functional harmony (was: reply to Carl Lumma)

>> [Paul Erlich, TD 512.14]
>> The dominant chord _is_ a functional harmony (according
>> to tonal analysis a la Forte), and that's exactly how
>> Barbershop uses it.

> [Carl Lumma, TD 520.7]
> I'm not familiar with Forte, or with a good definition of
> "functional harmony".

I'm not very familiar with Forte's work either (at least
not his work on *tonal* harmony), and also not sure that I
know enough about 'functional harmony' to offer a good
definition either, but here's my 2 cents on it:

AFAIK, the term originated with Riemann around 1880. It
refers to an analytical method which recognizes the Subdominant,
Tonic, and Dominant (or, as I would say, 3^(-1,0,1) as
the only basic 'forces' in musical harmony, and classifies
all other 'roots' as related to them.

The other roots are analyzable into either of two of the
categories, depending on context.

Thus,

chord 'root' category

VII Dominant or Subdominant
VI Tonic or Subdominant
V Dominant
IV Subdominant
III Tonic or Dominant
II Subdominant (sometimes Dominant, I think)
I Tonic

So typically, in an analysis, every chord is marked either
'T', 'S', or 'D'.

(The other important aspect to Riemann's early theories,
which he later abdicated, was that of 'dualism', which is
akin to Partch o- and u-tonal concepts. Earlier theorists
had used it, principally Oettingen. But that's a different
matter...)

> [Carl Lumma, TD 522.9]
> Barbershop songs modulate primarily by fifths, just as the
> songs of most genres. So if you wanted, you could describe
> most of the 7th chords as being dominants of their successors.
> But the successor is also a "dominant" 7th, and so on. Such
> an analysis wouldn't add much insight to the music, though.

But this kind of analysis is *very* useful in jazz. There's
a good exposition of this in a journal of jazz theory (don't
have it handy and thus can't cite it), which suggests using
'N' to symbolize the 'goal' of a string of dominants, and
'N-3', 'N-2', 'N-1', etc., to symbolize the dominants of the
dominants. 'N+1', etc., would symbolize 'root'-movement
by subdominants, which is much less common in jazz.

The paper uses 'All The Things You Are' (by Jerome Kern) to
illustrate the method, and it is very appropriate indeed for
a tune like that, instead of Roman numerals with loads of
accidentals (and which numerals don't really signify anything
pertinent to the chord movement in this song).

This type of analysis can be seen as a modification of the
'T/D/S' advocated by Riemann.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

________________________________________________________________
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>From: Joe Monzo <monz@juno.com>
>
>> [Carl Lumma, TD 520.7]
>> I'm not familiar with Forte, or with a good definition of
>> "functional harmony".
>
>
>I'm not very familiar with Forte's work either (at least
>not his work on *tonal* harmony), and also not sure that I
>know enough about 'functional harmony' to offer a good
>definition either, but here's my 2 cents on it:

If every two cents was as good as that we'd all be rich!

John Link

****************************************************************************

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featuring original compositions as well as arrangements of instrumental
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Monz - thanks for the links to previous threads on functional
harmony (like the one below). THey're really great, esp as I"m not
familiar with all the music theorists.

Its strikes me that, in addition to the force of I, IV, V mentioned
below, that another powerful force in functional harmony is the
powerful contrast provided by restating material in a minor key.
It's also interesting that, as the first 'force' (I, IV, V) is
related to the third harmonic, that the second force is related to
its double, the 6th harmonic (the 6/5 interval).

