Definition of Dissonance in auditory physics and psycho-physics.
As you know, the word dissonance is the opposite concept of consonance, that is harmony.
what is (un-)harmony?
Un-harmony level S, that is dissonant level,can be measured by the next standard.
Dissonance equation
un-harmony level S = A * N
;N = number (or quantity) of kind of notes (or pitch),
A is coefficient or operator.
If we can use entropy equation, dissonant level S is as the below.
S = k * log[ N ]
entropy = dis-order(= volume of noiz =complexity,fazzyness or chaos).
As you know, note or tone of every natural musical instruments have harmonic series (=integral freq series).
Why? for example, strings of guitar is fixed at both side of them, so the string can oscillate with only the ratios of whole numbers, or if not, the string can be splited.
so a note of all musical instruments includes high harmonics above fundamental tone as below.
Harmonics. now, if frequency of root note(=fundamental tone) is 262Hz =C, musical names of harmonics as the followings.
1 = C (= fundamental tone)
2 = C'
3 = G'
4 = C''
5 = E''
6 = G''
7 = bB''
8 = C'''
9 = D'''
10 = E'''
11 = F#'''
12 = G'''
(omitted the followings), here X'=X*2^1, X''=X*2^2. X'''= 2^n(n=3), 2^n = octave.
This structure of integral series is the base of consonance(=harmony). Pay your attention to harmonics from 1 to 7, particular 4,5,6,7. they are C,E,G,bB... This set is C7-chord.
If upper harmonics/root = 2^n(=Octave), this interval is perfect consonant. If we pick up only even number harmonics they consist of C,G and E, that is complete consonant three tones.
With this mannor. we can measure dissonant level of 12 notes into a octave with ratio of frequency of notes.
Now we can define the index of dissonance N' with molecular and denominator of the ratio of the harmonics as the below.
N'= molecular + denominato
musical note. ratio. N'.
C = 1/1 = 1 .. 2
bD = 16/15 = 1.06 32
D = 9/8 = 1.125 17
bE = 6/5 = 1.2 11
E = 5/4 = 1.25 9
F = 4/3 = 1.333 7
#F = 11/8 = 1.375 19
G = 3/2 = 1.5 5
bA = 8/5 = 1.6 13
A = 5/3 = 1.666.. 8
bB = 9/5 = 1.8 14
B = 15/8 = 1.875 23
C' = 2/1 = 2 3
# this ratio is the pure tuning though.
So the interval is more dissonant as N'is high.
then dissonant order of 12 notes are..
(1)bD =32,(2)B =23,(3)#F =19,(4)D =17,(5)bB =14,(6)bA =13,
(7)bE =11,(8)E =9,(9)A =8,(10)F =7,(11)G =5,(12)C =2.
* the average of N' = 13.333.....
And so, we can find out the reason of cycle of 4th in the structure. The Dominance chord C7 derivated from natural harmonics includes C,E,G,bB. and interval of E and bB (bB/E = #F/C = 1.375 :N'=19 > average 13.333...), that is tritone or leading notes, is very dissonant, so the combination tone must be resolved to more conssonant interval.
Then E moves to F and bB moves to A, so the chord C(=C,E,G,bB) changes F(F,A,C). this chord change is upper 4th progression.
So as the same, chain of the 4th progression G7(g,b,d,f) => C(7)(c,e,g(-b)) => F(f,a,c) produces the major scale (or Ionian=c,d,e,f,g,a,b).
G7 =
C(7)=
F =
And if we can set
F(6) =
Then we get next 4th chord progression cycle.
(F=) Dm7 -> G7 -> C -> F (=Dm7)
and if we can set
Fmj9(omitted root) = <(F),A,C,E,G> =
then we can get next chord progression cycle.
C -> (F9=)Am7 -> Dm7 -> G7 -> C
that is "the turn around chord progression".
This is the physics of the major scale on the functional chord structure, in other words, diatonic chord progression.
* In case of Over Drive Distortion Sound.
A musical note as color of the sound is defined by it's spectrum of power and frequency, that is, weighted harmonics by amplitude.
Over drive distortion sound or fuzz sound is boosted sound of high harmonics of the power.
So when we use this sound notes or chord are more dissonant or fuzzy than clear sound.
Because a tone or notes has boosted high harmonics interferences other hamonics of other notes so the conbination tone (=chord) is bursted.
In the exreme case, the notes can't produce harmony.
This explanation writen here can be found in texts auditory ,musical or psycho physics (cognitive&perceptual psycology).
In Jazz, Dissonant Chords & Scales are used for enphasis conssonant chord by to put disso-chord before consso-chrd.
caz Jazz music is composed of diso(as domi chrd) and conso(as tonic) rythm patern, sub-domi is neutral or floating.
THIS IS SWING, GROOOVE.
dB Level of Sounds
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