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An interval is the distance between two notes.
If the two notes sound at the same time, its called a harmonic interval. If they sound in sequence, it is a melodic interval. That’s just a way to complicate things. It makes no difference to the distance if the interval is harmonic or melodic.
There are a number of ways that an interval could be measured. In earlier posts, I talked about intervals as the ratio of two frequency. Thus, a unison has a 1:1 ratio, an octave has a 2:1 ration, and a perfect fifth (in theory) has a 3:2 ratio.
Musicians almost never think in those terms. Rather, musicians learn the diatonic distance between two notes, and this is usually calculated by reference to major scales and half steps.
There are two parts to the name for an interval: the number and the quality.
Number The number of an interval is easy, simply start count the letters going from the lower note to the higher note. Take C to A. The letters in between are C D E F G and A. There are six of them, so the interval is a sixth. This is all there is to finding the number.
Again take, G to F#. You would count seven note names, so this is a seventh. By the way, if the notes were G to F, the interval would also have the number of a seventh.
What if you don’t know the starting note. Simple, sing or play the major scale from the lower to the higher note. When you have hit the second note, you have your number by counting. If you go sharp in your major scale, then take off one. This may not be a perfect system, but it will work in well over 90% of the cases.
Quality
The quality of an interval is a much trickier subject.
There are five qualities that an interval can have: perfect, major, minor, augmented and diminished.
Perfect intervals appear at the 1st, 4th, 5th and Octave. With no alterations, these appear in both major and minor scale. I think that they are called perfect because they result from the simplest frequency ratios, and thus are the most consonant. They were also used almost exclusively in early church music, like Gregorian chants, and that might also explain their name.
The 2nd, 3rd, 6th and 7th can take on either a major or minor quality. In a major scale, they are all major. So the major scale goes Unison, Major 2nd, Major 3rd, Perfect 4th, Perfect 5th, Major 6th, Major 7th and Octave.
A natural minor scale, however, does not have all minor intervals. It has the minor 3rd, minor 6th and minor 7th, but a major 2nd. For our purposes, it might be easiest to say that a minor interval is simply a half step smaller than a major interval, and leave it at that.
A diminished interval occurs when you make a perfect or minor interval 1/2 step smaller.
An augmented interval occurs when you make a perfect or major interval 1/2 step larger.
It is possible to doubly diminish or augment an interval (though I have never seen a doubly augmented one in practice).
Complementary Intervals
A complementary interval is the interval that you need to add to an existing interval to make up an octave. For example, if you have a perfect fifth, you need to add a perfect fifth to get to the octave.
The numerical rule for complementary intervals is simple: they always add up to 9.
The quality rule is slightly more complicated. The complement of a perfect interval is perfect. The complement of a major interval is minor; of a minor interval is major; and of a diminished is augmented, or an augmented is diminished.
How do you find out the quality of an interval. You make reference to the major scale. Let’s say you have C to A, as in our first example. You count up in the key of C: C D E F G A. The A appears in the key at the sixth spot, so it is a major sixth.
How about G to F#. Again the F# appears in the seventh spot so it is a major seventh. G to F however, lowers the seventh a half step (one fret), so it is a minor seventh.
How about A to A#. Both are on the same letter name, so it is a unison, but it has been raised a half step, so it is an augmented unison. What about A to Bb? This is a second, but it is a B that appears in the A major scale, and this is lowered a half step, so this is a minor 2nd.
The last two is a type of example that drives people crazy. In equal temperament, A# and Bb are the same pitch. So here we have an interval that has two different names for the same pitch distance. This is known as enharmonic equivalence, and it can be very confusing. There are reasons for it, but none that a blues guitar player is ever likely to need.
As another example, take D to G#. In the D major scale the notes are D E F# G A… So this is a fourth, and it has been raised a half step, so it is not a perfect fourth, but an augmented fourth. What is its complement? There are two ways to do this. There hard way is to think of the G# major scale: G# A# B# C# D#. The D is a half step below the D#, on the fifth note, so it is a diminished fifth. The easy way is to use the complement rule. The first interval was an augmented fourth. 9-4 = 5, so the complement is a fifth. And the complement of augmented is diminished, so its a diminished fifth.
In the next few installments, I will talk about the shapes of these intervals on the guitar and why they are (more or less) important.
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wondering how to determine/build chord progressions ?..and is the term altered the same as augmented?.. think i recognize what diminished and half diminished (m7b5)if not mistaken is diminished with a flatted 5 ? I read some this stuff online ebooks but still a bit confused at times..guess i should focus on learning more theory between practicing here.
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Altered is not the same as augmented. Applied to a note, altered simply means changed, usually a half step in either direction. Applied to a note, augmented will mean raised a half step.
You sometimes see those terms in chord charts. Jazz players will use the ‘alt’ to signify that the fifth has been changed a half step. It also means that the jazz player should probably be playing on the altered scale (which contains all the notes that the Key’s major scale does not contain.) So lets say you are playing in the key of C, and you see a notation for Galt. That means you have something like a G7b5, or a G7#5. And instead of playing a C scale or a G mixolodian, you would likely play something like an F# major scale.
A diminished triad is a minor third on top of a minor third, or from the root a minor third and a diminished fifth. A diminished seventh chord adds another minor third on top, so its 1 b3 b5 bb7. A half diminished chord adds a major third on top, so it is 1 b3 b5 b7. The two have very different character from each other, and different uses. I will get to triads and chords later, but am more than happy to answer questions now, and these are all great questions.
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thank you kindly Mr Duffy! ..I kinda knew augmented meant up a half step interval in a chord.. but yeah sometimes I get confused,,guess i’ll keep at it,, study little more reading and understanding theory sure can help make practicing fun and easier.. I try these days being more sure about what it is i’m playing or at least have an idea/anticipate for what might fit in a progression.. peace out!
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