Yahoo Tuning Groups Ultimate Backup mills-tuning-list RE: Why x-ET?

>David, Let's discuss more if you like this topic as much as I.

Thanks for the invitation, Paul! This is one of those subjects that never
seems to end. Maybe it's too large for any one person to comprehend fully.

>...the greater the
>number of consonant harmonies you can make out of a small set of pitches and

>melodic intervals, the better.
>...
>a continuous-pitch paradigm is most
>desirable. However, individual musical ideas within such a paradigm are
>likely to employ simple sets of fixed pitches, ....

Brilliant analysis. That's an issue I hadn't thought of at all, even though
I have experienced the repercussions of it. It's by far the best reason I
have heard for pursuing ETs other than our beloved 12-tone. But I've even
found a great deal of pleasure in simple JI scales, usually diatonic. I
never try to play music composed for 12t-ET in a JI scale - I can't quite see
the point of that. I usually just fiddle till I get the feel of it and know
a little about how each member functions, and then improvise. Even with
7-note diatonic JI scales the results tend to be very much more satisfying
than with 12t-ET. I'm convinced I'll be able to record some
commercially-viable material that way in the near future. "JI - it's not
just for theorists anymore!"

>Just Intonation has no "puns", or notes
>taken in two different senses, and typical JI theory does not admit punning.
>...
>any single microtonal tuning will, by increasing pitch resources,
>lead to an unimaginable new universe of moods and sensations.

I think you may have rebutted yourself, there. With all the unexplored
possibilities of various tuning systems, who needs puns? Sure, they're
helpful for doing certain things. So, do other things - whatever the
functions of the tuning at hand provide. Easier said ... ;-)

>as long as the ET is _consistent_ within the particular
>harmonic limit you are trying to represent, _accurate_ enough to represent
>it, and does not have notes too close to each other (34 is just barely OK in

>this last respect), the dichotomy between consonance and dissonance is
>unambiguous and you have all the benefits of extended harmony enjoyed by JI
>of that harmonic limit (I speak of odd-, not prime-number, limits here).

A quick set of questions from my ignorance of standard terms: By "34 is just
barely OK", do you mean 34 cents? If so are those 100ths of the x th-root,
where xof ET divisions of whatever interval; or are "cents" always the
1200th root of the octave? Or perhaps you mean 34t-ET?

In any event, a very intriguing point and perspective. However, while you do
enjoy the benefits of extended harmony, you still don't enjoy the benefits of
heart-stopping in-tune-ness. The first time I played with a Phrygian JI
scale I had distilled from a series of
prime-number-series-numerator-over-power-of-two-denominator ratios (there's
probably a more concise and standard way to indicate that - hopefully you get
the drift) I had chills for a week. I had the feeling that it was prompting
some sort of "life-force" to well up within me. (Boy, that sound's weird,
but I can't think of a better way to describe it.) It's still one of my
favorites. I'm not very experienced with ETs other than 12t but, from what I
have heard and experimented with, you just can't get that same sort of primal
response to the music from an ET-derived scale.

The scale I referred to runs thusly: 1:1 (no kidding!), 17:16, 19:16, 4:3,
3:2, 51:32, 57:32. I put the 57:32 on note #11 and add 7:4 on note #10 so I
can throw that shocker in where appropriate. The note numbers refer to a 12t
keyboard. I found that harp or other ringing plucked-string sounds tend to
draw a good vibe out of this scale.

>...some non-just tuning,
>perhaps even an ET, might be the best way to work out harmonizations and
>developments of a given idea.

True enough. Depends on the idea. If you start with some seed of a musical
scheme that guides you by its nature in the direction of an ET for its best
realization, great. That seems a bit self-evident, though. Am I missing
your point? I don't suppose you're gonna help Marion make his previous point
by saying that most ideas are easier to work out in an ET?

In a #1063 posting, I explain in more detail there why I think JI scales are
more promising in the long run.

>Does the existing [12t-ET] repertoire have enough diversity to provide a
>lifetime of listening enjoyment of the most transcendent and sublime sort?

