Yahoo Tuning Groups Ultimate Backup tuning Decimal counterpoint

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., graham@m... wrote:
>
> /tuning/topicId_36539.html#36539
>
> > I've got some examples at
> > <http://x31eq.com/music/counterpoint.html> of two part
> > counterpoint using miracle temperament.
> >
> >
> > Graham
>
> ***Nice work, Graham!
>
> I remember when you said you were interested in studying species
> counterpoint, and now you're *doing* it! Great compositional
studies
> for more involved and "composerly" efforts later.
>
> congrats!
>
> Joseph

it's been a while since i've done species counterpoint -- *but* (or
perhaps *therefore*) i'm confused about some of these examples. a
written-out analysis of all of them would be very helpful. for
example, isn't second species supposed to start with a consonance?

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

/tuning/topicId_36539.html#36564

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > --- In tuning@y..., graham@m... wrote:
> >
> > /tuning/topicId_36539.html#36539
> >
> > > I've got some examples at
> > > <http://x31eq.com/music/counterpoint.html> of two
part
> > > counterpoint using miracle temperament.
> > >
> > >
> > > Graham
> >
> > ***Nice work, Graham!
> >
> > I remember when you said you were interested in studying species
> > counterpoint, and now you're *doing* it! Great compositional
> studies
> > for more involved and "composerly" efforts later.
> >
> > congrats!
> >
> > Joseph
>
> it's been a while since i've done species counterpoint -- *but* (or
> perhaps *therefore*) i'm confused about some of these examples. a
> written-out analysis of all of them would be very helpful. for
> example, isn't second species supposed to start with a consonance?

***Why, of course, Paul, you're entirely right!

Graham, I guess, was just employing a rather "loose" definition, i.e.
2 notes per 1 in the bass, etc.

GRAHAM: I think you're exercises would be more effective if you
could tailor them a bit more to "common practice" in species
counterpoint (a la Fux, for instance). Some of them are, but others
(like the very first for the second species) are off...

Waddya think??

Joseph

🔗graham@microtonal.co.uk

In-Reply-To: <aa2fh4+kb4l@eGroups.com>
jpehrson2 wrote:

> Graham, I guess, was just employing a rather "loose" definition, i.e.
> 2 notes per 1 in the bass, etc.

No, I'm employing a very strict definition but, because it's adapted to
decimal notation, not identical to Fux's. One difference, which is
probably what's throwing Paul off, is that I'm using more consonances. I
have a 6 level hierarchy as follows:

Consonance 1
1:1*, 3:2*, 5:4+

Consonance 2
4:3, 5:4, 6:5, 8:5, 5:3*, 7:4*, 7:6+

Consonance 3
all other 5-limit intervals
7:6, 7:5*, 10:7, 8:7, 9:8+, 9:5, 11:8+, 11:6+

Dissonance 1
all other 9-limit intervals
11:10+, 11:9, 11:8, 11:7, 11:6

Dissonance 2
all other 11-limit intervals
21:16+, 13:10+, 13:8+, 13:6+, 15:8+

Dissonance 3:
everything else

A * means you can add an arbitrary number of octaves, and a + means you
must add at least one octave.

Consonance 1 corresponds to Fux's perfect consonances. I avoid moving
directly between consonance levels 1 and 3, and should probably be
stricter about this. Consonance 3 can be brought in prematurely if it's
treated as a dissonance. I also avoid using the more extreme dissonances
with lower level consonances, but decided to allow all intervals within
the decimal scale anywhere dissonances are allowed.

> GRAHAM: I think you're exercises would be more effective if you
> could tailor them a bit more to "common practice" in species
> counterpoint (a la Fux, for instance). Some of them are, but others
> (like the very first for the second species) are off...

Fux is about Palestrina, not Common Practice.

I don't hear anything wrong with the first example. Second species,
cantus firmus 2, counterpoint in bass is a problem at the start. That's
because I moved too quickly to consonance 3, and probably because 8:7
should be demoted. The rest of them sound remarkably good considering it
was a purely theoretical exercise until I keyed them in at the weekend.

> Waddya think??

I'm going to carry on as I am. What specific things do you think don't
work?

Graham

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., graham@m... wrote:

/tuning/topicId_36539.html#36572

>
> > GRAHAM: I think you're exercises would be more effective if you
> > could tailor them a bit more to "common practice" in species
> > counterpoint (a la Fux, for instance). Some of them are, but
others (like the very first for the second species) are off...
>
> Fux is about Palestrina, not Common Practice.
>

****Well, Graham, in the above paragraph I said "common practice" in
species counterpoint (a la Fux). I wasn't refering to any specific
musical period. I don't even know, specifically, what somebody would
call "common practice" counterpoint. 18th Century? It might as well
be Fux, as far as I am concerned, since that's what is most commonly
taught.

> I don't hear anything wrong with the first example.

***I don't even believe Paul was commenting on the consonances. What
I think he meant, or at least what *I* mean, is that the first
example of "Second Species" counterpoint doesn't begin with a diad,
doesn't begin with a simultaneity. And, I believe, in the strict
definition of "second species" counterpoint, the exercises always
do.

That's about all there is to it. Certainly not a deprecation of
these interesting exercises!

Joseph

🔗graham@microtonal.co.uk

🔗emotionaljourney22 <paul@stretch-music.com>

--- In tuning@y..., graham@m... wrote:
> In-Reply-To: <aa2fh4+kb4l@e...>
> jpehrson2 wrote:
>
> > Graham, I guess, was just employing a rather "loose" definition,
i.e.
> > 2 notes per 1 in the bass, etc.
>
> No, I'm employing a very strict definition but, because it's
adapted to
> decimal notation, not identical to Fux's. One difference, which is
> probably what's throwing Paul off, is that I'm using more
consonances. I
> have a 6 level hierarchy as follows:
>
> Consonance 1
> 1:1*, 3:2*, 5:4+
>
> Consonance 2
> 4:3, 5:4, 6:5, 8:5, 5:3*, 7:4*, 7:6+
>
> Consonance 3
> all other 5-limit intervals
> 7:6, 7:5*, 10:7, 8:7, 9:8+, 9:5, 11:8+, 11:6+
>
> Dissonance 1
> all other 9-limit intervals
> 11:10+, 11:9, 11:8, 11:7, 11:6
>
> Dissonance 2
> all other 11-limit intervals
> 21:16+, 13:10+, 13:8+, 13:6+, 15:8+
>
> Dissonance 3:
> everything else
>
> A * means you can add an arbitrary number of octaves, and a + means
you
> must add at least one octave.

i'm confused about something:

11:10 is classified as a dissonance, but only if you add at least one
octave? isn't 11:5 more consonant than 11:10? same for 13:8, 15:8,
etc.

