Yahoo Tuning Groups Ultimate Backup makemicromusic sketch of 19-tet fugue

Hey all....I thought I'd share with you what I've been up to.

The link below is to an mp3 file of the exposition of a new fugue I've written
in "12 minor" (roughly g#-minor). Being the exposition, it's only the first
entrance of each voice doing the subject once, landing on the cadence which
will lead to developmentary material.

It's about 30 seconds long.

http://www.akjmusic.com/audio/19fugue.mp3

God, writing fugues is hard !!! Bach was a stud for doing the sheer amount of
them he did. Not to mention improvising them !

Also, on the way is my first work in 17-tet. Probably within the next couple
of weeks, I'd say.

Cheers,
--
Aaron Krister Johnson
http://www.dividebypi.com
http://www.akjmusic.com

🔗Jonathan M. Szanto <JSZANTO@...>

Aaron,

{you wrote...}
>God, writing fugues is hard !!! Bach was a stud for doing the sheer amount of
>them he did. Not to mention improvising them !

Exemplary so far, very well done. Form sounds very correct, including the elaboration/elongation at the end of the second statement of the fugue.

Not to mention I think it is interesting to hear this little 'works in progress' that have been popping up - good for all of us to hear the process along the way.

Looking forward to the complete fugue, as orchestrated by Leopold Stokowski...

Cheers,
Jon

🔗Paul Erlich <perlich@...>

Aaron, rock on. I absolutely love this beginning!

--- In MakeMicroMusic@yahoogroups.com, "Aaron K. Johnson"
<akjmicro@c...> wrote:
> Hey all....I thought I'd share with you what I've been up to.
>
> The link below is to an mp3 file of the exposition of a new fugue
I've written
> in "12 minor" (roughly g#-minor). Being the exposition, it's only
the first
> entrance of each voice doing the subject once, landing on the
cadence which
> will lead to developmentary material.
>
> It's about 30 seconds long.
>
> http://www.akjmusic.com/audio/19fugue.mp3
>
> God, writing fugues is hard !!! Bach was a stud for doing the sheer
amount of
> them he did. Not to mention improvising them !
>
> Also, on the way is my first work in 17-tet. Probably within the
next couple
> of weeks, I'd say.
>
> Cheers,
> --
> Aaron Krister Johnson
> http://www.dividebypi.com
> http://www.akjmusic.com

🔗tentothe99 <tentothe99@...>

🔗Gene Ward Smith <gwsmith@...>

🔗Carl Lumma <ekin@...>

🔗Jonathan M. Szanto <JSZANTO@...>

🔗Carl Lumma <ekin@...>

> {you wrote...}
> >Say, what's going on around the second entry? Is there
> >a half a beat missing or something?
>
> Hmmm, I took it as an interesting compositional device!

And you took my comment as a negative?

It was a simple question. I quite like this exposition,
in fact it was a friend I sent it to that first brought
this to my attention, as it sounds quite natural to me.

It doesn't seem to happen on the third entry. Does
Aaron see this 'stretto' happening again in the fugue?
etc.

-Carl

🔗Jonathan M. Szanto <JSZANTO@...>

{you wrote...}
> > Hmmm, I took it as an interesting compositional device!
>
>And you took my comment as a negative?

Not at all - I just thought it was intentional, not "missing". No slight intended, Carl.

>... to my attention, as it sounds quite natural to me.

As to me, while causing a smile as well.

Cheers,
Jon

🔗Aaron K. Johnson <akjmicro@...>

Hey thanks for all of your kind comments, all !!!

Yes, the missing beat was intentional. I don't know yet how significant it
will be as a sort of motive in the develoment (probably I won't overkill it)

But only time will tell. If it sounds good and organic, I might develop it
after all.

Best,
Aaron.

