tlhIngan-Hol Archive: Sun Sep 07 20:12:39 1997

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music scale (was Re: yu-bIm-'egh



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'







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