assuming you meant 11:5 is a consonance, etc., it looks like harmonic
entropy with good old s=1% is a great model of your interval
preferences. i chose this particular rendition to try to draw a line
demonstrating your preferences:

/tuning/files/dyadic/graham.jpg

this would indicate, that where beating is not a real factor (and yet
the timbres are appreciably harmonic), you (graham) might say (in
addition to the above),

*very tight tolerance required on the tuning of 8:7 and 12:5;
*10:7 might in fact be dissonant but i'm just used to assuming octave
equivalence in the 7-limit in my research;
*15:4 and especially 13:5 have to be absolutely just to be consonant,
and a just 9:7 might actually be comparable in consonance to these.

do these generally ring true if you test them out, graham?
if so, perhaps we could add a feature to your great linear
temperament program, which will print out the "graham-consonant"
intervals (including "second-best approximations" to ratios) present
in each MOS? i think that would be neato-burrito (i'm eating one
now) . . .

good on ya for delving into this stuff!
-paul

🔗graham@microtonal.co.uk

emotionaljourney22 wrote:
> i'm confused about something:
>
> 11:10 is classified as a dissonance, but only if you add at least one
> octave? isn't 11:5 more consonant than 11:10? same for 13:8, 15:8,
> etc.

Yes, 11:5 is a Dissonance 1 and 11:10 is a Dissonance 2, so 11:5 is less
dissonant than 11:10.

> assuming you meant 11:5 is a consonance, etc., it looks like harmonic
> entropy with good old s=1% is a great model of your interval
> preferences. i chose this particular rendition to try to draw a line
> demonstrating your preferences:
>
> /tuning/files/dyadic/graham.jpg

It still looks about right, and 8:7 is right on the line.

> this would indicate, that where beating is not a real factor (and yet
> the timbres are appreciably harmonic), you (graham) might say (in
> addition to the above),

The original ordering was worked out with different timbres, probably
sawtooths, to the ones used in the examples. But certainly harmonic. I'm
roughly following the integer limit as well. And fourths are worse than
they should be in line with tradition (the point of the exercise is to
extend tradition).

> *very tight tolerance required on the tuning of 8:7 and 12:5;
> *10:7 might in fact be dissonant but i'm just used to assuming octave
> equivalence in the 7-limit in my research;
> *15:4 and especially 13:5 have to be absolutely just to be consonant,
> and a just 9:7 might actually be comparable in consonance to these.

I don't know about tuning, I was taking them as I found them on the
keyboard. But certainly more complex intervals tend to require better
tuning. Not all 7-limit intervals within the octave are consonant. Looks
like 12:7 isn't. But there's still a bit of favouritism for the 7-limit
over 11. A chord involving 10:7 will probably involve other more
comprehensible 7-limit intervals. Plus it's a simple interval in miracle
temperament.

> do these generally ring true if you test them out, graham?
> if so, perhaps we could add a feature to your great linear
> temperament program, which will print out the "graham-consonant"
> intervals (including "second-best approximations" to ratios) present
> in each MOS? i think that would be neato-burrito (i'm eating one
> now) . . .

The hierarchy rang true when I worked it out. It's all provisional, but
there have to be strict rules for the counterpoint. Deliberate tests are
difficult because it all depends on the timbre, tuning and how I feel at
the time. The temperament finder's octave equivalent, and already works
with odd limits, so shouldn't have to change.

> good on ya for delving into this stuff!

Thanks. Slow progress is better than none at all.

Graham

🔗emotionaljourney22 <paul@stretch-music.com>

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., graham@m... wrote:

/tuning/topicId_36539.html#36596

> emotionaljourney22 wrote:
> > i'm confused about something:
> >
> > 11:10 is classified as a dissonance, but only if you add at least
one
> > octave? isn't 11:5 more consonant than 11:10? same for 13:8,
15:8,
> > etc.
>
> Yes, 11:5 is a Dissonance 1 and 11:10 is a Dissonance 2, so 11:5 is
less
> dissonant than 11:10.
>
> > assuming you meant 11:5 is a consonance, etc., it looks like
harmonic
> > entropy with good old s=1% is a great model of your interval
> > preferences. i chose this particular rendition to try to draw a
line
> > demonstrating your preferences:
> >
> >
/tuning/files/dyadic/graham.jpg
>
> It still looks about right, and 8:7 is right on the line.
>
> > this would indicate, that where beating is not a real factor (and
yet
> > the timbres are appreciably harmonic), you (graham) might say (in
> > addition to the above),
>
> The original ordering was worked out with different timbres,
probably
> sawtooths, to the ones used in the examples. But certainly
harmonic. I'm
> roughly following the integer limit as well. And fourths are worse
than
> they should be in line with tradition (the point of the exercise is
to
> extend tradition).
>
> > *very tight tolerance required on the tuning of 8:7 and 12:5;
> > *10:7 might in fact be dissonant but i'm just used to assuming
octave
> > equivalence in the 7-limit in my research;
> > *15:4 and especially 13:5 have to be absolutely just to be
consonant,
> > and a just 9:7 might actually be comparable in consonance to
these.
>
> I don't know about tuning, I was taking them as I found them on the
> keyboard. But certainly more complex intervals tend to require
better
> tuning. Not all 7-limit intervals within the octave are
consonant. Looks
> like 12:7 isn't. But there's still a bit of favouritism for the 7-
limit
> over 11. A chord involving 10:7 will probably involve other more
> comprehensible 7-limit intervals. Plus it's a simple interval in
miracle
> temperament.
>
> > do these generally ring true if you test them out, graham?
> > if so, perhaps we could add a feature to your great linear
> > temperament program, which will print out the "graham-consonant"
> > intervals (including "second-best approximations" to ratios)
present
> > in each MOS? i think that would be neato-burrito (i'm eating one
> > now) . . .
>
> The hierarchy rang true when I worked it out. It's all
provisional, but
> there have to be strict rules for the counterpoint. Deliberate
tests are
> difficult because it all depends on the timbre, tuning and how I
feel at
> the time. The temperament finder's octave equivalent, and already
works
> with odd limits, so shouldn't have to change.
>
> > good on ya for delving into this stuff!
>
> Thanks. Slow progress is better than none at all.
>
>
> Graham

***I wish somebody could write some of these exercises out in 72-tET
notation... I understand that better than "decimal," frankly.

