Yahoo Tuning Groups Ultimate Backup tuning As dumb as a unison

Ok Aaron. You and the rest of the world may like to think that a rock who
flunked the IQ test has an intelligence quotient of 0 and thus is able to
obtain a performance score measurable by everyday standards, but I'd still
keep saying that it is as dumb as a rock and has no intelligence
whatsoever - with or without the IQ test - provided that it has no
likelihood of ever gaining `intelligence` spontaneously. Blame me for my
exasperating logic.

A rock that has intelligence, however 0! It was a hoot the while it lasted.
However, I will not argue this matter any longer.

Surely, both the unison AND music in the broadest sense exist since billions
of years before a single human being was created.

Oz.

----- Original Message -----
From: "Aaron Wolf" <backfromthesilo@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 03 Mart 2006 Cuma 0:23
Subject: [tuning] Re: Unison is not a term to be defined emotionally

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Since when did the definition of unison entail actual acoustic
conditions of
> > pitch fluctuations, vibratos or glissandos in a real performance? We are
> > trying to pinpoint the theoretically correct explanation of unison here
that
> > applies to all ideal conditions.
> >
> > And never mind the minute variations that do not in the least affect our
> > conception. Glaring errors by any two musicians trying to sound a unison
is
> > not the fault of the unison.
> >
>
> That's exactly what I'm saying! Except for this: unison is a word. If we
have two different
> definitions, then we can figure out if we are explaining two different
things. If so, we need
> two different terms. It's just for communication. In other words, there
is absolutely no
> reason that two people, each descibing a different idea should either one
care what word
> is used to describe it, as long as they both end up with a way to
communicate their unique
> ideas. So there's no reason to argue. Just work together to clarify
meaning so we all have
> useful words. If "unison" alone doesn't express to me what you mean,
don't try to tell me
> that you've changed the definition of unison, unless everyone has agreed
to use that
> change. Because it's all about communication, right?
>
> I wasn't saying unison involves those performance issues, I was saying
that if those are
> factors in our musical discussion, we need words to define the difference
between
> perceptions based on those things and the other perceptions we're talking
about.
>
> Emotional does not equal perceptual. And if you are claiming that words
like unison or
> even the idea behind them even exist without perception, I have to
disagree. Unisons did
> not exist before people. Unison is an idea. Not a reality. Well- that
is unless we define
> unison as simply the existence of identical frequency waves coming from
discreet sources
> at the same moment in time. But if that's all it is, then what's with the
big discussion?
>
> -Aaron
>
>
>
>
>
>
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🔗Aaron Wolf <backfromthesilo@yahoo.com>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Ok Aaron. You and the rest of the world may like to think that a rock who
> flunked the IQ test has an intelligence quotient of 0 and thus is able to
> obtain a performance score measurable by everyday standards, but I'd still
> keep saying that it is as dumb as a rock and has no intelligence
> whatsoever - with or without the IQ test - provided that it has no
> likelihood of ever gaining `intelligence` spontaneously. Blame me for my
> exasperating logic.
>
> A rock that has intelligence, however 0! It was a hoot the while it lasted.
> However, I will not argue this matter any longer.
>
> Surely, both the unison AND music in the broadest sense exist since billions
> of years before a single human being was created.
>
> Oz.
>

I am not arguing about unison. I'm not involved in that discussion.

I will argue, however, about use of language as needing to be pragmatic. Unison is a
word. Music is a work. IQ test is a couple words. And the test it refers to is a human
construction. It is a ridiculous human flaw to think that because people come up with a
word like "Intelligence" that all of a sudden the existence of the word means that the
external universe actually fits into categories of more or less or existing or non-existing
intelligence. The universe is what it was before, regardless of inventing that word. The
practical question is only, how does the word help us communicate.

Thanks for the simple revelation that IQ tests are a simplistic way to define a complex
word like "intelligence." You've pointed out that anyone who views simple outputs of
simple tests and calls it truth is foolish. I agree.

The thing that lost me was: I didn't catch that someone stated something about unison in
such a similarly foolish way. But, assuming someone did... well, I would have responded
by asking what idea they were trying to get at. I can't imagine why someone would point
out that a rock would have intelligence, albiet 0. (which I agree is a misunderstanding to
even say that). But if anyone bothered to say that, I'd try to figure out if they had some
actual point or if they were just playing with words and being dumb. All I know about the
unison thing is that I could easily imagine someone talking about unison as an interval
who is trying to make some actual point. And so I'd wonder what that is. But if they were
just trying to say "don't forget unison is an interval too" and there was no point behind it,
then I'd just tell them to shut up and stop playing with words. And if *you* brought it up
by saying "you know, unison is not an interval" then I'd ask you, what's your point?

