Keyboard Patterns Observation

[phailes]

This is not a theory question but a mere observation. I see patterns in the black and white makeup of the keyboard....for instance.

Chromatically the notes from C to E are the mirror image of the notes from F# to B flat with F and B natural left out. If you number those notes from 1 to 5 in each pattern, the same number in each pattern is the Tri-tone.

C = 1, F# = 1....tri tone
I use this visual all the time to find my tritone substitutions.

Next pattern. Let's take the first five notes of the major scale.
These keys are mirror images of each other.
D flat and D
E flat and E
F and F#
A flat and A
B flat and B

Anybody else see any other patterns....or Willie has there been any texts written on this subject?

[nickrees]

I notice patterns all the time (I've been playing piano for thirty years and it's only since I have been trying to learn jazz in the last months that I have noticed these things).

I remember the tri-tone(s) B-F and F-B because it is the only tri-tone(s) with two white notes, All the others have one black and one white note as in your first pattern.

When I look at the cycle of fifths, I notice that all the black notes are consecutive Bb-Eb-Ab-Db-Gb, which I now use to help me remember the cycle. I tried to think about why all the black notes would be consecutive in this cycle. What I then saw was that the cycle of fifths consists of the two whole tone scales alternated

C - Bb - Ab - Gb - E - D
F - Eb - Db - B - A - G

It seems to be easier for me to always think of the cycle of fifths in the counter-clockwise direction (as I have given above). Normally I am thinking of the dominant to tonic direction so that is why it seems more natural in this direction. If you learn the cycle in this direction, it also gives you the ii-V-I sequence starting from any position as the ii chord. Or you can start two positions earlier and it gives you a iii-vi-ii-V-I turnaround sequence.

within the cycle of fifths the pattern B-E-A-D-G is repeated, first with all flats, then with all naturals, then you just have to add C & F and you have the whole cycle (that's how I remember it). It also helps that the first four letters of that sequence spells a word. Once you know the cycle and can picture it like the numbers on a clock as it is most often represented, you can look at the position directly opposite to get the tritone interval e.g. if C is at 12 O'clock, look at 6 O'clock to get its tritone interval.

When I was young, I used to hear people say all the time, there is a lot of mathematics in music. While I was learning maths I couldnt understand this because I thought of math as trigonemetry, algebra, calculus etc. which didnt seem to have anything to do with music, but after I learned about group theory I realized what people were talking about.

[phailes]

Also, let us take the pentatonic scale 1, b3, 4, 5, b7. These keys are the mirror image as far as black key white key notes.

C and Db
D and Eb (E and A are the same as D)
F and F#
G and Ab
Bb and B natural

I have never thought about the circle of fifths like that.....how interesting. Musicians do use math all the time without thinking about it. For example when transposing from one key to another, you take your scale and chord formulas and apply them to that key instead of just learning the key by rote.