J. Pehrson

🔗emotionaljourney22 <paul@stretch-music.com>

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> ***I wish somebody could write some of these exercises out in 72-
tET
> notation... I understand that better than "decimal," frankly.

if someone gives the decimal notation for these (or are they already
up?), i'll happily post the 'translation' on the miracle-tuning list
(an unnecessarily appendage of my cancerous plan to devour fertile
musical imagination wherever possible :)

i could see a parallel exercise going on for a few more of the 'best'
linear temperaments (including the default, meantone) . . .

in fact, not a bad topic for tuning-math -- i'll see you there {HA HA
HA HA HA} maybe tuning-math will end up composing some music ;)

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

/tuning/topicId_36539.html#36607

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > ***I wish somebody could write some of these exercises out in 72-
> tET
> > notation... I understand that better than "decimal," frankly.
>
> if someone gives the decimal notation for these (or are they
already
> up?), i'll happily post the 'translation' on the miracle-tuning
list
> (an unnecessarily appendage of my cancerous plan to devour fertile
> musical imagination wherever possible :)
>
> i could see a parallel exercise going on for a few more of
the 'best'
> linear temperaments (including the default, meantone) . . .
>
> in fact, not a bad topic for tuning-math -- i'll see you there {HA
HA HA HA HA} maybe tuning-math will end up composing some music ;)

Hi Paul!

I have enough respect for Tuning Math to know it's better than I stay
*here...* :)

🔗graham@microtonal.co.uk

In-Reply-To: <aa57ll+6p8h@eGroups.com>
emotionaljourney22 wrote:

> if someone gives the decimal notation for these (or are they already
> up?), i'll happily post the 'translation' on the miracle-tuning list
> (an unnecessarily appendage of my cancerous plan to devour fertile
> musical imagination wherever possible :)

I have hand written notes and MIDI files. The former could be scanned in,
but not right now. You can have the MIDI files, but you'll have to work
backwards from the keyboard mapping which won't be easy. I could knock up
some ASCII notation, as the rhythms are very simple. And do the
conversions myself. Do people really want this?

The examples themselves aren't anything special. The important thing is
that they sound okay, in so far as soulless exercises can be expected to.
That's why I put them up as audio files as the first priority.

I do intend to write up the rules sometime, and they're the interesting
thing.

> i could see a parallel exercise going on for a few more of the 'best'
> linear temperaments (including the default, meantone) . . .

Palestrina counterpoint is already a meantone system, of course. It may
be worth introducing more consonances, and allowing fuzzy tuning such that
a minor third can be either 6:5 or 7:6, a major second either 8:7 or 9:8,
and so on. This could also be done on a framework of harmony, rather than
counterpoint, as the functional rules would still work.

If anybody wants to pick a diatonic from the list Carl gave on
tuning-math, they could make real progress. I'm concentrating on miracle
now because I've liked it ever since its rediscovery and there's plenty
more work to do with it.

> in fact, not a bad topic for tuning-math -- i'll see you there {HA HA
> HA HA HA} maybe tuning-math will end up composing some music ;)

The criteria for selecting diatonics can be framed mathematically, so the
search is appropriate for tuning-math. But after you choose a tuning, it
doesn't take long before the mathematics becomes uninteresting and it's
all music. So any such quests would be best pursued here unless they
attract enough attention for a dedicated group to be set up.

Graham

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., graham@m... wrote:

/tuning/topicId_36539.html#36612

> The examples themselves aren't anything special. The important
thing is that they sound okay, in so far as soulless exercises can be
expected to.
> That's why I put them up as audio files as the first priority.
>
> I do intend to write up the rules sometime, and they're the
interesting thing.
>

***Hi Graham!

Well, that's the thing. If it were in 72-tET notation, I'd have an
idea about what you're trying to do, with reference to the new
counterpoint "rules" you've developed. I'm assuming you're using
the "entire" Miracle set and not a subset (??) Face it, the rules are
the interesting part, since counterpoint exercises never sound like
much! :) [I was told, though, when I was in school that my
counterpoint exercises sounded more like actual "compositions" but it
was mostly because I made mistakes... :) ]

Sorry about the Fux-up. Yes, it's true, the second species doesn't
have to start on a diad. I obviously haven't looked at the book for
a while, so thanks for getting me back into it with a new "twist!"

Joseph

🔗graham@microtonal.co.uk

In-Reply-To: <aa6c3g+3m6e@eGroups.com>
jpehrson2 wrote:

> Well, that's the thing. If it were in 72-tET notation, I'd have an
> idea about what you're trying to do, with reference to the new
> counterpoint "rules" you've developed. I'm assuming you're using
> the "entire" Miracle set and not a subset (??) Face it, the rules are
> the interesting part, since counterpoint exercises never sound like
> much! :) [I was told, though, when I was in school that my
> counterpoint exercises sounded more like actual "compositions" but it
> was mostly because I made mistakes... :) ]

The counterpoint rules make more sense in decimal notation. If you want
to use multiple-12 notation it might make more sense to base it around a
diatonic scale instead of the decimal one.

All the examples are within the standard Blackjack.

The rules aren't that difficult, so I can go over them. I've already
given the consonance levels. Mostly Fux's instructions carry over. The
extra rule is that you can't move directly between consonances 1 and 3 if
you want them both to sound like consonances. Unless you really want to.
Probably you shouldn't hang around in consonance 3 for too long either.

There are rules about preserving the integrity of the decimal scale. The
simple rule is that the only intervals found within the decimal scale can
be used. They're all a number of secors plus an optional quomma. This is
the bit that gets difficult if you change the notation.

To add variety, if three notes are all in rising or falling pitch
sequence, it doesn't matter if the interval between the second and the
third one is non-decimal, so long as those between the first note and the
other two are. So 0-1^-2 (C Dv D>) is allowed. As this is still
restrictive, I'm thinking about allowing the narrowed secors, like 1^-2
(Dv D> or C C#-), in any context. They can't be confused with unisons.
But you also have to think about decimal intervals over longer melodic
spans then. So 0^-1-2v (C> Db+ D) wouldn't be allowed in a fast passage
as the illegal 0^-2v (C> D) becomes too obvious. Sticking to Blackjack
mostly avoids this anyway.

There are other cases where Fux applies special rules to "steps". Any
interval of 1 decimal step is a "step". 3 decimal steps can always be
divided into two unequal "steps", so in 0-2-3 (C D> Ev) or 0-1-3 (C Db+
Ev), 0-2 (C D>) and 1-3 (Db+ Ev) are "steps". But a pair of two decimal
steps, like 0-2-4 (C D> F<), aren't "steps".

Parallel motion and the like should be avoided with all consonance 1
intervals. That includes 5:2. You should also avoid using the same
consonance twice in close succession, to give the sense of variety. You
could even try to avoiding a move from consonance 3 to consonance 2 by
parallel motion.

Special case rules apply at cadences, and I didn't really work out how
they should be translated. Probably you should end on a perfect
consonance by stepwise contrary motion.