If behind the discussion of words, there wasn't an idea to be communicated beyond the
words themselves then SHAME on everyone who wasted their time in the discussion. And
if people tried to inquire as to what the idea on the other side might be, only to have the
respondant refuse to get past the words to reveal the idea (or lack thereof) then that is
truly a shame. And if anyone gets hung up on my words here instead of doing their best
to interpret the idea, then you're obviously missing the whole point. So if this gets any
response, it better not be a single post referencing HOW I'm talking about this. Talk about
the ideas, instead.

And please try to apply this to all future discussions. We're trying to help each other
understand things here and communicate well.

-Aaron

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

The idea boils down to the coherent usage of terminology in music theory as
we recognize today, or in other words, that one cannot invert unison so that
it suddenly turns into the interval of an octave. I strongly urge the usage
of transformation for this particular case instead.

----- Original Message -----
From: "Aaron Wolf" <backfromthesilo@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 07 Mart 2006 Salï¿½ 1:39
Subject: [tuning] Re: As dumb as a unison

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Ok Aaron. You and the rest of the world may like to think that a rock
who
> > flunked the IQ test has an intelligence quotient of 0 and thus is able
to
> > obtain a performance score measurable by everyday standards, but I'd
still
> > keep saying that it is as dumb as a rock and has no intelligence
> > whatsoever - with or without the IQ test - provided that it has no
> > likelihood of ever gaining `intelligence` spontaneously. Blame me for my
> > exasperating logic.
> >
> > A rock that has intelligence, however 0! It was a hoot the while it
lasted.
> > However, I will not argue this matter any longer.
> >
> > Surely, both the unison AND music in the broadest sense exist since
billions
> > of years before a single human being was created.
> >
> > Oz.
> >
>
> I am not arguing about unison. I'm not involved in that discussion.
>
> I will argue, however, about use of language as needing to be pragmatic.
Unison is a
> word. Music is a work. IQ test is a couple words. And the test it
refers to is a human
> construction. It is a ridiculous human flaw to think that because people
come up with a
> word like "Intelligence" that all of a sudden the existence of the word
means that the
> external universe actually fits into categories of more or less or
existing or non-existing
> intelligence. The universe is what it was before, regardless of inventing
that word. The
> practical question is only, how does the word help us communicate.
>
> Thanks for the simple revelation that IQ tests are a simplistic way to
define a complex
> word like "intelligence." You've pointed out that anyone who views simple
outputs of
> simple tests and calls it truth is foolish. I agree.
>
> The thing that lost me was: I didn't catch that someone stated something
about unison in
> such a similarly foolish way. But, assuming someone did... well, I would
have responded
> by asking what idea they were trying to get at. I can't imagine why
someone would point
> out that a rock would have intelligence, albiet 0. (which I agree is a
misunderstanding to
> even say that). But if anyone bothered to say that, I'd try to figure out
if they had some
> actual point or if they were just playing with words and being dumb. All
I know about the
> unison thing is that I could easily imagine someone talking about unison
as an interval
> who is trying to make some actual point. And so I'd wonder what that is.
But if they were
> just trying to say "don't forget unison is an interval too" and there was
no point behind it,
> then I'd just tell them to shut up and stop playing with words. And if
*you* brought it up
> by saying "you know, unison is not an interval" then I'd ask you, what's
your point?
>
> If behind the discussion of words, there wasn't an idea to be communicated
beyond the
> words themselves then SHAME on everyone who wasted their time in the
discussion. And
> if people tried to inquire as to what the idea on the other side might be,
only to have the
> respondant refuse to get past the words to reveal the idea (or lack
thereof) then that is
> truly a shame. And if anyone gets hung up on my words here instead of
doing their best
> to interpret the idea, then you're obviously missing the whole point. So
if this gets any
> response, it better not be a single post referencing HOW I'm talking about
this. Talk about
> the ideas, instead.
>
> And please try to apply this to all future discussions. We're trying to
help each other
> understand things here and communicate well.
>
> -Aaron
>
>

🔗klaus schmirler <KSchmir@online.de>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

Oh but I did. Since inversion is transposing the bass note of a chord an
octave above, or the treble note an octave below when returning to the root
position, and since unison occupies both the bass and the treble positions
by definition (two or more tones, single pitch, no interval), you cannot
expect the unison to unfold to the interval of an octave by inversion, but
may only conceive of such by `transformation`.

