Yahoo Tuning Groups Ultimate Backup tuning Harmonic ornamentation

Hi tuners,

not sure how much you'll find of interest here but if this makes you bored, you can let me know. :-D

A few hours ago, I was thinking that while there's melodic ornamentation () and intonational ornamentation (), some properties of classical harmony could be described as harmonic ornamentation. If we think about the evolution of harmony, then we first find the use of fifths and fourths as consonances. Classical harmony might be, in a certain way, characterized as a 3D system because the so-called "consonant" triads contain something more than only fifths -- i.e. octaves work as equivalence intervals, fifths determine the "harmonic fundamental", and thirds determine major or minor "tonal gender" (I'm translating word for word from Czech, don't know if there's a proper English name for this). But there's something more to it. In the late Baroque times, seventh chords came into use. But they didn't bring any brand-new attributes to the "by-then-developed" system, they were used for something like "harmonic ornamentation" -- i.e. whether you played "G-D-G-B, C-C-E-C" or "G-D-F-B, C-C-E-C", the harmonic "meaning" of the phrase was more or less the same.

Now, if we think of it in terms of successive primes, then we get 2 as the interval of equivalence, 3 as the identifier of the harmonic fundamental, 5 as the identifier of "tonal gender", and 7 for harmonic ornamentation. Although I say this with some disappointment (since my meantone-like conditioning doesn't support this claim), it's pretty possible that the use of seventh chords arose from some ideas of approximating 7-limit intervals. OTOH, meantone supports a different view on the 7/4 (i.e. as an augmented sixth) and I have found chords using it in the most acoustically "correct" ways, even at some expense of breaking basic classical harmony rules )i.e. F-A-C-D#, E-B-G#-E). But even then, such a D# sounds to me like some "harmonic ornamentation" to the F major.

Interestingly enough, 7-limit ratios were never used in a similar way to the 5-limit ones. To make an audio test, I took my unnamed 5-limit example from 2006 and retuned it to a scale where all the 5s were replaced by 7s. You can find both the 5-limit and the 7-limit version in the Tuning Files in the PetrParizek folder. So if you wish, you can listen to M-JI and M-JI7 and judge for yourself.

Petr

🔗Marcel de Velde <m.develde@...>

Hi Peter,

A few hours ago, I was thinking that while there's melodic ornamentation ()
> and intonational ornamentation (), some properties of classical harmony
> could be described as harmonic ornamentation. If we think about the
> evolution of harmony, then we first find the use of fifths and fourths as
> consonances.
>

Do you mean fifths and thirds as consonances?
The fourth has almost allways been considered a dissonance (to the
fundamental bass / groundtone)

> Classical harmony might be, in a certain way, characterized as
> a 3D system because the so-called "consonant" triads contain something more
>
> than only fifths -- i.e. octaves work as equivalence intervals, fifths
> determine the "harmonic fundamental", and thirds determine major or minor
> "tonal gender" (I'm translating word for word from Czech, don't know if
> there's a proper English name for this). But there's something more to it.
> In the late Baroque times, seventh chords came into use. But they didn't
> bring any brand-new attributes to the "by-then-developed" system, they were
>
> used for something like "harmonic ornamentation" -- i.e. whether you played
>
> "G-D-G-B, C-C-E-C" or "G-D-F-B, C-C-E-C", the harmonic "meaning" of the
> phrase was more or less the same.
>
> Now, if we think of it in terms of successive primes, then we get 2 as the
> interval of equivalence, 3 as the identifier of the harmonic fundamental, 5
>
> as the identifier of "tonal gender", and 7 for harmonic ornamentation.
> Although I say this with some disappointment (since my meantone-like
> conditioning doesn't support this claim), it's pretty possible that the use
>
> of seventh chords arose from some ideas of approximating 7-limit intervals.
>
> OTOH, meantone supports a different view on the 7/4 (i.e. as an augmented
> sixth) and I have found chords using it in the most acoustically "correct"
> ways, even at some expense of breaking basic classical harmony rules )i.e.
> F-A-C-D#, E-B-G#-E). But even then, such a D# sounds to me like some
> "harmonic ornamentation" to the F major.
>

Yes very interesting, and I have been thinking about the same things up
untill some time ago.
However, after a lot of experimenting, thinking, and listening I now (again
and more than ever) truly beleive now that the minor third above the
fundamental bass is 19/16.
If the minor third above the fundamental bass is indeed 19/16 then the
5-limit intervals are not unique in determining "tonal gender".

