Vilen
2012-01-30 08:13:15 UTC
In last year November I tried to clear my questions about this matter
but the initiated discussion deviated in undesirable direction. I am
interesting why the handbooks, Internet sites , etc. consider only 3
orders from possible 6 although they all are used in practice. In try
to understand the matter I formed the table below. The scale
intervals(i) and corresponding distances in semitones(s) from bass
note are indicated in it for major triad c-e-g and its possible
inversions.
c-e-g > 4s/3i, 7s/5i
e-g-c > 3s/3i, 8s/6i C note upwards, 2 notes downwards
g-c-e > 5s/4i, 9s/6i 2 notes upwards, G note downwards
e-c-g > 8s/6i, 15s/9i E note downwards
c-g-e > 7s/5i, 16s/10i E note upwards
g-e-c > 9s/6i,17s/11i C note upwards, G note downwards
Let us consider presented in the table chords from 2 points of view
- greatest dissonances between third and even harmonics and
stability of missing fundamental (MF) (i.e. its clear articulation ).
Importance of dissonances is obvious. Importance of stability of MF
follows from the determined fact that brain includes an apparatus for
estimating missing fundamental which is tied with emotional
perception.
The pairs of chords with same bass notes would be compared as in
practice they determine the name of inversion.
For major chord c-e-g in root close position there is dissonance
between 4. harmonic of root C and 3. harmonic of E. MF of the chord is
2 octaves below root C.
For chord c-g-e there is dissonance between 8. harmonic of root C
and 3. harmonic of E. Missing fundamental of the chord is 2 octaves
below root note C as well.
For first inversion e-g-c there is dissonance between 2.
harmonic of C and 3. harmonic of E. MF of the chord is 3 octaves
below root note C, i.e. worse determined as by basic major chord, but
es may be improved through addition C note below chord notes. By it
melody note would be duplicated.
The chord e-c-g is considered as first inversion as well. It has
dissonance between 2. harmonic of C and 3. harmonic of E and MF 5
times below note E and hence 3 octaves below note C.
Second inversion g-c-e has dissonance between 4. harmonic of root C
and 3. harmonic of E. It has same MF as basic chord which is worth
determined thank to positions of notes C and E.
Second inversion g-e-c has dissonance between 2. harmonic of root C
and 3. harmonic of E. It determines MF somewhat worse as inversion g-c-
e thank to far position of note C.
The presented analysis permits to suppose that basic order c-e-g and
its most known inversions e-g-c and g-c-e have advantage in the
majority of cases.
Yuri Vilenkin
but the initiated discussion deviated in undesirable direction. I am
interesting why the handbooks, Internet sites , etc. consider only 3
orders from possible 6 although they all are used in practice. In try
to understand the matter I formed the table below. The scale
intervals(i) and corresponding distances in semitones(s) from bass
note are indicated in it for major triad c-e-g and its possible
inversions.
c-e-g > 4s/3i, 7s/5i
e-g-c > 3s/3i, 8s/6i C note upwards, 2 notes downwards
g-c-e > 5s/4i, 9s/6i 2 notes upwards, G note downwards
e-c-g > 8s/6i, 15s/9i E note downwards
c-g-e > 7s/5i, 16s/10i E note upwards
g-e-c > 9s/6i,17s/11i C note upwards, G note downwards
Let us consider presented in the table chords from 2 points of view
- greatest dissonances between third and even harmonics and
stability of missing fundamental (MF) (i.e. its clear articulation ).
Importance of dissonances is obvious. Importance of stability of MF
follows from the determined fact that brain includes an apparatus for
estimating missing fundamental which is tied with emotional
perception.
The pairs of chords with same bass notes would be compared as in
practice they determine the name of inversion.
For major chord c-e-g in root close position there is dissonance
between 4. harmonic of root C and 3. harmonic of E. MF of the chord is
2 octaves below root C.
For chord c-g-e there is dissonance between 8. harmonic of root C
and 3. harmonic of E. Missing fundamental of the chord is 2 octaves
below root note C as well.
For first inversion e-g-c there is dissonance between 2.
harmonic of C and 3. harmonic of E. MF of the chord is 3 octaves
below root note C, i.e. worse determined as by basic major chord, but
es may be improved through addition C note below chord notes. By it
melody note would be duplicated.
The chord e-c-g is considered as first inversion as well. It has
dissonance between 2. harmonic of C and 3. harmonic of E and MF 5
times below note E and hence 3 octaves below note C.
Second inversion g-c-e has dissonance between 4. harmonic of root C
and 3. harmonic of E. It has same MF as basic chord which is worth
determined thank to positions of notes C and E.
Second inversion g-e-c has dissonance between 2. harmonic of root C
and 3. harmonic of E. It determines MF somewhat worse as inversion g-c-
e thank to far position of note C.
The presented analysis permits to suppose that basic order c-e-g and
its most known inversions e-g-c and g-c-e have advantage in the
majority of cases.
Yuri Vilenkin