The psychology of the harmony intervals when the notes are sounding simultaneously or very close in time goes back to the ancient Greek Pythagoras and also the studies of the physicist Helmholtz is his studies and remarkable book "The theory of sound" see post 24. Here we will only make some remarks about not the harmony of the intervals but of the melodic dynamics, and only as long as the topic is not covered in the post 18.
Summarizing in a simplistic way the correspondence of melodic pitch dynamics and the 4-basic emotions in music (joy, sadness, anxiety, serenity) we have
1) Up pitch moves correspond to joy
2) Down pitch moves to sadness
3) Small pitch intervals of 1 or 2 semitones (chromatic or interval of 2nd) correspond to anxiety
5) Moving in the melody from intervals of 1,2 semitones to 7 (5th) , 12(octave) is moving from anxiety and stress to joy and serenity. (see post 78)
6) Ascending with larger steps that those of descending indicates favor of joy. E.g. Ascend with intervals of 2nd and major 3rd and descend with 2nds and minor 3rds.
7) Accelerating ascending indicates more joy, while decelerating ascending less joy. The converse with descending. E.g. Ascend by first intervals of 2nd then 3rd and finally 4th or 5th while descend at first with intervals of 5th or 4th, then 3rds and finally 2nds.
8) Melodies that move with steps of minor 2nds and minor 3rds mainly may be called minor feeling melodies, while melodies that move with steps of major 2nds and major 3rds mainly may be called major-feeling melodies.
OVERTONES-UNDERTONES AND HARMONICS-SUBHARMONICS
When we utilize the undertones or subharmonics the effect of minor sad chord apprears . In other words if a is a fundamental frequency the undertones are the 1/2a ,1/3 a, 1/4a , 1/5a etc
In a string of length l giving frequency a the undertones will be produced by multiplying the length of the string from l, to 2l , 3l 4l 5l etc.
Similarly a fretboard of n equal length l of frets will produce the n undertones of mini-string of length l (but not oft he whole string of n frets)
WHAT IS VERY INTERESTING IS THAT THE INITIAL MAJOR CHORD IN OVERTONES HAS A CORRESPONDING MINOR CHORD OF UNDERTONES!
This is also significant in understanding the sad emotion correlated with the minor chord as it is by contraction and lowering of a fundamental frequency compared to expansion and raising of fundamental frequency by overtones which gives the major chord.
HARMONIC POLES AND HARMONIC WAVING IN THE CHORD PROGRESSION AND STRUCTURE OF THEMES IN THE MELODY BASED ON THE EMOTION OF THE HARMONY OF THE INTERVALS:
The emotional parallel of the harmony of intervals, suggests that the chord progression and harmonic structure of the themes of the melody, waves (Harmonic waves) between the emotion of stress,intervals of 1 or 2 semitones to the pole of harmonic serenity ,intervals of 5 (4th) , 7 (5th) or 12 (octave) semitones.
We remind that in the post 30 we described the three relations of chord transitions corresponding to the intervals of 2nd, 3rd and 4th or 5th.
1) Resolution relation of chords
MELODIC MEANING : When such a pair of chords accompanies a melody then taking the themes of this melody either the theme is inside the chords is or is a bridge theme relating the two chords. This means that either the interval of 5 (4th) or 7 semitones (5th) appears as a shift or translation of the theme (chord-theme) or exists inside the theme (bridge-theme).
2) Relative chords
MELODIC MEANING: When such a pair of chords accompanies a melody then taking the themes of this melody either the theme is inside the chords is or is a bridge theme relating the two chords. This means that either the interval of 3 (minor 3rd) or 4 semitones (major 3rd) appears as a shift or translation of the theme (chord-theme) or exists inside the theme (bridge-theme).
MELODIC MEANING: When such a pair of chords accompanies a melody then taking the themes of this melody either the theme is inside the chords is or is a bridge theme relating the two chords. This means that either the interval of 3 (minor 3rd) or 4 semitones (major 3rd) appears as a shift or translation of the theme (chord-theme) or exists inside the theme (bridge-theme).