Examples:

E
C--C
G--G--G
E-- E
C

Cc
Cc

Transformation of unison to an octave:

c
Cc---C

Simple as that.

Oz.

----- Original Message -----
From: "klaus schmirler" <KSchmir@online.de>
To: <tuning@yahoogroups.com>
Sent: 07 Mart 2006 Salï¿½ 12:16
Subject: Re: [tuning] Re: As dumb as a unison

> Ozan Yarman wrote:
> > The idea boils down to the coherent usage of terminology in music theory
as
> > we recognize today, or in other words, that one cannot invert unison so
that
> > it suddenly turns into the interval of an octave. I strongly urge the
usage
> > of transformation for this particular case instead.
>
> You haven't said anything about the why and wherefore.
>
> klaus
>
>

🔗Aaron Wolf <backfromthesilo@yahoo.com>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Aaron Wolf <backfromthesilo@yahoo.com>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> So do we agree or not?
>

I agree that "inverting" a unison is really a very
inappropriate language to describe how intervals that
inverted within an octave can resolve to a unison
or to an octave.

The prevalent thinking that octaves and unisons are
truly "equivalent" seems faulty to me. It is a case
of exactly what I'm talking about: using names and
words instead of reality to prove a point. Just
because we use the same letter name, doesn't mean
it is the same note. However, there's obviously
a real idea behind it that is based on actual
perception.

So rather than argue with people about how you can't
invert a unison, I'd try to say, yeah, you're point
about octave-inverted large intervals resolving to
unisons versus octaves is a good point. Here's a
better way I'd suggest to talk about it though...

And if there's confusion, we can point out why
discussing inversion of unison is confusing
or how it keeps the thinking in an artificial
box, not open to all the possibilities of musical
understanding.

I think that it isn't "unison" that is the problem,
it's the word "inversion" and how that isn't clear.
There's the implication usually that we're talking
about octave based inversion. But that isn't always
specified. So what are we really talking about?
This leads to discussion about the significance of
octaves. I think that is useful discussion. It's
important in my mind to pin-down what it is about
the octave that we're valuing and perceiving. It's
a long and interesting discussion, so I won't start
into that.

If we can identify more clearly and precisely what
the perception is that we're identifying with the
word "interval" and the word "inversion" then maybe
we could agree that if we apply a similar perceptual
event to a unison it will become an octave. If so,
then maybe we'll end up accepting that the term
"inversion," while clearly illogical to apply to a
unison, is in fact the easiest way to relate the
unison vs. octave perception in this context (though
I don't like those sorts of compromises that use
such illogical confusing language, they are a fact
of language, and sometimes we do compromise). On the
other hand, maybe with discussion, we will discover
that the perception we're talking about with "interval"
and "inversion" doesn't actually apply to unisons,
and then we could clear say that unisons don't exhibit
the behaviour of the other intervals in these regards.

This is all obviously somewhat subjective.

My overall point being that rather than try to argue
about which boxes everything belongs in, we should
use every point of confusion like this as an
opportunity to clarify what it that we're really
talking about. If inversion is only a name for
something people saw patterns of in notation, then
that's not very significant or applicable. That
would be like the idea I mentioned where people
see patterns like "oh, I see, chords are every other
note in a scale." If we apply patterns like that
to everything, it really isn't appropriate. I'm glad
that I understand why and how chords really come to
be. My sense is that inversions and octaves also
relate to real perceptual phenomena. Whether these
perceptions also apply to unisons isn't clear to me,
especially when we use words like "inversion" which
absolutely doesn't, as a *word*, apply to the idea
of unison.

Ok, so we recognize silly innapropriate words.
Fine. Instead of arguing about it, everyone needs to:

1. accept and admit that those words are illogical
to apply to this circumstance

2. Figure out with other ways what we're really talking
about

3. Decide if it will be best to compromise and accept
the illogical words or rather come up with new words
or clarify or modify definitions.

