This chapter is about the distances between notes, which are called ‘intervals’, and knowing them helps in the communication with other musicians.
For example, when you are rehearsing a tune and you find the key way too high for your liking. The pianist may say: “how about taking it a perfect fourth down?” Instead of having to leave the scene faking you have an urgent phone call, once you know the intervals you could reply: “or maybe a major third will do” and look cool; which is the whole purpose of singing jazz :)
Relative
A week is a week. A week from Sunday is a Sunday. Regardless of which Sunday is meant and regardless whether you’re going back in time or forward.
It’s like that with intervals. A perfect octave interval is a perfect octave interval; for example the distance between ‘c’ and the nearest ‘c’, or in numbers ‘1’ and the nearest ‘1’, or ‘b5’ and the nearest ‘b5’. Intervals are relative distances.
However, how many days is it from Sunday to Wednesday? Three? You must be thinking of the Wednesday that follows Sunday. The Wednesday before Sunday is four days away. Still, in this question, there’s no way of telling which Sunday or Wednesday is referred to.
In short: directions, upwards or downwards, are important when thinking and talking about intervals.
Perfect
The names of intervals derive from the numbers of the major scale. A distance like the one between 1 and 4* is called a perfect fourth interval.
* this now automatically means upwards within one octave of the major scale, since that’s how the numbers work, remember? The next octave starts on 8 and continues from there
So what’s with the addition of perfect in front of the name of an interval? Not every interval is perfect. The perfect intervals are considered the purest and most natural intervals that could be easily achieved (through simple integer divisions) and used for tuning instruments, long before the digital age.
The perfect unison interval = the distance between a tone and itself. Produced by an undivided string (or air column).
The perfect octave interval = the distance between a tone and the nearest ‘copy’ of itself. The difference between the tone produced by the original undivided string and the tone produced by half or double that string: the frequency of this octave is twice or half that of the ‘original’.
The perfect fifth interval = the distance between a tone and the nearest ‘copy’ of itself.The difference between the tone produced by the original undivided string and the tone produced by a third of the original string. The frequency of 5 lies at the center of the 1 and 8 (octave interval). If 1 is 100Hz, 8 = 200Hz, 5 = 150Hz.
The perfect fourth interval = the difference between a perfect fifth interval and a perfect octave interval.
The intervals and their most commonly used names along with the amount of semitones they span.
0 Perfect unison
1 Minor second or semitone
2 Major second or whole tone
3 Minor third
4 Major third
5 Perfect fourth
6 Diminished fifth / Tritone / Augmented fourth
7 Perfect fifth
8 Minor sixth
9 Major sixth
10 Minor seventh
11 Major seventh
12 Perfect octave
Transpose
Suppose you find a song but it’s not in the right key for you. Then you need to put it in a different key, which means you have to ‘transpose’ the song.
If it’s in an app like iRealPro it’s only a matter of changing the key to change all chords. If it’s not, you could enter it in iRealPro as is and then transpose it afterwards, or you could write a new chart in a different key by transposing all chords by the same interval.
Suppose the song is just a bit too high and you decide a whole tone interval lower would suit you better. This means you have to ‘transpose’ each chord by a whole tone interval downwards. Luckily this means you have to ‘transpose’ only the capital letters (upper cases) as the rest remains the same. For example, C6-Dm7-G7 then becomes Bb6-Cm7-F7.
If you also wanted to transpose the melody you could do the same with each note or enter the notes as they are in a music notation program or apps like Sibelius (www.sibelius.com) for example; and then have the software transpose the melody.
