Got a couple of questions about this:
Yes please do write more about intervals, I don’t quite understand when you add and subtract, I will check out the rest of this that you emailed here, thanks.
-Gil
Thank you, Neal,
I am writing by ear and feeling of music and lyrics. I liked the GF#E on piano , so I wrote it in Gmaj on piano and was ready to record sax section when I thought about transposing issue.
I clearly need more theory.
-Kate
A sax player cannot play multiple notes at once. But once you play a note, it continues to ring and it stays in the ear of the listener. If you play one note and then another, you can distinctively hear the interval.
And you also play at the same time other musicians are playing other notes, that creates intervals too.
Let’s look at the intervals that exist within an octave.
Minor second, major second, minor third, major third, perfect fourth, tritone (aka augmented fourth or diminished fifth), perfect fifth, minor sixth, major sixth, minor seventh, major seventh, octave.
It can be useful to think of musical examples for the different intervals. These are some of the examples I think of for the intervals, with songs that I’m familiar with. If you have other suggestions, please feel free to share them in comments.
Here I’m listing the intervals from smallest distance between notes to largest distance.
The smallest distance (in Western music) is the half step. All the intervals are made up of some number of half steps.
A minor second is one half step. A major second is two half steps. A minor third is three half steps. A major third is four half steps. Two half steps would make one ‘whole step’.
So the number of half steps
Minor second: 1
Major second: 2
Minor third: 3
Major third: 4
Perfect fourth: 5
Tritone: 6
Perfect fifth: 7
Minor sixth: 8
Major sixth: 9
Minor seventh: 10
Major seventh: 11
Octave: 12
Twelve half steps is the same as six whole steps. To check the mathematics.
C major scale has the notes
C D E F G A B C
The intervals between consecutive notes are:
W W H W W W H
1 + 1 + 1/2 + 1 + 1 +1 +1/2 = 6
Six whole steps is twelve half steps.
Mathematically, everything lines up. So we can deal with intervals mathematically, especially for transposition (a computer program can do this very quickly too!)
We also want to know what the intervals sound like. For that, it’s good to have musical examples.
Ascending Interval Examples:
A minor second repeated…. that’s the theme from Jaws.
A major second is like the beginning of Frère Jacques
A minor third is in the James Bond theme.
A major third at the start of ‘When the Saints Go Marching In’
The perfect fourth- that’s the beginning of ‘here come’s the bride’.
There’s a tritone in the Simpsons Theme and in Purple Haze (Jimmy Hendrix)
Perfect fifth at the beginning of the Star Wars Main Theme, also in Twinkle Twinkle.
Minor sixth in Black Orpheus and also in ‘The Entertainer’ by Scott Joplin.
Major sixth in Take the A Train, also in the NBC three notes.
Minor seventh in ‘Somewhere’ from West Side Story
Major seventh in Ceora melody, Lee Morgan.
Octave in Somewhere Over the Rainbow.
To list all those intervals starting from C,
C to Db is minor second
C to D is major second
C to Eb is major second
C to E is a major third
C to F is a perfect fourth
C to F# is a tritone
C to G is a perfect fifth
C to Ab is a minor sixth
C to A is a major sixth
C to Bb is a minor seventh
C to B is a major seventh
C to C (8va) is an octave.
Within the major scale:
If you can play a major scale, you’re already playing a number of intervals.
Let’s look at the notes and intervals of C major, starting from C.
The notes: C, D, E, F, G, A, B, C
C to D is major second
C to E is a major third
C to F is a perfect fourth
C to G is a perfect fifth
C to A is a major sixth
C to B is a major seventh
C to C (8va) is an octave.
These come from the major scale, so many have ‘major’ in the interval names. Fourths and fifths are called ‘perfect’ though.
If you play the notes of the C major scale, but start on D, you have a D Dorian scale, which is a minor scale.
The notes and intervals starting from D.
D to E is a major second
D to F is a minor third
D to G is a perfect fourth
D to A is a perfect fifth
D to B is a major sixth
D to C is a minor seventh
Mathematics
The foundation theoretically to move between intervals starts with the major scales for me. Learning the major scales gives you context for intervals.
To get a major interval, perfect fourth, or perfect fifth, you simply can count up the major scale.
Perfect fourth of C, you count C, D, E, F. The perfect fourth of C is F.
To move downward a minor third, you can get to what would be a major third down and then move up by a half step.
Bob says
Don’t know if anyone can use this but my simple help for knowing which key is right when transposed is visualizing a keyboard (concert pitch) with my Bb Instruments above the keyboard (as a cross with the big t-sax vertical and my sop sax or clarinet as the horizontal above my head) and my alto as being below the keyboard. Then it’s just remembering 2 up 3 down when sitting at the keyboard (take C major concert and go 2 half steps up for D major for the Bb Instruments, or three half-steps down to A for the alto. Vica-versa if you’re on a horn – from the tenor to concert , go two half steps down, e.g. F# to F to E Concert, or the alto to concert three up. e.g. A to A# to B to C.
The above of course, just gets you into the right key…not in the right octave (for instance the alto is actually up a major sixth so it would be the A above the middle C, not below it). But to find the right key signature you needn’t make it complicated.
Of course the extension of the above means 5 up from alto to tenor or 5 down from tenor to alto – again disregarding octaves, just finding the right key.
Fellow for simpletons who do well with visualizations: two up three down.
KT says
Neal, I saw the math of music first time I sat at a piano. The logic and connections. I get playing notes, chords, bass notes. Starting to get theory after re-reading your response to Gil.
I think it may seem like a need to know basis re learning intervals. I need to know some. If I already knew and understood, I could just play and write.
Got my goal and my starting point. Thanks.
By no means have I mastered it, I will have think and play etc until it becomes one step not two in my mind.
Thanks. I think knowing this will free me up when trying to play by ear…sound and built in logic. I have a friend who only plays by ear and memory of songs he has heard. I envy him. He wishes he could read music. Feels like with solid theory, a little by ear and a little reading will take me a long way.
Gil says
OK, I need to listen to the Theme of Jaws, to get the gist of what your saying.
Neal says
Just embedded the Jaws theme on this page. It’s a half step. So the distance between any two notes in a chromatic scale.
C to C#, D to Eb, etc.
The different intervals have different emotions connected to them. The minor second has a bit of dissonance. A perfect fifth sounds like it fits with less tension.
Gil says
I do appreciate you sending all this, but it seems overwhelming to me, so much to remember or memorize, how is it practically done, I guess practice, practice, seems like learning a language. A little at a time seems to be my key in learning, especially all of this.
I dont know if anyone else feels like I do but this is a lot, I know part of it I never had much Music Theory.
Neal says
Hey Gil,
Just take it a piece at a time. In terms of intervals, I would say start with the minor second and get a feel for what that sounds like.
Music has a lot to it!
Gil Ross says
Hi Neal, I still don’t understand.