Intervals and Chords

Intervals in music are important for understanding the sounds of chords and dyads. Even melodies can benefit from a clear understanding of intervals. Unfortunately, a lot of the information I have found out there is confusing. I’m trying to unravel it for myself and you may get something out of it as well.

Last updated: April 23rd, 2021

Intervals are the differences in pitch of two sounds. Some sound good (melodic) and some sound not so good (dissonant). To make this simpler, I’m classifying intervals as differences in notes on the diatonic scale. Think of them as two distinct notes on a keyboard, for example.

If you put more than two of these together, you will get chords. If you have only two of them, they call that a “dyad” which is a two-note chord but two notes is also known as an “interval” so you can call them that also. Dyad kind of sounds cooler though.

Things can get complex rather quickly, so to simplify it, there is notation. Unfortunately, there are different kinds of notation. But, I put them both on a sheet so they are easily translatable.

The two different kinds of notation I am familiar with are

  1. Number of half steps – start at a note and move to the very next one and that is one (1) half-step. For example, starting at C and moving one half step would get you to C# (a.k.a. Db). If you don’t move at all that is not a half step, so it is zero (0).
  2. Relative notation – start at the root note of a key and call it “1” then move to the next whole note in the key and call it “2” and so on. If you are in the key of C Major, you would start at C and that would be 1, then D would be 2, E would be 3, and so on. What about the black keys in this case? Those would be named with a flat symbol. For example C# (a.k.a. Db) would be known as 2b.

This sounds hopelessly complex, but it becomes easier to see with a picture. See below.

Here I show the half steps starting from C. C is a convenient place to start, so just use that key while learning this because if you don’t it becomes incredibly complicated (in my opinion).

I also show the relative notation for the C Major scale. I bolded those because they become important.

Now, the rest of this is just learning the number of half steps for each chord and then translating it to the relative notation, then to the actual notes. I did this all with the C Major scale. I realize this is super small to see on a webpage like this, so I included the Excel file here for you to download.

I like the simplest first, so here are the intervals or dyads as they are sometimes called by the cool people. These are simply two notes. You can see that they are basic, and the Octave is probably the dumbest, but important because my notation for the notes shows C-C*. That C* is the next higher octave (duh, I know, right).

The next group I like are the Major and Suspended chords. Major sounds upbeat and I like that. Suspended sounds cool too and they are used a lot by deadmau5 and other artists. Cthulhu by Xfer Records has a feature where you can change all the chords to suspended ones. That’s probably not by accident, as deadmau5 was a primary user of it.

Augmented and Diminished chords are okay, but I’m not really fond of them.

Notation here is interesting because I put parenthesis after some of these. This is because you can play them on the next octave up if you wanted, or you can just play them within the same octave (the lower number, not in parenthesis), or anywhere else (like an octave lower, etc.). This playing of the notes out of order is called “inversion.” It is a fancy way of saying that you can play the notes wherever you want and call them an inversion. They really sound different when played in different locations on the keyboard, and I would highly recommend you try it to get different sounds.

Minor chords are downers, but sometimes necessary to have counterpoint to the major ones, so here they are. Dominant chords don’t sound so good to my ears, but can be useful, again, if used in counter to other chords.

The real kicker here is that these in the tables are all in C Major scale. If you switched to D, for example, that scale would have the relative 1 note not as C, but as D. This gets crazy hard to understand. Fortunately, the people at Hooktheory are really good at explaining it and that is who I used to understand the relative notation.

Also, relative notation is super cool because, for example if you want a Major 6th chord, you build it using the 1-3-5 of a major triad, and add the 6 in relative notation. 6 = sixth chord. Get it. Nice, huh?

So if you can understand the relative notation, you will go far. Hooktheory is great at explaining it. I have a long way to go to understand, but I think they are the best teachers for the self-taught.

Two (More?) Ways

A musical interval is a distance between two tones, we’ve established that. But, you can also think of the interval as frequency ratios relative to their nearest neighbor (note) such as this:

  • First interval = the octave or a 2:1 relationship of frequency. For example, C1=32.705Hz and C2, an octave above, is 65.41 Hz. That is two times the C1 frequency or a relationship of 2:1. Here’s a list of notes and frequencies: https://pages.mtu.edu/~suits/notefreqs.html
  • Second interval = the fifth or a 3:2 relationship of frequency.
  • Third interval = the fourth or a 4:3 relationship.
  • Fourth interval = the major third of 5:4.
  • Fifth interval = the minor third of 6:5.
  • Then a second of 9:8 or 10:9.
  • Then smaller ones of quarter tone of 36:35, shruti, comma, apotome, and so on.
  • They have whole books on this, but here’s a great list: http://www.huygens-fokker.org/docs/intervals.html

Or, another way to look at these intervals aforementioned is to compare them to the fundamental (absolute) of which they relate. This gives you ratios like this:

  • An octave is 2:1. No surprise here. The fundamental is C1 so the octave is C2 at 2x, just like in the relative approach above.
  • A fifth is 3:1. Wait – a surprise. But think of it this way – a C1 is 32.705 Hz, so 3x that is 98.115Hz or G2. C1 and G1 is a ratio of 3:2, and C1 and G2 is a ratio of 3:1. C and G together, no matter where on the scale make up a fifth.
  • Another octave is 4:1.
  • A major third is 5:1.
  • Another fifth is 6:1.
  • A seventh is 7:1.
  • Another octave is 8:1.
  • A second is 9:1.
  • A third is 10:1.
  • A tritone is 11:1.
  • And so on.

You can probably Wikipedia most of this, but the point is not to get lost in the endless complexity of the interval, but to find out what to do with them. Find out what chords sound good to you and use them in your music.

Chords, Intervals, and Their Sounds

Here is a list of chords, intervals, and what they sound like to me:

  • Major – happy
  • Minor – sad
  • Perfect 4th or 5th – confident (and deadmau5-ian)
  • Seventh – mischievous
  • Sixth – moody maybe jazz-like
  • Suspended – melancholy tension (also deadmau5-ian)
  • Added – a richness
  • Augmented – unresolved