This is like the idea that musicians use ordinal names:
major second, perfect FIFTH, and also cardinal names:
I-IV-V (one-four-five) but it's all confusing and weird.
See we say that ONE step away is an interval of a SECOND.
That's ridiculous. Every beginning student in the world
gets confused at first about this. Should we change it?
Maybe that's like Esperanto... language has come to be
and we need to accept it to some degree even when it
doesn't make sense. That NEVER means, however, that we
should argue that it DOES make sense!
I tell my students why and more importantly THAT our
musical numbering system is illogical confusing and
sometimes inconsistent. Then I teach it to them anyway
because they need to communicate with other musicians.

Ok, anyway, long answer. Ozan, it seems we agree about
the problems with the words. But I'm trying not to get
hung up on the words. I'll be optimistic and assume
that people talking about inverting the unison have
something of substance they are trying to communicate.
I don't know what it is really, and I don't have time
for the discussion at the moment. But it could be
interesting.

My humble advice on the politics of it all is to
get people to admit to the confusion of the words, but
always leave open the idea that what they are saying
might have validity, outside of the confusing words.
Then try to get at that substance. Or like me, say
you don't have time. People butt heads when someone
says "unisons can't be inverted!!" instead of saying
"the word inversion is illogical to apply to unisons."
The difference being that nobody will take the second
one as a statement that their entire idea they were
trying to communicate is false.

-Aaron

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

I am the daring author of the argument "you cannot invert a unison, since
it's not an interval".

All that discussion about zero was to facilitate the understanding of this
very point.

Inversion is a very simple concept though. It just applies to intervals, not
unison.

BTW, call me Oz.

Oz.

----- Original Message -----
From: "Aaron Wolf" <backfromthesilo@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 07 Mart 2006 Salï¿½ 20:31
Subject: [tuning] Re: As dumb as a unison

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > So do we agree or not?
> >
>
> I agree that "inverting" a unison is really a very
> inappropriate language to describe how intervals that
> inverted within an octave can resolve to a unison
> or to an octave.
>
> The prevalent thinking that octaves and unisons are
> truly "equivalent" seems faulty to me. It is a case
> of exactly what I'm talking about: using names and
> words instead of reality to prove a point. Just
> because we use the same letter name, doesn't mean
> it is the same note. However, there's obviously
> a real idea behind it that is based on actual
> perception.
>
> So rather than argue with people about how you can't
> invert a unison, I'd try to say, yeah, you're point
> about octave-inverted large intervals resolving to
> unisons versus octaves is a good point. Here's a
> better way I'd suggest to talk about it though...
>
> And if there's confusion, we can point out why
> discussing inversion of unison is confusing
> or how it keeps the thinking in an artificial
> box, not open to all the possibilities of musical
> understanding.
>
> I think that it isn't "unison" that is the problem,
> it's the word "inversion" and how that isn't clear.
> There's the implication usually that we're talking
> about octave based inversion. But that isn't always
> specified. So what are we really talking about?
> This leads to discussion about the significance of
> octaves. I think that is useful discussion. It's
> important in my mind to pin-down what it is about
> the octave that we're valuing and perceiving. It's
> a long and interesting discussion, so I won't start
> into that.
>
> If we can identify more clearly and precisely what
> the perception is that we're identifying with the
> word "interval" and the word "inversion" then maybe
> we could agree that if we apply a similar perceptual
> event to a unison it will become an octave. If so,
> then maybe we'll end up accepting that the term
> "inversion," while clearly illogical to apply to a
> unison, is in fact the easiest way to relate the
> unison vs. octave perception in this context (though
> I don't like those sorts of compromises that use
> such illogical confusing language, they are a fact
> of language, and sometimes we do compromise). On the
> other hand, maybe with discussion, we will discover
> that the perception we're talking about with "interval"
> and "inversion" doesn't actually apply to unisons,
> and then we could clear say that unisons don't exhibit
> the behaviour of the other intervals in these regards.
>
> This is all obviously somewhat subjective.
>
> My overall point being that rather than try to argue
> about which boxes everything belongs in, we should
> use every point of confusion like this as an
> opportunity to clarify what it that we're really
> talking about. If inversion is only a name for
> something people saw patterns of in notation, then
> that's not very significant or applicable. That
> would be like the idea I mentioned where people
> see patterns like "oh, I see, chords are every other
> note in a scale." If we apply patterns like that
> to everything, it really isn't appropriate. I'm glad
> that I understand why and how chords really come to
> be. My sense is that inversions and octaves also
> relate to real perceptual phenomena. Whether these
> perceptions also apply to unisons isn't clear to me,
> especially when we use words like "inversion" which
> absolutely doesn't, as a *word*, apply to the idea
> of unison.
>
> Ok, so we recognize silly innapropriate words.
> Fine. Instead of arguing about it, everyone needs to:
>
> 1. accept and admit that those words are illogical
> to apply to this circumstance
>
> 2. Figure out with other ways what we're really talking
> about
>
> 3. Decide if it will be best to compromise and accept
> the illogical words or rather come up with new words
> or clarify or modify definitions.
>
> This is like the idea that musicians use ordinal names:
> major second, perfect FIFTH, and also cardinal names:
> I-IV-V (one-four-five) but it's all confusing and weird.
> See we say that ONE step away is an interval of a SECOND.
> That's ridiculous. Every beginning student in the world
> gets confused at first about this. Should we change it?
> Maybe that's like Esperanto... language has come to be
> and we need to accept it to some degree even when it
> doesn't make sense. That NEVER means, however, that we
> should argue that it DOES make sense!
> I tell my students why and more importantly THAT our
> musical numbering system is illogical confusing and
> sometimes inconsistent. Then I teach it to them anyway
> because they need to communicate with other musicians.
>
> Ok, anyway, long answer. Ozan, it seems we agree about
> the problems with the words. But I'm trying not to get
> hung up on the words. I'll be optimistic and assume
> that people talking about inverting the unison have
> something of substance they are trying to communicate.
> I don't know what it is really, and I don't have time
> for the discussion at the moment. But it could be
> interesting.
>
> My humble advice on the politics of it all is to
> get people to admit to the confusion of the words, but
> always leave open the idea that what they are saying
> might have validity, outside of the confusing words.
> Then try to get at that substance. Or like me, say
> you don't have time. People butt heads when someone
> says "unisons can't be inverted!!" instead of saying
> "the word inversion is illogical to apply to unisons."
> The difference being that nobody will take the second
> one as a statement that their entire idea they were
> trying to communicate is false.
>
> -Aaron
>
>

