Yahoo Tuning Groups Ultimate Backup tuning jonathan glasier - youtube

He makes a curious comment at about 6:40, saying that 19-edo has a "perfect minor third" and "perfect major sixth" instead of perfect fifths and fourths. It appears he's alluding to the fact those are the particularly good non-octave approximations in 19-edo, not that that's what makes perfect intervals "perfect." Was he just being poetic?

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:
>
> Jonathan Glasier has just begun a video lecture series
> on how to play 19edo mapped onto the standard Halberstadt
> (7-white/5-black) keyboard. Here's part 1 of 3:
>
> http://www.youtube.com/watch?v=D0WKTb2V7_k
>
> You can search for it on Youtube using "microtonal piano".
>
>
> -monz
> http://tonalsoft.com/tonescape.aspx
> Tonescape microtonal music series
>

🔗monz <joemonz@...>

It's not curious, but you've figured it out:
the minor-3rds and major-6ths of 19-edo are
extremely close to the ratios 6:5 and 5:3, respectively.

On the contrary, the 5ths and 4ths in 19-edo are
much farther away from ratios 3:2 and 4:3, and they
are also much farther away than the 5ths and 4ths
of 12-edo (which are close to the just ratios).

So you figured it out correctly. :)

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "leopold_plumtree" <leopold_plumtree@...> wrote:
>
> He makes a curious comment at about 6:40, saying that 19-edo has a "perfect minor third" and "perfect major sixth" instead of perfect fifths and fourths. It appears he's alluding to the fact those are the particularly good non-octave approximations in 19-edo, not that that's what makes perfect intervals "perfect." Was he just being poetic?
>
>
> --- In tuning@yahoogroups.com, "monz" <joemonz@> wrote:
> >
> > Jonathan Glasier has just begun a video lecture series
> > on how to play 19edo mapped onto the standard Halberstadt
> > (7-white/5-black) keyboard. Here's part 1 of 3:
> >
> > http://www.youtube.com/watch?v=D0WKTb2V7_k
> >
> > You can search for it on Youtube using "microtonal piano".
> >
> >
> > -monz
> > http://tonalsoft.com/tonescape.aspx
> > Tonescape microtonal music series
> >
>

🔗leopold_plumtree <leopold_plumtree@...>

True, but he said in 19-edo we don't call a perfect fourth a perfect fourth and likewise for the perfect fifth, instead calling the minor third and major sixth perfect. There seem to be conflicting senses of "perfect" being used in close proximity. Perfect fourths and fifths aren't so-called because how closely any particular tuning system gets them to 4:3 and 3:2, so why wouldn't we continue to refer to them as perfect in 19-edo as per conventional interval nonmenclature? His wording makes it sound as though he's trying to transfer "perfect" in one sense (interval name) and apply it in other sense to 19-edo minor thirds and major sixths, changing the term to mean close to Just. That's the curious bit.

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:
>
> It's not curious, but you've figured it out:
> the minor-3rds and major-6ths of 19-edo are
> extremely close to the ratios 6:5 and 5:3, respectively.
>
> On the contrary, the 5ths and 4ths in 19-edo are
> much farther away from ratios 3:2 and 4:3, and they
> are also much farther away than the 5ths and 4ths
> of 12-edo (which are close to the just ratios).
>
> So you figured it out correctly. :)
>
> -monz
> http://tonalsoft.com/tonescape.aspx
> Tonescape microtonal music software
>
>
> --- In tuning@yahoogroups.com, "leopold_plumtree" <leopold_plumtree@> wrote:
> >
> > He makes a curious comment at about 6:40, saying that 19-edo has a "perfect minor third" and "perfect major sixth" instead of perfect fifths and fourths. It appears he's alluding to the fact those are the particularly good non-octave approximations in 19-edo, not that that's what makes perfect intervals "perfect." Was he just being poetic?
> >
> >
> > --- In tuning@yahoogroups.com, "monz" <joemonz@> wrote:
> > >
> > > Jonathan Glasier has just begun a video lecture series
> > > on how to play 19edo mapped onto the standard Halberstadt
> > > (7-white/5-black) keyboard. Here's part 1 of 3:
> > >
> > > http://www.youtube.com/watch?v=D0WKTb2V7_k
> > >
> > > You can search for it on Youtube using "microtonal piano".
> > >
> > >
> > > -monz
> > > http://tonalsoft.com/tonescape.aspx
> > > Tonescape microtonal music series
> > >
> >
>