John

--- In tuning@yahoogroups.com, Joe Monzo <monz@j...> wrote:
>
> >> [Paul Erlich, TD 512.14]
> >> The dominant chord _is_ a functional harmony (according
> >> to tonal analysis a la Forte), and that's exactly how
> >> Barbershop uses it.
>
> > [Carl Lumma, TD 520.7]
> > I'm not familiar with Forte, or with a good definition of
> > "functional harmony".
>
>
> I'm not very familiar with Forte's work either (at least
> not his work on *tonal* harmony), and also not sure that I
> know enough about 'functional harmony' to offer a good
> definition either, but here's my 2 cents on it:
>
>
> AFAIK, the term originated with Riemann around 1880. It
> refers to an analytical method which recognizes the Subdominant,
> Tonic, and Dominant (or, as I would say, 3^(-1,0,1) as
> the only basic 'forces' in musical harmony, and classifies
> all other 'roots' as related to them.
>
> The other roots are analyzable into either of two of the
> categories, depending on context.
>
> Thus,
>
> chord 'root' category
>
> VII Dominant or Subdominant
> VI Tonic or Subdominant
> V Dominant
> IV Subdominant
> III Tonic or Dominant
> II Subdominant (sometimes Dominant, I think)
> I Tonic
>
> So typically, in an analysis, every chord is marked either
> 'T', 'S', or 'D'.
>
> (The other important aspect to Riemann's early theories,
> which he later abdicated, was that of 'dualism', which is
> akin to Partch o- and u-tonal concepts. Earlier theorists
> had used it, principally Oettingen. But that's a different
> matter...)
>
>
>
> > [Carl Lumma, TD 522.9]
> > Barbershop songs modulate primarily by fifths, just as the
> > songs of most genres. So if you wanted, you could describe
> > most of the 7th chords as being dominants of their successors.
> > But the successor is also a "dominant" 7th, and so on. Such
> > an analysis wouldn't add much insight to the music, though.
>
>
> But this kind of analysis is *very* useful in jazz. There's
> a good exposition of this in a journal of jazz theory (don't
> have it handy and thus can't cite it), which suggests using
> 'N' to symbolize the 'goal' of a string of dominants, and
> 'N-3', 'N-2', 'N-1', etc., to symbolize the dominants of the
> dominants. 'N+1', etc., would symbolize 'root'-movement
> by subdominants, which is much less common in jazz.
>
> The paper uses 'All The Things You Are' (by Jerome Kern) to
> illustrate the method, and it is very appropriate indeed for
> a tune like that, instead of Roman numerals with loads of
> accidentals (and which numerals don't really signify anything
> pertinent to the chord movement in this song).
>
> This type of analysis can be seen as a modification of the
> 'T/D/S' advocated by Riemann.
>
>
> -monz
>
> Joseph L. Monzo Philadelphia monz@j...
> http://www.ixpres.com/interval/monzo/homepage.html
> |"...I had broken thru the lattice barrier..."|
> | - Erv Wilson |
> --------------------------------------------------
>
> ________________________________________________________________
> YOU'RE PAYING TOO MUCH FOR THE INTERNET!
> Juno now offers FREE Internet Access!
> Try it today - there's no risk! For your FREE software, visit:
> http://dl.www.juno.com/get/tagj.

Good grief, fellas, you ever talk about music here?!?! After
seeing your thread "new member question...", sort of made me want to
puke...not from trying to understand it --you've really developed
this stuff!-- but from how far removed it seems from music making or
even thinking about music. Sort of confirms my observation that
computer/math types and music types, at their core, are often
fundamentally different... Or maybe you need to be stoned (Monz!)
to hear some of the '11-limit' and other things you mention?

