Yahoo Tuning Groups Ultimate Backup crazy_music What makes a tuning sound the way it does?

FROM: mclaren
TO: New practical microtonality group
SUBJECT: What makes a tuning sound the way it does?

Joseph Pehrson's discussion of the overall number of
pitches per octave prove particularly imporant for JI
tunings.

For ALL tunings, JI or ET or NJNET, tunings with
very large numbers of steps per octave will all tend to
sound much more alike, all other factors being equal.
For example -- 41 note Pythagorean sounds very
simliar to Partch's 43-note 11-limit JI tuning in real
music in the real world. Since the human ea/brain
system contains no integer ratio detectors, ratios
are beside the point when listeners hear music.
They hear primarilyt he musical style, then the
overall timbre/tuning combo, then the step size.
If you play two radically different tuning with
lots of steps per octave (say, 30 equal and
29 note Pythagorean) listeners will tend to say
"Those sound very similar" as compared to other
factors.
Accordingly, the total number of pitches in the
octave plays a significant role.

FOR JI TUNINGS:
The pratt & Moran limits apply. This means that
there exists no such thing as "THE" perfectf fifth
in JI, only a range from around 680 cents to 720
cents. As an exercise, you might want to amuse
yourself by figuring out the ratios which correspond
to those limits. There exist many, many, many possible
ratios, in many different limits.

JI "limits" are in my experience not audible. The reason
for this is that the human ear/brain contains no integer-
ratio detectors. We hear by logarithmic interval width.
We also use plenty of categorical perception. As a result,
listeners will invariably confuse the 19/16 with the 6/5,
or the 16/13 with the 11/9, or hte 5/4 with the 24/19,
and so on. There's simply nothing special or even audible
about a particular integer in a ratio -- the human ear/brain
system merely detects the overall interval width (see
the article by Plomp & Mimpen in the Brit. Journ. of
Statistics detailing their reserach and findings to prove
this back in 1962).
As a result, "limit" proves meaningless in catregorizing
JI tuning.
My own hands-on experience seems to show that
the lumpiness of a tuning plays the most important
role -- define "lumpiness" as "ratio twixt largest and
smallest scale step." Tunings with a lumpiness of
around 5:1 have a characteristic "sound" different
from tunings with a lumpiness close to 2:1. Examples
include 29-note Pythagorean vs. 1/4-comma meantone.
However, the:lumpiness must be considered in
combination with the overall size of the smallest scale-step,
and that's where Joseph Pehrson's point becomes
particularly insightful for JI tunings -- at least in my limited
experience. At present, I have only composed in JI
tunings from 3 limit through 101 limit, but hope to go
higher soon.
With more hands-on experience, it should be possible
to narrow down these issues and clarify them. The one
thing all my JI experience seems to show is that the
classical measures (harmonic series integers, "limit,"
and son) prove meaningless and inaudible for cateogrizing
JI tunings. 35-note 61-limits sounds much more similar
to 41-note 3-limit Pythagorean than, say, a 14-note
59-limit. According to Partch and the mathematiicians,
this should nto be so. But it clearly and audibly is so.
Alas, Partch madehis claims based on a near total
lack of hands-on experience in tunings other than the
handful he used. As a result, Partch simply had to take
on faith the claims of earlier non-musicains, like
Helmholtz, and that resulted in a great deal of confusion
and led to a great many dead ends.
JI tunings tend to share in common a kind of acoustic "moire effect" where you can hear the overtones shifting into and out of various lock-in positions. This does _not_ equate to musical consonance, since musical consonance is a far more complex phenomenon which relates style and cultural conditions to issues like the melodic root movement of chord progressions and the overall arc of a melody -- whether in JI or not. Acoustic roughness and musical consonance have little to do with one another -- acoustically rough tonal combiantions can and do often function as musical consonances, like acoustically smooth (beatless) tonal combinations can and often do function as musical consonances. Exmaples of rough tonal complexes function as musical consonances include the 7th and 9th and 11th chords used in jazz, as well as innumerable major second dyads used in Central European folks music, along with the tone clusters beloved on post-1950 Euro-North American art music.
Examples of smotoh tonal complexes sounding and functioning as dissonances include the perfect fourth, and major triads or perfect ffiths used out of key.
Norman Cazden shows a fine example of Bach using a C major triad as a powerful dissonance in one of his articles. It's easy to see how a C major triad can function as a dissonance if we consider the key of (say) Db major. Introducing a C major triad as an unexpected conclusion to a plain-vanilla Db-major harmonic progressions produces a powerful musical sense of unrest and disturbance.
So the issue with JI tunings remains complex. Certainly more complicated than with ET tunings.
More hands-on experience with a wider variety of JI tunings is needed before anything definitive can be said about the exact factors which influence the overall "sound" or "sonic fingerprint" of a JI tuning. However, just off the top of my head, I'd have to say that the overall number of JI pitches in the octave seems one of the most important factors.
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--mclaren

What makes a tuning sound the way it does?

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