🔗monz <joemonz@...>

hi leopold,

i guess i didn't think about my response carefully enough.
yes, Glasier is using the word "perfect" here in a poetic
sense, which describes the tempered interval's proximity
to the just interval, and not in the usual theoretical sense
of "perfect" vs. "imperfect".

historically, these terms refer to intervals which come
from the diatonic scale, and "perfect" intervals
(prime, 4th, 5th, 8ve) are those which come in only
one basic size, while the "imperfect" intervals
(2nd, 3rd, 6th, 7th) come in two basic sizes and must
be further qualified as either "major" or "minor".

the whole procedure is confusing to begin with, because
he's using one set of interval names for the physical
keyboard based on 12-edo, and another set of interval names
for the aural interval distance being heard in 19-edo.
that's exactly why he made the video, so that you could
see and hear what's going on simultaneously.

one criticism i have is that when he equates 4 degrees
of 19-edo (i.e., what looks like a 12-edo "major-3rd" on
Glasier's keyboard) with the 7:6 ratio, he never explains how
far off the 19-edo approximation is, and continues
to use the ratio name to describe the interval. 4 degrees
of 19-edo is ~253 cents, and the 7:6 ratio is ~267 cents.
So the 19-edo "septimal-3rd" is ~14 cents smaller than
the real 7:6 ratio. i think he should have noted the
difference and then referred to the 19-edo interval
as the "septimal-3rd". (this 19-edo interval is actually
much closer to the 5-limit ratio 125:108, but the 7:6
is much more familiar than that one.)

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "leopold_plumtree" <leopold_plumtree@...> wrote:
>
> True, but he said in 19-edo we don't call a perfect fourth a perfect fourth and likewise for the perfect fifth, instead calling the minor third and major sixth perfect. There seem to be conflicting senses of "perfect" being used in close proximity. Perfect fourths and fifths aren't so-called because how closely any particular tuning system gets them to 4:3 and 3:2, so why wouldn't we continue to refer to them as perfect in 19-edo as per conventional interval nonmenclature? His wording makes it sound as though he's trying to transfer "perfect" in one sense (interval name) and apply it in other sense to 19-edo minor thirds and major sixths, changing the term to mean close to Just. That's the curious bit.

🔗Chris <chrisvaisvil@...>

I found it valuable from the standpoint of hearing another way to think about 19 edo

Thanks

Chris
Sent via BlackBerry from T-Mobile

-----Original Message-----
From: "monz" <joemonz@yahoo.com>
Date: Sat, 26 Dec 2009 18:59:45
To: <tuning@yahoogroups.com>
Subject: [tuning] Re: jonathan glasier - youtube - 19edo on halberstadt keyboard

hi leopold,

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

🔗leopold_plumtree <leopold_plumtree@...>

I agree; if you're going to call 4 degrees of 19-edo a 7:6, you might as well call 4 degrees of 12-edo a 5:4. :)

> one criticism i have is that when he equates 4 degrees
> of 19-edo (i.e., what looks like a 12-edo "major-3rd" on
> Glasier's keyboard) with the 7:6 ratio, he never explains how
> far off the 19-edo approximation is, and continues
> to use the ratio name to describe the interval. 4 degrees
> of 19-edo is ~253 cents, and the 7:6 ratio is ~267 cents.
> So the 19-edo "septimal-3rd" is ~14 cents smaller than
> the real 7:6 ratio. i think he should have noted the
> difference and then referred to the 19-edo interval
> as the "septimal-3rd". (this 19-edo interval is actually
> much closer to the 5-limit ratio 125:108, but the 7:6
> is much more familiar than that one.)

🔗hpiinstruments <aaronhunt@...>

Well, although this idea of what is "Perfect" isn't a simple thing
historically, it's a fact that theorists of ages past used the term
"Perfect thirds" to describe meantone thirds which are close to
beatless. Also, in other languages, "Perfect" is called "Just"
(such as in Portuguese "Juste") so you get a J5 instead of a P5. In
my own nomenclature, there are Perfect versions of all intervals,
which are achieved using JNDs to correct intonation until it's as
near to beatless as possible.