Graham

🔗emotionaljourney22 <paul@stretch-music.com>

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., graham@m... wrote:

/tuning/topicId_36539.html#36572

> In-Reply-To: <aa2fh4+kb4l@e...>
> jpehrson2 wrote:
>
> > Graham, I guess, was just employing a rather "loose" definition,
i.e.
> > 2 notes per 1 in the bass, etc.
>
> No, I'm employing a very strict definition but, because it's
adapted to
> decimal notation, not identical to Fux's. One difference, which is
> probably what's throwing Paul off, is that I'm using more
consonances. I
> have a 6 level hierarchy as follows:
>
> Consonance 1
> 1:1*, 3:2*, 5:4+
>
> Consonance 2
> 4:3, 5:4, 6:5, 8:5, 5:3*, 7:4*, 7:6+
>
> Consonance 3
> all other 5-limit intervals
> 7:6, 7:5*, 10:7, 8:7, 9:8+, 9:5, 11:8+, 11:6+
>
>

***I'm not "getting" "Consonance 3..."

Isn't an 8:7 kind of like a "traditional" major second??

That's considered a "mild dissonance" in 12-tET music, isn't it??

Or is this category a bit of the, dare I say, "middlesex" AC-DC
variety??

Perhaps we could call these intervals "disconsonances..." ??

J. Pehrson

🔗Carl Lumma <carl@lumma.org>

🔗graham@microtonal.co.uk

In-Reply-To: <aa74il+qu5k@eGroups.com>
Me:
> > There are other cases where Fux applies special rules to "steps".
> Any
> > interval of 1 decimal step is a "step". 3 decimal steps can always
> be
> > divided into two unequal "steps", so in 0-2-3 (C D> Ev) or 0-1-3 (C
> Db+
> > Ev), 0-2 (C D>) and 1-3 (Db+ Ev) are "steps".

Paul:
> does this follow from the fux rules? what does fux say about this? it
> would seem to be "illegal pentatonicism" in a diatonic context -- no?

Fux defines (or maybe simple assumes) "steps" to be any kind of second.
In a decimal context, "seconds" aren't defined. There are 1 step
intervals, but they don't get as big. So some alternative definition has
to be found so that the special rules about "steps" make sense, and I use
the one above.

Graham

🔗graham@microtonal.co.uk

In-Reply-To: <aa7lr3+igi7@eGroups.com>
jpehrson2 wrote:

> ***I'm not "getting" "Consonance 3..."
>
> Isn't an 8:7 kind of like a "traditional" major second??

Sort of. It's wider than the traditional tuning of a major second. In
Palestrina's day it was well approximated by the diminished third of
keyboard tunings. But it doesn't seem to have been exploited as such.

> That's considered a "mild dissonance" in 12-tET music, isn't it??

It's a dissonance, plain and simple. But it isn't in 12-tET. Much the
same as 7:4, which is in consonance 2. Traditional harmony only
recognises 5-limit consonance, and everything else is lumped together as
dissonance. 16th-17th Century examples are interesting, in that only a
few kinds of dissonance were actually used. But they weren't the 7-limit
chords that are hidden away in meantone. So harmony as observed by
Palestrina and taught by Fux doesn't deal with the 7-limit at all.

Looked at another way, the 12-equal dissonances can all be thought of as
9-limit intervals. Well, except for minor seconds and major sevenths
which would have to be 15-limit. So the consonance/dissonance cutoff for
traditional harmony is roughly between the 5-limit and the 9-limit. You
don't have to consider the 11-limit because it's outside the notation.

Miracle temperament is excellent in both the 7- and 11-limits, but nothing
special in the 5-limit. So the obvious way to cut it up is for the
7-limit to be consonant and the rest of the 11-limit to be dissonant.
Intervals outside the 11-limit would be extreme dissonances, not to be
used harmonically unless you really want to.

If you want only 5-limit consonance, you're better off staying in
meantone. Remember that the first species can only use consonances. So
for the system to make sense on its own terms I had to increase the set of
consonances. I don't follow the simple 7-limit cutoff because when you
reach that level of complexity you do have to consider octave specificity.
I also allowed the 4 secor interval to be a "respectable" dissonance
because it's a prominent interval in the tuning, and sounds okay to me
despite being outside the 11-limit. To be fair, I allowed some more
intervals in as well.

> Or is this category a bit of the, dare I say, "middlesex" AC-DC
> variety??

In some contexts it is treated as a dissonance. What do you have against
English counties and Australian rock bands?

> Perhaps we could call these intervals "disconsonances..." ??

Traditional harmony has three levels of sonance I know of: perfect
consonance, imperfect consonance and dissonance. There's also the special
case of perfect fourths, which can be either consonant or dissonant
depending on context and who you ask. I'm using 6 levels of sonance, and
I don't have names for them all. Possibly that consonance 3 could be
called "assonance" which is a historical term, although originally applied
to thirds.

Graham

🔗emotionaljourney22 <paul@stretch-music.com>

--- In tuning@y..., graham@m... wrote:
> In-Reply-To: <aa74il+qu5k@e...>
> Me:
> > > There are other cases where Fux applies special rules
to "steps".
> > Any
> > > interval of 1 decimal step is a "step". 3 decimal steps can
always
> > be
> > > divided into two unequal "steps", so in 0-2-3 (C D> Ev) or 0-1-
3 (C
> > Db+
> > > Ev), 0-2 (C D>) and 1-3 (Db+ Ev) are "steps".
>
> Paul:
> > does this follow from the fux rules? what does fux say about
this? it
> > would seem to be "illegal pentatonicism" in a diatonic context --
no?
>
> Fux defines (or maybe simple assumes) "steps" to be any kind of
second.
> In a decimal context, "seconds" aren't defined.

not defined??? why on earth?

> There are 1 step
> intervals,

so they are defined!

> but they don't get as big.

so? this is microtonality, after all. and these steps average 120
cents -- not all that small, really!

> So some alternative definition has
> to be found so that the special rules about "steps" make sense, and
> I use the one above.

this deprives the special rules about 'steps' of *all* their sense,
IMO. you're not giving the 'decimality' of the scale a chance to show
itself -- and 'decimality', we seem to have agreed, is the only hope
blackjack has of taking on a 'white-note' or melodically coherent
character. why not just let the decimal step take the place of the
diatonic step?

btw, how exactly did you 'translate' the cantus firmi?