On Sunday 04 July 2004 01:55 pm, Carl Lumma wrote:
> > {you wrote...}
> >
> > >Say, what's going on around the second entry? Is there
> > >a half a beat missing or something?
> >
> > Hmmm, I took it as an interesting compositional device!
>
> And you took my comment as a negative?
>
> It was a simple question. I quite like this exposition,
> in fact it was a friend I sent it to that first brought
> this to my attention, as it sounds quite natural to me.
>
> It doesn't seem to happen on the third entry. Does
> Aaron see this 'stretto' happening again in the fugue?
> etc.
>
> -Carl
>
>
>
>
> [MMM info]------------------------------------------------------
> More MMM music files are at http://www.microtonal.org/music.html
> ------------------------------------------------------[MMM info]
> Yahoo! Groups Links
>
>
>

--
Aaron Krister Johnson
http://www.dividebypi.com
http://www.akjmusic.com

🔗hstraub64 <hstraub64@...>

Talking about fugues, there comes a question into my mind I have been
thinking about earlier: how do you guys handle counterpoint in other
tunings? Depending on the tuning system, the traditional counterpoint
rules may apply only in a limited way or not at all - after all, there
are other kinds of intervals, and those that appear in traditional
counterpoint may not appear at all (there are no fifth parallels if
there are no fifths!).
I have seen quite some amount of melodic and harmonic theory for
generalized tunings - I wonder if there is something like a
generalized counterpoint theory? Maybe in the spirit of Paul's
decatonic scales or so?
Well, maybe this belongs more into tuning or tuning-math. I already
looked there, but did not find much til now.
--
Hans Straub
http://home.datacomm.ch/straub

🔗Rick McGowan <rick@...>

Hans Straub asked...

> Talking about fugues, there comes a question into my mind I have been
> thinking about earlier: how do you guys handle counterpoint in other
> tunings?
> ...
> I wonder if there is something like a
> generalized counterpoint theory?

The principles of western counterpoint are fairly easily stated more
generally than they are usually written in traditional counterpoint texts.
Rather than express the consonant intervals in terms such as "3rds and
6ths" you can pick a set of intervals and clusters that you are going to
consider as consonant or semi-consonant intervals. Use them in the way that
traditional counterpoint texts tell you to use 3rds and 6ths, etc. Avoid
parallel octaves and parallel things that *function* like 5ths. The
principles of good voice leading are likewise pretty general, not really
dependent on the tuning per se.

Basically I think there isn't any *need* for a "generalized counterpoint
theory" because the principles underlying the picky rules about certain
intervals given in some texts are already general enough.

For a fugue, which is basically focussed on what you do at the voice
entries, pick related interval that functions something like a 5th.

> Well, maybe this belongs more into tuning or tuning-math. I already
> looked there, but did not find much til now.

Counterpoint I think is probably more relevant here than in tuning math,
because counterpoint isn't math, and isn't dependent on particular tunings.

Rick

🔗Paul Erlich <perlich@...>

--- In MakeMicroMusic@yahoogroups.com, Rick McGowan <rick@u...> wrote:

> Basically I think there isn't any *need* for a "generalized
counterpoint
> theory" because the principles underlying the picky rules about
certain
> intervals given in some texts are already general enough.

It can be hard to dig deep enough to these underlying principles,
which can be especially troublesome when you're throwing out the
diatonic scale. My paper that was referred to in this thread tries to
do so -- for example, by generalizing the role of the tritone with
the term "characteristic dissonance".

> Counterpoint I think is probably more relevant here than in tuning
math,
> because counterpoint isn't math, and isn't dependent on particular
tunings.

Well, even if that's somehow true, counterpoint is highly dependent
on the *scale* you're using -- for example, so much of counterpoint
is about *stepwise* motion, which means one step in the *scale*. Lots
of the discussion on tuning-math has been about *scales*, but this
list might have some tolerance for it too. All three lists have a
role to play . . .

🔗Carl Lumma <ekin@...>

>Talking about fugues, there comes a question into my mind I
>have been thinking about earlier: how do you guys handle
>counterpoint in other tunings? Depending on the tuning
>system, the traditional counterpoint rules may apply only
>in a limited way or not at all

I've always found writing counterpoint by the rules, though
valuable as an exercise, too painstaking in practice.
Fortunately, like anything else, if you listen to and play
enough counterpoint, it starts to come naturally.