I had no idea Jonathan was going to make this video. Thanks for
posting the link here. I'm writing a blog about the video at the H-Pi
site:<http://www.h-pi.com/wordpress>

Cheers,
AAH
=====

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:
>
> hi leopold,
>
> i guess i didn't think about my response carefully enough.
> yes, Glasier is using the word "perfect" here in a poetic
> sense, which describes the tempered interval's proximity
> to the just interval, and not in the usual theoretical sense
> of "perfect" vs. "imperfect".
>
> historically, these terms refer to intervals which come
> from the diatonic scale, and "perfect" intervals
> (prime, 4th, 5th, 8ve) are those which come in only
> one basic size, while the "imperfect" intervals
> (2nd, 3rd, 6th, 7th) come in two basic sizes and must
> be further qualified as either "major" or "minor".
>
> the whole procedure is confusing to begin with, because
> he's using one set of interval names for the physical
> keyboard based on 12-edo, and another set of interval names
> for the aural interval distance being heard in 19-edo.
> that's exactly why he made the video, so that you could
> see and hear what's going on simultaneously.
>
> one criticism i have is that when he equates 4 degrees
> of 19-edo (i.e., what looks like a 12-edo "major-3rd" on
> Glasier's keyboard) with the 7:6 ratio, he never explains how
> far off the 19-edo approximation is, and continues
> to use the ratio name to describe the interval. 4 degrees
> of 19-edo is ~253 cents, and the 7:6 ratio is ~267 cents.
> So the 19-edo "septimal-3rd" is ~14 cents smaller than
> the real 7:6 ratio. i think he should have noted the
> difference and then referred to the 19-edo interval
> as the "septimal-3rd". (this 19-edo interval is actually
> much closer to the 5-limit ratio 125:108, but the 7:6
> is much more familiar than that one.)
>
>
> -monz
> http://tonalsoft.com/tonescape.aspx
> Tonescape microtonal music software
>
>
>
>
> --- In tuning@yahoogroups.com, "leopold_plumtree" <leopold_plumtree@> wrote:
> >
> > True, but he said in 19-edo we don't call a perfect fourth a perfect fourth and likewise for the perfect fifth, instead calling the minor third and major sixth perfect. There seem to be conflicting senses of "perfect" being used in close proximity. Perfect fourths and fifths aren't so-called because how closely any particular tuning system gets them to 4:3 and 3:2, so why wouldn't we continue to refer to them as perfect in 19-edo as per conventional interval nonmenclature? His wording makes it sound as though he's trying to transfer "perfect" in one sense (interval name) and apply it in other sense to 19-edo minor thirds and major sixths, changing the term to mean close to Just. That's the curious bit.
>

🔗Carl Lumma <carl@...>

What about the augmented 4th / diminished 5th?

Even if that were the case, Jonathan could argue that 19
is a kleismic system where the minor 3rd is analogous to
the 4th/5th in 12 (ditto the associated subscales in
each system).

But I think the "perfect" nomenclature probably traces back
to a time when 3rds were not considered consonant. So
we might say it is a euphemism for the 3-limit.

Then again, it's probably not worth arguing about. :)

-Carl

🔗monz <joemonz@...>

🔗leopold_plumtree <leopold_plumtree@...>

>
> What about the augmented 4th / diminished 5th?
>
> Even if that were the case, Jonathan could argue that 19
> is a kleismic system where the minor 3rd is analogous to
> the 4th/5th in 12 (ditto the associated subscales in
> each system).
>
> But I think the "perfect" nomenclature probably traces back
> to a time when 3rds were not considered consonant. So
> we might say it is a euphemism for the 3-limit.
>
> Then again, it's probably not worth arguing about. :)
>
> -Carl
>

That's possible. Perhaps the "perfect/imperfect" classification is altogether unnecessary(?). Is there a good reason for it, with a range of validity that extends beyond perfect intervals being syntonic generators? Would minor fourth and major fifth work just as well (with the unison/diapason being the only intervals that are neither major nor minor)?

