IntroductionHave you ever innocently strolled into a conversation between you and a few other good musicians, or even a thread in MT, feeling pretty sound in your knowledge of theory, being able to keep up with and discuss everything that their talking about? It feels good, doesn't it? Then suddenly you hit a stumbling block, they mention something about harmonization and ask you what interval you usually harmonize with. You have no knowledge about intervals or harmonization, you don't know what to do. Err, minor 2nd? You suggest, hoping that it's a real interval. You are thrown by the surprise this causes and you start to think that it isn't but the conversation continues and you realise it must be (the real reason of surprise being how unusual this interval is to harmonize with). In this article I will try to show you how different intervals relate to each other, how to work out what an interval is and how to apply your use of intervals to create harmonies in your own songs. This article is mainly for players with little knowledge about intervals, but knowing basic theory like the notes will help you understand this article. A knowledge of keys would be good, or at least knowing what keys are, because this will help you apply intervals and harmonisation successfully in your own music.
The BasicsSo, what is an interval? Well, an interval is basically the gap between two notes, which can be expressed anyway you want (in number of frets, for example) but intervals have special names in theory which are widely recognised and will help you communicate with other musicians. Most musician think it notes much more than in semitones, so using the classical names for intervals will make it easier for them to think of that interval (and it will make you sound smarter too, which is always a good thing). Intervals are always calculated from the lower note, regardless of note order. This means that if you played the open A string then the open E string, then the interval would be worked out starting at the E. There would also be no difference in the interval if the E was played first but there would be if the E was played on the 7th fret on the A string because this would mean that the A was the lower note.
The NamesI will list the names of the intervals with the number of semitones for reference but I recommend that you don't memorise this list because the whole point of using the classical names is to get you to think in notes, not semitones (which are not much use for thinking in keys to write songs). 00 semitones: Unison 01 semitone: Minor 2nd 02 semitones: Major 2nd 03 semitones: Minor 3rd 04 semitones: Major 3rd or Diminished 4th 05 semitones: Perfect 4th 06 semitones: Augmented 4th or Diminished 5th 07 semitones: Perfect 5th 08 semitones: Augmented 5th or Minor 6th 09 semitones: Major 6th 10 semitones: Minor 7th 11 semitones: Major 7th 12 semitones: Octave
The Intervals of the ScalesYou may know that most scales are written according to their notes, which are referred to as numbers (bare with me, there is a point to all of this). However, these numbers can also be seen as intervals. The standard numbers make up the major scale:
1 2 3 4 5 6 7These numbers don't correlate to the semitones but to the major scale, so the gap between 3 and 4 is smaller than 1 and 2. The minor scale is written like this:
1 2 b3 4 5 b6 b7Note that there are no two numbers that are the same. This is because even thought it could be expressed with two of the same numbers (5 #5, for example) but you are not allowed to do this. The same goes for intervals, in a minor key you will never find a augmented 5th because there is already a perfect 5th, so this interval is always a minor 6th. See what I mean?
The Intervals of the Major ScaleThe intervals of the major scale are very important for working out what the interval between two notes is. If you know how the major scale is formed (which you should) then you might be able to work these out but I'll tell you anyway. All of these intervals are from the first note to another.
1st note to 1st note = Unison 1st note to 2nd note = Major 2nd 1st note to 3rd note = Major 3rd (starting to see a pattern) 1st note to 4th note = Perfect 4th (that just messed up your pattern) 1st note to 5th note = Perfect 5th 1st note to 6th note = Major 6th 1st note to 7th note = Major 7th 1st note to 8th note = Octave
Working Out IntervalsYou could work out intervals by counting semitones but that way is very slow and requires you to know which 12 intervals correspond to how many semitones, which is unnecessary when you can do it another way, which will also help you thinking about keys. So this is how you do it: Get your two notes, I'll start with E and B. Now think of E as the beginning of the E major scale. Now count how which number note in the E major scale B is (remember the table above?).
E-F#-G#-A-BThat's 5 notes, which makes B the 5th note of the E major scale. Now look at the chart about the major scale intervals and you'll see that from the 1st note to the 5th note is a Perfect 5th, so from E to B is a perfect 5th. Easy, isn't it? Well it gets easier with practise. Try this one: Bb to A.
Bb-C-D-Eb-F-G-AThat's 7 notes, so look at the chart and, yes, it's a major 7th. You can now feel free to feel good about yourself. Now stop, there's more to come.
Sir, It Doesn't Always WorkIndeed, try this one: A to F. Easy, you think to yourself, and begin to work it out:
A-B-C#-D-E-F#.Wait, that can't be write, you think to yourself, I'll try again.
A-B-C#-D-E-F#.Wait, there is no F in the A major scale. No there isn't, so how will you work it out. Well to do this you'll have to be able to work out intervals that aren't in the major scale. How to do that Well, there isn't that much more to it than before but you do have to know these simple rules. These rules are all about changes of one semitone:
Make a major interval smaller (by one semitone) and it becomes minor. Make a major interval bigger (by one semitone) and it becomes augmented. Make a minor interval smaller (by one semitone) and it becomes diminished. Make a minor interval bigger (by one semitone) and it becomes major. Make a perfect interval smaller (by one semitone) and it becomes diminished. Make a perfect interval bigger (by one semitone) and it becomes augmented.Got that? Now I'll explain how to use it. Think about the previous example. A to F. Count it again.
A-B-C#-D-E-F#.Again there's no F, but there is an F# which is 1 semitone smaller (you can also use E but the same note is usually easier). So F# is 6 notes away which makes it a major 6th. Now look at the rule above - a major interval made one semitone smaller is a minor interval. Therefore a major 6th one semitone smaller is a minor 6th. So A to F is A minor 6th. Try another one: C to Gb
C-D-E-F-GThat's 5 notes so C to G is a perfect 5th. Make that one semitone smaller and, according to our rule, it becomes a diminished 5th. Therefore C to Gb is a diminished 5th. See, it's not too hard.