I'll never forget the state of mystical transport that I was in after hearing
a live performance of Brahm's Requiem when I was in school. I was affected
similarly by performing, as part of a choir, Bach's Christmas Oratorio and
several pieces by Mendelssohn. But I'm beginning to find that there is even
more power in music with "pure," resonant chords and scales. It seems that
there is more potential there, and I believe that is because it reflects more
closely the way that we are made.

As to diversity - I'm torn there. So many musicians seem to have given up on
the idea of harmonic originality, choosing the easier route of sonic shock
value (e.g., Nirvana). But just when you think you've heard it all, some
genius comes up with a gem that was lying right in front of our eyes (or
ears) all the time. (Jerry Rafferty's changes, simple as they were - mostly
triadic, still blow my mind.) How much longer can that go on? Hard to say.
But clearly, we can improve our chances with any system that expands our
choices.

Just tune it!

David J. Finnamore

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🔗"Collins, Gordon" <CollinG@...>

Greg Schiemer wrote:

>What is the term Phrygian JI scale ? I presume David that you mean a mode
>that begins on the third degree of a JI scale (I looked for confirmation
>in Doty's primer to no avail and my past experience of the terms dorian
>phrygian lydian is based on 12-TET where each of these modes is an octave
>of white notes starting on D, E, F and so on). I was unaware that these
>terms still apply in the world of JI.

Whoa! Perhaps it's time to remind folks that Western music, at least before
the 20th century, is not - repeat NOT - based on 12TET! (I'm not singling
out Greg here - I've seen quite a few posts recently reflecting this
assumption.) It is based on the diatonic scale and the concept of tonality
without a great deal of concern for the particular tuning used. When the
church modes were invented, the scale was tuned in Pythagorean tuning (3-
limit JI), with only eight notes per octave: C, D, E, F, G, A, Bb, and B.
(Come to think of it, the Bb might be even later than that.) Centuries
later, 5-limit tuning was used, to make the thirds pure (at the expense of
the D-A fifth, among other things) and more "fictitious" notes were accepted
as sharps and flats. By the time mean-tone came into use, the church modes
were being replaced by hexachords and major/minor scales and there were more
than 12 pitches per octave in use. Well-temperaments reduced that number to
12 only in the 18th century. So the modes have almost *always* been used in
JI, and *never* in 12TET!

Gordon Collins
gordon_collins@jhuapl.edu

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🔗mr88cet@texas.net (Gary Morrison)

🔗"Collins, Gordon" <CollinG@...>

🔗Daniel Wolf <DJWOLF_MATERIAL@...>

Gordon Collins wrote:

''But the church modes have not been *used* in all that time,
either as a basis for theory or as a basis for practical music.''

- a remark which I cannot follow at all, unless one wishes to limit ''music
theory'' and ''practical music'' to what what happened in art music in
German-speaking countries (and even there (here, I should say)), there is
plenty of ''modal'' music to be found in both ''composed'' and folk
traditions.

Even if you intend to limit the definition of the church modes to their
treatment under species counterpoint, then you must account for the fact
that composing in various modes has been a continuous and central part of
musical training in the western classical tradition.

That said, I believe it is worthwhile to discuss what aspects of modal
theory are indeed useful for a musical training in which a wider variety of
pitch relations are to be included. From my personal experience, I find it
more efficient for a beginner to concentrate on mastering (singing,
dictating, and tuning up) _intervals_, and then contructing collections of
pitches (among them tetrachords, hexachords, and proper scales) and only
then locating modes within the collections. I find too often that young
musicians focus on ''scales'' which are simply not directly relevant to a
lot of real musics. Most music that I know tends to focus locally on
collections smaller than scales (something I learned first by listening to
Stravinsky and Sibelius, but then reconfirmed in my ethnological work), and
music that makes even the most simple modulations will soon depart from the
limits of a single scale.