🔗hpiinstruments <aaronhunt@...>

🔗monz <joemonz@...>

As i already explained, the historical classification of
"perfect" and "imperfect" has to do with the idea that
a diatonic scale has:

* some intervals which come in only
one basic size (perfect): prime, 4th, 5th, 8ve), and

* the rest of the intervals, whose basic size
must be further classified as either small (minor)
or large (major): 2nd, 3rd, 6th, 7th.

If one keeps in mind the meaning of the Latin terms
(minor = small, major = big), it makes more sense.

The idea of using "perfect" to represent the closeness
of approximation of a tempered interval from its just
equivalent is a much more recent addition to the definition.

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "leopold_plumtree" <leopold_plumtree@...> wrote:
>
>
> >
> > What about the augmented 4th / diminished 5th?
> >
> > Even if that were the case, Jonathan could argue that 19
> > is a kleismic system where the minor 3rd is analogous to
> > the 4th/5th in 12 (ditto the associated subscales in
> > each system).
> >
> > But I think the "perfect" nomenclature probably traces back
> > to a time when 3rds were not considered consonant. So
> > we might say it is a euphemism for the 3-limit.
> >
> > Then again, it's probably not worth arguing about. :)
> >
> > -Carl
> >
>
> That's possible. Perhaps the "perfect/imperfect" classification is altogether unnecessary(?). Is there a good reason for it, with a range of validity that extends beyond perfect intervals being syntonic generators? Would minor fourth and major fifth work just as well (with the unison/diapason being the only intervals that are neither major nor minor)?
>

🔗Daniel Forro <dan.for@...>

Maybe this idea of perfect/imperfect has something to do with the considering and using those intervals as a base for music works (in medieval parallel organum). They are perfect because they have only one size. Those times perfect intervals were considered consonant, the other dissonant (thirds and sixths came into the use much later and slowly started to be considered consonant, and seconds and sevenths are still not considered consonant).

Daniel Forro

On 29 Dec 2009, at 12:26 AM, monz wrote:

>
> As i already explained, the historical classification of
> "perfect" and "imperfect" has to do with the idea that
> a diatonic scale has:
>
> * some intervals which come in only
> one basic size (perfect): prime, 4th, 5th, 8ve), and
>
> * the rest of the intervals, whose basic size
> must be further classified as either small (minor)
> or large (major): 2nd, 3rd, 6th, 7th.
>
> If one keeps in mind the meaning of the Latin terms
> (minor = small, major = big), it makes more sense.
>
> The idea of using "perfect" to represent the closeness
> of approximation of a tempered interval from its just
> equivalent is a much more recent addition to the definition.
>
> -monz
> http://tonalsoft.com/tonescape.aspx
> Tonescape microtonal music software
>
>

🔗Tony <leopold_plumtree@...>

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:
>
> As i already explained, the historical classification of
> "perfect" and "imperfect" has to do with the idea that
> a diatonic scale has:
>
> * some intervals which come in only
> one basic size (perfect): prime, 4th, 5th, 8ve), and
>
> * the rest of the intervals, whose basic size
> must be further classified as either small (minor)
> or large (major): 2nd, 3rd, 6th, 7th.

But what about the other basic size that generally appears in the diatonic scale; the augmented fourth?

>
> The idea of using "perfect" to represent the closeness
> of approximation of a tempered interval from its just
> equivalent is a much more recent addition to the definition.

It seems that way. Which brings me back to wondering if the major/minor prefixes should be applied to fourths and fifths. If you have a "perfect minor third" and "perfect major sixth," what prefixes does that leave for fourths and fifths, which weren't doubly-prefixed to start?