Of course with many alternate scales there aren't existing
works to listen to or practice playing. So you have to
write your own practice material as you go. Fortunately I
suspect the underlying skill of hearing multiple voices at
once should carry over to any scale, once you get that scale
in your ear.

>after all, there are other kinds of intervals, and those
>that appear in traditional counterpoint may not appear at
>all (there are no fifth parallels if there are no fifths!).

My contribution here is limited to what I call the
"diatonic property" -- the presence of a generic interval
class in the scale that yields different consonances
depending on what mode you're in.

For example, in the diatonic scale, the thirds alternate
between major and minor. So you can use them in parallel
without it starting to sound like synthesis. Try it with
fifths and what you get sounds very much like a single
timbre. Like heavy-metal guitar playing melodies with
power chords.

With a "diatonic" interval, it's easy to improvise
harmonies -- you just sing the same melody in a different
mode.

Graham has pointed out that in counterpoint this should
matter less, since you're avoiding parallelism anyway.
This is a good point, but I still feel like the ability
to do local parallel moves is important. The only way
to tell, though, is to write a lot of music and see...

-Carl

🔗Paul Erlich <perlich@...>

--- In MakeMicroMusic@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
> >Talking about fugues, there comes a question into my mind I
> >have been thinking about earlier: how do you guys handle
> >counterpoint in other tunings? Depending on the tuning
> >system, the traditional counterpoint rules may apply only
> >in a limited way or not at all
>
> I've always found writing counterpoint by the rules, though
> valuable as an exercise, too painstaking in practice.
> Fortunately, like anything else, if you listen to and play
> enough counterpoint, it starts to come naturally.
>
> Of course with many alternate scales there aren't existing
> works to listen to or practice playing. So you have to
> write your own practice material as you go. Fortunately I
> suspect the underlying skill of hearing multiple voices at
> once should carry over to any scale, once you get that scale
> in your ear.

The problem is that it's hard to get a new scale truly in your ear if
you aren't strict about using the scale, because it seems almost
everyone just gravitates to things that approximate what they're
familiar with, so they may essentially work with whatever
approximation of the diatonic scale they can find, for example,
without even realizing that that's what they're doing. I had a
similar problem in my "composing in the style of Bach" class, because
I kept, unknowingly, using pentatonic ideas. Being really strict
about the rules helped me greatly to internalize much of what
traditional European style is fundamentally about.

> >after all, there are other kinds of intervals, and those
> >that appear in traditional counterpoint may not appear at
> >all (there are no fifth parallels if there are no fifths!).
>
> My contribution here is limited to what I call the
> "diatonic property" -- the presence of a generic interval
> class in the scale that yields different consonances
> depending on what mode you're in.
>
> For example, in the diatonic scale, the thirds alternate
> between major and minor. So you can use them in parallel
> without it starting to sound like synthesis. Try it with
> fifths and what you get sounds very much like a single
> timbre.

Well, there's another reason for that. Fifths are simpler ratios, so
they sound much more like they could be a single timbre. There are
scales, like Tcherepnin's, where you can run the whole thing in
parallel major thirds, but it still doesn't have anything like
the "synthesis" effect of parallel fifths.

> Like heavy-metal guitar playing melodies with
> power chords.

Well, there you've got distortion, which fills in the "missing
fundamental" physically for you, as well as many of its
overtones . . .

🔗Carl Lumma <ekin@...>

>Well, there's another reason for that. Fifths are simpler
>ratios, so they sound much more like they could be a single
>timbre. There are scales, like Tcherepnin's, where you can
>run the whole thing in parallel major thirds, but it still
>doesn't have anything like the "synthesis" effect of
>parallel fifths.

The other day I played with that scale a bit, FWIW.