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., graham@m... wrote:

/tuning/topicId_36539.html#36624

> In-Reply-To: <aa7lr3+igi7@e...>
> jpehrson2 wrote:
>
> > ***I'm not "getting" "Consonance 3..."
> >
> > Isn't an 8:7 kind of like a "traditional" major second??
>
> Sort of. It's wider than the traditional tuning of a major
second. In
> Palestrina's day it was well approximated by the diminished third
of
> keyboard tunings. But it doesn't seem to have been exploited as
such.
>
> > That's considered a "mild dissonance" in 12-tET music, isn't it??
>
> It's a dissonance, plain and simple. But it isn't in 12-tET. Much
the
> same as 7:4, which is in consonance 2. Traditional harmony only
> recognises 5-limit consonance, and everything else is lumped
together as
> dissonance. 16th-17th Century examples are interesting, in that
only a
> few kinds of dissonance were actually used. But they weren't the 7-
limit
> chords that are hidden away in meantone. So harmony as observed by
> Palestrina and taught by Fux doesn't deal with the 7-limit at all.
>
> Looked at another way, the 12-equal dissonances can all be thought
of as
> 9-limit intervals. Well, except for minor seconds and major
sevenths
> which would have to be 15-limit. So the consonance/dissonance
cutoff for
> traditional harmony is roughly between the 5-limit and the 9-
limit. You
> don't have to consider the 11-limit because it's outside the
notation.
>
> Miracle temperament is excellent in both the 7- and 11-limits, but
nothing
> special in the 5-limit. So the obvious way to cut it up is for the
> 7-limit to be consonant and the rest of the 11-limit to be
dissonant.
> Intervals outside the 11-limit would be extreme dissonances, not to
be
> used harmonically unless you really want to.
>
> If you want only 5-limit consonance, you're better off staying in
> meantone. Remember that the first species can only use
consonances. So
> for the system to make sense on its own terms I had to increase the
set of
> consonances. I don't follow the simple 7-limit cutoff because when
you
> reach that level of complexity you do have to consider octave
specificity.
> I also allowed the 4 secor interval to be a "respectable"
dissonance
> because it's a prominent interval in the tuning, and sounds okay to
me
> despite being outside the 11-limit. To be fair, I allowed some
more
> intervals in as well.
>
> > Or is this category a bit of the, dare I say, "middlesex" AC-DC
> > variety??
>
> In some contexts it is treated as a dissonance. What do you have
against
> English counties and Australian rock bands?
>
> > Perhaps we could call these intervals "disconsonances..." ??
>
> Traditional harmony has three levels of sonance I know of: perfect
> consonance, imperfect consonance and dissonance. There's also the
special
> case of perfect fourths, which can be either consonant or dissonant
> depending on context and who you ask. I'm using 6 levels of
sonance, and
> I don't have names for them all. Possibly that consonance 3 could
be
> called "assonance" which is a historical term, although originally
applied
> to thirds.
>
>
> Graham

***Thanks for the clarifications, Graham! This is a mighty
interesting post.... I think it goes into my folder of
printed "keepers..."

Joseph

🔗graham@microtonal.co.uk

In-Reply-To: <aa9pgf+nhhn@eGroups.com>
emotionaljourney22 wrote:

> > Fux defines (or maybe simple assumes) "steps" to be any kind of
> second.
> > In a decimal context, "seconds" aren't defined.
>
> not defined??? why on earth?
>
> > There are 1 step
> > intervals,
>
> so they are defined!

No, 9:8 is a second but it's 2 decimal steps. 8:7 is usually classed as a
supermajor second, and that's also 2 steps. 7:6 is an augmented second in
meantone, and it's 2 steps again. Apart from the last two being
inconsistent usages, the best equivalent would be either 1 or 2 decimal
steps as a diatonic step.

> > but they don't get as big.
>
> so? this is microtonality, after all. and these steps average 120
> cents -- not all that small, really!

I don't find long strings of semitones make for good melody, and melody is
an important feature of counterpoint.

> > So some alternative definition has
> > to be found so that the special rules about "steps" make sense, and
> > I use the one above.
>
> this deprives the special rules about 'steps' of *all* their sense,
> IMO. you're not giving the 'decimality' of the scale a chance to show
> itself -- and 'decimality', we seem to have agreed, is the only hope
> blackjack has of taking on a 'white-note' or melodically coherent
> character. why not just let the decimal step take the place of the
> diatonic step?

When did we agree what? I find the decimal scale to be the equivalent of
the 12 note chromatic scale, not the 7 note diatonic. If you want to
show the decimalness, you can add the intermediate notes as ornamentation.
Species counterpoint is about equal rhythms, and equal step sizes make it
sound bland.

> btw, how exactly did you 'translate' the cantus firmi?

Make intervals equivalent, when notes repeat try to make them really
repeat, take out the accidentals and make sure it follows the melodic
rules.

Graham

🔗emotionaljourney22 <paul@stretch-music.com>

--- In tuning@y..., graham@m... wrote:

> > > but they don't get as big.
> >
> > so? this is microtonality, after all. and these steps average 120
> > cents -- not all that small, really!
>
> I don't find long strings of semitones

well, they can be altered!

> make for good melody, and melody is
> an important feature of counterpoint.

i think this is because you're used to diatonic melody, and if you're
not willing to abandon your diatonic tendencies, the whole decimal
thing is never going to have a chance to live its own musical life.
you'll just end up with badly bruised diatonic melodies, a result of
trying to fit a heptatonic peg into a decimal hole. imho.

> Species counterpoint is about equal rhythms, and equal step sizes
make it
> sound bland.

i thought you were altering the step sizes pretty freely, within the
bounds of blackjack. i endorse that -- thus, the step sizes won't be
equal.

> > btw, how exactly did you 'translate' the cantus firmi?
>
> Make intervals equivalent,

meaning you tried to preserve the rough cents values?

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., graham@m... wrote:

/tuning/topicId_36539.html#36643

why not just let the decimal step take the place of the
> > diatonic step?
>
> When did we agree what? I find the decimal scale to be the
equivalent of the 12 note chromatic scale, not the 7 note diatonic.

***I would tend to agree with this. The 116 step secor lends
a "traditional" chromaticism to Blackjack.

So, Graham, what is your "equivalent" to a "diatonic major second"
again??

Or, you're saying there are *several* of them possible...

Tx,

Joseph

🔗Carl Lumma <carl@lumma.org>

>>>***I wish somebody could write some of these exercises out in 72-
>>>tET notation... I understand that better than "decimal," frankly.
>>
>>J. Pehrson
>>
>>That would be wrong, since they are studies within the decimal
>>scale, not the diatonic scale. Notation in the diatonic scale
>>is fine, but should properly be called tablature.
>>
>>-Carl
>
>***I believe I would prefer to call *decimal* the "tablature"...
>since I've studied our "regular" 12-tET system as a reference all my
>life, as have most other musicians.

It isn't a matter of your preference, it's a matter of definition.
A tablature is defined as a notation which shows how to play something
on a particular instrument, while being non-ideal at showing the
structure of the music, which is exactly what you're requesting.