(One caveat to the above: if the student is interested in learning a music
based upon a fixed drone pitch (as in Karnatic or Hindustani musics), then
one begins directly with the modes as fixed melodic types, each with fixed
ornamentation, and the abstract study of intervals is less relevant.)

In the west, the modal traditions are defined rather more coarsly than on
the Indian subcontinent, and modal melodic types are not fixed to
particular ornaments nor may they be assigned single intonations. Indeed,
the modes - like the genera of the classical tetrachords - are broadly
defined and invariant to specific tunings; and in polyphgonic settings may
indeed require a larger number of exact pitches. Perhaps it is most
efficient to retain a definition of the modes in terms of ''whole steps''
and ''half steps''? From my experience it is centainly sufficient to limit
the practice to the four most common modes (dorian, phrygian, lydian, and
mixolydian), to focus on the tetrachords and hexachords from which they are
built, and precisely tuning the intervals within these smaller units. This
kind of practice should then also be sufficient for tonal repertoire as
well (by recombining the tetra- or hexachords).

Daniel Wolf
Frankfurt

DR DANIEL WOLF / MATERIAL PRESS / FRANKFURT AM MAIN
http://ourworld.compuserve.com/homepages/DJWOLF_MATERIAL

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🔗"Collins, Gordon" <CollinG@...>

Daniel Wolf wrote:

>Gordon Collins wrote:
>
>''But the church modes have not been *used* in all that time,
>either as a basis for theory or as a basis for practical music.''
>
>- a remark which I cannot follow at all, unless one wishes to limit ''music
>theory'' and ''practical music'' to what what happened in art music in
>German-speaking countries (and even there (here, I should say)), there is
>plenty of ''modal'' music to be found in both ''composed'' and folk
>traditions.

Well, if you take my comment out of the context of this thread, then it does
need qualification. I was referring to Western music, but not just in
German-speaking areas.

>Even if you intend to limit the definition of the church modes to their
>treatment under species counterpoint, then you must account for the fact
>that composing in various modes has been a continuous and central part of
>musical training in the western classical tradition.

By the 18th century, the theorists had caught up with the composers in
accepting the consolidation of several modes into the major and minor keys.
I don't see how you can claim that the church modes continued to be
"central" to that music. One does not see references to a "Chopin Etude in
the Dorian Mode", for instance. Some people do refer to the major
and minor keys as "modes", but that is misleading.

Gordon Collins

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🔗Daniel Wolf <DJWOLF_MATERIAL@...>

My words were chosen very carefully:

'' composing in various modes has been a continuous and central part of
>_musical training_''

Although the art repertoire indeed became Major/minor, the training with
the church modes remained quite traditional. Composers learned with Fux
well into the nineteenth century (and again in the late twentieth century:
indeed, the fashionable Schenkerian training is fundamentally Fuxian), and
the further one gets from the German repertoire the more one is likely to
encounter ''modal'' practices. You'll find plenty of examples in French,
English, Spanish, Northern, and Eastern European art musics, and Schumann -
to go to the center of the German tonal repertoire was extremely fond of
modal writing. (I don't know quite what to say about the German chorale
tradition where old, distinctively modal melodies are harmonized tonally -
this is still a standard exercise for music students). Above and beyond
this, the folk repertoires tend to be either only exceptionally or
nominally tonal! If the example of contemporary vernacular idioms is at all
relevant, one may be easily persuaded that modulating, functional tonality
held a leading position for a limited time in only a select repertoire, and
the greater part of music heard has been modal since - as my great
grandfather put it - Hector was a pup.

You wrote:

''By the 18th century, the theorists had caught up with the composers...''