-Marcel

🔗Daniel Forró <dan.for@...>

Hi, Peter,

1. Seventh chords were used good 350 years before Late Baroque.

2. There IS difference between triad dominant and seventh dominant -
second chord itself has more tension thanks to tritone inside, and
resolution of this chord to another chords is more tight and stronger
(depending to which chord it goes). Basic harmonic function is the
same, of course, and again depends on resolution (you know well
Janáček's resolution G-B-D-F ----> Ab-Db-Db-F).
There is difference also between any triad and seventh chord based on
it, again in the sound (depends on intervallic structure, as we have
12 types of seventh chord) and in the resolution.

3. During history of European music and music theory using of higher
chords of triadic structure (seventh, ninth, eleventh, thirteenth,
later even crossing two octaves border and using of 12tone triadic
chords) came in my opinion just as logical development of adding more
tones, which is not necessarily connected with harmonic series. But
it's as well possible ithere's a connection.
I think that only piano composers like Chopin, Liszt, Debussy, Ravel,
Skriabin found (probably thanks to using of pedal) some beauty in the
chord based on harmonic series (13/11+) and used this intentionally
in some of their works. But they used as well whole tone scale (and
harmony) and diminished scale (and harmony)...

4. You can't understand higher tones of triadic chords bigger than
triads just as some "ornamentation" or additional, purely
"decorative" tones to basic triad, adding only some color to it. All
tones of such chords are equal and have some reason why composers use
them. Maybe we can find some examaples of purely timbral using of
such chords in some styles of the music of 20th century...

5. There are many ways how to resolve seventh chords, in my personalharmonic theory to any of 24 triads, and of course we can connect
them with more complex chords than triads.

BTW what's wrong with resolution F-A-C-D# to E-G#-B-E? It's standard
harmonic progression, especially in Classicism period, where the
first chord can be subdominant or flatted VI grade in major key, or
VI grade in minor key.

Daniel Forro

On 29 Aug 2009, at 3:20 AM, Petr Pařízek wrote:

>
> Hi tuners,
>
> not sure how much you'll find of interest here but if this makes
> you bored,
> you can let me know. :-D
>
> A few hours ago, I was thinking that while there's melodic
> ornamentation ()
> and intonational ornamentation (), some properties of classical
> harmony
> could be described as harmonic ornamentation. If we think about the
> evolution of harmony, then we first find the use of fifths and
> fourths as
> consonances. Classical harmony might be, in a certain way,
> characterized as
> a 3D system because the so-called "consonant" triads contain
> something more
> than only fifths -- i.e. octaves work as equivalence intervals, fifths
> determine the "harmonic fundamental", and thirds determine major or
> minor
> "tonal gender" (I'm translating word for word from Czech, don't
> know if
> there's a proper English name for this). But there's something more
> to it.
> In the late Baroque times, seventh chords came into use. But they
> didn't
> bring any brand-new attributes to the "by-then-developed" system,
> they were
> used for something like "harmonic ornamentation" -- i.e. whether
> you played
> "G-D-G-B, C-C-E-C" or "G-D-F-B, C-C-E-C", the harmonic "meaning" of
> the
> phrase was more or less the same.
>
> Now, if we think of it in terms of successive primes, then we get 2
> as the
> interval of equivalence, 3 as the identifier of the harmonic
> fundamental, 5
> as the identifier of "tonal gender", and 7 for harmonic ornamentation.
> Although I say this with some disappointment (since my meantone-like
> conditioning doesn't support this claim), it's pretty possible that
> the use
> of seventh chords arose from some ideas of approximating 7-limit
> intervals.
> OTOH, meantone supports a different view on the 7/4 (i.e. as an
> augmented
> sixth) and I have found chords using it in the most acoustically
> "correct"
> ways, even at some expense of breaking basic classical harmony
> rules )i.e.
> F-A-C-D#, E-B-G#-E). But even then, such a D# sounds to me like some
> "harmonic ornamentation" to the F major.
>
> Interestingly enough, 7-limit ratios were never used in a similar
> way to the
> 5-limit ones. To make an audio test, I took my unnamed 5-limit
> example from
> 2006 and retuned it to a scale where all the 5s were replaced by
> 7s. You can
> find both the 5-limit and the 7-limit version in the Tuning Files
> in the
> PetrParizek folder. So if you wish, you can listen to M-JI and M-
> JI7 and
> judge for yourself.
>
> Petr
>
>
>