I agree that the effect is weaker, but it's still stronger
than the diatonic scale with its alternating thirds -- as is
just playing random parallel minor thirds -- to my ear.

It's also about as much weaker with 4ths, but traditional
counterpoint rules forbid them too.

>> Like heavy-metal guitar playing melodies with
>> power chords.
>
>Well, there you've got distortion, which fills in the "missing
>fundamental" physically for you, as well as many of its
>overtones . . .

There's no distortion on my slide guitar, which exhibits the
same effect, even with bare major 3rds.

-Carl

🔗Paul Erlich <perlich@...>

--- In MakeMicroMusic@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
> >Well, there's another reason for that. Fifths are simpler
> >ratios, so they sound much more like they could be a single
> >timbre. There are scales, like Tcherepnin's, where you can
> >run the whole thing in parallel major thirds, but it still
> >doesn't have anything like the "synthesis" effect of
> >parallel fifths.
>
> The other day I played with that scale a bit, FWIW.
>
> I agree that the effect is weaker, but it's still stronger
> than the diatonic scale with its alternating thirds -- as is
> just playing random parallel minor thirds -- to my ear.
>
> It's also about as much weaker with 4ths, but traditional
> counterpoint rules forbid them too.

Forbid parallel 4ths? No, they don't. Traditional counterpoint
*thrives* on parallel fourths.

> There's no distortion on my slide guitar, which exhibits the
> same effect, even with bare major 3rds.

Tuned justly?

🔗Carl Lumma <ekin@...>

>> >Well, there's another reason for that. Fifths are simpler
>> >ratios, so they sound much more like they could be a single
>> >timbre. There are scales, like Tcherepnin's, where you can
>> >run the whole thing in parallel major thirds, but it still
>> >doesn't have anything like the "synthesis" effect of
>> >parallel fifths.
>>
>> The other day I played with that scale a bit, FWIW.
>>
>> I agree that the effect is weaker, but it's still stronger
>> than the diatonic scale with its alternating thirds -- as is
>> just playing random parallel minor thirds -- to my ear.
>>
>> It's also about as much weaker with 4ths, but traditional
>> counterpoint rules forbid them too.
>
>Forbid parallel 4ths? No, they don't. Traditional counterpoint
>*thrives* on parallel fourths.

What theory class did you take? I'd be interested in any
example of counterpoint with parallel fourths. Howabout 2
bars, any two voices.

>> There's no distortion on my slide guitar, which exhibits the
>> same effect, even with bare major 3rds.
>
>Tuned justly?

Yes.

-Carl

🔗Paul Erlich <perlich@...>

--- In MakeMicroMusic@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
> >> >Well, there's another reason for that. Fifths are simpler
> >> >ratios, so they sound much more like they could be a single
> >> >timbre. There are scales, like Tcherepnin's, where you can
> >> >run the whole thing in parallel major thirds, but it still
> >> >doesn't have anything like the "synthesis" effect of
> >> >parallel fifths.
> >>
> >> The other day I played with that scale a bit, FWIW.
> >>
> >> I agree that the effect is weaker, but it's still stronger
> >> than the diatonic scale with its alternating thirds -- as is
> >> just playing random parallel minor thirds -- to my ear.
> >>
> >> It's also about as much weaker with 4ths, but traditional
> >> counterpoint rules forbid them too.
> >
> >Forbid parallel 4ths? No, they don't. Traditional counterpoint
> >*thrives* on parallel fourths.
>
> What theory class did you take?

A bunch of them. Got A's in all of them too ;)

> I'd be interested in any
> example of counterpoint with parallel fourths.

It's everywhere. Most typical in sequences of first-inversion triads.

> Howabout 2
> bars, any two voices.

Maybe were thinking 2-voice counterpoint. Counterpoint with more than
2 voices is riddled with parallel fourths -- it's those sequences of
first-inversion triads.

> >> There's no distortion on my slide guitar, which exhibits the
> >> same effect, even with bare major 3rds.
> >
> >Tuned justly?
>
> Yes.

