Re: [tuning] Re: O beautiful

Jacky Ligon wrote,

> this represents a wonderful musical example from which to ask these
kinds of questions, because of the familiar tune. At first exposure, I
felt I could almost qualify it as a flattly tuned fourth, but after
hearing it repeatedly, I still want to call it a wide major 3rd.

Thanks for listening and weighing in Jacky! I find that if I play the
little "O Beautiful" descending minor 3rd motif as a major 3rd, then
it really sounds 100%, obstinately WRONG... I used the descending
10:13 as it seemed to me to project an acceptable recasting of the
expected minor third *proportion wise* -- not quite as removed or
"remote" sounding as a fourth, and not nearly as wrongish sounding as
a major 3rd. I completely agree with you that context is everything
(and if forced to call the an isolated 10:13 dyad something, I'd have
to say some flavor of 4th), and in the context of this piece I clearly
hear the descending melodic 10:13 as an interval unto itself:
definitely not a major third in the traditional or comparative sense,
but not quite a fourth either.

> The context IS everything - and this really shows it to be true,
because - for contrast, if you play an arpeggio on a piano sound
alone, of 1/1, 13/10 and 3/2 - just a first position triad, well this
really wants to behave like a major triad.

I think I'd more agree that the 13:15 sounds more like a minor third
than a major second! Staccato? Maybe... Legato? I'm mostly hearing it
as its own thing again, independent of either the 3rd or a 4th... it
would be interesting to know other folks observations and feelings for
these "no man's land" intervals. (Maybe an interesting experiment for
Joseph Pehrson's Tuning Lab would be to take a slate of some of Paul
Erlich's various local dyadic maxima and have folks offer there
opinion of what those intervals most resemble?) The 13/10 really seems
to me to sit pretty firmly on the fence... certainly more so than say
the 11/9, to which my gut reaction is almost always, "minor third,"
followed by some mild indecision and general misgivings! Perhaps it's
because the 13/10 stubbornly lies between two so clearly defined
interval classes?

> I love using intervals that creat this kind of ambiguity, as a
deliberate compositional choice. And I think that the context of their
use really does affect the quality of perception, either nakedly or in
a veiled sort of way. To me this is a more "veiled", approach, in that
it uses a familiar piece, and the part under analysis is a melody that
you expect to do certain things. That is the delightful part of what
you've done here!!!

Thanks for all the kind comments Jacky, I do appreciate it. I think it
really is the super strong expectation of a minor 3rd here that makes
the "10:13 as a major 3rd" so untenable to me in this particular
context... but that very same expectation also allows one the freedom
to extrapolate its dynamic, or its motific and proportional
implications, into a kaleidoscopic array of microtonal possibilities
that lie completely outside the omnipresent confines of 12-tET...
montani semper liberi! Rash adventurers unite!

ds

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:

http://www.egroups.com/message/tuning/12447

and in the context of this piece I clearly hear the descending
melodic 10:13 as an interval unto itself:
> definitely not a major third in the traditional or comparative
sense,but not quite a fourth either.
>

This is what I'm getting so far as well, but I want to take some more
time with it...

>(Maybe an interesting experiment for Joseph Pehrson's Tuning Lab
>would be to take a slate of some of Paul Erlich's various local
>dyadic maxima and have folks offer there opinion of what those
>intervals most resemble?)

I think that's going to part of the "Audible Harmonic Entropy"
experiment that we're going to do when Paul has the time for it...

__________ ____ __ __ _ _
Joseph Pehrson

--- In tuning@egroups.com, "Joseph Pehrson" <pehrson@p...> wrote:
> --- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:
>
> and in the context of this piece I clearly hear the descending
> melodic 10:13 as an interval unto itself:

I think this statement "an interval unto itself", is really the best
way to look at the Neutral Ratio Intervals. The fun comes in when you
do this comparative listening research into an intervals "12-tET"
correlatives - because, obviously the quantizing of intervals to 12-
tET and their associated names and meanings (minorness and
majorness), aurally, these meanings/definitions come up short in
being able to explain what the ear detects.