-Carl

🔗emotionaljourney22 <paul@stretch-music.com>

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., graham@m... wrote:
>
> /tuning/topicId_36539.html#36643
>
> why not just let the decimal step take the place of the
> > > diatonic step?
> >
> > When did we agree what? I find the decimal scale to be the
> equivalent of the 12 note chromatic scale, not the 7 note diatonic.
>
> ***I would tend to agree with this. The 116 step secor lends
> a "traditional" chromaticism to Blackjack.
>
> So, Graham, what is your "equivalent" to a "diatonic major second"
> again??
>
> Or, you're saying there are *several* of them possible...

well, my personal reaction is we're likely to learn more from these
exercises if we define "step" as any of the intervals where the
decimal name increments by 1 -- this would include the 83.3, 116.7,
and 150-cent intervals in blackjack. that way we'll be projecting
something of the 'fuzzy 10' that you, pierre, and i see as the
melodic 'ethos' of blackjack.

when i was taking my intermediate analysis and composition classes,
my first few exercises imitating the counterpoint of bach came back
with a lot of red marks. it turned out that i was relying too much
(read: at all) on my improvisational intuition, which was largely
blues-based, and hence 'pentatonic'. i was *used* to hearing major
seconds and minor thirds both as *steps*, since they are steps in the
pentatonic scale. the counterpoint i wrote sounded fine to me, but
since technically it followed leaps with steps in the same direction,
it 'broke the rules'. once i corrected this tendency, i actually
learned something -- i internalized the distinction between modern,
pentatonic-infused melody and 'classical', strictly diatonic melody --
as well as the ability to create nice counterpoint in the latter
language. the ability to do so has served me very well ever since.

what i'm suggesting is that, if we can abandon our diatonic
tendencies, we may find something more like a coherent new language,
as opposed to some mutation of our current habits. if we want to
stick with a diatonic conception of melody, i don't see that
blackjack is the right tuning for us at all. an exception might be if
we were to treat the mohajira scale as the set of 'naturals' in
blackjack, and let our definition of 'step' be based on that . . .

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

/tuning/topicId_36539.html#36656

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > --- In tuning@y..., graham@m... wrote:
> >
> > /tuning/topicId_36539.html#36643
> >
> > why not just let the decimal step take the place of the
> > > > diatonic step?
> > >
> > > When did we agree what? I find the decimal scale to be the
> > equivalent of the 12 note chromatic scale, not the 7 note
diatonic.
> >
> > ***I would tend to agree with this. The 116 step secor lends
> > a "traditional" chromaticism to Blackjack.
> >
> > So, Graham, what is your "equivalent" to a "diatonic major
second"
> > again??
> >
> > Or, you're saying there are *several* of them possible...
>
> well, my personal reaction is we're likely to learn more from these
> exercises if we define "step" as any of the intervals where the
> decimal name increments by 1 -- this would include the 83.3, 116.7,
> and 150-cent intervals in blackjack. that way we'll be projecting
> something of the 'fuzzy 10' that you, pierre, and i see as the
> melodic 'ethos' of blackjack.
>
> when i was taking my intermediate analysis and composition classes,
> my first few exercises imitating the counterpoint of bach came back
> with a lot of red marks. it turned out that i was relying too much
> (read: at all) on my improvisational intuition, which was largely
> blues-based, and hence 'pentatonic'. i was *used* to hearing major
> seconds and minor thirds both as *steps*, since they are steps in
the
> pentatonic scale. the counterpoint i wrote sounded fine to me, but
> since technically it followed leaps with steps in the same
direction,
> it 'broke the rules'. once i corrected this tendency, i actually
> learned something -- i internalized the distinction between modern,
> pentatonic-infused melody and 'classical', strictly diatonic
melody --
> as well as the ability to create nice counterpoint in the latter
> language. the ability to do so has served me very well ever since.
>
> what i'm suggesting is that, if we can abandon our diatonic
> tendencies, we may find something more like a coherent new
language,
> as opposed to some mutation of our current habits. if we want to
> stick with a diatonic conception of melody, i don't see that
> blackjack is the right tuning for us at all. an exception might be
if
> we were to treat the mohajira scale as the set of 'naturals' in
> blackjack, and let our definition of 'step' be based on that . . .

****Frankly, Paul, I think you're more on target when you say we
shouldn't try to "pidgeonhole" Blackjack into some kind of previous
conception, i.e. find some kind of "diatonic" equivalent.

Maybe we should just formulate contrapuntal rules for *Blackjack*
within its own context??

J. Pehrson

🔗graham@microtonal.co.uk

emotionaljourney22 wrote:

> well, my personal reaction is we're likely to learn more from these
> exercises if we define "step" as any of the intervals where the
> decimal name increments by 1 -- this would include the 83.3, 116.7,
> and 150-cent intervals in blackjack. that way we'll be projecting
> something of the 'fuzzy 10' that you, pierre, and i see as the
> melodic 'ethos' of blackjack.

If you're going to preserve the nature of the decimal scale, you should
avoid the 83.3 cent interval and only use the 15 cent interval for 10% of
your steps. So it'd be the 116.7 cent interval 90% of the steps, which
will dominate the melody.

If you want to use your own rules of counterpoint based around the melodic
ethos of blackjack, that's fine. I'm basing mine around the ethos of the
decimal scale, and free use of steps ranging from 83 to 150 cents (or 2 to
4 steps of 31-equal) would destroy that.

You also get a couple of 183 cent decimal 1-steps in Blackjack.

> when i was taking my intermediate analysis and composition classes,
> my first few exercises imitating the counterpoint of bach came back
> with a lot of red marks. it turned out that i was relying too much
> (read: at all) on my improvisational intuition, which was largely
> blues-based, and hence 'pentatonic'. i was *used* to hearing major
> seconds and minor thirds both as *steps*, since they are steps in the
> pentatonic scale. the counterpoint i wrote sounded fine to me, but
> since technically it followed leaps with steps in the same direction,
> it 'broke the rules'. once i corrected this tendency, i actually
> learned something -- i internalized the distinction between modern,
> pentatonic-infused melody and 'classical', strictly diatonic melody --
> as well as the ability to create nice counterpoint in the latter
> language. the ability to do so has served me very well ever since.

But Palestrina did that all the time. Does that mean his music wasn't
strictly diatonic? Pentatonic melody is also typical of medieval music,
which Palestrina was 150 years closer to than Bach. Nothing I'm doing is
stopping somebody moving to a stricter decimal melody in 150 years time.
It's isn't stopping you doing so now, for that matter.

60% of the steps in the pentatonic scale are also in the diatonic scale.
Only 29% of steps in the diatonic scale are in the decimal scale. So
decimal steps will sound much more chromatic than diatonic.

> what i'm suggesting is that, if we can abandon our diatonic
> tendencies, we may find something more like a coherent new language,
> as opposed to some mutation of our current habits. if we want to
> stick with a diatonic conception of melody, i don't see that
> blackjack is the right tuning for us at all. an exception might be if
> we were to treat the mohajira scale as the set of 'naturals' in
> blackjack, and let our definition of 'step' be based on that . . .

I've been using alternative tunings for a few years now, and I was playing
with free atonality before that. So if I still have diatonic tendencies I
expect my listeners will as well.

