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Word: Octave/Nonave

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Description/Reason:

A 2:1 frequency ratio, the distance from two musical pitches that share the same name.


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3 thoughts on “Octave/Nonave

  1. De'vID says:

    But wait, shouldn’t Klingons have a 3:1 frequency ratio?

     

    • Rhona Fenwick says:

      We only know that the number 3 is important to Klingons, not that it governs everything they do 🙂

      Though there seems to be a lot of debate on the topic, the most rational reason I could find is that in the real pitch of most musical instruments (i.e. not electronic instruments like the theremin, which produces a simple sine wave), the frequency peak of the first harmonic overtone of any fundamental musical note is equivalent to the peak frequency of the note one octave above it, which is why A₁ is consonant with A₂. Assuming that yu₁ and yu₂ are so named by Klingons because they’re consonant, the 2:1 relationship is the only one of the two that works on the basis of pure physics; the tone that stands in a 3:1 relationship with the fundamental doesn’t match any of the overtone frequencies of the fundamental.

    • Jeffrey Clark says:

      Frequencies that are powers of 2 have the unique property that whenever the lowest frequency completes a cycle, all the upper frequencies are also completing their cycles. Since the human ear tends to measure spectral distance from the lowest sound to the highest sound — this has unique significance to us. There’s no reason to think that the Klingon ear works differently — especially given the canon fragments of music that we have.

      A 3:1 frequency ratio is the same as 2:1 + 3:2 — an octave and a fifth. In this case, it takes 2 cycles of the lower note before the frequencies phase-align — this it is more complex.

      This presents another issue with trying to understand the span of yu to yu… if as assume a 3:1 ratio, then Klingon has 9 notes in span of Human’s 16 (assuming diatonics — which there is good precedent to do so). This can be demonstrably disproved by looking at existing music fragments; which more clearly follow Human tendencies towards forms of heptatonia.

      Just for the sake of argument we can also examine the 3:2 ratio (being a naturally-occurring 3-base). This is a more interesting arrangement:

      In Western music (and much of non-western music can generally fit inside of the Western chromatic system since it is often all based on harmonics). Again, a cursory examination of known Klingon music shows that it tends to also fit inside of the chromatic system. An interesting feature of most musical scales is that they are asymmetrical around their mid-point. Now, since we known that (at least some) Klingon melodies can fit neatly inside of the heptaonia prima system, if we try to fit nine notes within the 3:2 ratio we end up having difficulty with the asymmetry.

      However, that doesn’t discount some type of overlapping nona-chordal system akin to the hexachordal theory of the middle ages; however based on the description of the scale in KGT I find it unconvincing.

      My personal theory is that Klingons have a system that follows our heptaonia prima similarly but with a mutable note somewhere that has an independent name (like Germans have B and H, rather than being B# and Bb as it is more usually called). I’m planning an analytical paper to examine some known Klingon music and try to prove my theory.

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