3) Complementary transition of chords
MELODIC MEANING: When such a pair of chords accompanies a melody then taking the themes of this melody either the theme is inside the chords is or is a bridge theme relating the two chords. This means that either the interval of 1 (minor 2nd) or 2 semitones (major 2nd) appears as a shift or translation of the theme (chord-theme) or exists inside the theme (bridge-theme).
Much of the remarkable art of scale butterflying improvisation (see post 55) and in general of melodies and their pitch dynamic patterns (see post 18 ) is that it can create the emotions of sadness, joy etc not through harmonic simultaneous sounding of notes, and common harmonics, but through progressions of intervals.
As we have remarked small interval like 1 semitone is closer to sadness than longer intervals like 1 tone etc.
But what is more effective is the acceleration or deceleration in the movement of the pitch.
Ascending pitch is of course correlated to joy and descanting to sadness. But the acceleration amplifies it.
So an ascending sequence of tones (measured in semitones) 2-2-2 will become even more joyful if it accelerates. That is like this 2-3-5. And a descending sequence of notes will become even more sad if it accelerates 2-2-2 becoming 2-3-5. An ascending sequence of notes will become more sad if it decelerates.
So an ascending 3-2-1 is more sad than the ascending 2-2-2. And when descending the deceleration reduces sadness. So the descending 2-2-2 is more sad than the descending 3-2-1.
See also post 59 for the basic melodic moves spike, scaling, waving, isokratic waving.
1) up/down spike (=large interval of 5th or larger in one or very few steps, extreme emotional effect, excitement , emotional intensity)
2) up/down waving (also called in this blog butterflying, emotional effect of playing either sad of with joy, emotional complication and ambiguity)
3) up/down scaling (direct ascending or descending of notes in a monotone order without waving, emotional effect straight usually with simplicity, emotional clarity)
4) Iso-kratic waving (=horizontal waving with repeating same note, peculiar emotional effect of internal symmetry , and emotional stability )
From these 4 patterns the 1) and 3) are simple and with emotional clarity. The 2) and 4) are with emotional complication and ambiguity.
Another classification would make them 5!
1) Straight scaling up or down (including spikes) in one or more of the melodic speeds (straight sadness or joy). Here the notes of the simplicial submelody are the starting and ending notes.
MORE PITCH DYNAMICS AND THEIR PSYCHOLOGY
We may create more complex pitch dynamic patterns than these basic with recognizable psychological meaning. Eg. a melodic theme that has a spike up but then falls back to the same pitch level corresponds ton an emotion of "complaining" or "crying" or angry protest that turns to sadness"
In general when the melody is ascending through repetitive descending melodic themes (resisting ascension), or is descending through ascending repetitive melodic themes (resisting descending) , the emotion (either joyful or sad) is more dark emotion compared to than when the the melody is ascending through repetitive ascending melodic themes (irresistible ascension) , or is descending through descending repetitive melodic themes (irresistible descending) , the emotion (either joyful or sad) in which latter case it is an emotion more straight and transparent.
See also post 59 for the basic melodic moves spike, scaling, waving, isokratic waving.
1) up/down spike (=large interval of 5th or larger in one or very few steps, extreme emotional effect, excitement , emotional intensity)
2) up/down waving (also called in this blog butterflying, emotional effect of playing either sad of with joy, emotional complication and ambiguity)
3) up/down scaling (direct ascending or descending of notes in a monotone order without waving, emotional effect straight usually with simplicity, emotional clarity)
4) Iso-kratic waving (=horizontal waving with repeating same note, peculiar emotional effect of internal symmetry , and emotional stability )
From these 4 patterns the 1) and 3) are simple and with emotional clarity. The 2) and 4) are with emotional complication and ambiguity.
Another classification would make them 5!
1) Straight scaling up or down (including spikes) in one or more of the melodic speeds (straight sadness or joy). Here the notes of the simplicial submelody are the starting and ending notes.