Jacky Ligon

--- In tuning@egroups.com, "Jacky Ligon" <jacky_ekstasis@y...> wrote:
> http://www.egroups.com/message/tuning/12452
>
> ... obviously the quantizing of intervals to 12-tET and their
> associated names and meanings (minorness and majorness), aurally,
> these meanings/definitions come up short in being able to explain
> what the ear detects.

Amen. As Partch put it: 'The ability of the human ear is
vastly underestimated.'.

'Minorness and majorness' are artefacts of 5-limit JI theorizing,
say around 1300-1500 in Europe (and of course after and almost
everywhere else).

The realization was most often in a meantone, which still
reflected 5-limit JI theory. But before this period most of
the tuning and all of the theorizing was Pythagorean, which is
dramatically different, as it does not produce 'minorness and
majorness', because the '3rds' and '6ths' aren't consonant.

If you read the article of mine that Joe Pehrson's been studying:

http://www.ixpres.com/interval/monzo/article/article.htm

the order of my presentation should give you a pretty good feel
for this transition.

I, personally, *do* believe that 5-limit tuning was used *way*
before medieval Europe, probably as far back as the Sumerians.
But after the Germanic invasions of the former Roman Empire
in the late 400s, the Pythagorean tuning, based on Boethius's
presentation, became quite firmly entrenched in European music,
at least in theory, for about 1000 years.

So there was at least a millenium without 'minorness and
majorness', and most likely, those concepts hadn't developed
in the earlier 5-limit music either.
(believe me, I'm investigating...)

Marchetto of Padua was one of the earliest European theorists
to introduce new non-Pythagorean tuning concepts. Because of
Marchetto's vague mathematics, I've found a study of his work
very interesting. Here's my still-developing webpage on him:

http://www.ixpres.com/interval/monzo/marchet/marchet.htm

in case anyone's interested in that.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

Jacky Ligon wrote,

>> ... obviously the quantizing of intervals to 12-tET and their
>> associated names and meanings (minorness and majorness), aurally,
>> these meanings/definitions come up short in being able to explain
>> what the ear detects.

Monz wrote,

>Amen. As Partch put it: 'The ability of the human ear is
>vastly underestimated.'.

>'Minorness and majorness' are artefacts of 5-limit JI theorizing,
>say around 1300-1500 in Europe (and of course after and almost
>everywhere else).

>The realization was most often in a meantone, which still
>reflected 5-limit JI theory. But before this period most of
>the tuning and all of the theorizing was Pythagorean, which is
>dramatically different, as it does not produce 'minorness and
>majorness', because the '3rds' and '6ths' aren't consonant.

But in this case, Jacky's referring not to consonant intervals or to otonal
vs. utonal triads but to all the intervals classes in 12-tET, including
major and minor seconds and sevenths.

I would argue that these distinctions would have been well in force
throughout the medieval era, and even part of the ancient era, since the
music was based on diatonic scales in Pythagorean tuning, which have major
and minor seconds, thirds, etc.

In fact, the distinctions in Pythagorean are a bit closer to the modern
12-tET ones than the meantone ones are.

Only in something like the Thai 7-tET system would one experience "seconds",
"thirds", "sixths", and "sevenths" which are all divorced from a sense of
"majorness" and "minorness". Also, in many Arabic scales, many of these
intervals are "neutral" - between "major" and "minor".

Granted, these 12-tET-like classifications fall short when it comes to
describing the properties of microtonal music, but unfortunately, the vast
majority Western musicians have learned to hear all intervals in terms of
these categories, and this tendency is well-documented by rigorous
psychological studies. Generally these categories begin and end at the
"quartertones", except for the unison and octave, which can only be detuned
by 25 or 30 cents before they are perceived as a "minor second" and "major
seventh" or "minor ninth".

