The Connection Between Math and Music.
Musical notes are denoted by letters (A-G) map to specific frequencies. But their relation to each other can be more simply referenced with the numbers 1-8 if the melody is within the same scale.
This numerical map allows anyone to change keys at will due to the constant relationship between the map and the scale.
The 1 note is the root and it determines the active key being used.
If C is the root, then 1 can represent C. When 1-3-5 is played on an instrument, the C major chord (C,E,G) is played.
Another way to denote the distance between notes in a scale is to describe the difference between notes as a whole step or a half step. On the piano, a whole step requires a musician to skip one key. Half steps are the distance between every neighboring key.
Major Scale Examples:
Key of C major map: --------------- 1 2 3 4 5 6 7 8 C D E F G A B C _ w w h w w w h ---------------
Do-Re-Mi, Sound of Music 1 2 3 1 3 1 3 2 3 4 4 3 2 4 Doe a deer a female deer. Ray a drop of golden sun.
The Way You Make Me Feel, Michael Jackson
3 3 3 4 5 5
The way you make me feel
3 3 3 4 5 5
You really turn me on
3 3 3 4 4 5 5 3 2 1
You knock me off of my feet (now baby)
3 3 3 4 5 5
My lonely days are gone
Note Jackson's use of that 5 note. The 5 note of greatest tension and listeners ears want to hear the root note a.k.a the 1 note to relieve that tension. Jackson waits until the third verse to get to the root in the chorus, but ends on the 5th! Such torture makes you want to either listen to the rest of the song, or buy the album so you are absolutely sure he ends no songs on the 5th.
Minor Scale with a surprise:
What about the minor scale for those sad lonely sounding songs? Well just add a "b" after the number and know that we are only moving a half step.
Key of C minor map: ------------------ 1 2 3b 4 5 6b 7b 8 C D Eb F G Ab Bb C _ w h w w h w w ------------------
Billie Jean, Michael Jackson
8 8 7b 5 8 8 7b 5
Billie Jean is not my lo-ver
8 8 8 7b 5 8 10b 11 10b 9 8
She's just a girl who claims that I am the one
8 8 12 11 11 8 6b 5
But the ki-d is not my son
Hotline Bling, Drake
7b 7b 5 5 7b 7b 8
I know when that hotline bling
3b 5 4 3b 4 4 5
That can only mean one thing
WTF am I doing writing numbers above 8 (surprise)? Did I just smoke crack?!? No, no, my young musical jedi, I just added 7 to any notes above the highest note in the map. Check this out.
Key of C minor map: ----------------------------------------- 1 2 3b 4 5 6b 7b 8 9 10b 11 12 13b 14b 15 C D Eb F G Ab Bb C D Eb F G Ab Bb C _ w h w w h w w w h w w h w w -----------------------------------------
As you go outside of the scale into the higher notes, you just keep increasing the numbers in the map and maintaining the whole and half relationships.
I threw Drake into the mix just to see why his Hotline Bling is so catchy. If you see the chorus snippet I included, he ends on the 5 which creates tension. And pulls listeners in until he gets back to the root and resolves the tension.
Notes:
- This method of melody mapping doesn't take into account rhythm, which is why I chose popular songs where the rhythm is most likely memorized. - Image of the piano is from commons.wikimedia.org
I've come across some really badass stuff before on the connections between sacred geometry math & music before. Here are a couple interesting ones:
http://www.harmonisphere.com/SacredGeometryOfMusic.htm
http://thespiritscience.net/2014/03/15/sacred-geometry-of-sound-and-vibration/
Math = Music = Entropy-defeating-tool
Bach's air on G String is my favourite example (best appreciated in a meditative state)
This is really interesting- I'm going to take my time going over it again. Nice work!
Thanks! Let me know if you have questions.
This is the second time in a few days time that I have run across this numbering system. A few days ago I overheard a couple musicians I was performing with talking about this very thing. Now after reading your post, it all makes sense to me. Thanks.
It really helps when you have to solo. You can just pull together melodies everyone knows and see if they can recognize them.
Loved the post. On my last birthday, my daughter and my wife bought me a guitar, and the lessons came soon after. While I was with my guitar teacher one evening, we were discussing key changes and the Fibonacci Sequence. This brought me back to that discussion in a good way.
I have featured this post on my blog this evening. Thanks for the great content.
I don't see this as a math relationship so much as transposing a traditional musical notation naming relationship to numbers. There is indeed a lot of "math" in music, whether it's frequencies, fibonacci numbers, or even some more contrived notions. But, not quite getting the math behind your post.
Thanks for posting it though. Maybe the title should be more like A Connection Between Music and Numbers: A useful naming system for music?
Hi i really think there is good intentions on your post but it simplifies too much everything and you are wrong about the way you analyze melodies. Things are not as simples . Thats not because you use the 5 that it creates tensions .
If you are in a modal harmony the notes will be the same but the tensions won't be the same . For example if your song is in G Mixolydian what you call 5 won't be a tension but a resolution . More important than that is the relationship between your chords and your melodie . C is 1 but will be the fourth of a G chords and i don't think we'll consider your 1 as a resolution note.