🔗Mike Battaglia <battaglia01@...>

Hello Petr,

I like the way you think about this stuff... I was throwing some
similar ideas around earlier this year, and apparently I'd reached the
conclusion that the 13:4 sonority and the 7:4 sonority were closer in
"harmonic flavor" than 7:4 and 11:4, when used in an otonal sonority.

> i.e. octaves work as equivalence intervals, fifths
> determine the "harmonic fundamental", and thirds determine major or minor
> "tonal gender" (I'm translating word for word from Czech, don't know if
> there's a proper English name for this).

They would usually refer to it as the chord "quality", I think,
although that could also refer to whether it's a 7th chord, or a 9th
chord, or an aug#11, or what have you. I don't know if there's a term
that refers specifically to which type of third the chord uses.

> i.e. whether you played
> "G-D-G-B, C-C-E-C" or "G-D-F-B, C-C-E-C", the harmonic "meaning" of the
> phrase was more or less the same.

How about G-C#-F-B, C-C-E-C? And if we had more than 4 notes in here,
I'd throw in a b9 for good measure too :)

> Now, if we think of it in terms of successive primes, then we get 2 as the
> interval of equivalence, 3 as the identifier of the harmonic fundamental, 5
> as the identifier of "tonal gender", and 7 for harmonic ornamentation.
> Although I say this with some disappointment (since my meantone-like
> conditioning doesn't support this claim), it's pretty possible that the use
> of seventh chords arose from some ideas of approximating 7-limit intervals.

So would you describe the extended and altered harmonies incorporating
b9's and #9's to be 17- and 19- limit intervals? Would a #11 be a
ratio of 11, or perhaps a 23?

If you look at it that way, it's interesting to see the tendency
people have to actually strengthen the fundamental of dominant chords
with these higher-limit ratios. You would expect a triad like
4:5:6:7:17/2:19/2:23/2 to be extremely accordant and resonate well as
a 1 chord, but this added resonance is much more often used within the
context of a V chord (or an aug6 chord), with it often resolving to a
far simpler form of I chord. You do of course see b7's and #11's and
#9's as 1 chords in certain contexts (like the very end of a song
sometimes)...

And even more interesting about this approach is that (especially in
early American pop music) these extended harmonies are often in a way
that sounds completely natural and intuitive, even though it
completely steps outside the realm of whatever scale or mode the song
is in. Of course, for some reason, when I try to throw 13/4 right in
like that, it doesn't always sit right. (maybe I'm just biased towards
12-tet intervals).

> OTOH, meantone supports a different view on the 7/4 (i.e. as an augmented
> sixth) and I have found chords using it in the most acoustically "correct"
> ways, even at some expense of breaking basic classical harmony rules )i.e.
> F-A-C-D#, E-B-G#-E). But even then, such a D# sounds to me like some
> "harmonic ornamentation" to the F major.

What classical rule does that break?

> Interestingly enough, 7-limit ratios were never used in a similar way to the
> 5-limit ones. To make an audio test, I took my unnamed 5-limit example from
> 2006 and retuned it to a scale where all the 5s were replaced by 7s. You can
> find both the 5-limit and the 7-limit version in the Tuning Files in the
> PetrParizek folder. So if you wish, you can listen to M-JI and M-JI7 and
> judge for yourself.
>
> Petr
>
>
>
>
>
> ------------------------------------
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🔗Daniel Forró <dan.for@...>

