Specifically we will define all these intervals:
C - D
C - E
C - F
C - G
C - A
C - B

To give them their name, we will rely on their higher degree by changing the name in some pseudo-intellectual way:

C - D, degree I and degree II => two => second
C - E, degree I and degree III => three => third
C - F, degree IV => four => fourth
C - G => five => fifth
C - A => sixth
C - B => seventh

Note that this naming system works with any major scale. In A major, for example, the second is B the third is C #, the fourth is D etc...

Let's add the adjectives now. We find two types of intervals: those that are perfect, and those that are major / minor. The following is to be learnt by heart: the fourths and fifths are perfect, the others (seconds, thirds, sixths, sevenths) are major or minor. As we are in the major scale, all intervals are perfect or major, not minor at this time. So now we can already quantify the intervals we have just seen by counting the intervals between the notes:

C - D = ​​major second = 1 tone = 2 half-tones
C - E = major third = 2-tones = 4 half-tones
C - F = perfect fourth = 2.5 tons = 5 half-tones
C - G = 3.5 tones = perfect fifth = 7 half-tones
C - A = major sixth = 4.5 tons = 9 half-tones
C - A = 5.5 tons = major seventh = 11 half-tones
(Feel free to recalculate all this, also in other scales, it makes you work)

So as you can see, there are "holes", we have no names for some intervals like : 3 halftones, 6 halftones, etc. ...

To give names to these intervals, we will use the adjectives:

• a major interval, we can change it to minor by lowering it of one half-tone
• for ALL intervals, we can make it "diminished" or "augmented". For the perfect intervals, it's easy: we add or remove one half-tone. For the major / minor intervals, the diminished is a half-tone below the minor, the augmented a half-tone above the major.

To summarize in a somehow graphic way we have:
augmented = perfect + one half-tone
perfect
diminished = perfect - one half-tone

or :
augmented = major + 1 half-tone
major
minor = major - 1 half-tone
diminished = minor - 1 half-tone = 2 half-tones


From there, you can easily create a list of all possible intervals, there will not be any single hole. For example:

• major third interval = between C and E = 2 tones.
• minor third = 1.5 tons (2 tons - a half-tone)
• augmented third = 2.5 tons (2 tones + 1 half-tone)
• diminished third = minor - 1 half-tone = major - 2 half-tones

As you can see, the augmented third is an enharmonic interval of the perfect fourth and the diminished third is the enharmonic interval of the major second. Of course, since there are many enharmonic intervals, some of them will be more common that others. Here is a list (not very exhaustive though, it depends on styles etc ...) of the main enharmonic intervals to know:

• Major and minor seconds
• Major and minor third
• Perfect and augmented fourth
• Diminished, perfect and augmented fifth,
• Major and minor sixth
• The major, minor and diminished seventh

The others are rare.

You are not supposed to know them all by heart, but you should be able to re-calculate them quite quickly so that later, you are able to recognize them easily and instantaneously.

Well of course all this is about defining the names of the intervals, but it is not limited to the C major scale. You can try calculating the augmented fourth of an F #, or a minor seventh of a G, or whatever you want. This is precisely the purpose.

Normally, you understood everything so far. If it's not ultra-clear, read, write down, try before taking the next courses.

We just saw here the basics to understand the intervals, but we can add 2-3 other concepts (not necessarily important, but curiosity brings fun). The following is therefore OPTIONAL.

More concepts about intervals

The unison and the octave

I have not spoken about this earlier, but there are intervals of unison (0 tone, ie the gap between a note and itself) and intervals of an octave (6 tones, the gap between a note and the same note one octave higher). These two intervals are considered as perfect, and thus, they can be augmented or diminished (to get weird things, like a diminished unison that makes -1 half-tone and that kind of crap). Generally we do not put an adjective for these intervals, we just talk about unison and octave.

Single interval and double interval (or compound)

A single interval is less than one octave, a double interval more than one octave. Example: the interval between C and G: if the G is somewhere between the C and the C an octave above, it's a single interval. If the G is higher than the C an octave above, it is called double interval. It's still the same names (a perfect fifth in our case). I take this opportunity to say that we will speak later (when we're in the harmonization course) about intervals of the ninth, eleventh and thirteenth, which are compound intervals.

Sus-augmented ou sub-diminished intervals

An interval can be sus-augmented (a half-tone over an augmented interval), or sub-diminished (a half-tone under the diminished). But personally, I have never seen a case where it was useful.

The enharmonic

We will FINALLY have a reason to tell the difference between sharps and flats. Example: the minor third is a half-tone below the major third. In C major, the major third is the C- E interval. Thus, 2 tones. So the minor third is 1.5 tons. Therefore it's a D # or an Eb. And that's where the name of the note will be important: the E flat is the major third (E), which, with the flat, is diminished by a half-tone. The D # is the second major (D) which is increased by a half-tone thanks to the sharp.
But in the end yes, it is still nothing useful, it is only a naming convention.

Additional intervals

For each interval, there is an additional interval that completes the octave. Example: A major third (between C and E) is 2 tones, the additional interval will be between E and C, and will therefore be 4 tones (so that between C and C there are 6 tones).
The interesting thing to note is that the name of the interval + the name of the additional interval will always be 9. The additional interval to the third we just saw is a sixth. Third (= 3) + Sixth (= 6) = 9.
 

Triton:

It's the augmented fourth or diminished fifth interval which is 3 tones (hence the name). It has the specificity to separate the octave (6 tons) into two equal parts. Therefore, the additional interval of the triton is the triton.

Let's summarize

• we start from the C major scale
• we name each interval between each degree and C
• the adjectives are perfect or major
• then we get from there the minors, augmented and diminished

Train yourself, recalculate all the intervals, make a complete list of all possible intervals, do that with other scales (with lots of sharps and flats to make your head work), take a note randomly and choose randomly an interval, and try to find the second corresponding note.

Again, take the time to work on all this before you move on!