This is one of only a few references to minor fourths/major fifths I could find...

http://books.google.com/books?id=IsQPAAAAYAAJ&pg=PA26&lpg=PA26&dq=interval+%22minor+fourth%22&source=bl&ots=MXkDNuJBkS&sig=V7Fd7HraBu99veqa_w8FtO9b4yk&hl=en&ei=0g03S7X_D9G6lAf-xrmgBw&sa=X&oi=book_result&ct=result&resnum=3&ved=0CBAQ6AEwAg#v=onepage&q=&f=false

🔗Tony <leopold_plumtree@...>

🔗Mario Pizarro <piagui@...>

Daniel Forro's message makes me to remember another group of consonant figures whose validities are without question: The 612 cells of the progression in the octave range which are cyclically linked by the products of two commas (J, U) and the schisma (32805/32768). Interesting powers of the progression reveal that it is not a common set of fractional numbers comprised between 1 and 2. For instance, one of its powers is that any cell when multiplied by a perfect fifth (1.5) or by a perfect fourth (4/3) the exact frequency of another cell is obtained.

Six consecutive cells (#48....#53) worked as two independent equations to solve 2 equations with 4 variables to get K and P semitone factors (cells # 49 and #52) of the three Piagui scales, since one Piagui triad presented a small imperfection, K and P provided a second scale named Justharm. The cell frequency values expanded along the geometrical progression by the exclusive and cyclical products of the mentioned commas and schisma.

I believe that any scale formed by equal tempered semitones contain some number of dissonant tones, out of consonance and roots of discordant chords.

I know that part of the list members do not rely on the progression, they have the right to think that way.

Thanks

Mario Pizarro
piagui@...
Lima, December 28
xxxxxxxxxxxxxxxxxxxxxxxxxxxx
----- Original Message ----- From: "Daniel Forro" <dan.for@...>
To: <tuning@yahoogroups.com>
Sent: Monday, December 28, 2009 11:31 AM
Subject: Re: [tuning] Re: jonathan glasier - youtube - 19edo on halberstadt keyboard

>
> Maybe this idea of perfect/imperfect has something to do with the
> considering and using those intervals as a base for music works (in
> medieval parallel organum). They are perfect because they have only
> one size. Those times perfect intervals were considered consonant,
> the other dissonant (thirds and sixths came into the use much later
> and slowly started to be considered consonant, and seconds and
> sevenths are still not considered consonant).
>
> Daniel Forro
>
>
> On 29 Dec 2009, at 12:26 AM, monz wrote:
>
>>
>> As i already explained, the historical classification of
>> "perfect" and "imperfect" has to do with the idea that
>> a diatonic scale has:
>>
>> * some intervals which come in only
>> one basic size (perfect): prime, 4th, 5th, 8ve), and
>>
>> * the rest of the intervals, whose basic size
>> must be further classified as either small (minor)
>> or large (major): 2nd, 3rd, 6th, 7th.
>>
>> If one keeps in mind the meaning of the Latin terms
>> (minor = small, major = big), it makes more sense.
>>
>> The idea of using "perfect" to represent the closeness
>> of approximation of a tempered interval from its just
>> equivalent is a much more recent addition to the definition.
>>
>> -monz
>> http://tonalsoft.com/tonescape.aspx
>> Tonescape microtonal music software
>>
>>
>
>
>
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🔗Carl Lumma <carl@...>

Citation? You haven't respond to the point about
augmented/diminished 4th/5th? Wikipedia says, "The term
perfect identifies it as belonging to the group of perfect
intervals (perfect fourth, octave) so called because of
their simple pitch relationships and their high degree of
consonance.", citing Piston & DeVoto 1987.

-Carl

🔗monz <joemonz@...>

Hi Carl,

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> Citation? You haven't respond to the point about
> augmented/diminished 4th/5th? Wikipedia says, "The term
> perfect identifies it as belonging to the group of perfect
> intervals (perfect fourth, octave) so called because of
> their simple pitch relationships and their high degree of
> consonance.", citing Piston & DeVoto 1987.
>
> -Carl

Ahem ... i really don't think that a 1987 publication
is a good _historical_ citation for terms that were
current in the 1300s!

Here's a paper which gives a good overview,
from which i quote:

Mark Jerome Yeary
March 28, 2004
_Back and Fourth: Tracing the Theoretical Categorization
of the Perfect Fourth in Medieval and Renaissance Treatises_

http://home.uchicago.edu/~yeary/papers/yeary-fourth.pdf

_Discantus positio vulgaris_ (CoussemakerH, Anon.3), c. 1230

[p. 6]

This treatise ... defines a continuum of consonances,
rather than a discrete set. The unison, fifth, and octave
are listed as the perfect consonances, ...