Carl gave a whole list of diatonics that you could use for a system of
counterpoint. I'm using the fuzzy decimal scale. One problem with
mohajira, as an MOS of fixed neutral thirds, is that the steps sizes are
close in size, same as with the decimal scale. And without chromaticism,
you have to admit the neutral third as a consonance. If you're going to
allow chromaticism within blackjack, you may as well start with the 7 from
decimal scale instead.

Graham

🔗graham@microtonal.co.uk

jpehrson2 wrote:

> So, Graham, what is your "equivalent" to a "diatonic major second"
> again??
>
> Or, you're saying there are *several* of them possible...

As a major second can be either 9:8 or 10:9, it'd be either 2 secors flat
by a quomma (12/72 octaves) or a secor sharp by two quommas (11/72
octaves). But as the latter is forbidden in decimal melody, it'd have to
be the former. There's also the 2 secor interval (14/72 octaves) that
approximates 8:7, which is a supermajor second. So two secors plus or
minus any number of quommas is the closest equivalent of a major second.
But only the 9:8 approximation is diatonic.

Graham

🔗emotionaljourney22 <paul@stretch-music.com>

--- In tuning@y..., graham@m... wrote:

> > that way we'll be projecting
> > something of the 'fuzzy 10' that you, pierre, and i see as the
> > melodic 'ethos' of blackjack.
>
> If you're going to preserve the nature of the decimal scale,

no, that isn't what i'm suggesting.

> you should
> avoid the 83.3 cent interval

this is a very useful interval, especially when changing melodic
direction.

> and only use the 15 cent interval for 10% of
> your steps. So it'd be the 116.7 cent interval 90% of the steps,
which
> will dominate the melody.

oh dear. you must have missed the 'fuzzy' bit above.

> I'm basing mine around the ethos of the
> decimal scale,

oh, so that's what you meant above.

> and free use of steps ranging from 83 to 150 cents (or 2 to
> 4 steps of 31-equal) would destroy that.

i'm claiming that treating 0-1-3 and 0-2-3 as just as valid as 0-1-2
in all circumstances will 'destroy the ethos of the decimal scale',
since the whole thing is likely to dissolve into diatonicity in the
listener's ear. the same thing is true (perhaps even more so) of the
decatonic scale in 22-equal.

> You also get a couple of 183 cent decimal 1-steps in Blackjack.

right, i forgot to mention those.

🔗graham@microtonal.co.uk

Me:
> > If you're going to preserve the nature of the decimal scale,

Paul:
> no, that isn't what i'm suggesting.

Well that's what I'm suggesting, and I started this thread, decided on the
rules and provided the examples. You'll notice the subject line also says
"decimal" counterpoint.

Me:
> > you should
> > avoid the 83.3 cent interval

Paul:
> this is a very useful interval, especially when changing melodic
> direction.

Changing direction? Well, that's not covered by the current rules. But
they aren't set in stone, so long as the decimal orientation is preserved.

Me:
> > and only use the 15 cent interval for 10% of
> > your steps. So it'd be the 116.7 cent interval 90% of the steps,
> which
> > will dominate the melody.

Paul:
> oh dear. you must have missed the 'fuzzy' bit above.

What do you mean "missed the 'fuzzy' bit"? That's a precise description
of a fuzzy set.

Paul:
> i'm claiming that treating 0-1-3 and 0-2-3 as just as valid as 0-1-2
> in all circumstances will 'destroy the ethos of the decimal scale',
> since the whole thing is likely to dissolve into diatonicity in the
> listener's ear. the same thing is true (perhaps even more so) of the
> decatonic scale in 22-equal.

So what if it does "dissolve into diatonicity"? So long as it's heard as
a subset of a 10 note chromatic. The trick to that is making sure each
decimal interval class is clearly distinguished.

> > You also get a couple of 183 cent decimal 1-steps in Blackjack.
>
> right, i forgot to mention those.

So you've got steps ranging from 83 to 183 cents, and you expect the
listener to know they're all the same interval class??

Graham

🔗graham@microtonal.co.uk

Me:
> > But Palestrina did that all the time.

Paul:
> do you have any examples?

Specifically of minor thirds followed by steps in the same direction?
Jeppesen (p.86) gives the opening theme of Ad te levavi which includes
F-D-C on "-vi o-cu-".

On the first page of the Stabat Mater, the first chorus tenor starts out
C#-D-F on "Sta-bat Ma-" and the first chorus tenor goes F-D-C# on
"-lo-ro-sa". The second chorus alto starts E-G-A on "Jux-ta cru-".

It would break the rules if there were a passing dissonance, but you
didn't say anything about that.

> i've only seen extremely specious arguments to that effect.

Okay, we'll leave the middle ages to one side.

Me:
> > So if I still have diatonic tendencies I
> > expect my listeners will as well.

Paul:
> yes, they will. that's why we need to work especially hard to avoid
> these tendencies, in my opinion.

Why, so they don't like the melodies? How about we emancipate the
dissonances and have the whole thing based an a single tone row as well?

Besides, you said minor thirds as steps were going against strict diatonic
melody before. So surely the same must be true of approximations to 7:6.

Graham

🔗Carl Lumma <carl@lumma.org>

🔗emotionaljourney22 <paul@stretch-music.com>

--- In tuning@y..., graham@m... wrote:
> Me:
> > > But Palestrina did that all the time.
>
> Paul:
> > do you have any examples?
>
> Specifically of minor thirds followed by steps in the same
direction?

well no, i meant of more extensive pentatonicism. the "rules" are
always more restrictive than what most actual composers used,
but they point you in a certain stylistic direction.

> It would break the rules if there were a passing dissonance,

so it doesn't even break the rules? well then i'm not sure why you
brought him up.

> > i've only seen extremely specious arguments to that effect.
>
> Okay, we'll leave the middle ages to one side.
>
> Me:
> > > So if I still have diatonic tendencies I
> > > expect my listeners will as well.
>
> Paul:
> > yes, they will. that's why we need to work especially hard to
avoid
> > these tendencies, in my opinion.
>
> Why, so they don't like the melodies?

maybe not at first, but you'll end up with a more unique musical
style, which will go farther in the long run.

> How about we emancipate the
> dissonances and have the whole thing based an a single tone
>row as well?

well clearly that's not something either one of us is interested in,
but it's a perfect example of how a set of rules can be useful for
preliminary exercises in a new style.

> Besides, you said minor thirds as steps were going against
>strict diatonic melody before.

not when treated under the accepted rules for leaps in species
counterpoint, or when occuring as part of an arpeggiated
gesture in diatonic music.

> So surely the same must be true of approximations to 7:6.

yes, 7:6s would be great melodic intervals to use with a similar
set of rules.

🔗graham@microtonal.co.uk

emotionaljourney22 wrote:

> well no, i meant of more extensive pentatonicism. the "rules" are
> always more restrictive than what most actual composers used,
> but they point you in a certain stylistic direction.

