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: 14-November-2025
Intervals are the differences in the pitch of two sounds. Some sound good (melodic), and some sound not so good (dissonant). To simplify this, 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. Two notes are also known as an “interval,” so you can call them that, too. 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
- The 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).
- 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, which 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 2b. The “b” reads as “flat.”
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 will become important in how you think about the notes. Later, you can change to a different scale just by substituting the new root note for C.
Now, the rest of this is just learning the number of half steps for each chord and then translating it to relative notation and 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 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).
Boards of Canada created some of their tracks, such as “Pete Standing Alone,” “Telepath,” “Energy Warning,” “Oscar See Through Red Eye,” “Come to Dust,” “Split Your Infinities,” “Sundown,” “Palace Posy,” “Sick Times,” and others, using fifths. Some, like “Cold Earth,” use both fifths and fourths.
The next group I like is the Major and Suspended chords. Major sounds upbeat, and I like that.
Suspended sounds cool, too, and it is 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.
Boards of Canada use Sus2 chords, which can be found in their tracks “Under the Coke Sign” and “Chromakey Dreamcoat,” while Sus4 chords can be found in “Hi Scores.” Even more elaborate are the Sus4Add9 chords, which are found in “Hey Saturday Sun,” or the Add9 found in “Dayvan Cowboy.”
Augmented and Diminished chords are okay, but I’m not fond of them.
The 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 sound different when played in various locations on the keyboard, and I highly recommend you try them to get different sounds.
Minor chords are downers, but sometimes necessary to have a 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 the tables are all in the 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 it, 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 the 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
As mentioned earlier, another way to view these intervals is to compare them to the fundamental (absolute) unit to which they relate. This gives you ratios like this:
- An octave is 2:1. This is no surprise. 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 98.115 Hz 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.
- The 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 and, strangely, BoC-ian)
- Added – a richness
- Augmented – unresolved