(For the record, total musical noob also trying to make convinient formulas to avoid remembering stuff - this is for intervals within an octave)
(given x is the lower/root pitch note wise, regardlesss of letter)
Example:
f(x,y) =
if Y>X
return dist(X,Y) + 1 # +1 is to handle starting at 1 (A=1)
else
return 8 - dist(X,Y)
f(C,F) -> Y>X -> dist(X,Y) + 1-> Y - X + 1 -> 6-3+1 = 4th Interval
f(F,C) -> X>Y -> 8 - dist(X,Y) -> 8 - (6-3) -> 8 - 3 -> 5th interval
If Y>X but x is of lower letters, say A-D you can use
f(B,G) --> (A = B - 1 -> G - 1 = 6th, less hassle)
Any bigger X just count it, its max 3 steps if Y>X
**Note sum is always 9 together.**
For X>Y,
We can internalize this table to calculate more easly:
dist(x,y) + 1 |
Quantity |
2 |
7 |
3 |
6 |
4 |
5 |
5 |
4 |
6 |
2 |
7 |
2 |
- 2<->7
- 3<->6
- 4<->5
Example:
F(G, D) -> dist(G,D) -> (7-4+1) = 4 --> pair of 4<->5 [Always equal 9 together] --> 5th Interval
Not sure this is easier at all, but I learned it quiet thoroughly ^ _ ^
Interval Quality:
I don't have a convinient formula for the quality but I use this:
Major Second: Accidental matches, except root E/B where it’s raised one
Major Third: Accidental raised one, except root F/C/G where it matches
Perfect Fourth: Accidental matches, except root F where it’s lowered one
Perfect Fifth: Accidental matches, except root B where it’s raised one
Major Sixth: Accidental matches, except for root A/E/B where it’s raised one
Major Seventh: Accidental raised one except for root F/C where it matches
Always calculate the major/perfect interval and then apply any minor/aug/etc, super efficient :)
(source: https://www.musical-u.com/learn/spell-intervals-fast-tips-tricks/)
%
in many programming languages). For the "quality" component, however, it seems to me that a lookup table would be far simpler than a formula. $\endgroup$