Well there you go. With 12-equal's major thirds, the "synthesis"
effect is a whole lot weaker.

🔗Paul Erlich <perlich@...>

--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:

> > I'd be interested in any
> > example of counterpoint with parallel fourths.
>
> It's everywhere. Most typical in sequences of first-inversion
triads.

Another common example is where the Neapolitan chord resolves to a
second-inversion tonic chord. The top two voices very often descend
in parallel fourths:

b2 -> 1
b6 -> 5

but never in parallel fifths.

🔗Carl Lumma <ekin@...>

> > I'd be interested in any
> > example of counterpoint with parallel fourths.
>
> It's everywhere. Most typical in sequences of
> first-inversion triads.

Everywhere ain't an example.

> > Howabout 2
> > bars, any two voices.
>
> Maybe were thinking 2-voice counterpoint.
> Counterpoint with more than 2 voices is
> riddled with parallel fourths -- it's
> those sequences of first-inversion triads.

Example?

> > >> There's no distortion on my slide guitar,
> > >> which exhibits the same effect, even with
> > >> bare major 3rds.
> > >
> > >Tuned justly?
> >
> > Yes.
>
> Well there you go. With 12-equal's major thirds,
> the "synthesis" effect is a whole lot weaker.

But this thread is about microtonal counterpoint...

-Carl

🔗Carl Lumma <ekin@...>

> > > I'd be interested in any example of counterpoint
> > > with parallel fourths.
> >
> > It's everywhere. Most typical in sequences of first-
> > inversion triads.
>
> Another common example is where the Neapolitan chord resolves
> to a second-inversion tonic chord. The top two voices very
> often descend in parallel fourths:
>
> b2 -> 1
> b6 -> 5
>
> but never in parallel fifths.

Ah, you're thinking of isolated movements. Yes, you're
right.

-Carl

🔗Paul Erlich <perlich@...>

--- In MakeMicroMusic@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:

> > > I'd be interested in any
> > > example of counterpoint with parallel fourths.
> >
> > It's everywhere. Most typical in sequences of
> > first-inversion triads.
>
> Everywhere ain't an example.

Sorry, I don't have any sheet music here. But you can find such
sequences all over the place. Why don't you find such sequences of
root-position triads? Parallel fifths. To avoid parallel fifths, put
the triads in first inversion. You get parallel fourths, and there's
no prohibition against parallel fourths.

> > > >> There's no distortion on my slide guitar,
> > > >> which exhibits the same effect, even with
> > > >> bare major 3rds.
> > > >
> > > >Tuned justly?
> > >
> > > Yes.
> >
> > Well there you go. With 12-equal's major thirds,
> > the "synthesis" effect is a whole lot weaker.
>
> But this thread is about microtonal counterpoint...

So? Does "microtonal" automatically mean "just" to you? Where in the
context of this thread was this leap taken?

🔗Paul Erlich <perlich@...>

--- In MakeMicroMusic@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
> > > > I'd be interested in any example of counterpoint
> > > > with parallel fourths.
> > >
> > > It's everywhere. Most typical in sequences of first-
> > > inversion triads.
> >
> > Another common example is where the Neapolitan chord resolves
> > to a second-inversion tonic chord. The top two voices very
> > often descend in parallel fourths:
> >
> > b2 -> 1
> > b6 -> 5
> >
> > but never in parallel fifths.
>
> Ah, you're thinking of isolated movements.

As well as long, extended sequences.

🔗Aaron K. Johnson <akjmicro@...>

On Thursday 08 July 2004 07:28 pm, Paul Erlich wrote:
> --- In MakeMicroMusic@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
> > > > I'd be interested in any
> > > > example of counterpoint with parallel fourths.
> > >
> > > It's everywhere. Most typical in sequences of
> > > first-inversion triads.
> >
> > Everywhere ain't an example.
>
> Sorry, I don't have any sheet music here. But you can find such
> sequences all over the place. Why don't you find such sequences of
> root-position triads? Parallel fifths. To avoid parallel fifths, put
> the triads in first inversion. You get parallel fourths, and there's
> no prohibition against parallel fourths.