What else do you mean by pentatonicism? So far you've only said following
a major third by a step in the same direction, and Palestrina does that.
The rules as given by Fux and Jeppesen are deduced from Palestrina's
music, so that music is the ultimate authority on what is or isn't a rule.
He was very consistent.

> > It would break the rules if there were a passing dissonance,
>
> so it doesn't even break the rules? well then i'm not sure why you
> brought him up.

You said a leap followed by a step in the same direction broke the rules
of Bach counterpoint. I said that it's commonplace in Palestrina, so it
can't be necessary for diatonic melody.

> maybe not at first, but you'll end up with a more unique musical
> style, which will go farther in the long run.

I'll keep on with what sounds good to me. I'm already allowing
consecutive semitones in diatonic music, and subminor thirds treated as
steps. So it is a unique style, if similar to diatonicism in some
respects.

> > Besides, you said minor thirds as steps were going against
> >strict diatonic melody before.
>
> not when treated under the accepted rules for leaps in species
> counterpoint, or when occuring as part of an arpeggiated
> gesture in diatonic music.

If they're treated as steps then they can't be leaps, can they?

And what do you mean by "accepted rules"? There are different rules for
different eras. According to Jeppesen, Kirnberger does allow passing
notes to be introduced or quitted by leaps. As my rules don't allow for a
passing note to be both introduced and quitted by a 2-step, they could
well be in line with the adaptation you suggest for Bach counterpoint,
which you say is what you learned. Do any of my examples sound wrong in
this context?

In addition, there's no way a minor third can be followed by a semitone in
the same direction in a major scale. So the primary rule of passing
dissonances -- that they should pass through a third -- can't be followed
if the note is introduced or quitted by a minor third. That it can in
decimal counterpoint (and the 7 from decimal MOS) is a break with
diatonicism. Hence:

> yes, 7:6s would be great melodic intervals to use with a similar
> set of rules.

But how about if they're treated as steps? Isn't treating 7:6 as a step
exactly the example you gave of breaking strict diatonic melody? But when
I do it, it's selling out to diatonic melody.

Anyway, I am using a 7 note mode now, which is sickeningly diatonic but
does at least mean my contrapuntal steps are also scale steps.

Graham

🔗emotionaljourney22 <paul@stretch-music.com>

--- In tuning@y..., graham@m... wrote:
consistent.
>
> > > It would break the rules if there were a passing
dissonance,
> >
> > so it doesn't even break the rules? well then i'm not sure why
you
> > brought him up.
>
> You said a leap followed by a step in the same direction broke
the rules
> of Bach counterpoint.

no, not that in itself -- that was just part of it. but the fux rules are
certainly strict enough to prevent a sense of pentatonicism from
arising. all i was objecting to was that you seemed to be altering
those rules a bit relative to a 'literal translation' . . . weren't you, in
the context of what moves are allowed in a passing-tone
context?

>
> > > Besides, you said minor thirds as steps were going
against
> > >strict diatonic melody before.
> >
> > not when treated under the accepted rules for leaps in
species
> > counterpoint, or when occuring as part of an arpeggiated
> > gesture in diatonic music.
>
> If they're treated as steps then they can't be leaps, can they?

right -- to be unambiguously "treated as steps" in the sense i
meant, they must flagrantly violate the accepted rules for leaps.

> Do any of my examples sound wrong in
> this context?

i wasn't listening particularly for that -- when i can listen again, i
will.

> In addition, there's no way a minor third can be followed by a
semitone in
> the same direction in a major scale. So the primary rule of
passing
> dissonances -- that they should pass through a third -- can't be
followed
> if the note is introduced or quitted by a minor third.

i'm not following.

> That it can in
> decimal counterpoint (and the 7 from decimal MOS) is a break
with
> diatonicism.

can you show with examples?

>> Hence:
>
> > yes, 7:6s would be great melodic intervals to use with a
similar
> > set of rules.
>
> But how about if they're treated as steps? Isn't treating 7:6 as a
step
> exactly the example you gave of breaking strict diatonic
melody?

not that i recall -- remind me if i'm forgetting something.

> But when
> I do it, it's selling out to diatonic melody.

not as far as i can see. not according to anything i've said, either,
right?

🔗graham@microtonal.co.uk

In-Reply-To: <aai51m+a246@eGroups.com>
emotionaljourney22 wrote:

> no, not that in itself -- that was just part of it. but the fux rules
> are certainly strict enough to prevent a sense of pentatonicism from
> arising. all i was objecting to was that you seemed to be altering
> those rules a bit relative to a 'literal translation' . . . weren't
> you, in the context of what moves are allowed in a passing-tone context?

The rules I use are the best translation I can find for diatonic steps in
a decimal scale. The diatonic steps will translate to 16:15, 10:9 or 9:8
(maybe even 25:24 or 8:7). As decimal interval classes, these are either
1 or 2 steps. However, 2 decimal steps can get a larger than a typical
diatonic step, to cover 8:7 and 7:6. So to balance this, I don't allow
two 2-step intervals in a row to both translate as diatonic steps. That
means two steps can still be a third, which keeps the spirit of the
passing dissonance rule.

I don't know what to do about isolated 2-steps where a diatonic step is
expected. Now I'm using a 7 note scale, probably based on that. I didn't
get as far as appoggiaturas in the free decimal examples. Possibly they
would make more sense resolving by single decimal steps.

1 or 2 decimal steps being a contrapuntal step is also consistent with 1
or 2 chromatic steps being a diatonic step. I'm treating the fuzzy
decimal scale as a chromatic because it's too big and too shapeless to be
a diatonic.

The increased number of dissonances, and complexity of the rules, is a
looser translation. I felt it was the only way of treating the decimal
scale on its own terms. You can twist the scale to give lots of 5-limit
intervals, but then it really will end up sounding diatonic.

Fux uses step size for other rules. Leaps greater than a minor sixth are
forbidden (I broke this in a recent example, should fix it) except for
octaves in a particular context, and leaps greater than a third are enough
to obscure parallel fifths in another context. As "steps" are generalized
by their size, the same can be done for these other cases. If diatonic
steps were mapped to decimal steps, I'd have to decide whether leaps
should be illegal if greater than 5 or 8 (10-2) steps.

The pattern 8-0-1 counts as consecutive steps by my rule. The 8-0
interval approximates 7:6 and the 0-1 approximates 15:14, so the whole 8-1
approximates 5:4. In meantone, that'd be C-D#-E, including an augmented
second which lies outside the diatonic scale, and is rarely used as a
melodic interval in 16th century music. So the generalisation of diatonic
steps still gives results that would be impossible in a diatonic context,
because it is framed in terms of decimal steps. A more direct translation
would have been to allow 0-2v as a step, but rarely 0-2 and never 0v-2.

Graham