Yahoo Tuning Groups Ultimate Backup tuning RE: [tuning] "Partch's Folly" Re: Defining Just intonation (summi ng up)

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/16340

> >> As for the frenetic pace of much of Western music up to New Age
> >>music, I believe it is partly to conceal this beating but also to
> >>prevent the building up of standing wave resonances in rooms with
> >>parallel pairs of reflective surfaces (walls, floors and
ceilings).
>
> >This is very interesting... I had never thought of it!
>
> I don't see the logic in this argument.

This is funny. The more I thought about this, the less sense it
made!
It seems Paul is right here. If there is a lot of beating in
chords... there's going to be even MORE beating when the harmonic
motion is greater. :) It's good Paul's around to help us think
straight!
________ ___ __ _
Joseph Pehrson

🔗John F. Sprague <jsprague@dhcr.state.ny.us>

Think baroque. For an average tempo, whole notes are sustained enough to let you hear beats. Eighth notes are probably not, perhaps not even quarter notes. But for the more sustained tones, vibrato is generally used, at least since the violin family replaced the viol family. This shifts pitches just rapidly enough to obscure the beats and possibly enough to break up the formation of standing waves and the consequent resonant peaks.
Of course, there are other reasons for music to move right along. One is to allow musicians to show off their technical prowess. Another is to avoid boredom. The latter can also result from excessive repetition with limited variation, but that is common is much popular and ethnic music and some classical music. Few bother to speak out against it, so it appears to be a sort of cultural norm.

>>> josephpehrson@compuserve.com 12/07/00 11:15PM >>>
--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/16340

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🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗John F. Sprague <jsprague@dhcr.state.ny.us>

That depends on the dimensions of the room and its temperature. Assume the speed of sound to be about 1130 feet per second at 68 degrees Fahrenheit (20 degrees Celsius). The half wave length reinforcement for a ten foot ceiling (parallel to the floor) would thus be 66.5 Hz, for example. Not only parallel surfaces result in standing waves, but also diagonals out of right angle intersections (i.e., wall and floor) and corners. There is a formula devised by Lord Rayleigh for computing all of these for a rectangular type room. As the frequency increases, the number of resonances increases, becoming closer together. Depending on the proportions of the room, these may be well or poorly spaced. If well spaced, the transmission characteristic of the room may be fairly smooth, once there are enough resonances per octave to reinforce most tones fairly evenly. (The diagonal reinforcements are not as strong as the ones between parallel surfaces.)
As an experiment, you may wish to try the following: if you have a test record or CD with the usual 1000 Hz tone (about two octaves above middle C) and play it through stereo speakers, you will almost certainly cause standing waves in almost any room. If you move your head about three inches to either side, the apparent source of the sound will appear to shift from one speaker to the other.

>>> PERLICH@ACADIAN-ASSET.COM 12/08/00 02:42PM >>>
John Sprague and Joseph Pehrson, the part of the argument I didn't see the
logic in was the part about standing wave resonances. At what frequency and
with what probability would you expect these to build up in typical
performance venues in early music and in later music? Really . . .

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

John Sprague, that's all correct, but I thought you were correlating the
opportunities for room resonances historically with the different tunings
used in different periods. Sorry if I misunderstood you. The part that
really didn't make sense to me was this:

>The idea that both harmonic and inharmonic partials work against any sort
of JI is >probably just a smokescreen created by the defenders of 12 tet who
are trying to >conceal that the real problem with 12 tet is the beating of
the fundamentals, >especially the semitone. Such beating works against any
"scale" other than one of >octaves only and even then the inharmonic
partials work against it. With most >instruments, the partials are weaker
by far than the fundamentals and this beating is >not a very significant
problem.

🔗Joseph Pehrson <josephpehrson@compuserve.com>

--- In tuning@egroups.com, "John F. Sprague" <jsprague@d...> wrote:

http://www.egroups.com/message/tuning/16360

> Think baroque. For an average tempo, whole notes are sustained
enough to let you hear beats. Eighth notes are probably not, perhaps
not even quarter notes. But for the more sustained tones, vibrato is
generally used, at least since the violin family replaced the viol
family. This shifts pitches just rapidly enough to obscure the beats
and possibly enough to break up the formation of standing waves and
the consequent resonant peaks.
> Of course, there are other reasons for music to move right along.
One is to allow musicians to show off their technical prowess.
Another is to avoid boredom. The latter can also result from
excessive repetition with limited variation, but that is common is
much popular and ethnic music and some classical music. Few bother
to speak out against it, so it appears to be a sort of cultural norm.