Hey, I gave the example of Beethoven op2 #3 piano sonata, last mvt., for 'faux
bourdon' motion of first inversion triads.

Comment: one does find root position motion of triads in post romantic, 20th
century composers, and some transitional composers as well (I can think of
examples in Debussy, Mompou, Milhaud, Stravinsky, Nancarrow, etc. as well as
some stuff like Holst, Vaughn Williams) Through it all, the concept of
counterpoint survives, illustrating the somewhat arbitrary cultural bias
against parrallel fifth (and octaves). Hey, Perotin's counterpoint doesn't
suffer from being filled with parallel octaves and fifths !!!!

But yes, we are correct when we observe that common practice classical
composers generally avoid parallel fifths, although on rare occasions they
break this 'rule' for effect, or out of neccessity. A good example is
Mozart's last piano sonata in D major, last movement, where he has parallel
fifth in an imitative, developmental section.

Aaron Krister Johnson
http://www.dividebypi.com
http://www.akjmusic.com

🔗Aaron K. Johnson <akjmicro@...>

On Thursday 08 July 2004 07:15 pm, Carl Lumma wrote:
> > > I'd be interested in any
> > > example of counterpoint with parallel fourths.
> >
> > It's everywhere. Most typical in sequences of
> > first-inversion triads.
>
> Everywhere ain't an example.
>

Here's a great one: a typical example of what is caled 'faux bourdon' in
classical voice leading: Beethoven sonata in C major, op2 #3 , last mvt,
first 2 measures.....

Aaron Krister Johnson
http://www.dividebypi.com
http://www.akjmusic.com

🔗Carl Lumma <ekin@...>

🔗Paul Erlich <perlich@...>

🔗Carl Lumma <ekin@...>

>> >> Ah, you're thinking of isolated movements.
>> >
>> >As well as long, extended sequences.
>>
>> Of parallel 4ths? "I don't think so..."
>
>Was the Beethoven example not long enough for you?

Aaron's post didn't reach me until after I had posted that.

""Here's a great one: a typical example of what is caled 'faux
bourdon' in classical voice leading: Beethoven sonata in
C major, op2 #3 , last mvt, first 2 measures.....""

Here I am with my trusty Dover edition, ed. Shenker. These
are triads, with the 3rds-confusion thing outweighing any
4ths-fusion thing.

>Oh wait,
>I'm seeing something about the Duetto from Bach's 78th Cantata,
>mm. 58-59 . . .

http://lumma.org/stuff/bach78.png

Does look like there are some 4ths there.

Clearly, though, parallel 3rds and 6ths *far* outweigh 4ths
or 5ths.

-Carl

🔗Dante Rosati <dante@...>

🔗Prent Rodgers <prentrodgers@...>

🔗Carl Lumma <ekin@...>

>Great discussion.
>
>I recently studied the rules of counterpoint by Kent Wheeler Keenan,

I think that's Kennan.

>in his book "Counterpoint, based on eighteenth century practice". It
>has all kinds of interesting ways to move from tone to tone with many
>parts. It starts simple and gets interesting very quickly. Parts of my
>Resolution in Blue is based on his ideas.

Cool, I dig that piece. I'm not familiar with this book, though,
yet...

-Carl

🔗tentothe99 <tentothe99@...>

--- In MakeMicroMusic@yahoogroups.com, "hstraub64"
<hstraub64@t...> wrote:
> Talking about fugues, there comes a question into my mind I
have been
> thinking about earlier: how do you guys handle counterpoint in
other
> tunings? Depending on the tuning system, the traditional
counterpoint
> rules may apply only in a limited way or not at all - after all,
there
> are other kinds of intervals, and those that appear in traditional
> counterpoint may not appear at all (there are no fifth parallels if
> there are no fifths!).
> I have seen quite some amount of melodic and harmonic
theory for
> generalized tunings - I wonder if there is something like a
> generalized counterpoint theory? Maybe in the spirit of Paul's
> decatonic scales or so?
> Well, maybe this belongs more into tuning or tuning-math. I
already
> looked there, but did not find much til now.
> --
> Hans Straub
> http://home.datacomm.ch/straub

i'm sure you could generalize counterpoint to ratios. i've seen
one treatment of this (Harmonic Experience-Mathieu) which
manages to be very thorough and effective with its little singing
examples, while being totally indigestible. i love that book more
for its encyclopedic nature.