On 29 Aug 2009, at 1:53 PM, Mike Battaglia wrote:
> > i.e. octaves work as equivalence intervals, fifths
> > determine the "harmonic fundamental", and thirds determine major > or minor
> > "tonal gender" (I'm translating word for word from Czech, don't > know if
> > there's a proper English name for this).
>
> They would usually refer to it as the chord "quality", I think,
>
> although that could also refer to whether it's a 7th chord, or a 9th
>
> chord, or an aug#11, or what have you. I don't know if there's a term
> that refers specifically to which type of third the chord uses.
>

Peter was talking here only about the third of the chord, which determines major or minor tonality,
not about the other "thirds" which build triadic chord.
>
> How about G-C#-F-B, C-C-E-C?
>

Proper spelling should be G-Db-F-B, as basic shape of this seventh chord 7/5- is G-B-Db-F. When you use C#, structure of chord is not triadic, but quartal. Quite different world :-) Nice to see how near triadic and quartal structure can be - sometimes it depends on the way how chord is written.

> If you look at it that way, it's interesting to see the tendency
> people have to actually strengthen the fundamental of dominant chords
> with these higher-limit ratios.
>

Not only dominant chord...

> You would expect a triad like
> 4:5:6:7:17/2:19/2:23/2 to be extremely accordant and resonate well as
> a 1 chord,
>

For chord functions in functional harmony it's better to use Roman numerals - I, II... For I, IV and V we usually use T, S and D. Your writing "1" is confusing.

> but this added resonance is much more often used within the
> context of a V chord (or an aug6 chord), with it often resolving to a
> far simpler form of I chord. You do of course see b7's and #11's and
> #9's as 1 chords in certain contexts (like the very end of a song
> sometimes)...
>

This kind of using of higher triadic chords has direct relation to harmonics series, for sure (provided there's 13/11+/9/7, like 13th, 11th, 9th and 7th harmonic tone). It serves really as colorization of ending T chord in some jazz styles (or other chords in the song).
>
> And even more interesting about this approach is that (especially in
> early American pop music)
>

What do you mean by this? Could you specify?

> > OTOH, meantone supports a different view on the 7/4 (i.e. as an > augmented
> > sixth) and I have found chords using it in the most acoustically > "correct"
> > ways, even at some expense of breaking basic classical harmony > rules )i.e.
> > F-A-C-D#, E-B-G#-E). But even then, such a D# sounds to me like some
> > "harmonic ornamentation" to the F major.
>
> What classical rule does that break?
>
I have asked him the same, as I'm sure it's quite OK in the classical music.

Daniel Forro

🔗Petr Parízek <p.parizek@...>

🔗Petr Pařízek <p.parizek@...>

Daniel Forró wrote:

> 1. Seventh chords were used good 350 years before Late Baroque.

Could you give an example of such a thing?

> 2. There IS difference between triad dominant and seventh dominant -
> second chord itself has more tension thanks to tritone inside, and
> resolution of this chord to another chords is more tight and stronger
> (depending to which chord it goes). Basic harmonic function is the
> same, of course, and again depends on resolution (you know well
> Janáček's resolution G-B-D-F ----> Ab-Db-Db-F).

Maybe I should have said, at the very beginning of this thread, that I was excluding music of the impressionism and newer periods, which would mean that this „tritonic“ progression doesn’t fit into this „model“. Secondly, seventh chords started appearing long before 12-equal, while that particular progression of Janáček is (as are some of the favored jazz progressions) clearly coming from 12-equal and would be hard to do properly in, say, meantone temperament.

> 4. You can't understand higher tones of triadic chords bigger than
> triads just as some "ornamentation" or additional, purely
> "decorative" tones to basic triad, adding only some color to it. All
> tones of such chords are equal and have some reason why composers use
> them. Maybe we can find some examaples of purely timbral using of
> such chords in some styles of the music of 20th century...

Probably this is where our oppinions differ. Of course, second chords do have their particular „flavor“ and strength and tension and whatever (and this is why musicians use them) but the overall meaning doesn’t change a great deal whether you play „G-G-B-D, E-G-C-G“ or „F-G-B-D, E-G-C-G“. It just adds some higher significance or higher importance to the harmonic phrase -- similarly as if you first say „I enjoyed having met them“ and then „I was so happy to have met them that it was just an unforgettable experience to me“.