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> http://www.egroups.com/message/tuning/12463
>
> I would argue that these distinctions ['minorness and majorness']
> would have been well in force throughout the medieval era, and
> even part of the ancient era, since the music was based on
> diatonic scales in Pythagorean tuning, which have major and
> minor seconds, thirds, etc.

The distinctions were there *aurally*, but, I would argue, only
gradually developed *conceptually*.

The Greeks didn't classify the '6th' and '7ths' at all, since
the units they used were based on tetrachords and the larger
'perfect' intervals ('8ve', '12th', 'double 8ve').

Here's a table of names for the intervals they did classify
that were not considered consonant:

common-practice ancient Greek = English meaning

minor second semitone 1/2-tone
major second tone tone
minor third trihemitone three 1/2-tones
major third ditone 2 tones

So they didn't use the concept of 'major/minor' at all - they
thought of all the small intervals as related to the 'tone'.

Gradually, beginning around 1100 in England and slowly spreading
to the rest of Europe (Margo, help!) theorists began recognizing
the consonance of the '3rds' and classifying them as 'major/minor'.
This supports my argument that those concepts derive from 5-limit
theory, which is exactly what this development was in the process
of becoming.

> In fact, the distinctions in Pythagorean are a bit closer to
> the modern 12-tET ones than the meantone ones are.

Yes, that's a good point.

What you say after this falls in line with the current discussion
of the 'neutral' intervals.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> Jacky Ligon wrote,
>
> >> ... obviously the quantizing of intervals to 12-tET and their
> >> associated names and meanings (minorness and majorness), aurally,
> >> these meanings/definitions come up short in being able to explain
> >> what the ear detects.
>
> Monz wrote,
>
> >'Minorness and majorness' are artefacts of 5-limit JI theorizing,
> >say around 1300-1500 in Europe (and of course after and almost
> >everywhere else).
>
>
> But in this case, Jacky's referring not to consonant intervals or
to otonal
> vs. utonal triads but to all the intervals classes in 12-tET,
including
> major and minor seconds and sevenths.

Correct.

>
> Only in something like the Thai 7-tET system would one
experience "seconds",
> "thirds", "sixths", and "sevenths" which are all divorced from a
sense of
> "majorness" and "minorness". Also, in many Arabic scales, many of
these
> intervals are "neutral" - between "major" and "minor".
>
> Granted, these 12-tET-like classifications fall short when it comes
to
> describing the properties of microtonal music, but unfortunately,
the vast
> majority Western musicians have learned to hear all intervals in
terms of
> these categories, and this tendency is well-documented by rigorous
> psychological studies. Generally these categories begin and end at
the
> "quartertones", except for the unison and octave, which can only be
detuned
> by 25 or 30 cents before they are perceived as a "minor second"
and "major
> seventh" or "minor ninth".

Paul and Monz,

Since our hearing is also very sensitive to distortions in the tuning
of 3/2 and 4/3, at what point as you tune away from these tonality
creating intervals, generally do we begin to
experience "minorness", "majorness" and "neutralness (perhaps this
could be another entry into the tuning lexicon about this valid
category of intervallic quality)"? It seems that the ear is much more
forgiving of distuning of about all the other scale degrees. This is
back to the idea that there is a sort of gradient scale of
tonality/consonance relative to the harmonic series. Would it be
correct to assume that there is a much broader band of the perception
of "minorness", "majorness" and "neutralness" around the 2nds, 3rds,
6ths and 7ths? It is extremely interesting to me that "Generally
these categories begin and end at the "quartertones"", because as we
are discussing here, it can become very paradoxical for the neutral
intervals. Something interesting that I observed recently in my
exploration of a huge number of different Neutral Ratio, is that
there is also a broad band of perception of ratios, of which your ear
can perceive as a Neutral Ratio as well. I roughly categorized them
into 10 cents shifts away from the 12tET pitches: 50-40, 40-30 cents.
I'm sure, as stated above that the quality of neutralness is greatly
influenced by the other pitches that neighbor it.

Thanks,

Jacky