Yahoo Tuning Groups Ultimate Backup tuning Chromatic chords

One student asked me why a CmM7 is more dissonant than Cm7. There is nothing wrong inside: just some thirds, a major seventh and a perfect fifths. The dissonance seems to come from m6 between m3 and M7 but m6 is a consonant interval for example in the inversion of a major triad. So it seems there is no reason for dissonance.

I've done this explanation:

This chord comes from a chromatically altered scale for example an harmonic minor (eolian +7) or a melodic minor (dorian +7). These chromatic alteration are melodically based and normally they are near fondamental, octave or fifth of the scale. They also reduce the harmonic stability of the scales because the major number of fifths and fourths are always founded in a consecutive chain of fifths. So I think there are "harmonic scales" which beside melody preserve harmony, and "melodic scales" which are unbalanced on melodic effects.

So if we play a major seventh we are naturally inclined to perceive a major third even if not played; at the same way a minor third "calls" a minor seventh. The compresence of m3 and M7 give us the perception that the scale of this chord is wider than 7 notes and includes at least a chromatic passage of two consecutive semitones resulting more dissonant.

Actually melodic and harmonic scales had these genesis because the ascending mode was different from descending resulting in a chromatic melodic material.

So there are three kind of chords: pentatonic, diatonic and chromatic.
Pentatonic chords are founded inside a chain of five fifths, diatonic are inside a chain of 7 fifths and chromatic inside 12 fifths.

CmM7 is a chromatic chord even if it comes from a seven notes scale.

Should my student change teacher? :-))

Lorenzo

🔗jjensen142000 <jjensen14@hotmail.com>

--- In tuning@yahoogroups.com, "Lorenzo Frizzera"
<lorenzo.frizzera@c...> wrote:
> One student asked me why a CmM7 is more dissonant than Cm7. There
is nothing wrong inside: just some thirds, a major seventh and a
perfect fifths. The dissonance seems to come from m6 between m3 and
M7 but m6 is a consonant interval for example in the inversion of a
major triad. So it seems there is no reason for dissonance.

CmM7 is the notes C-Eb-G-B right? and Cm7 = C-Eb-G-Bb?
Then there is a much simpler explanation:

The harmonics of the B beat more strongly against those
of C than Bb does, since B is closer to the 2nd harmonic of
C -- that's all there is to it!

--JEff

🔗George D. Secor <gdsecor@yahoo.com>

That interval between Eb and B is not a minor 6th (a consonance), but
an augmented 5th (a dissonance). If you think that so-
called "enharmonically equivalent" intervals are one and the same
(particularly in 12-ET), then please read this:

/tuning/topicId_48499.html#49594

--George

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Lorenzo,

An excellent explanation!

Your statement "So if we play a major seventh we are naturally inclined to
perceive a major third even if not played [my emphasis]; at the same way a
minor third "calls" a minor seventh." mirrors my own feelings exactly.

And you have also provided a good rationale for naming some scales
"harmonic" and others "melodic".

Regards,
Yahya
-----Original Message-----
From: Lorenzo Frizzera [mailto:lorenzo.frizzera@cdmrovereto.it]
Sent: Saturday 22 January 2005 0:40 am
To: tuning@yahoogroups.com
Subject: [tuning] Chromatic chords

One student asked me why a CmM7 is more dissonant than Cm7. There is
nothing wrong inside: just some thirds, a major seventh and a perfect
fifths. The dissonance seems to come from m6 between m3 and M7 but m6 is a
consonant interval for example in the inversion of a major triad. So it
seems there is no reason for dissonance.

I've done this explanation:

This chord comes from a chromatically altered scale for example an
harmonic minor (eolian +7) or a melodic minor (dorian +7). These chromatic
alteration are melodically based and normally they are near fondamental,
octave or fifth of the scale. They also reduce the harmonic stability of the
scales because the major number of fifths and fourths are always founded in
a consecutive chain of fifths. So I think there are "harmonic scales" which
beside melody preserve harmony, and "melodic scales" which are unbalanced on
melodic effects.

So if we play a major seventh we are naturally inclined to perceive a
major third even if not played; at the same way a minor third "calls" a
minor seventh. The compresence of m3 and M7 give us the perception that the
scale of this chord is wider than 7 notes and includes at least a chromatic
passage of two consecutive semitones resulting more dissonant.

Actually melodic and harmonic scales had these genesis because the
ascending mode was different from descending resulting in a chromatic
melodic material.

So there are three kind of chords: pentatonic, diatonic and chromatic.
Pentatonic chords are founded inside a chain of five fifths, diatonic are
inside a chain of 7 fifths and chromatic inside 12 fifths.

CmM7 is a chromatic chord even if it comes from a seven notes scale.