> BTW what's wrong with resolution F-A-C-D# to E-G#-B-E?

There’s nothing wrong with it, there’s just the fact that the early classical harmony rules didn’t allow parallel fifths more or less anywhere but they DID allow them in this one case. I have some sort of „personal“ explanation how this thing may have evolved regarding the „sonic“ properties of these chords, but I’m going to post this in another thread later so I won’t go into the detail here.

Petr

🔗Daniel Forró <dan.for@...>

On 29 Aug 2009, at 6:40 PM, Petr Pařízek wrote:

> Daniel Forró wrote:
>
> > 1. Seventh chords were used good 350 years before Late Baroque.
>
> Could you give an example of such a thing?
>
Guillaume de Machaut, and generally late 14th century, especially
manneristic Ars subtilior...

> > 2. There IS difference between triad dominant and seventh dominant -
> > second chord itself has more tension thanks to tritone inside, and
> > resolution of this chord to another chords is more tight and
> stronger
> > (depending to which chord it goes). Basic harmonic function is the
> > same, of course, and again depends on resolution (you know well
> > Janáček's resolution G-B-D-F ----> Ab-Db-Db-F).
>
> Maybe I should have said, at the very beginning of this thread,
> that I was excluding music of the impressionism and newer periods,
> which would mean that this „tritonic“ progression doesn’t fit
> into this „model“. Secondly, seventh chords started appearing
> long before 12-equal, while that particular progression of Janáček > is (as are some of the favored jazz progressions) clearly coming
> from 12-equal and would be hard to do properly in, say, meantone
> temperament.
>

What about Solage's "Fumeaux fume", and all that Italian chromatic madrigal, Lasso, Rore, Marenzio, Gesualdo,... with similar crazy
harmonic progressions?

> > 4. You can't understand higher tones of triadic chords bigger than
> > triads just as some "ornamentation" or additional, purely
> > "decorative" tones to basic triad, adding only some color to it. All
> > tones of such chords are equal and have some reason why composers
> use
> > them. Maybe we can find some examaples of purely timbral using of
> > such chords in some styles of the music of 20th century...
>
> Probably this is where our oppinions differ. Of course, second chords
>

I didn't mentioned "second chords" at all...

> do have their particular „flavor“ and strength and tension and
> whatever (and this is why musicians use them) but the overall
> meaning doesn’t change a great deal whether you play „G-G-B-D, E-
> G-C-G“ or „F-G-B-D, E-G-C-G“. It just adds some higher
> significance or higher importance to the harmonic phrase --
> similarly as if you first say „I enjoyed having met them“ and
> then „I was so happy to have met them that it was just an
> unforgettable experience to me“.
>

Yes, in those two examples meaning of harmonic function is the same,
of course. But originally you have compared pure triad and seventh
chord...

> > BTW what's wrong with resolution F-A-C-D# to E-G#-B-E?
>
> There’s nothing wrong with it, there’s just the fact that the
> early classical harmony rules didn’t allow parallel fifths more or
> less anywhere but they DID allow them in this one case.
>
Yes, "Mozartian fifths" they are called. BTW, Mozart was very
"advanced" concerning fifths, I have discovered nice example of them...

I have found another interesting connection, it's and inversion of
previous one: F-G#-B#-D# to E-A-C#-E... so there are also parallel
fifths. Should be also allowed in that restrictive classical harmony,
shouldn't be?

> I have some sort of „personal“ explanation how this thing may
> have evolved regarding the „sonic“ properties of these chords,
> but I’m going to post this in another thread later so I won’t go
> into the detail here.
>
> Petr
>
OK.

Daniel Forro

🔗Mike Battaglia <battaglia01@...>

>> How about G-C#-F-B, C-C-E-C?
>>
>
> Proper spelling should be G-Db-F-B, as basic shape of this seventh
> chord 7/5- is G-B-Db-F. When you use C#, structure of chord is not
> triadic, but quartal. Quite different world :-) Nice to see how near
> triadic and quartal structure can be - sometimes it depends on the
> way how chord is written.