Thanks, John, for this commentary. Paul Erlich and I were also
discussing this briefly off list. Certainly, the idea of the long
notes beating is no mystery... The question I had concerned whether
the beating really had any affect as far as the construction of music
with a greater harmonic motion... I would tend to think maybe not...
that the other factors you cite, like the need for variety would play
a greater part, since when a lot of instruments are playing together,
there is so much tuning "confusion" anyway, that the beating matter
would become rather mute... (??)

_________ ___ __ _
Joseph Pehrson

🔗Joseph Pehrson <josephpehrson@compuserve.com>

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/16365

> John Sprague and Joseph Pehrson, the part of the argument I didn't
see the logic in was the part about standing wave resonances. At what
frequency and with what probability would you expect these to build
up in typical performance venues in early music and in later music?
Really . . .

Actually, the more I thought about it, Paul, I didn't even see the
logic in the notion of the beating contributing to greater harmonic
motion. When a group of traditional non-electronic instruments are
playing together, isn't there enough tuning "confusion" to make the
beating/non-beating issue a mute one??
________ ___ __ _ _
Joseph Pehrson

🔗Paul Erlich <PERLICH@ACADIAN-ASSET.COM>

--- In tuning@egroups.com, "Joseph Pehrson" <josephpehrson@c...>

> Actually, the more I thought about it, Paul, I didn't even see the
> logic in the notion of the beating contributing to greater harmonic
> motion. When a group of traditional non-electronic instruments are
> playing together, isn't there enough tuning "confusion" to make the
> beating/non-beating issue a mute one??

Nah . . . I believe a fine ensemble in the 16th to early 18th
centuries would keep pretty close to a form of adaptive JI close to
meantone tuning, while a fine ensemble in the last two centuries
would keep the thirds pretty close to 12-tET . . . certainly the
latter is true based on what I've heard from classical groups (not
counting early music groups).

🔗John F. Sprague <jsprague@dhcr.state.ny.us>

Make that 72 degrees Fahrenheit. A further correction for differences in temperature is about 1.1 feet per second faster for each degree Fahrenheit warmer. This assumes sea level, such as New York City (not near the top of one of its tall buildings). For Denver, a further correction would be necessary for the altitude, assuming the same temperature.
The Rayleigh formula is really an application of the Pythagorean theorem, to compute the four diagonals given the length, width and height of a rectangular room. Not only the lowest resonance (66.5 Hz in the example) but all integer multiples of it will form standing waves (two times, three times, etc.). The worst case would be a cube, because of the common dimensions causing the resonances to be bunched rather than spread out. Smaller rooms will have more uneven bass reinforcement than a well designed large auditorium might, because the latter will have subsonic resonances and when the audible range is reached, the resonances may be spaced well enough to reinforce all the tones of the scale in the lowest octave rather than only one or two.

>>> jsprague@dhcr.state.ny.us 12/08/00 05:06PM >>>
That depends on the dimensions of the room and its temperature. Assume the speed of sound to be about 1130 feet per second at 68 degrees Fahrenheit (20 degrees Celsius). The half wave length reinforcement for a ten foot ceiling (parallel to the floor) would thus be 66.5 Hz, for example. Not only parallel surfaces result in standing waves, but also diagonals out of right angle intersections (i.e., wall and floor) and corners. There is a formula devised by Lord Rayleigh for computing all of these for a rectangular type room. As the frequency increases, the number of resonances increases, becoming closer together. Depending on the proportions of the room, these may be well or poorly spaced. If well spaced, the transmission characteristic of the room may be fairly smooth, once there are enough resonances per octave to reinforce most tones fairly evenly. (The diagonal reinforcements are not as strong as the ones between parallel surfaces.)
As an experiment, you may wish to try the following: if you have a test record or CD with the usual 1000 Hz tone (about two octaves above middle C) and play it through stereo speakers, you will almost certainly cause standing waves in almost any room. If you move your head about three inches to either side, the apparent source of the sound will appear to shift from one speaker to the other.

🔗John F. Sprague <jsprague@dhcr.state.ny.us>

Certainly when a variety of instruments are playing simultaneously, each with its own overtone structure (which varies with frequency as well), there could be a confusion obscuring the beats. However, before they start, any group of musicians using tunable instruments will "tune up" to reach a reasonable degree of unison. Imagine how it might sound if they didn't!

>>> josephpehrson@compuserve.com 12/09/00 10:42AM >>>
--- In tuning@egroups.com, "John F. Sprague" <jsprague@d...> wrote:

http://www.egroups.com/message/tuning/16360

_________ ___ __ _
Joseph Pehrson