2) Ascending or descending waving (complex sadness or joy). Here the notes of the simplicial submelody are the starting and ending notes.
3) Flat equilibrium waving (serenity and equilibrium emotion).Here the notes of the simplicial submelody are the upper level and lower level ofthe flat channel.
4) Flat diminishing waving (serenity and diminishing emotions). Here the notes of the simplicial submelody are the starting upper or lower level and h ending note of the diminishing channel
5) Flat expanding waving resolving up or down (serenity emotions exploding to either sadness or joy). Here the notes of the simplicial submelody are the starting note and the ending note at the upper or lower level of the expanding channel.
MORE PITCH DYNAMICS AND THEIR PSYCHOLOGY
We may create more complex pitch dynamic patterns than these basic with recognizable psychological meaning. Eg. a melodic theme that has a spike up but then falls back to the same pitch level corresponds ton an emotion of "complaining" or "crying" or angry protest that turns to sadness"
In general when the melody is ascending through repetitive descending melodic themes (resisting ascension), or is descending through ascending repetitive melodic themes (resisting descending) , the emotion (either joyful or sad) is more dark emotion compared to than when the the melody is ascending through repetitive ascending melodic themes (irresistible ascension) , or is descending through descending repetitive melodic themes (irresistible descending) , the emotion (either joyful or sad) in which latter case it is an emotion more straight and transparent.
Natural major and minor explained with the psychology of the progression of intervals
This is somehow the reason why the mode of the diatonic scale 2-1-2-2-1-2 is called natural minor while the cyclic permutation of it 2-2-1-2-2-2 is called natural major . The former has twice deceleration in ascending 2-1 at the beginning , which is preemptive in the perception with a bias to the deceleration thus sadness, and 2-1 towards the end, while the latter starts with non-deceleration which is again preemptive in the perception towards balance rather than sadness and has only one deceleration 2-1 in the middle!
This explains also why the tetra-chord 1-3-1 of the Harmonic minor and Romani double minor sounds so sad.
They accelerate at the beginning 1-3 as ascending but then suddenly they decelerate fast by 3-1.
The same with the melodic minor 1-2-1.
Also the same principle explains why a minor chord sounds sad, while a major sounds happy. The human harmonic perception starts its analysis of the chord from its highest pitch, that in the normal position is called also dominant note , not without a reason! So for example the chord C major c-e-g , is analyzed by the brain, starting from g, then e, then c, and here the intervals are in a sequence which accelerates, from 3 semitones (minor 3rd) to 4 semitones (major 3rd) thus it sounds with joy. While the A minor a-c-e, is analyzed by the brain from e then c then a, and its a deceleration , from major 3rd interval of 4 semitones to a minor 3rd interval of 3 semitones that decelerating, therefore it induces sadness.
Actually there is another factor , probably more robust that explains the different feeling of the sounds of a major and minor chord.
One may ask, a major triad sounds more harmonious and joyful than a minor triad which sounds more sad? The answer is that the same harmonic score (see post 40 ) of the minor 3rd interval (3 semitones) sounds less harmonious when it is in lower frequencies, than when it is in higher frequencies. And this explains the different feeling of the major and minor chord, although they have the same harmonic score!
Another more simple explanation is the harmonics of the root. For a major triad we need only 5-harmonics to derive all the 3 roots, while for the minor triad, we need 19 harmonics to derive the roots!
To derive the 7 notes of the diatonic scale in major mode, requires more harmonics (of a single note) that one may imagine.
Another aspect of the psychology of the intervals progression in melodies is of course the pitch dynamics waving pattern (butterflying) which is described in detail in post 18.
The psychology of such waving patterns have also been studied in the psychology of the speech of married couples by the research group of the professor Gottman https://www.gottman.com/ http://www.amazon.com/The-Mathematics-Marriage-Nonlinear-Bradford/dp/0262572303 .