......

[p. 7]

Philippe de Vitry, c. 1320
_Ars contrapunctus secundum Philippum de Vitriaco_

Johannes de Muris, c. 1340
_Ars contrapunctus secundum Johannes de Muris_

In these theoretical treatises one finds the blueprint
for 14th-century counterpoint: a twofold stratification
of consonances as perfect (unison, octave, fifth) and
imperfect (thirds and sixths).

Augmented and diminished 4ths and 5ths are
naturally-occurring elements of any diatonic scale,
but are so obviously not concordant or consonant
that they have always been clearly differentiated
from the "perfect" 4ths and 5ths - and this began
at least as far back as c.1800 BC with the Babylonian
"tuning tablet" CBS10996. A good citation for this is:

Dumbrill, Richard J. 2005. Trafford Publishing.
_The Archaeomusicology of the Ancient Near East_.

What makes the minor and major intervals "imperfect"
is that the two different sizes of each generic interval
have very nearly the same degree of concordance, but
one must still differentiate between one or the other.

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:

> > Citation? You haven't respond to the point about
> > augmented/diminished 4th/5th? Wikipedia says, "The term
> > perfect identifies it as belonging to the group of perfect
> > intervals (perfect fourth, octave) so called because of
> > their simple pitch relationships and their high degree of
> > consonance.", citing Piston & DeVoto 1987.
>
> Ahem ... i really don't think that a 1987 publication
> is a good _historical_ citation for terms that were
> current in the 1300s!

I didn't mean to imply it was a good reference, just pointing
out it's what wikipedia currently says.

> Here's a paper which gives a good overview,
> from which i quote:
>
> Mark Jerome Yeary
> March 28, 2004
> _Back and Fourth: Tracing the Theoretical Categorization
> of the Perfect Fourth in Medieval and Renaissance Treatises_
>
> http://home.uchicago.edu/~yeary/papers/yeary-fourth.pdf
>
> _Discantus positio vulgaris_ (CoussemakerH, Anon.3), c. 1230
>
> This treatise ... defines a continuum of consonances,
> rather than a discrete set. The unison, fifth, and octave
> are listed as the perfect consonances, ...
>
> Philippe de Vitry, c. 1320
> _Ars contrapunctus secundum Philippum de Vitriaco_
> Johannes de Muris, c. 1340
> _Ars contrapunctus secundum Johannes de Muris_
>
> In these theoretical treatises one finds the blueprint
> for 14th-century counterpoint: a twofold stratification
> of consonances as perfect (unison, octave, fifth) and
> imperfect (thirds and sixths).

So far this looks consistent with the meaning Aaron Hunt
and I suggested.

> Augmented and diminished 4ths and 5ths are
> naturally-occurring elements of any diatonic scale,
> but are so obviously not concordant or consonant
> that they have always been clearly differentiated
> from the "perfect" 4ths and 5ths

Ok, so your argument is that 5ths have only one _consonance_
in the diatonic scale, whereas 3rds have two.

> What makes the minor and major intervals "imperfect"
> is that the two different sizes of each generic interval
> have very nearly the same degree of concordance, but
> one must still differentiate between one or the other.

I still don't see anything supporting this. If it's correct,
why are the treatises Yeary cites all about whether the 4th
is perfect or not? In fact, the Yeary paper is all about the
term being used to describe the _consonance_ of intervals, not
their scalar properties, e.g.

""
Johannes de Garlandia, De mensurabili musica, c. 1250

This treatise provides the most comprehensive categorization of
consonances and dissonances of its time, and the definitions
within continue to resurface in treatises of the following
century, most notably Franco of Cologne's Ars cantus mensurabilis.
The fourth and fifth are given the status of "medial consonance",
below the perfect consonances of the unison and fifth, but above
the imperfect *consonances* [emphasis added] of the major and
minor thirds. The two intervals are not on equal footing, however,
as the fifth is seen as more perfect than the fourth based on
their numerical ratios.
""