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

--- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@...> wrote:

> For what it's worth I absolutely cannot imagine accepting the idea
that a unison can be
> inverted... That's even more foolish than the naive idea that
chords are essentially built by
> using every other note in a scale, as simplistic theory texts say.

The mathematician's point of view on such questions is to stick with
simplicity and generality.

You might be asking for an inversion of an interval, or for the
inversion of an interval of pitch classes, and this isn't the same
question. For intervals and chords, the simplest notion of inversion
is applying an inversive mapping to each note, which does not
correspond to musical vocabulary. In other words, choosing a unison,
apply x |--> 1/x to each note, and your chord is converted into
another chord. If we now take this to be applied to pitch classes, we
can reduce to the octave. Aside from the unison, this can be obtained
from x |--> 2/x, which maps the octave 1 <= x < 2 to itself if we make
an exception and say the unision is mapped to a unison, and not an octave.

None of this, of course, corresponds to musical terminology practice.
You get something more like musical practice if we look at what
happens when we apply the inversive mapping, either modulo octaves or
not, to classes of chords. Then the class of intervals of a fifth is
mapped to the class of intervals of a fourth when we are not looking
modulo octaves, whereas fifths and fourths are identified mod octaves.
The class of major triads in close root position is mapped to the
class of minor triads in close root position and vice versa not modulo
octaves, whereas all you can say mod octaves is that major triads are
mapped to minor triads and vice versa.

Using these definitions, the class of unison intervals maps to itself,
not to octaves.

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

On Tue, 07 Mar 2006, Aaron Wolf wrote:
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> > The idea boils down to the coherent usage of terminology in music theory
as
> > we recognize today, or in other words, that one cannot invert unison so
that
> > it suddenly turns into the interval of an octave. I strongly urge the
usage
> > of transformation for this particular case instead.
>
> For what it's worth I absolutely cannot imagine accepting the idea that a
unison can be
> inverted... That's even more foolish than the naive idea that chords are
essentially built by
> using every other note in a scale, as simplistic theory texts say.

Hi Aaron and Ozan,

For what it's worth, I see no _logical_ reason to reject
the idea of inverting any interval whatsoever, including
unison. I also see no _lgical_ reason to reject calling a
unison between two parts an interval.

