Beautiful Just Intonation 7s.


Just Intonation (JI) 7s are 7/4, 7/5, and 7/6.
They divide the octave into four logical divisions.
They do not use equal divisions:
    All of which would be equal minor thirds,
    And which are out of tune.
Rather they define Extremely Beautiful relationships.
Playing in Just Intonature with a Drone is Pure Tone.

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Converting Just Intonations to Cents:
1200*log2 (m/n) where 1 < m/n < 2 is your ratio.

Note that I rounded log2 calculations to 3 decimal places for clarity:

[Blue m3, 7/6] 266.870 + [Bright 2nd, 8/7] 231.174 = [Pure 4th, 4/3] 498.045
Note: Log2(7/6) + Log2(8/7) = Log2((7*8)/(6*7)) = log2(56/42) = log2(4/3)
    *** Harmonic Intervals are Natural Logarithms!!!

[Pure 4th, 4/3] 498.045 + [Major 2nd, 9/8] 203.910 = [Pure 5th, 3/2] 701.955

[Bright m3 6/5] 315.641 + [Pure M3, 5/4] 386.314 = [Pure 5th, 3/2] 701.955

[Blue m3 , 7/6] 266.870 + [Bright m3, 6/5] 315.641 = [Blue b5, 7/5] 582.512

[Blue b5, 7/5] 582.512+ [Pure M3 5/4] 386.314 = [Blue m7, 7/4] 968.826


Therefore a few examples to the Octave:

[Blue m3, 7/6] 266.870 + [Bright 6th, 12/7] 933.128 = {Octave] 1200

[Blue b5, 7/5] 582.512 + [Bright b5, 10/7] 617.487 = {Octave] 1200

[Blue m7, 7/4] 968.826 + [Bright 2nd, 8/7] 231.174 = [Octave] 1200

[Blue b5, 7/5] 582.512+ [Pure M3 5/4] 386.314 + [Bright 2nd, 8/7] 231.174 = [Octave] 1200

[Blue m3 , 7/6] 266.870 + [Bright m3, 6/5] 315.641 + [Pure M3 5/4] 386.314 + [Bright 2nd, 8/7] 231.174 = [Octave] 1200

Therefore Just Intonations Harmonics is an Infinite Set!!!
Actually the Natural Logarithm itself without the 1200 cents of music.
12 being the Equal Temperament choice since it is divisible by 2, 3, 4, and 6.
The combination of these determine the Timbre of an instrument.

The Nature of Just Intonation Music is Harmonic and Healing!!!

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