Golden Chord Generator (Ableton 12 Max for Live Device)

The 'golden ratio' is associated with natural growth and is found all throughout the natural world. I made this Midi Transformer Tool to find the closet musical note and/or the closet interval of time that corresponds to the golden ratio.

'↕' or 'Chord Button': you select two notes and it will calculate the musical note that is the closest to the golden ratio between them.

• Can use a Logarithmic or Linear Algorithm (Log is a more complex kind of calculation that uses the same kind of math for how a musical scale is divided across the frequency spectrum and aligned more with the subjective experience of sound. It will tend to sound more 'musical' especially at larger intervals, while Linear is more strait forward of a calculation and in a sense 'objective'.

• This is an approximation and how close it is to a perfect golden ratio is shown in the 'deviation from Phi in Hz:' section at the bottom.
• Will also calculate the golden ratio length between the notes if they vary in length. This is automatic and there's currently no setting to adjust this.

↔ or 'Time Button': You select a single note and it will divide it into two two notes having the cut point at a golden ratio distance between the start and end point.

• You can (for the chord button as well) click 'Top-Down' or 'Down-Top' to 'invert' the algorithm.
• Linear/Logarithmic are meaningless since it is always exact (or as exact as it can be in a digital domain). 'Deviation from Phi' is also unaffected by this for that reason and only holds the value for the chord generator portion.

Specs:
Live 12/Max for Live 9.07

Math:

Phi = 0.6180339887

LOGARITHMIC PHI NOTE:

Lowest Note:
ALog = log2(note 1)

Highest Note:
BLog = log2(note 2)

'A' from Top:
GoldenLogA = 2^(BLog − (1 − Phi) × (BLog − ALog)) Hz
'A' from Bottom:
GoldenLogB = 2^(BLog + (ALog − BLog) × Phi) Hz

Check:
GoldenLogA / GoldenLogB
(GoldenLogA − GoldenLogB) / GoldenLogB



LINEAR PHI NOTE:

L = note 2 − note 1
A = (1 − Phi ) × L
B = L − A

'A' from Top:
AT = note 2 − A
'A' from Bottom:
AB = A + note 1

Check:
B / A
L / A −1
L / B