For Julia -- JI and microtonality

Hello, everyone, and I might have a few comments on the JI dialogue,
and specifically on your paper, Julia.

First of all, as I'm often inclined to point, a lot of the "JI
vs. 12-tET" discussion tends to make very specific historical and
musical assumptions which don't apply to a lot of what I do, although
they would indeed apply to the performance of 16th-19th century
European composed music.

Specifically, the assumption is that major and minor thirds will have
"just" ratios of 5: that is, 5:4 major thirds (~386.31 cents) and 6:5
minor thirds (~315.64 cents). By comparison, 12-tET has these thirds
at 400 cents and 300 cents, so that it is "not so accurate" and has a
rather "busy" quality by comparison with 5-limit just intonation, or
for that matter an historical meantone temperament where major and
minor thirds are at or quite close to pure.

However, in much of my music, usual or "common" ratios for major and
minor thirds are around 14:11 (~417.51 cents) and 13:11 (~289.21
cents) or 33:28 (~284.45 cents). In just intonation with pure 3:2
fifths, 14:11 goes together with 33:28. In a mildly tempered system,
however, with slightly wide fifths, it's not untypical to have major
thirds very close to 14:11 and minor thirds closer to 13:11 than 33:28
(with the same minor third serving to represent both ratios).

From my perspective, 12-tET tempers fifths by about the right amount,
but in the less interesting direction. This gives me a different
perspective on "justness" and "temperament" alike.

One difficulty of a discussion about "just intonation," Julia, which
your article might reflect, is the very different meanings and
overtones (pun intended!) this term can carry for different people.
To one person, it means using only a few "simple" and "pure" ratios in
a "concordant and natural" music as a corrective to the "dissonance"
practiced for the last century in European and related compositional
traditions. To another, such as LaMonte Young, it means finding new
and strikingly complex and different sonorities based on unfamiliar
harmonics and synergistic effects requiring extremely accurate tuning.

We might come up with a crude typology like this, not to exhaust or
adequately to represent the field, but indeed to show why some of the
"contradictions" you discuss in your paper could actually represent
differences of viewpoint as to what "JI" means, rather than
inconsistencies between a limiting theory and a more creative
practice:

Conventional Unconventional
__________________________________________________
| | |
| Simple JI music | Complex JI (Young) |
Just | | |
| 1.1 | 1.2 |
|________________________|_______________________|
| | |
Tempered | Tempered "tonal" | Tempered microtonal |
| | |
| 2.1 | 2.2 |
|________________________|_______________________|

Here it's significant that the "just/tempered" variable is not
necessarily the most important one in determining a composer's or
listener's philosophy and orientation. A JI composition using new and
unfamiliar ratios (category 1.2), and a composition likewise using
some tempered microtonal system (category 2.2), could invite
comparably favorable responses from those seeking novelty and
innovation.

Further, I find that in my own musical explorations I sometimes
combine aspects of 2.1 and 2.2. Consider, for example, the matter of
the tempered 23:31:35:39 sonority in one of my favorite tuning
systems, with fifths about 2.14 cents wide, and two 12-note chains of
such fifths arranged about 58.68 cents apart to generate some pure 7:6
intervals.

Anyway, 23:31:35:39 (in its pure form, about 0-516.76-726.87-914.21
cents) has the interesting feature of including above the lowest voice
both a 517-cent fourth (wide by 93:92 or about 18.72 cents) and a
727-cent fifth (wide by 70:69 or about 24.91 cents). In conventional
European terms, both intervals would be "Wolves," dissonant fifths or
fourths said to recall the howling of wolves.

In contrast to these somewhat exotic intervals, 39:23 is represented
in the tuning I'm applying here as a usual garden-variety major sixth
at about 912.29 cents, which also represents the more routine ratio of
22:13 (~910.79 cents). The difference in size between the theoretical
ratios of 39:23 and 22:13 also forms an elegant superparticular ratio,
507:506 (~3.42 cents).

The interesting thing about 23:31:35:39 from an "isoharmonic" point of
view is that the successive terms of the ratio all have differences of
either 4 or 8, which might lead to a certain synergistic kind of
concord with sufficiently accurate tuning. Theorists such as Erv
Wilson and George Secor have discussed this general kind of effect,
although it remains an open question as to whether inaccuracies as
great as a couple of cents might still such an effect in a tempered
tuning.

What LaMonte Young has done is to use _extremely_ accurate tuning
technologies to create new musical architectures with very high
harmonic ratios. This is indeed innovative music, in practice and
theory, based on the harmonic series as an organizing factor.

Julia, your article raises for me an interesting question: to what
degree does the effect of the extended JI music you like draw
specifically on complex "justness" (precisely tuned integer ratios, or
relations between partials), and to what degree mainly on the
refreshing novelty of the intervals and melodic steps, "just" or
otherwise?