John

--- In tuning@yahoogroups.com, "edfg555" <edfg555@y...> wrote:
>
> Monz - thanks for the links to previous threads on functional
> harmony (like the one below). THey're really great, esp as I"m
not
> familiar with all the music theorists.
>
> Its strikes me that, in addition to the force of I, IV, V
mentioned
> below, that another powerful force in functional harmony is the
> powerful contrast provided by restating material in a minor key.
> It's also interesting that, as the first 'force' (I, IV, V) is
> related to the third harmonic, that the second force is related to
> its double, the 6th harmonic (the 6/5 interval).
>
> John
>
> --- In tuning@yahoogroups.com, Joe Monzo <monz@j...> wrote:
> >
> > >> [Paul Erlich, TD 512.14]
> > >> The dominant chord _is_ a functional harmony (according
> > >> to tonal analysis a la Forte), and that's exactly how
> > >> Barbershop uses it.
> >
> > > [Carl Lumma, TD 520.7]
> > > I'm not familiar with Forte, or with a good definition of
> > > "functional harmony".
> >
> >
> > I'm not very familiar with Forte's work either (at least
> > not his work on *tonal* harmony), and also not sure that I
> > know enough about 'functional harmony' to offer a good
> > definition either, but here's my 2 cents on it:
> >
> >
> > AFAIK, the term originated with Riemann around 1880. It
> > refers to an analytical method which recognizes the Subdominant,
> > Tonic, and Dominant (or, as I would say, 3^(-1,0,1) as
> > the only basic 'forces' in musical harmony, and classifies
> > all other 'roots' as related to them.
> >
> > The other roots are analyzable into either of two of the
> > categories, depending on context.
> >
> > Thus,
> >
> > chord 'root' category
> >
> > VII Dominant or Subdominant
> > VI Tonic or Subdominant
> > V Dominant
> > IV Subdominant
> > III Tonic or Dominant
> > II Subdominant (sometimes Dominant, I think)
> > I Tonic
> >
> > So typically, in an analysis, every chord is marked either
> > 'T', 'S', or 'D'.
> >
> > (The other important aspect to Riemann's early theories,
> > which he later abdicated, was that of 'dualism', which is
> > akin to Partch o- and u-tonal concepts. Earlier theorists
> > had used it, principally Oettingen. But that's a different
> > matter...)
> >
> >
> >
> > > [Carl Lumma, TD 522.9]
> > > Barbershop songs modulate primarily by fifths, just as the
> > > songs of most genres. So if you wanted, you could describe
> > > most of the 7th chords as being dominants of their successors.
> > > But the successor is also a "dominant" 7th, and so on. Such
> > > an analysis wouldn't add much insight to the music, though.
> >
> >
> > But this kind of analysis is *very* useful in jazz. There's
> > a good exposition of this in a journal of jazz theory (don't
> > have it handy and thus can't cite it), which suggests using
> > 'N' to symbolize the 'goal' of a string of dominants, and
> > 'N-3', 'N-2', 'N-1', etc., to symbolize the dominants of the
> > dominants. 'N+1', etc., would symbolize 'root'-movement
> > by subdominants, which is much less common in jazz.
> >
> > The paper uses 'All The Things You Are' (by Jerome Kern) to
> > illustrate the method, and it is very appropriate indeed for
> > a tune like that, instead of Roman numerals with loads of
> > accidentals (and which numerals don't really signify anything
> > pertinent to the chord movement in this song).
> >
> > This type of analysis can be seen as a modification of the
> > 'T/D/S' advocated by Riemann.
> >
> >
> > -monz
> >
> > Joseph L. Monzo Philadelphia monz@j...
> > http://www.ixpres.com/interval/monzo/homepage.html
> > |"...I had broken thru the lattice barrier..."|
> > | - Erv Wilson |
> > --------------------------------------------------
> >
> > ________________________________________________________________
> > YOU'RE PAYING TOO MUCH FOR THE INTERNET!
> > Juno now offers FREE Internet Access!
> > Try it today - there's no risk! For your FREE software, visit:
> > http://dl.www.juno.com/get/tagj.

--- In tuning@yahoogroups.com, "edfg555" <edfg555@y...> wrote:
>
> Good grief, fellas, you ever talk about music here?!?!

If you look at what Paul wrote, there isn't any heavy math in it, but
a lot of stuff like "dominant chord", "functional harmony", and the
like. In other words, music theory.

After
> seeing your thread "new member question...", sort of made me want to
> puke...not from trying to understand it --you've really developed
> this stuff!-- but from how far removed it seems from music making or
> even thinking about music. Sort of confirms my observation that
> computer/math types and music types, at their core, are often
> fundamentally different...

Oh, please. The computer/math people do as much as anyone on this list
when it comes to actually writing music.

Or maybe you need to be stoned (Monz!)
> to hear some of the '11-limit' and other things you mention?

Get stoned, listen to some Partch (not a computer/math geek,
incidentally), and tell us what you conclude.

hi John,

--- In tuning@yahoogroups.com, "edfg555" <edfg555@y...> wrote:

> Good grief, fellas, you ever talk about music here?!?!
> After seeing your thread "new member question...", sort of
> made me want to puke...not from trying to understand it
> --you've really developed this stuff!-- but from how far
> removed it seems from music making or even thinking about
> music. Sort of confirms my observation that computer/math
> types and music types, at their core, are often fundamentally
> different... Or maybe you need to be stoned (Monz!)
> to hear some of the '11-limit' and other things you mention?

i hear the same stuff in tunings whether i'm stoned or not.
don't really get where you're going with that ...

-monz

I've had those moments too, but people like what they like. Let
them have their kicks. It was a math type who made the Moog (he was
not a musician in any way), and pretty much every other synth ever
conceived. Even if you can't get into what they're talking about,
you can benefit from the results.

