tlhIngan-Hol Archive: Sun Sep 07 20:12:39 1997
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music scale (was Re: yu-bIm-'egh
- From: "William H. Martin" <[email protected]>
- Subject: music scale (was Re: yu-bIm-'egh
- Date: Sun, 7 Sep 1997 23:12:54 -0400 ()
- Priority: NORMAL
On Fri, 22 Aug 1997 13:16:23 -0700 (PDT) Guido
<[email protected]> wrote:
> >Incidentally, Western music fits a twelve-tone tuning system. Since a
> >pentatonic scale has five notes, that leaves seven, or a little over half a
> >dozen. And since all 12 pitches are not often found in a melody, it is
> >likely that less than 6 pitches not in a pentatonic scale can be found in
> >*any* melody at all...
Hmmm. But if our diatonic scales based on an octave really have
seven notes, then why would a Klingon scale be based upon a
nontave if it is nonatonic? Shouldn't it be based upon a scale
with TEN notes with the tenth note being a repeat of the first
note?
Well, this would not be a problem if my model of the Klingon
scale were adopted. What I suggest is that the Klingon scale
does not repeat across a broader scale.
What I mean is, we use an octave (a doubling of frequency) to be
the range of notes in a diatonic scale which have unique names
(except that the top and bottom of the scale is really the same
note in different octaves). A major scale goes:
C, D, E, F, G, A, B
and then it repeats itself "an octave higher", and it can keep
repeating itself octaves higher for the full range of human
hearing. Most human voices (without specialized training) can't
really sing a broader range than an octave and a fifth (think of
it as an octave and a half). This is a tripling of the
frequency. Klingons like threes, so having this be a tripling of
frequency and the normal extreme range of a singer's voice is
convenient.
What if Klingons took this tripling of a base frequency as the
full range of any musical instrument, be it voice, chuS 'ugh, or
whatever. Different instruments would have different base
frequencies, but all instruments would be limited to a scale of
that breadth. There is a nine note scale for each instrument
spanning from a base frequency to triple that frequency.
Now, walk up to a piano. Ignore all the white keys. Start at any
black key and count nine keys. You have just spanned a frequency
range from that original base frequency to triple that frequency.
We call it a pentatonic scale because you play five notes before
you begin to repeat yourself in a higher octave, but Klingons
don't have to see scales that way. For them, a scale is the
range of notes you sing or play. There are no repeats. You never
go lower than your base frequency and you never go higher than
triple that base frequency. That is the scale.
This avoids the whole issue of why western music and its
diatonic scales really have seven notes in a scale that spans an
"octave", since we insist on repeating the first note "an octave
higher" in order to complete the scale. Meanwhile, the repeat of
the scale does not begin on the first note after the last note
of the previous scale. It is instead a repeat of that last note.
This sounds weirder than it is, though it is weird.
So, my proposal has two parts: The Klingon scale is based upon
the tripling of frequency instead of the doubling of it, and the
scale does not repeat in different nontaves. The scale is simply
complete.
Klingon music can contain a wide range of frequencies because
different instruments and different voices begin at different
base frequencies. This would make for famous performance groups
because the music written for each singer has its scale written
for the base frequency for that person's voice. If a different
group wants to sing the same music, they have to find singers
with the same relative dispersion of base frequencies as the
original performers. There is no absolute pitch in Klingon music
in the way that our orchestrated pieces are written in piano
clef, though we do have our own equivalents.
It is very much the way, in our orchestra, a Bb trumpet has
music written as if the trumpeter were playing in C when he is
in fact playing in Bb. The notation the trumpeter reads shows
different notes than the notes shown in a piano score of the
same melody. A full score will show a different key signature
for the trumpets than for most of the rest of the orchestra.
Klingon music would be an extention of this. Every instrument
would have its own key signature. Every voice would have its own
key signature. Complex harmonies and unusual dissonances would
occur as each voice stays within a very consonant pentatonic
scale across a nine note range. It would be polytonic music
based upon melodies strictly adhering to pentatonic scales.
This would be massively cool.
> >Qermaq
>
> Frequency distribution fortunately doesn't have to map at all to any other
> scale. Refer to http://www-math.cudenver.edu/~jstarret/microtone.html to get
> an idea of what I mean. If Klingon music were based on any scale other than
> our own, it would sound to us (even to most traditionally trained musicians)
> as out of tune, but merely would be harmonizing over different frequency ratios.
That's partly true. The missing element is that natural
harmonics tend to press us toward our diatonic scales, and then
toward our chromatic scale. If you create a scale which ignores
natural harmonics, you can't play keyless wind instruments, like
bugles or early trumpets, or stringed instruments like the
tromba marina, which all depend upon natural harmonics. You also
hear a lot of beats occurring between notes (which is what we
hear as being "out of tune").
I think that the likelihood is less that Klingon music would be
based upon notes between the twelve tones of our chromatic scale
than that they would be based upon a different subset of those
notes than the subsets we now choose for our diatonic scales
(mostly Major and Minor, since Dorian and Mixolydian have fallen
out of fashion and Locrian never made it to the top of the
charts).
We don't have to hit notes between the chromatic tones to make
strange music. Polytonic music based upon pentatonic scales of
fixed range of an octave and a fifth starting on different notes
would be wonderfully strange. I want to hear it, even now. It
would have a very distictive sound which would certainly bend a
lot of conventional rules about parallel motion of perfect
intervals, and the cadences would be quite interesting, given
the "missing notes" in each scale, and the interleaving patterns
of scales starting on notes a pentatonic interval apart.
I can see a Klingon chorus tuning up now. The lowest pitched
voice sings his scale slowly. Each other singer tries to sing
each note, waiting to start until the lowest singer gets high
enough for their lowest note. That will be their starting pitch.
Once that singer has hit the top of his scale, if there are any
singers who can't sing yet, the last singer to come in, sings
his scale for the remainders to find their lowest pitch.
It beats the hell out of that little round pitch pipe WE use.
Orchestras would similarly tune starting with the lowest pitched
instruments, though standardized instruments already know their
relative range to other players. And then, again, a Klingon
accordian orchestra doesn't worry all that much about pitch,
anyway, right?
> Guido
charghwI'