A very useful remark for improvisation of melody within a particular chord is the next.
Suppose we are at a note y1 of the melody which fits the underlying chord with notes x1x2x3 (whatever that may mean), then depending on the particular position of y1 relative to the x1x2x3, a shift by an interval of 3rd, 4th, 5th, and 6th wil lead to a note y2 that will again fit the chord!. This is because the relative positions of the notes x1x2x3 of the chord are intervals of major, minor 3rd and pure 5th, and their complementary intervals relative to the octave are minor or major 6th, and pure 4th
We must emphasize a basic philosophy here that when playing the musical instrument, we do not only produce musical sounds but also independently emotions in us. And I do not mean that the musical sounds produce the emotions I mean that our self is producing the emotions parallel and in fitness with the musical sounds
This explains also why the tetra-chord 1-3-1 of the Harmonic minor and Romani double minor sounds so sad.
They accelerate at the beginning 1-3 as ascending but then suddenly they decelerate fast by 3-1.
The same with the melodic minor 1-2-1.
Also the same principle explains why a minor chord sounds sad, while a major sounds happy. The human harmonic perception starts its analysis of the chord from its highest pitch, that in the normal position is called also dominant note , not without a reason! So for example the chord C major c-e-g , is analyzed by the brain, starting from g, then e, then c, and here the intervals are in a sequence which accelerates, from 3 semitones (minor 3rd) to 4 semitones (major 3rd) thus it sounds with joy. While the A minor a-c-e, is analyzed by the brain from e then c then a, and its a deceleration , from major 3rd interval of 4 semitones to a minor 3rd interval of 3 semitones that decelerating, therefore it induces sadness.
Actually there is another factor , probably more robust that explains the different feeling of the sounds of a major and minor chord.
One may ask, a major triad sounds more harmonious and joyful than a minor triad which sounds more sad? The answer is that the same harmonic score (see post 40 ) of the minor 3rd interval (3 semitones) sounds less harmonious when it is in lower frequencies, than when it is in higher frequencies. And this explains the different feeling of the major and minor chord, although they have the same harmonic score!
Another more simple explanation is the harmonics of the root. For a major triad we need only 5-harmonics to derive all the 3 roots, while for the minor triad, we need 19 harmonics to derive the roots!
To derive the 7 notes of the diatonic scale in major mode, requires more harmonics (of a single note) that one may imagine.
Thus the 7-notes of the diatonic scale in major mode, require 27 harmonics. And the correspondence is the next. The notes are of course lowered to be within one octave, while the harmonics in many higher)
C---1 harmonic
D---9
E---5
F---11
G---3
A---27
B---15
C---2
So a major scale like C-E-G, requires only the first 5 harmonics
While a minor scale e.g. C-Eb-G requires 19 harmonics as Eb is obtained as the 19th harmonic.
Another aspect of the psychology of the intervals progression in melodies is of course the pitch dynamics waving pattern (butterflying) which is described in detail in post 18.
The psychology of such waving patterns have also been studied in the psychology of the speech of married couples by the research group of the professor Gottman https://www.gottman.com/ http://www.amazon.com/The-Mathematics-Marriage-Nonlinear-Bradford/dp/0262572303 .
A very useful remark for improvisation of melody within a particular chord is the next.
Suppose we are at a note y1 of the melody which fits the underlying chord with notes x1x2x3 (whatever that may mean), then depending on the particular position of y1 relative to the x1x2x3, a shift by an interval of 3rd, 4th, 5th, and 6th wil lead to a note y2 that will again fit the chord!. This is because the relative positions of the notes x1x2x3 of the chord are intervals of major, minor 3rd and pure 5th, and their complementary intervals relative to the octave are minor or major 6th, and pure 4th
We must emphasize a basic philosophy here that when playing the musical instrument, we do not only produce musical sounds but also independently emotions in us. And I do not mean that the musical sounds produce the emotions I mean that our self is producing the emotions parallel and in fitness with the musical sounds