Should my student change teacher? :-))

Lorenzo

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🔗Jacob <jbarton@rice.edu>

--- In tuning@yahoogroups.com, "Lorenzo Frizzera" <lorenzo.frizzera@c...> wrote:
> One student asked me why a CmM7 is more dissonant than Cm7. There is nothing
wrong inside: just some thirds, a major seventh and a perfect fifths. The dissonance seems
to come from m6 between m3 and M7 but m6 is a consonant interval for example in the
inversion of a major triad. So it seems there is no reason for dissonance.

Technically that's not a m6 but an augmented fifth, e.g. Eb to B. Which is reached by
going eight fifths in one direction. Which fits nicely with your explanation.

🔗jjensen142000 <jjensen14@hotmail.com>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
>
> --- In tuning@yahoogroups.com, "Lorenzo Frizzera"
> <lorenzo.frizzera@c...> wrote:
> > One student asked me why a CmM7 is more dissonant than Cm7. There
> is nothing wrong inside: just some thirds, a major seventh and a
> perfect fifths. The dissonance seems to come from m6 between m3 and
> M7 but m6 is a consonant interval for example in the inversion of a
> major triad. So it seems there is no reason for dissonance.
>
> That interval between Eb and B is not a minor 6th (a consonance),
but
> an augmented 5th (a dissonance). If you think that so-
> called "enharmonically equivalent" intervals are one and the same
> (particularly in 12-ET), then please read this:
>
> /tuning/topicId_48499.html#49594
>
> --George

Hi George

I agree with you about what you said in message 49594 that
the context can cue the listener to interpret intervals as
parts of different chords, particularly in a cadence.

However, I don't think that applies here, because there
is only one chord (CmM7) or (Cmm7); it is not said to
be part of a progression. Now, if we were talking about
C7 (C-E-G-Bb) then I could believe that chord standing alone
could suggest a cadence to F.

A major 7th ( c - b) is a highly dissonant interval!

--Jeff
So what you are saying is that we have the strong cadence
CmM7 = C7 ---> F

🔗jjensen142000 <jjensen14@hotmail.com>

🔗Lorenzo Frizzera <lorenzo.frizzera@cdmrovereto.it>

>The harmonics of the B beat more strongly against those
>of C than Bb does, since B is closer to the 2nd harmonic of
>C -- that's all there is to it!

Any of my student never told me that a Cmaj7 is dissonant even if it includes a B.
You can find a lot of maj7 chords in pop music, for example, but a mM7 is really less used probably because it is more dissonant.

Also I absolutely agree with George and Jacob:

>That interval between Eb and B is not a minor 6th (a consonance), >but an augmented 5th (a dissonance).

(and i'm quite embarassed...) :)

And also with the message George linked where I read:

>in 12-ET the intervals are exactly the same sizes, but the harmonic >context makes all the difference.

What I was trying to do was exactly to define that "harmonic context" which I consider actually a portion of the chain of fifth stopped each time on the shorter step respect tonic: 2 steps = fourth, 5 steps = tone, 7 steps = half tone, 12 steps = comma).

Lorenzo

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Hi all,

Another approach is simply to calculate the total beating roughness of each
chord, in the fashion pioneered by Helmholtz, then compare the roughness
measures to say which is the more consonant or dissonant of the two.
Of course, since my arrival on this list I have seen many other measures of
harmonic consonance alluded to, which presumably offer improvements on
Helmholtz' methods.

If any member could give me some concise directions to references on the
development of the subject since Helmholtz' day, I'd be most obliged. (It's
not every day you get to advance your thinking by more than a century ...!)

Regards,
Yahya
-----Original Message-----
From: Jeff Jensen

Hi George

I agree with you about what you said in message 49594 that
the context can cue the listener to interpret intervals as
parts of different chords, particularly in a cadence.

A major 7th ( c - b) is a highly dissonant interval!

--Jeff
So what you are saying is that we have the strong cadence
CmM7 = C7 ---> F

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🔗jjensen142000 <jjensen14@hotmail.com>

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
> Hi all,
>
> Another approach is simply to calculate the total beating roughness
of each
> chord, in the fashion pioneered by Helmholtz, then compare the
roughness
> measures to say which is the more consonant or dissonant of the two.
> Of course, since my arrival on this list I have seen many other
measures of
> harmonic consonance alluded to, which presumably offer improvements
on
> Helmholtz' methods.
>
> If any member could give me some concise directions to references
on the
> development of the subject since Helmholtz' day, I'd be most
obliged. (It's
> not every day you get to advance your thinking by more than a
century ...!)

There is a lot of stuff, but here are some good enty points
(on the web, rather than digging through the university library!)

Ernst Terhardt
http://www.mmk.e-technik.tu-muenchen.de/persons/ter.html

and William Sethares, who was just posting to this list not too
long ago:
http://eceserv0.ece.wisc.edu/~sethares/consemi.html

I hope this helps,
Jeff
(and by no means is that an exhaustive list! I left out a lot
of people, some of whom read this list and now presumably
hate me, but that's life...)