For an alternative reading of the relationship between composers and
theorists, the chapter on ''Professional Theorists and their Influence'' in
Milton Babbitt's _Words about Music_ is certainly worth a look. We tend
nowadays to place theorists and composers in fixed positions with regard to
one another, and this simply does not bear up historically. In considering
any single theorist, one must be very careful to distinguish the aims and
limits of his (sadly, not often _her_) work and the audience to which the
work is addressed. One must often pry deeply to decide if a theoretical
work is descriptive or prescriptive, or if it is historical or speculative.
And then one must evaluate the influence - if any - that a work has had on
real music making. The persistance of species, modal counterpoint as an
element of musical training well into eras when the fashionable idiom was
very different is, on one hand, a testament to the value of the training in
the development of general musicianship, but is perhaps an expression of
deeper structural connections among repertoires whose material surfaces are
radically different. This is a point that intonational theorists and
microtonal composers desperately need to consider in detail (and is
fundamentally connected to the constant plea by list members for better
compositions!): devising new musical materials - a tuning, for example - is
not difficult at all; devising ''interesting'' or ''effective'' or
''convincing'' or ''musical'' ways of using those materials is extremely
difficult.

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🔗alves@orion.ac.hmc.edu (Bill Alves)

>Daniel Wolf wrote:
>>Even if you intend to limit the definition of the church modes to their
>>treatment under species counterpoint, then you must account for the fact
>>that composing in various modes has been a continuous and central part of
>>musical training in the western classical tradition.
>
Gordon Collins replied:
>By the 18th century, the theorists had caught up with the composers in
>accepting the consolidation of several modes into the major and minor keys.
>I don't see how you can claim that the church modes continued to be
>"central" to that music. One does not see references to a "Chopin Etude in
>the Dorian Mode", for instance. Some people do refer to the major
>and minor keys as "modes", but that is misleading.
>
I have to agree with Dan, who, after all, said that "church" modes
continued to be central to music _education_. But even so, diatonic modes
other than major or minor return most obviously to art music in France in
the late nineteenth century, as in pieces by Chabrier, Debussy, Satie,
Faure, and in the twentieth century by many composers, including Ravel,
Bartok, Copland, Vaughan Williams and so on. And as Dan points out, many
European folk songs are in diatonic modes other than major or minor.

I don't see why refering to major and minor as modes is misleading. In my
definition of modes in the European tradition, they include at least the
following defining characteristics:

1) A tuning system, though it may be somewhat flexible as long as the
general pattern of intervals (below) remains recognizable.

2) A subset of pitches from that tuning system, or, put another way, a
pattern of intervals. (In the European tradition this means the diatonic
set.)

3) A tonal center within that subset.

Given that there are seven pitches in the diatonic set, there are thus
seven possible diatonic modes, of which major and minor are only two. I
don't see how they are different than the other diatonic modes. (Well, the
existence of multiple "minor scales" is a rather arbitrary theoretical
construction that has more to do with harmony and counterpoint than modes
per se. I don't think the altered scale degrees fundamentally change the
impression of diatonicism -- see below.)

In other non-European (or earlier European) traditions, there are
theoretical pitch constructions that roughly correspond to "mode," but they
often involve further defining characteristics. Thus, you can either
jettison the term "mode" (as many do), or augment the definition with some
of these other defining characteristics:

4) A range.

5) Characteristic melodic motives.

6) Characteristic methods of ornamentation ("ornamentation" here defined
broadly).

7) A further hierarchy of pitches or other categorization of pitch
functionality.

8) Extramusical associations.

As long as we're on the subject:

Some modes have what I would call "auxiliary tones" (though they are not
usually part of what defines a mode as I see it). I think of them as tones
that lie outside of the pitch set that are used more or less as occasional
passing tones or temporary substitutes for notes in the pitch set for
various musical reasons (such as the sharpened leading tone in minor). I
sometimes compare the pitch sets of various modes using a shorthand
notation:

Number of pitches in the tuning system/number of pitches in the
subset/number of commonly used auxiliary tones.

(Note: I should qualify the below numbers with the statement that the
distinction between auxiliary tones and other pitch inflections is not
always clear, that when a pitch is within or outside of the pitch set is
likewise sometimes a subjective judgment, and that the use of modes
depends, of course, on the music itself, so understand that these are
generalizations.)