However, as is so often the case, applying these logical
ideas to the creation of _music_ doesn't always result
in something satisfying. For example, when two parts
cross by stepwise contrary or oblique motion, the
_logical_ interval between them at some point is most
definitely a unison, although playing or singing that will
often create an unmusical result, through the sudden
thinning of the texture - probably due as much to the
loss of interaction of the upper partials of the two
notes as to the absence of a second fundamental in the
mix.

While discussing the logical idea of inversion (in any
interval, commonly an octave), may I point out that it's
not vastly different from the logical idea of reflection
about the midpoint of that interval (commonly a tritone).
eg inverting the diatonic melodic fragment:
CDEE DEFF EFAG FGBA
in its octave (at c) produces:
cBAA BAGG AGEF GFDE
which is exactly the same result as reflecting it in the
tritone at F#.

In the first method, we invert the (note at the) _prime_
C in the (interval) octave C-c to get the (note at the)
octave c.

Hmmm, I notice that I'm talking about the prime here
(a note), rather than the unison (an interval).

In the second method, we reflect the (note at the)
_prime_ C in the midpoint of the (interval) octave C-c,
that is F#, 3 and a half scale degrees away, to get the
(note at the) octave c, 3 and a half scale degrees away
on the other side.

Interesting that a non-scale note (F#) is useful in
working this out!

Regards,
Yahya

--
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🔗Ozan Yarman <ozanyarman@ozanyarman.com>

SNIP

>
> You might be asking for an inversion of an interval, or for the
> inversion of an interval of pitch classes, and this isn't the same
> question. For intervals and chords, the simplest notion of inversion
> is applying an inversive mapping to each note, which does not
> correspond to musical vocabulary. In other words, choosing a unison,
> apply x |--> 1/x to each note, and your chord is converted into
> another chord. If we now take this to be applied to pitch classes, we
> can reduce to the octave. Aside from the unison, this can be obtained
> from x |--> 2/x, which maps the octave 1 <= x < 2 to itself if we make
> an exception and say the unision is mapped to a unison, and not an octave.
>

Indeed.

> None of this, of course, corresponds to musical terminology practice.
> You get something more like musical practice if we look at what
> happens when we apply the inversive mapping, either modulo octaves or
> not, to classes of chords. Then the class of intervals of a fifth is
> mapped to the class of intervals of a fourth when we are not looking
> modulo octaves, whereas fifths and fourths are identified mod octaves.
> The class of major triads in close root position is mapped to the
> class of minor triads in close root position and vice versa not modulo
> octaves, whereas all you can say mod octaves is that major triads are
> mapped to minor triads and vice versa.
>
> Using these definitions, the class of unison intervals maps to itself,
> not to octaves.
>
>

Exactly, unless you somehow use unison synonymously with octaves.

Oz.

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

SNIP

> Hi Aaron and Ozan,
>
> For what it's worth, I see no _logical_ reason to reject
> the idea of inverting any interval whatsoever, including
> unison.

How can one invert a unison? An example if you please?

I also see no _lgical_ reason to reject calling a
> unison between two parts an interval.
>

Between a lower and an upper pitch. This certainly does not apply to unison.

> However, as is so often the case, applying these logical
> ideas to the creation of _music_ doesn't always result
> in something satisfying. For example, when two parts
> cross by stepwise contrary or oblique motion, the
> _logical_ interval

rendezvouz point, rather.

between them at some point is most
> definitely a unison, although playing or singing that will
> often create an unmusical result, through the sudden
> thinning of the texture - probably due as much to the
> loss of interaction of the upper partials of the two
> notes as to the absence of a second fundamental in the
> mix.
>
> While discussing the logical idea of inversion (in any
> interval, commonly an octave), may I point out that it's
> not vastly different from the logical idea of reflection
> about the midpoint of that interval (commonly a tritone).
> eg inverting the diatonic melodic fragment:
> CDEE DEFF EFAG FGBA
> in its octave (at c) produces:
> cBAA BAGG AGEF GFDE
> which is exactly the same result as reflecting it in the
> tritone at F#.
>

This is a diatonical melodic inversion. Where is the unison inverted?

