replies to bill arnold, lawrence ball, joseph pehrson, joe monzo, david beardsley, robert walker

bill arnold wrote:

"Question four: What is the starting point, I guess you all would say,
note on a piano? Either where it all began, or a tuner begins? Does
the scale or system begin at Middle C, or some other note? And if
so, does the system progress from some Zero point and progress
infinitely, technically, through the range of the human ear? Or does
the system start in the middle, at Middle C, and move down through
the lower notes, and move up through the upper notes, away from some
starting point in the middle?"

any pitch on the piano is equally valid as a starting point. the entire system looks exactly the same from the vantage point of any pitch as "center". that's how equal temperament works -- all the consecutive intervals are 2^(1/12), and no single pitch is differentiated as the "center". most piano music, however, uses a particular pitch as the "tonic" or "center", at least for a while, before changing to a different "center". we could discuss this at length, but this is really a general music question, not a tuning question . . .

lawrence ball wrote,

"PIANO/SAROD IMPROV CONCERTS OCT. 23 and 26"

how are the pianos being tuned for these concerts?

joseph pehrson wrote,

"***I would also like to add the phenominon of the "shrinking
interval..." After listening to 1/6th tones for a while, for
example, quartertones start sounding like *semitones!*"

yes, this too is a real phenomenon, described in a different form by gary morrison, for example. this seems symptomatic of trying to write melodies with teensy tiny intervals -- then the good old-fashioned intervals seem really large. it's amazing how, in only a few weeks, one can get oneself into a state where the western diatonic scale -- defended for generations as some kind of supra-humanly eternal entity -- can sound distorted and gross beyond all expectations.

joseph also wrote,

"***Don't forget, too, that if you start with the lowest C on the
piano and make a circle of fifths, the circle closes exactly the time
you reach the very *highest* C on the piano! Surely, that can't be
just coincidence!"

yes, that's just a coincidence.

joe monzo wrote,

"the 5-limit consistency for various popular EDOs ...
at least, i *hope* that's what they show!"

well, the term "consistency" is already overworked and has too many meanings . . . "5-limit consistency" is already defined and is a simple yes/no for any given equal temperament, with a "level" as an optional additional parameter . . . i suggest you think of a different term for what you're illustrating here, perhaps something using the words "just" and "rounding" . . . also, i've e-mailed you off-list with more specific comments about this page and your equal temperament page . . .

david beardsley wrote (of monz' solar system chord):

"So what's the tuning - in ratios?"

david, if one fires a dart at the real number line, the probability of hitting a rational number is exactly zero. so i'm not sure why you would assume that the chord was, or should be, expressed in ratios. the orbits of neptune and pluto are indeed in a resonant ratio, 3:2 if i recall correctly, but the other planets don't interact strongly enough with one another to pull their periods into "just" relationships. meanwhile, the comment was made that the chord resembled a major triad, so if you're going to force it into a set of ratios, i think you already know what the answer is . . .

robert walker provided a link that told us:

"In 1867 a typewriter pioneer first set up the QWERTY arrangement so his salesman could peck out the word typewriter quickly and easily. The letters that spell typewriter all lie on the top row. Just think! That's the logic that shaped your computer keyboard. "

thanks robert, for dispelling (no pun intended) all the myths about how this arrangement came about! so it's really all about the word "typewriter". wow!

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--- In tuning@y..., wally paulrus <wallyesterpaulrus@y...> wrote:

/tuning/topicId_39325.html#39325

> joseph also wrote,
>
> "***Don't forget, too, that if you start with the lowest C on the
> piano and make a circle of fifths, the circle closes exactly the
time
> you reach the very *highest* C on the piano! Surely, that can't be
> just coincidence!"
>
> yes, that's just a coincidence.
>

***Are you absolutely certain, Paul? Can you cite anything? Since
piano tuners tune by fifths and are always obsessed about the
Pythagorean comma (I know, from my piano tuning studies!) wouldn't it
seem quite logical for them to establish a *standard* keyboard length
at some point in time that went, basically *once* through the circle
of fifths?? It seemed pretty obvious to me, once I *noticed* it... :)

Joseph

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@y..., wally paulrus <wallyesterpaulrus@y...> wrote:
>
> /tuning/topicId_39325.html#39325
>
> > joseph also wrote,
> >
> > "***Don't forget, too, that if you start with the lowest C on the
> > piano and make a circle of fifths, the circle closes exactly the
> time
> > you reach the very *highest* C on the piano! Surely, that can't
be
> > just coincidence!"
> >
> > yes, that's just a coincidence.
> >
>
> ***Are you absolutely certain, Paul? Can you cite anything?

keyboard instruments gradually expanded in range, concurrently with
improving means of tone production at the extremes, until it hit a
practical endpoint.

> Since
> piano tuners tune by fifths and are always obsessed about the
> Pythagorean comma (I know, from my piano tuning studies!) wouldn't
it
> seem quite logical for them to establish a *standard* keyboard
length
> at some point in time that went, basically *once* through the
circle
> of fifths?? It seemed pretty obvious to me, once I *noticed*
it... :)

keyboards have been around for a long, long time . . . the seven-
octave keyboard doesn't really stand out in history as much of
a "standard", especially not coming from piano tuners(?).

> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, October 08, 2002 9:38 PM
> Subject: [tuning] Re: replies to bill arnold, lawrence ball, joseph
pehrson, joe monzo, david beardsley, robert walker
>
>
> keyboard instruments gradually expanded in range, concurrently with
> improving means of tone production at the extremes, until it hit a
> practical endpoint.
>
> --- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
>
> > Since piano tuners tune by fifths and are always obsessed
> > about the Pythagorean comma (I know, from my piano tuning
> > studies!) wouldn't it seem quite logical for them to establish
> > a *standard* keyboard length at some point in time that
> > went, basically *once* through the circle of fifths??
> > It seemed pretty obvious to me, once I *noticed* it... :)
>
> keyboards have been around for a long, long time . . . the
> seven-octave keyboard doesn't really stand out in history
> as much of a "standard", especially not coming from piano
> tuners(?).

paul's right, Joe ... all keyboards had a much smaller range
in the earlier part of their history, and it was only the
demands Beethoven made in his piano sonatas that caused
piano manufacturers to expand it at each end, and that was
only in the early 1800s. the Halberstadt design originated
almost 500 years before that, and the piano itself had already
been around for nearly a century.

i saw a whole bunch of old harspichords and pianos (including
one of the original ones made by the piano's inventor,
Cristofori) at a musical instrument museum in Rome last
year, and most of them had a range of only 4 or 5 octaves.

-monz
"all roads lead to n^0"