Thus traditional diatonic modes are:

12/7/0

Minor with sometimes a raised seventh or sixth scale degree:

12/7/2

Pelog patet:

7/5/1

Slendro patet (most of the time):

5/5/0

Chinese pentatonic modes (according to some theoretical sources):

12/5/2

Defining raga this way gets tricky, depending if you think of a 12 or 22
pitch tuning system and which tones are "auxiliary." (In the North Indian
tradition, Bhatkande has already made these judgments for us.) Here's my
take on Hindustani raga des:

12/7/1

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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🔗Daniel Wolf <DJWOLF_MATERIAL@...>

Bill Alves' classification of modes based upon

''Number of pitches in the tuning system/number of pitches in the
subset/number of commonly used auxiliary tones.''

is very useful, and recalls Wilson's MOS scheme.

However, the first number in the classification applies only to
temperaments. If the diatonic scale is in pythagorean intonation, there is
a convenient MOS at 12, but the number of pitches available through
modulations by fifths in either direction is potentially infinite. The
Javanese modes are similar in that the temperament of the metallophones
settles on 5 or 7 pitches (or pitch areas - as the instruments tend not to
be tuned to exact unison or octaves, which must affect the
''digestability'' (thank you, Klaerentz Barlough) of the temperament), but
this restriction need not be applied to voices and instruments of variable
pitch. I would classify the auxillary tones differently for the Javanese
modes as well with Slendro as 5/4/1 + 4 miring (in between) pitches. I hear
pelog as 7/5/0 with the use of pitches 3 and 4 in pelog nem/lima being
heard as real modulations and the gender bem (which has no key 4) being an
example of idiomatic instrumental realization and not a modal auxillary
pitch (there is something similar in Gagaku when the wind instruments play
''wrong'' pitches when the core melody contains a tone not available on the
instrument). In pelog barang, the use of pitch 1 in place of 7 is similar.

If the first number in the classification can be taken as nominal pitch
areas with exact intonation unspecified, then the Karnatic 72 melakarta
scheme gives 72 modes in the form 12/7/0, or, with the raised ma modes
taken as auxillaries (which does not conform to practice, however) 36 modes
of 12/7/1. Interestingly, consecutive pieces in Karnatic recitals - or
between sections of a single Raga Malaka - often stand at one ''key
signature'' distance from one another thus reinforcing the ''12-ness'' of
the system, and some recitalists like to include one strategic disjunction
in the series (i.e. to a mode two or more accidentals away or to one that
doesn't correspond to a diatonic possibility). Thus you will often hear
Kalyani (with Ma #) next to Sankarabharanam (no sharps or flats). The
subject of the consecutive ragas in a program or within a Raga Malaka seems
not to have received any attention. What have others observed?

(I should note that the ragas whose pitch content corresponds to our
diatonic modes make up the majority of the ragas found in frequent use, but
students all begin studying the music with the mode s rb g m p db n s -
with two augmented seconds. K.S. Subramanian explained that the augmented
intervals made it more ''unnatural'' and thus more difficult to control,
and so it was considered important to master such a raga first, before
learning those with easier intervals. In fact, however, I found it fairly
easy to sing because the ''difficult pitches'' were all neighbors of tones
in a major triad, which is easy to sing against a drone, and all of the
gamakas (ornaments) reflected this. This made an intonationally interesting
effect however, in that three pitches were well defined as consonant to the
drone, and the remaining were defined by their melodic distance from these
pitches, not by their harmonic consonance or dissonance.

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RE: Why x-ET?

🔗DFinnamore@aol.com

🔗"Collins, Gordon" <CollinG@...>

🔗mr88cet@texas.net (Gary Morrison)

🔗"Collins, Gordon" <CollinG@...>

🔗Daniel Wolf <DJWOLF_MATERIAL@...>

🔗"Collins, Gordon" <CollinG@...>

🔗Daniel Wolf <DJWOLF_MATERIAL@...>

🔗alves@orion.ac.hmc.edu (Bill Alves)

🔗Daniel Wolf <DJWOLF_MATERIAL@...>