> In the first method, we invert the (note at the) _prime_
> C in the (interval) octave C-c to get the (note at the)
> octave c.
>
> Hmmm, I notice that I'm talking about the prime here
> (a note), rather than the unison (an interval).
>

You are trying to apply the principles of invertible counterpoint, which
does not mean at all that the unison is an interval to begin with.

> In the second method, we reflect the (note at the)
> _prime_ C in the midpoint of the (interval) octave C-c,
> that is F#, 3 and a half scale degrees away, to get the
> (note at the) octave c, 3 and a half scale degrees away
> on the other side.
>

So what does the voices become?

> Interesting that a non-scale note (F#) is useful in
> working this out!
>
> Regards,
> Yahya
>

Oz.

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

Hi Oz,

On Thu, 9 Mar 2006, Ozan Yarman wrote:
>
> SNIP
> > Hi Aaron and Ozan,
> >
> > For what it's worth, I see no _logical_ reason to reject
> > the idea of inverting any interval whatsoever, including
> > unison.
>
> How can one invert a unison? An example if you please?

Same two ways as one inverts any other
melodic interval (and Yes! It is!):

1. by subtracting its scale degree number from
that of the interval of inversion; or
2. by reflecting the scale degrees about a (real
or imagined) midpoint.

Both methods result in the self-same pitches.

> I also see no _lgical_ reason to reject calling a
> > unison between two parts an interval.
>
> Between a lower and an upper pitch. This certainly does not apply to
unison.

That's your view, and you're welcome to it.
But personally, I enjoy the added convenience
of being able to call all intervals "intervals",
and not having to contstantly make special
mention of unison when no exceptions apply
to it.

"It looks like an interval; it sounds like an
interval; it behaves like an interval; ... it IS
an interval!"

In much the same way, really, Oz, you ought
to accept that the whole world calls zero a
number because it works better that way.

Are you forgetting that Baghdad taught
Europe the conept of zero as a number and
a great convenience in counting, since it
enables place notation? That was in, let me
see, the XIIIth century or so ...

> > However, as is so often the case, applying these logical
> > ideas to the creation of _music_ doesn't always result
> > in something satisfying. For example, when two parts
> > cross by stepwise contrary or oblique motion, the
> > _logical_ interval
>
> rendezvouz point, rather.

I said what I mean. Please don't put words
in my mouth.

> between them at some point is most
> > definitely a unison, although playing or singing that will
> > often create an unmusical result, through the sudden
> > thinning of the texture - probably due as much to the
> > loss of interaction of the upper partials of the two
> > notes as to the absence of a second fundamental in the
> > mix.
> >
> > While discussing the logical idea of inversion (in any
> > interval, commonly an octave), may I point out that it's
> > not vastly different from the logical idea of reflection
> > about the midpoint of that interval (commonly a tritone).
> > eg inverting the diatonic melodic fragment:
> > CDEE DEFF EFAG FGBA
> > in its octave (at c) produces:
> > cBAA BAGG AGEF GFDE
> > which is exactly the same result as reflecting it in the
> > tritone at F#.
>
> This is a diatonical melodic inversion.

I said so, didn't I?

> Where is the unison inverted?

Did I say this example included one?

But I'm sure you are capable of extending this
example to include a final note c in the melody,
which will invert in the octave, naturally enough,
to give C.

> > In the first method, we invert the (note at the) _prime_
> > C in the (interval) octave C-c to get the (note at the)
> > octave c.
> >
> > Hmmm, I notice that I'm talking about the prime here
> > (a note), rather than the unison (an interval).
>
> You are trying to apply the principles of invertible counterpoint, ...

Not at all. I *am* applying them.

> ... which
> does not mean at all that the unison is an interval to begin with.

Nor was that my argument. But it is one.

> > In the second method, we reflect the (note at the)
> > _prime_ C in the midpoint of the (interval) octave C-c,
> > that is F#, 3 and a half scale degrees away, to get the
> > (note at the) octave c, 3 and a half scale degrees away
> > on the other side.
>
> So what does the voices become?

You weren't paying attention! Both methods
lead to identical results. Which is another
reason I spelt them out for you above.

Regards,
Yahya

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🔗Ozan Yarman <ozanyarman@ozanyarman.com>

Here is a late reply:

SNIP

> > How can one invert a unison? An example if you please?
>
> Same two ways as one inverts any other
> melodic interval (and Yes! It is!):
>
> 1. by subtracting its scale degree number from
> that of the interval of inversion; or
> 2. by reflecting the scale degrees about a (real
> or imagined) midpoint.
>
> Both methods result in the self-same pitches.
>

`Reflection` seems to be a term more suitable, seeing as inversion has many
confounded meanings in music theory.