-Carl

🔗monz <joemonz@...>

Hi Carl,

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> > Here's a paper which gives a good overview,
> > from which i quote:
> >
> > Mark Jerome Yeary
> > March 28, 2004
> > _Back and Fourth: Tracing the Theoretical Categorization
> > of the Perfect Fourth in Medieval and Renaissance Treatises_
> >
> > http://home.uchicago.edu/~yeary/papers/yeary-fourth.pdf
> >
> > _Discantus positio vulgaris_ (CoussemakerH, Anon.3), c. 1230
> >
> > This treatise ... defines a continuum of consonances,
> > rather than a discrete set. The unison, fifth, and octave
> > are listed as the perfect consonances, ...
> >
> > Philippe de Vitry, c. 1320
> > _Ars contrapunctus secundum Philippum de Vitriaco_
> > Johannes de Muris, c. 1340
> > _Ars contrapunctus secundum Johannes de Muris_
> >
> > In these theoretical treatises one finds the blueprint
> > for 14th-century counterpoint: a twofold stratification
> > of consonances as perfect (unison, octave, fifth) and
> > imperfect (thirds and sixths).
>
> So far this looks consistent with the meaning Aaron Hunt
> and I suggested.
>
> > Augmented and diminished 4ths and 5ths are
> > naturally-occurring elements of any diatonic scale,
> > but are so obviously not concordant or consonant
> > that they have always been clearly differentiated
> > from the "perfect" 4ths and 5ths
>
> Ok, so your argument is that 5ths have only one _consonance_
> in the diatonic scale, whereas 3rds have two.
>
> > What makes the minor and major intervals "imperfect"
> > is that the two different sizes of each generic interval
> > have very nearly the same degree of concordance, but
> > one must still differentiate between one or the other.
>
> I still don't see anything supporting this.

The point is that the only intervals that were considered
"consonant" from ancient times were the prime, octave,
perfect-4th, and perfect-5th ... and octave-plus-4th,
octave-plus-5th, and double-octave. When the 3rds and 6ths
were first admitted to this group in the 1300s, they were
called "imperfect consonances".

> If it's correct,
> why are the treatises Yeary cites all about whether the 4th
> is perfect or not?

Yeary's paper is focused on the change of attitude
towards the perfect-4th, it being originally a consonance,
then later a dissonance. Of course, the quotes from
his citations are deliberately chosen to support his debate.

Anyway, i'm just trying to shed what light i can
on the two different meanings of "perfect".
I don't have the time to go any farther with an
argument about this -- digging up those citations
already cost me a whole evening during which i should
have been doing other work.

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

🔗Tony <leopold_plumtree@...>

> Ok, so your argument is that 5ths have only one _consonance_
> in the diatonic scale, whereas 3rds have two.

>
> This treatise provides the most comprehensive categorization of
> consonances and dissonances of its time, and the definitions
> within continue to resurface in treatises of the following
> century, most notably Franco of Cologne's Ars cantus mensurabilis.
> The fourth and fifth are given the status of "medial consonance",
> below the perfect consonances of the unison and fifth, but above
> the imperfect *consonances* [emphasis added] of the major and
> minor thirds. The two intervals are not on equal footing, however,
> as the fifth is seen as more perfect than the fourth based on
> their numerical ratios.
> ""

That's basically the 'problem' of the intervals being classified as perfect according to their consonance. Only a particular fifth being consonant is one thing, but to take it to be perfect based on that automatically means the fourth mooches its way into the perfect party by way of its inverse relationship. At different times in history the fourth has been, and sometimes still is, treated as a dissonance, while the augmented fourth almost becomes a consonance of sorts with the right application.

🔗Marcel de Velde <m.develde@...>

> That's basically the 'problem' of the intervals being classified as perfect
> according to their consonance. Only a particular fifth being consonant is
> one thing, but to take it to be perfect based on that automatically means
> the fourth mooches its way into the perfect party by way of its inverse
> relationship. At different times in history the fourth has been, and
> sometimes still is, treated as a dissonance, while the augmented fourth
> almost becomes a consonance of sorts with the right application.
>

The fourth can sometimes be consonant (for instance as an inversion of the
fifth) and sometimes dissonant (for instance between A - D in C major).
I don't think the rules allways work very well in JI, though often they do
and they may well have this consonance dissonance as their origin.

Marcel