Correction

> - Beat 154:4:469, an A-C tuned at 377.5 cents

Oops, that should be 277.5

--kw

Many thanks to Paul Erlich for pointing out some errors in my paragraphs on
the Tuvans. If I'm understanding this correctly, the Tuvans are actually
changing the shape of their vocal cavity to align the vocal cavity
overtones in simple integer ratios... at which point they reinforce the
naturally occuring integer-ratio overtones from the vibrating vocal chords
and, when this happens, the "whistling effect" takes place...

I should have "run this by" you guys before I sent it off to the little
mag... I'll give more lead time next time. [I think it still can be
corrected...]

Also, Paul, thanks for your INCREDIBLY THOROUGH analysis of practically
every single topic to appear on this list (!!) It's amazing. Some of
these posts were from a few weeks ago (!) I also appreciate the response
concerning the tuning websites...

In any case, here is the rewrite... I'm hoping this is more accurate (??!)

Any closed space, in this case the throat cavity, contains certain defined
acoustical properties. If set to vibrate or make a sound, there are
certain tones that are naturally produced, depending on shape and size of
the space. In addition to the "fundamental" note, there are "overtones,"
multiples of the basic frequency that "go along for the ride." These
"little sounds" of higher frequency are at multiples of the fundamental
frequency. They are always there in any vibrating space or produced sound,
unless it is the rare vibration that is so precise and pure that no
overtones come along with it. Such sounds are generally pretty dull.

It so happens that pitches made by the vocal cords also set up their OWN
series of overtones, at simple, integer relations to the basic vocal pitch.
These are in addition to the set of resonating overtones in the throat
cavity. It is the tradition of the Tuvan throat singers, mostly through
changing the size of the vocal cavity with the tongue, to adjust the throat
so that the overtones from the resonating vocal cavity ALIGN in simple
harmonic ratios with the overtones of the vocal cords. When this happens
there is magic -- the simple-ratio harmonics of the voice are strongly
enforced, resulting in a disembodied "whistling" effect that sounds quite a
bit different from anything we would expect to hear coming from a human
mouth.

Thanks! and any further comments are greatly appreciated!

Joseph Pehrson

Joseph Pehrson wrote,

>Many thanks to Paul Erlich for pointing out some errors in my paragraphs on
>the Tuvans. If I'm understanding this correctly, the Tuvans are actually
>changing the shape of their vocal cavity to align the vocal cavity
>overtones in simple integer ratios... at which point they reinforce the
>naturally occuring integer-ratio overtones from the vibrating vocal chords
>and, when this happens, the "whistling effect" takes place...

More precisely, they change the shape of the vocal cavity to accentuate
resonance at one specific frequency . . . when that frequency is the same as
one of the overtones from the vibrating vocal cords, the "whistling effect"
takes place...

>In any case, here is the rewrite... I'm hoping this is more accurate (??!)

>[big snip]

I didn't see any change from the previous version . . . all my previous
objections still apply (did you make a copying error)?

My post:

> Bob, the topic was the _Pythagorean third, which requires that the third is
> high because of the piling of four 2:3 fifths. My "demo" suggests that the
> ear prefers the high third upon the sounding of _one third.

should have read:

"_one fifth." I hope the error was obvious and caused no confusion.

Jerry

Oops...in Bach's estate, after his death, he had only 1 lute/clavier, not 2 as I thought...but, he also had a lute, which is even more evidence that he liked equal temperament....cause I'm sure he played it...Hstick

--- In tuning@yahoogroups.com, <microstick@...> wrote:
>
> Oops...in Bach's estate, after his death, he had only 1
lute/clavier, not 2 as I thought...but, he also had a lute, which is
even more evidence that he liked equal temperament....cause I'm sure
he played it...Hstick
>

What makes it certain that he played it in *equal* temperament,
though? Lute frets are merely tied-on pieces of gut, and they can be
moved around (or angled) to taste; ditto for violas da gamba.
Furthermore, the open strings don't have to be tuned to equal
temperament's 1/12th comma points, either, necessarily.

As food for thought, here's a modern lute builder/player who says he
prefers putting his into 1/6th comma:
http://www.wadsworth-lutes.co.uk/frets.htm

Brad Lehman

--- In tuning@yahoogroups.com, <microstick@...> wrote:
>
> Oops...in Bach's estate, after his death, he had only 1 lute/
clavier, not 2 as I thought...but, he also had a lute, which is even
more evidence that he liked equal temperament....cause I'm sure he
played it...Hstick
>

Bach greatly admired the lute virtuoso and composer Sylvius Leopold
Weiss, and his interest in the Lautenwerk reflects his interest in
the sound of the instrument (in addition to a small numebr of solo
works, he included lute in the St. John Passion), a return, if you
will to the origins of much musical technique later adopted by
keyboard instruments.

Bach's critiques of Silvermann's initial design for the Lautenwerk at
first upset Silvermann, but the instrument maker later reconciled
himself to Bach's opinion and improved the design of the gut strung
instrument. Bach owned a large collection of instruments, some
obviously for personal or family use, but many for rental, from which
he added to his income. A keyboard virtuoso and competent violist
and violinist, there is, however, no evidence that he actually played
lute.

The use of the lute (or viola da gamba), with tied frets, does not
necessarily imply equal temperament. Mark Lindley's Lutes, Viols, &
Temeraments is certainly a place to begin investigating this topic,
and the earlier history of the lute, fretted or unfretted, and with
its deep connections to the ud is fascinating.

djw

--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@...> wrote:
>
>
> As food for thought, here's a modern lute builder/player who says he
> prefers putting his into 1/6th comma:
> http://www.wadsworth-lutes.co.uk/frets.htm
>

Any of the meantone-like temperaments frets beautifully with straight
frets, but the viol consort presents some problems in accomodating
both the bass/treble and the tenor. The subject of lyra viol tunings
(with more than 60 different scordatura!) introduces even more
complications.

djw

Graham,

I should correct myself. My formula for the consonance value of an interval does not use or depend on prime numbers. For the selection of notes for my 12 key tuning system however prime numbers *are* a factor, although I did not realise this until much later.

John.