as far as counterpoint, you could probably generalize the theory
even for things like ryhthm and timbre, ie. if the kick drum goes
twice as fast, the hihat should not go twice as fast (paralell
octaves). hey, it's a stretch, but what the hell.

what about counterpoint for sliding pitches? they tend to
combine into one sound if they go at the same rate, but, here's
the rub, IF they are panned the same way. one part of my
technique now is to modify melodies timbrally and pan them
away from each other, non-symmetrically. you could extend
counterpoint theory to that, too. it makes sense to me. a paralell
unison pan (of two voices) from hard left to right will sound
weaker than one starting hard left and ending center and the
other starting center and ending hard right.

🔗Prent Rodgers <prentrodgers@...>

🔗Paul Erlich <perlich@...>

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> ""Here's a great one: a typical example of what is caled 'faux
> bourdon' in classical voice leading: Beethoven sonata in
> C major, op2 #3 , last mvt, first 2 measures.....""
>
> Here I am with my trusty Dover edition, ed. Shenker. These
> are triads, with the 3rds-confusion thing outweighing any
> 4ths-fusion thing.

Sure -- but the point is that according to the "rules", at least in
my classes and books, you can do this triad-sequence thing with
parallel 4ths, but *not* with parallel 5ths, even though in both
cases, the 3rds will vary. That was my point, that parallel fourths
are allowed in three- or more-voiced textures, including
counterpoint, not that "fusion" or loss of independence is allowed
when produced by 4th rather than 5ths (if that's what you thought I
was saying).

> Clearly, though, parallel 3rds and 6ths *far* outweigh 4ths
> or 5ths.

If you see parallel 3rds *and* 6ths *simultaneously* in three voices,
there will *have* to be parallel 4ths in there, because there can't
be parallel 5ths or 8ves. There's no other way.

🔗Paul Erlich <perlich@...>

🔗Carl Lumma <ekin@...>

> > ""Here's a great one: a typical example of what is caled 'faux
> > bourdon' in classical voice leading: Beethoven sonata in
> > C major, op2 #3 , last mvt, first 2 measures.....""
> >
> > Here I am with my trusty Dover edition, ed. Shenker. These
> > are triads, with the 3rds-confusion thing outweighing any
> > 4ths-fusion thing.
>
> Sure -- but the point is that according to the "rules", at least
> in my classes and books, you can do this triad-sequence thing
> with parallel 4ths, but *not* with parallel 5ths, even though
> in both cases, the 3rds will vary. That was my point, that
> parallel fourths are allowed in three- or more-voiced textures,
> including counterpoint,

Agreed. But I still don't think you'll find an example of
two voices going in 4ths while other voices are doing
something else -- contrary motion, etc. (that's why I said
"any two voices").

> > Clearly, though, parallel 3rds and 6ths *far* outweigh
> > 4ths or 5ths.
>
> If you see parallel 3rds *and* 6ths *simultaneously* in
> three voices, there will *have* to be parallel 4ths in
> there, because there can't be parallel 5ths or 8ves.
> There's no other way.

Sorry, bad use of "or" and "and". I didn't mean at the
same time. I just meant, if you were to do a count
over all counterpoint, the average length of any two
voices in parallel 3rds or 6ths would be far greater
than of 5ths or 4ths.

-Carl

🔗Carl Lumma <ekin@...>

> > http://lumma.org/stuff/bach78.png
> >
> > Does look like there are some 4ths there.
>
> That's two-voice counterpoint? Not was I was talking
> about,

I believe that is the relevant section. I didn't
display the other parts, but they're just accompaniment
to the duet shown, at least at that point in the
piece.