Ok, so you can `reflect` any PITCH in relation to a midpoint by the
`interval of inversion`. That will yield either another interval, but not a
unison. How about that?

Note: I like Dave Keenan's method of considering the fraction sign when
typing ratios to denote pitches (relative frequencies) not intervals. He
assigns the colon sign for the intervals.

>
> > I also see no _lgical_ reason to reject calling a
> > > unison between two parts an interval.
> >
> > Between a lower and an upper pitch. This certainly does not apply to
> unison.
>
> That's your view, and you're welcome to it.
> But personally, I enjoy the added convenience
> of being able to call all intervals "intervals",
> and not having to contstantly make special
> mention of unison when no exceptions apply
> to it.
>
> "It looks like an interval; it sounds like an
> interval; it behaves like an interval; ... it IS
> an interval!"
>

As you like.

> In much the same way, really, Oz, you ought
> to accept that the whole world calls zero a
> number because it works better that way.
>

I never said anything to the contrary. Zero just denotes the absence of
whatever is being counted in the world of integers.

> Are you forgetting that Baghdad taught
> Europe the conept of zero as a number and
> a great convenience in counting, since it
> enables place notation? That was in, let me
> see, the XIIIth century or so ...
>

I very well remember the Mutezilite contributions to European Renaissance,
especially in mathematics, geometry and physics.

>
> > > However, as is so often the case, applying these logical
> > > ideas to the creation of _music_ doesn't always result
> > > in something satisfying. For example, when two parts
> > > cross by stepwise contrary or oblique motion, the
> > > _logical_ interval
> >
> > rendezvouz point, rather.
>
> I said what I mean. Please don't put words
> in my mouth.
>

I wouldn't dare think of it.

>
> > between them at some point is most
> > > definitely a unison, although playing or singing that will
> > > often create an unmusical result, through the sudden
> > > thinning of the texture - probably due as much to the
> > > loss of interaction of the upper partials of the two
> > > notes as to the absence of a second fundamental in the
> > > mix.
> > >
> > > While discussing the logical idea of inversion (in any
> > > interval, commonly an octave), may I point out that it's
> > > not vastly different from the logical idea of reflection
> > > about the midpoint of that interval (commonly a tritone).
> > > eg inverting the diatonic melodic fragment:
> > > CDEE DEFF EFAG FGBA
> > > in its octave (at c) produces:
> > > cBAA BAGG AGEF GFDE
> > > which is exactly the same result as reflecting it in the
> > > tritone at F#.
> >
> > This is a diatonical melodic inversion.
>
> I said so, didn't I?
>

So that would make F# the focal point for unison. Try reflecting or
inverting that.

>
> > Where is the unison inverted?
>
> Did I say this example included one?

You pointed out the pitch of the `tritone` as the midpoint.

>
> But I'm sure you are capable of extending this
> example to include a final note c in the melody,
> which will invert in the octave, naturally enough,
> to give C.

Let's pretend that I am not, and let's see you produce an example!

>
>
> > > In the first method, we invert the (note at the) _prime_
> > > C in the (interval) octave C-c to get the (note at the)
> > > octave c.
> > >
> > > Hmmm, I notice that I'm talking about the prime here
> > > (a note), rather than the unison (an interval).
> >
> > You are trying to apply the principles of invertible counterpoint, ...
>
> Not at all. I *am* applying them.
>
>

Then why not give a concrete example from established composers such as
Telemann, Handel or Bach?

> > ... which
> > does not mean at all that the unison is an interval to begin with.
>
> Nor was that my argument. But it is one.
>

Nope.

>
> > > In the second method, we reflect the (note at the)
> > > _prime_ C in the midpoint of the (interval) octave C-c,
> > > that is F#, 3 and a half scale degrees away, to get the
> > > (note at the) octave c, 3 and a half scale degrees away
> > > on the other side.
> >
> > So what does the voices become?
>
> You weren't paying attention! Both methods
> lead to identical results. Which is another
> reason I spelt them out for you above.
>

Nowhere did I see how the unison was inverted.

>
> Regards,
> Yahya
>

Cordially,
Oz.