Most appreciatively,

Margo Schulter
mschulter@value.net

Hi Margo.

Thanks for your thoughts and comments, and please forgive me for taking this
long to reply.

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:

> One difficulty of a discussion about "just intonation," Julia, which
> your article might reflect, is the very different meanings and
> overtones (pun intended!) this term can carry for different people.
> To one person, it means using only a few "simple" and "pure" ratios in
> a "concordant and natural" music as a corrective to the "dissonance"
> practiced for the last century in European and related compositional
> traditions. To another, such as LaMonte Young, it means finding new
> and strikingly complex and different sonorities based on unfamiliar
> harmonics and synergistic effects requiring extremely accurate tuning.
>
This is true. When stripped down to this level, I would seem to have my basic
impetus more-or-less in common with JI-ers who fall in this second category, even
if the music and aesthetic is so very different, as well as the logic and means with
which we choose our pitches.

> We might come up with a crude typology like this, not to exhaust or
> adequately to represent the field, but indeed to show why some of the
> "contradictions" you discuss in your paper could actually represent
> differences of viewpoint as to what "JI" means, rather than
> inconsistencies between a limiting theory and a more creative
> practice:
>

Certainly, especially in the context of this list, I'm sure that the differing viewpoints
about what JI means are the source of many stimulating discussions for members,
and represent a nice plurality. From my point of view, though, there still seem to
be some inconsistencies within the philosophical positions of certain practitioners
and also within the basic theoretical premise - when that basic premise is a
mandate of acoustical, harmonic "correctness." (Which at this point is a topic I
have probably beaten into the ground.)

>
> Conventional Unconventional
> __________________________________________________
> | | |
> | Simple JI music | Complex JI (Young) |
> Just | | |
> | 1.1 | 1.2 |
> |________________________|_______________________|
> | | |
> Tempered | Tempered "tonal" | Tempered microtonal |
> | | |
> | 2.1 | 2.2 |
> |________________________|_______________________|
>
>
> Here it's significant that the "just/tempered" variable is not
> necessarily the most important one in determining a composer's or
> listener's philosophy and orientation. A JI composition using new and
> unfamiliar ratios (category 1.2), and a composition likewise using
> some tempered microtonal system (category 2.2), could invite
> comparably favorable responses from those seeking novelty and
> innovation.
>
> Further, I find that in my own musical explorations I sometimes
> combine aspects of 2.1 and 2.2. Consider, for example, the matter of
> the tempered 23:31:35:39 sonority in one of my favorite tuning
> systems, with fifths about 2.14 cents wide, and two 12-note chains of
> such fifths arranged about 58.68 cents apart to generate some pure 7:6
> intervals.
>
> Anyway, 23:31:35:39 (in its pure form, about 0-516.76-726.87-914.21
> cents) has the interesting feature of including above the lowest voice
> both a 517-cent fourth (wide by 93:92 or about 18.72 cents) and a
> 727-cent fifth (wide by 70:69 or about 24.91 cents). In conventional
> European terms, both intervals would be "Wolves," dissonant fifths or
> fourths said to recall the howling of wolves.
>
> In contrast to these somewhat exotic intervals, 39:23 is represented
> in the tuning I'm applying here as a usual garden-variety major sixth
> at about 912.29 cents, which also represents the more routine ratio of
> 22:13 (~910.79 cents). The difference in size between the theoretical
> ratios of 39:23 and 22:13 also forms an elegant superparticular ratio,
> 507:506 (~3.42 cents).
>
> The interesting thing about 23:31:35:39 from an "isoharmonic" point of
> view is that the successive terms of the ratio all have differences of
> either 4 or 8, which might lead to a certain synergistic kind of
> concord with sufficiently accurate tuning. Theorists such as Erv
> Wilson and George Secor have discussed this general kind of effect,
> although it remains an open question as to whether inaccuracies as
> great as a couple of cents might still such an effect in a tempered
> tuning.
>
> What LaMonte Young has done is to use _extremely_ accurate tuning
> technologies to create new musical architectures with very high
> harmonic ratios. This is indeed innovative music, in practice and
> theory, based on the harmonic series as an organizing factor.
>
> Julia, your article raises for me an interesting question: to what
> degree does the effect of the extended JI music you like draw
> specifically on complex "justness" (precisely tuned integer ratios, or
> relations between partials), and to what degree mainly on the
> refreshing novelty of the intervals and melodic steps, "just" or
> otherwise?

Absolutely. Of course, by now you probably know my interpretation of the JI
pieces *I* like. I know that, for example, I enjoy Ezra Sims' melodies not because
they contain more accurate harmonies than 12-note ET music does (which I don't
believe they do), but because Ezra chooses relationships I perceive as refreshing,
and, even more importantly, because of the expressive qualities of his melodies,
the artistry of his writing with these new intervals.

Thanks again, Margo.

-Julia