I've always hated spelling a #11 chord as a b5. This is because that
chord will often have a #11 AND a natural 5 in it, and will
furthermore be derived from a scale that has a raised fourth degree
rather than a lowered fifth. And I've never seen a chord that has both
a 4 and a #4 in it, but I've seen plenty of chords that have a 5 and a
#4. So a full spelling of the chord above would be G-B-D-F-A-C#, not
G-B-D-F-A-Db.

>> You would expect a triad like
>> 4:5:6:7:17/2:19/2:23/2 to be extremely accordant and resonate well as
>> a 1 chord,
>>
>
> For chord functions in functional harmony it's better to use Roman
> numerals - I, II... For I, IV and V we usually use T, S and D. Your
> writing "1" is confusing.

Hahaha, nothing gets past you, does it? That was a typo, written at 1
in the morning :)

>> And even more interesting about this approach is that (especially in
>> early American pop music)
> What do you mean by this? Could you specify?

Sure, these types of harmonies were used almost exclusively in
American pop music around the 30s, 40s, and to some extent the 50s...
The type of music that Frank Sinatra would sing. Music by composers
such as Cole Porter, George Gershwin, Harry Warren, etc, would use
(and sometimes overuse) extended, altered, or aux. diminished
harmonies as part of the tonal language of their song. If these
harmonies are more well known for their prevalence in jazz, it's only
because the jazz repertoire drew on the music of the "Great American
Songbook", as it's called, where these types of harmonies were
employed to the point of becoming idiomatically recognizable as a part
of the music of that time period.

🔗Daniel Forró <dan.for@...>

On 29 Aug 2009, at 11:34 PM, Mike Battaglia wrote:
> I've always hated spelling a #11 chord as a b5. This is because that
> chord will often have a #11 AND a natural 5 in it, and will
> furthermore be derived from a scale that has a raised fourth degree
> rather than a lowered fifth. And I've never seen a chord that has both
> a 4 and a #4 in it, but I've seen plenty of chords that have a 5 and a
> #4. So a full spelling of the chord above would be G-B-D-F-A-C#, not
> G-B-D-F-A-Db.
>

Sorry, it was not totally clear from four notes chord if there was 5- or 11+, I agree this must be differentiated. But discussion was about seventh chord, so I supposed 5-.

Anyway - classical tonality rules don't allow to change notes of tonic chords (in this case C-E-G), so sharpened fourth C# in dominant chord (which is in the same time root note of tonic chord) is not possible. Only Db is allowed in C major tonality. But jazz harmony is more flexible...

> > For chord functions in functional harmony it's better to use Roman
> > numerals - I, II... For I, IV and V we usually use T, S and D. Your
> > writing "1" is confusing.
>
> Hahaha, nothing gets past you, does it? That was a typo, written at 1
> in the morning :)
>

:-)
>
> >> And even more interesting about this approach is that > (especially in
> >> early American pop music)
> > What do you mean by this? Could you specify?
>
> Sure, these types of harmonies were used almost exclusively in
> American pop music around the 30s, 40s, and to some extent the 50s...
> The type of music that Frank Sinatra would sing. Music by composers
> such as Cole Porter, George Gershwin, Harry Warren, etc, would use
> (and sometimes overuse) extended, altered, or aux. diminished
> harmonies as part of the tonal language of their song. If these
> harmonies are more well known for their prevalence in jazz, it's only
> because the jazz repertoire drew on the music of the "Great American
> Songbook", as it's called, where these types of harmonies were
> employed to the point of becoming idiomatically recognizable as a part
> of the music of that time period.
Yes, you are right, of course. I've just never met a term "early American pop" for this music...

Daniel Forro

Harmonic ornamentation - i.e. classical harmony as a 3D system

🔗Petr Pařízek <p.parizek@...>

🔗Marcel de Velde <m.develde@...>

🔗Daniel Forró <dan.for@...>

🔗Mike Battaglia <battaglia01@...>

🔗Daniel Forró <dan.for@...>

🔗Petr Parízek <p.parizek@...>

🔗Petr Pařízek <p.parizek@...>

🔗Daniel Forró <dan.for@...>

🔗Daniel Forró <dan.for@...>

🔗Mike Battaglia <battaglia01@...>

🔗Daniel Forró <dan.for@...>