CreateMotif
The further away from 1, the stronger the desire to return to 1.
If we snap back to 1, the tension is gone, it is resolved unto the tonic
So there is a tension budget
0.5 does not have the same pull to resolve as .9
At .9 we almost guarantee the next note will resolve
There’s only 0.1 room for resolution
For a ii-V-i - 0.5, 0.8, 1.0
Here there is a strengthening desire to resolve
Furthermore, the ol V-I is a “perfect cadence”, it finishes an idea.
Some common progressions as reported by the internet:
1-5-6-4
1-4-5-4
2-5-1
1-1-1-1, 4-4-1-1, 5-4-1-1
1-6-4-5
1-5-6-3, 4-1-4-5
Converted into resolution weights:
1.0, 0.8, 0.3, 0.6
The total possible resolution for this would be 1, 1, 1, 1 = 4;
Total Possible Resolution: 4.0
Sum of Actual Resolution in the above chord progression: 2.7
Delta: 1.3
1.3 / 4.0 = 0.325
This gives us a 30% total tension budget for this chord progression.
What I need to do is to decide which notes can be chosen that will end up hitting that 30% note budget while in a for loop.
Look again at this:
1.0, 0.8, 0.3, 0.6
We start at 1.0. Tension is 0. Full 30% tension available.
Then 0.8. That’s 1.8 of a possible 2.0.
0.3 making 2.1 of a possible 3.0
And finally 2.7 of 4.0.
1.0 - 1.0 = 0.0; 0 / 1.0 = 0; Below budget - 0.3 remaining
2.0 - 1.8 = 0.2; 0.2 / 2.0 = 0.1; Below budget - 0.2 remaining
3.0 - 2.1 = 0.9; 0.9 / 3.0 = 0.3; On budget - 0.0 remaining
4.0 - 2.7 = 1.3; 1.3 / 4.0 = 0.325; Just above budget - -0.25 remaining
Can we reverse this logic?
0.3 - 0.2 = 0.1; 0.1 * 2.0 = 0.2; 2.0 - 0.2 = 1.8; 1.8 - 1.0 = 0.8
Total budget - Desired Remaining = This Note Budget
This Note Budget * Cumulative Possible Total = Optimal Tension
Cumulative Possible Total - Optimal Tension = Current Note Tension
Current Note Tension - Total Actual Tension = Optimal Candidate Note Tension
So with the Optimal Candidate Note Tension of 0.8, we map that to the 5th.
But we don’t necessarily want to choose the optimal mapping. But we do want to weight it higher.
If we have the following allowable notes: [1, 2, 4, 5, 6 ]
It maps to tension weights of [ 0, 0.5, 0.6, 0.8, 0.3 ]
Deviation from Optimal Candidate Note Tension = [ 0.2, 0.3, 0.2, 0, 0.5 ]
Chance to Select = (100 - (Deviation * 100)); [ 80, 70, 80, 100, 50 ]
Sum of all of those is 380;
Random range select 1 - 380:
[ 1-80, 81-150, 151-230, 231-330, 331-380 ]
[ 21%, 18%, 21%, 26%, 13% ]
I think I want to overweight the Optimal. If we doubled the deviation:
[ 0.4, 0.6, 0.4, 0, 1.0 ]
[ 60, 40, 60, 100, 0 ]
[ 23%, 15%, 23%, 38%, 0% ]
So that kind of works. Except that 0.3 on the second beat is just as valid as the optimal 0.8.
Looking at others:
1.0, 0.6, 0.8, 0.6
- 4.0 - 3.0 = 1.0 tension budget
- 1 / 4 = 0.25
0.5, 0.8, 1.0
- 3.0 - 2.3 = 0.7 tension budget
- 1 / 3 = 0.333
1.0, 1.0, 1.0, 1.0 - 0.6, 0.6, 1.0, 1.0 - 0.8, 0.6, 1.0, 1.0
1.0, 0.3, 0.6, 0.8
- 4.0 - 2.7 = 1.3
- 0.325
1.0, 0.8, 0.3, 0.4 - 0.6, 1.0, 0.6, 0.8
- 4.0 - 2.5 = 1.5, 1.0
- 0.375, 0.25
Tension budget percent range [ 23% - 37.5% ]
What we establish with this is that for common chord progressions, there is about 30% cumulative tension.
Things that jump out at me:
The 4th is a common, versatile chord. Seems like excellent “glue” chord
Works well with the 6th, but only in terms of 6→4, not 4→6.
7, 2, 3, chords are surprisingly rare
I suppose this because the 3 is mainly reserved for modifying the shape of each chord in each of those progressions. In the above example, there’s no distinction between minor or major 6th, we’re just defining the root note.
I think the 7th works the same way, It would only really work as a lead in to the root.
The other thing is that these are very much chord progressions. They are common progression in terms of the chords they would produce. You’ll put a 7 in any chord you want, for flavor, but you rarely have a 7th chord.
Additionally, there are emotional evocations for each key:
Major Keys
- C Major: Pure, joyful, innocent
- G Major: Friendly, happy, pastoral
- D Major: Triumphant, bright, bold
- A Major: Joyful, confident, spirited
- E Major: Powerful, brilliant, resilient
- B Major: Optimistic, bright, intense
- F♯ Major: Majestic, ecstatic
- D♭ Major: Warm, dreamy, elegant
- A♭ Major: Graceful, tender
- E♭ Major: Heroic, strong, noble
- B♭ Major: Harmonious, cheerful
- F Major: Calm, simple, rural
Minor Keys
- A Minor: Sorrowful, melancholic, reflective
- E Minor: Mournful, restless, poignant
- B Minor: Dark, brooding, dramatic
- F♯ Minor: Mysterious, intense
- C♯ Minor: Depressed, reflective
- G♯ Minor: Agitated, intense
- D♯ Minor: Desperate, poignant
- B♭ Minor: Gloomy, lamenting
- F Minor: Serious, pensive
- C Minor: Tragic, heroic, passionate
- G Minor: Discontented, restless
- D Minor: Grave, serious, solemn
Why does this matter? We’re creating a motif- a motif is a musical idea, the strength of that idea is the emotional resonance that idea evokes, and how well that idea integrates with the rest of the composition.