-Chuckk

--- In tuning@yahoogroups.com, "edfg555" <edfg555@y...> wrote:
>
> Good grief, fellas, you ever talk about music here?!?! After
> seeing your thread "new member question...", sort of made me want
to
> puke...not from trying to understand it --you've really developed
> this stuff!-- but from how far removed it seems from music making
or
> even thinking about music. Sort of confirms my observation that
> computer/math types and music types, at their core, are often
> fundamentally different... Or maybe you need to be stoned (Monz!)
> to hear some of the '11-limit' and other things you mention?
>
> John
>
> --- In tuning@yahoogroups.com, "edfg555" <edfg555@y...> wrote:
> >
> > Monz - thanks for the links to previous threads on functional
> > harmony (like the one below). THey're really great, esp as I"m
> not
> > familiar with all the music theorists.
> >
> > Its strikes me that, in addition to the force of I, IV, V
> mentioned
> > below, that another powerful force in functional harmony is the
> > powerful contrast provided by restating material in a minor
key.
> > It's also interesting that, as the first 'force' (I, IV, V) is
> > related to the third harmonic, that the second force is related
to
> > its double, the 6th harmonic (the 6/5 interval).
> >
> > John
> >
> > --- In tuning@yahoogroups.com, Joe Monzo <monz@j...> wrote:
> > >
> > > >> [Paul Erlich, TD 512.14]
> > > >> The dominant chord _is_ a functional harmony (according
> > > >> to tonal analysis a la Forte), and that's exactly how
> > > >> Barbershop uses it.
> > >
> > > > [Carl Lumma, TD 520.7]
> > > > I'm not familiar with Forte, or with a good definition of
> > > > "functional harmony".
> > >
> > >
> > > I'm not very familiar with Forte's work either (at least
> > > not his work on *tonal* harmony), and also not sure that I
> > > know enough about 'functional harmony' to offer a good
> > > definition either, but here's my 2 cents on it:
> > >
> > >
> > > AFAIK, the term originated with Riemann around 1880. It
> > > refers to an analytical method which recognizes the
Subdominant,
> > > Tonic, and Dominant (or, as I would say, 3^(-1,0,1) as
> > > the only basic 'forces' in musical harmony, and classifies
> > > all other 'roots' as related to them.
> > >
> > > The other roots are analyzable into either of two of the
> > > categories, depending on context.
> > >
> > > Thus,
> > >
> > > chord 'root' category
> > >
> > > VII Dominant or Subdominant
> > > VI Tonic or Subdominant
> > > V Dominant
> > > IV Subdominant
> > > III Tonic or Dominant
> > > II Subdominant (sometimes Dominant, I think)
> > > I Tonic
> > >
> > > So typically, in an analysis, every chord is marked either
> > > 'T', 'S', or 'D'.
> > >
> > > (The other important aspect to Riemann's early theories,
> > > which he later abdicated, was that of 'dualism', which is
> > > akin to Partch o- and u-tonal concepts. Earlier theorists
> > > had used it, principally Oettingen. But that's a different
> > > matter...)
> > >
> > >
> > >
> > > > [Carl Lumma, TD 522.9]
> > > > Barbershop songs modulate primarily by fifths, just as the
> > > > songs of most genres. So if you wanted, you could describe
> > > > most of the 7th chords as being dominants of their
successors.
> > > > But the successor is also a "dominant" 7th, and so on. Such
> > > > an analysis wouldn't add much insight to the music, though.
> > >
> > >
> > > But this kind of analysis is *very* useful in jazz. There's
> > > a good exposition of this in a journal of jazz theory (don't
> > > have it handy and thus can't cite it), which suggests using
> > > 'N' to symbolize the 'goal' of a string of dominants, and
> > > 'N-3', 'N-2', 'N-1', etc., to symbolize the dominants of the
> > > dominants. 'N+1', etc., would symbolize 'root'-movement
> > > by subdominants, which is much less common in jazz.
> > >
> > > The paper uses 'All The Things You Are' (by Jerome Kern) to
> > > illustrate the method, and it is very appropriate indeed for
> > > a tune like that, instead of Roman numerals with loads of
> > > accidentals (and which numerals don't really signify anything
> > > pertinent to the chord movement in this song).
> > >
> > > This type of analysis can be seen as a modification of the
> > > 'T/D/S' advocated by Riemann.
> > >
> > >
> > > -monz
> > >
> > > Joseph L. Monzo Philadelphia monz@j...
> > > http://www.ixpres.com/interval/monzo/homepage.html
> > > |"...I had broken thru the lattice barrier..."|
> > > | - Erv Wilson |
> > > --------------------------------------------------
> > >
> > >
________________________________________________________________
> > > YOU'RE PAYING TOO MUCH FOR THE INTERNET!
> > > Juno now offers FREE Internet Access!
> > > Try it today - there's no risk! For your FREE software, visit:
> > > http://dl.www.juno.com/get/tagj.