> because 4ths are always considered "dissonances"
> anyway in two-voice texture.

Yes.

-Carl

🔗Paul Erlich <perlich@...>

--- In MakeMicroMusic@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:

> Agreed. But I still don't think you'll find an example of
> two voices going in 4ths while other voices are doing
> something else -- contrary motion, etc. (that's why I said
> "any two voices").

If you mean three or more consecutive 4ths, not arising in the
context of a sequence (a sequence implies parallel motion in the
other voice(s)), you may be right. But I think that would be because
the other rules of counterpoint don't allow any such solutions --
it's not because there's any prescribed or implied prohibition
against parallel 4ths.

🔗Carl Lumma <ekin@...>

>> Agreed. But I still don't think you'll find an example of
>> two voices going in 4ths while other voices are doing
>> something else -- contrary motion, etc. (that's why I said
>> "any two voices").
>
>If you mean three or more consecutive 4ths, not arising in the
>context of a sequence (a sequence implies parallel motion in the
>other voice(s)), you may be right. But I think that would be because
>the other rules of counterpoint don't allow any such solutions --
>it's not because there's any prescribed or implied prohibition
>against parallel 4ths.

There are 'non-sequence' parallel 6ths in Bach, I'm pretty
sure. Gimme a bit to find the example. :)

-Carl

🔗Joseph Pehrson <jpehrson@...>

--- In MakeMicroMusic@yahoogroups.com, "Aaron K. Johnson"

/makemicromusic/topicId_7021.html#7021

<akjmicro@c...> wrote:
> Hey all....I thought I'd share with you what I've been up to.
>
> The link below is to an mp3 file of the exposition of a new fugue
I've written
> in "12 minor" (roughly g#-minor). Being the exposition, it's only
the first
> entrance of each voice doing the subject once, landing on the
cadence which
> will lead to developmentary material.
>
> It's about 30 seconds long.
>
> http://www.akjmusic.com/audio/19fugue.mp3
>
> God, writing fugues is hard !!! Bach was a stud for doing the sheer
amount of
> them he did. Not to mention improvising them !
>
> Also, on the way is my first work in 17-tet. Probably within the
next couple
> of weeks, I'd say.
>
> Cheers,
> --
> Aaron Krister Johnson
> http://www.dividebypi.com
> http://www.akjmusic.com

***Nothing like a microtonal fugue to brighten the day/evening! Nice
work Aaron! Looking forward to hearing the rest of the piece...!

Joe Pehrson

🔗Joseph Pehrson <jpehrson@...>

--- In MakeMicroMusic@yahoogroups.com, "hstraub64" <hstraub64@t...>

/makemicromusic/topicId_7021.html#7038

wrote:
> Talking about fugues, there comes a question into my mind I have
been
> thinking about earlier: how do you guys handle counterpoint in other
> tunings? Depending on the tuning system, the traditional
counterpoint
> rules may apply only in a limited way or not at all - after all,
there
> are other kinds of intervals, and those that appear in traditional
> counterpoint may not appear at all (there are no fifth parallels if
> there are no fifths!).
> I have seen quite some amount of melodic and harmonic theory for
> generalized tunings - I wonder if there is something like a
> generalized counterpoint theory? Maybe in the spirit of Paul's
> decatonic scales or so?
> Well, maybe this belongs more into tuning or tuning-math. I already
> looked there, but did not find much til now.
> --
> Hans Straub
> http://home.datacomm.ch/straub

***It seems like there would be general principles for this, but I'm
not sure they could be codified. For example, even repetition in a
non ET would cause different intervals at different pitch levels.

So one would rely on the old compositional standards, such as ideas
of unity, variety, and that vague term "interest..."

However, in any given non-12 tuning system, I'm sure a lot could be
said on this topic in a theory course, and it would be an interesting
one...

J. Pehrson