Diatonic Analysis Insufficient, from Gary

From: Gary Morrison

> > > ...tone should be considered a "wandered" tonic, or the major
> > > third of the V of ii (near C# in C) should be considered a
> > > "wandered" tonic. "
> > Frankly I wouldn't buy that. If the harmony makes clear
> > that you're playing a vi chord, then its third is the tonic.
> > That's built into the definition of diatonic triads.
> Sure, but definitions are not music. I say let the
> music make the definitions, not the reverse. ...
> If a diatonic analysis is crippled enough to confuse 81/80
> with 1/1, then it doesn't fall within the realm of usefulness.

Well, then I recommend you avoid diatonic-triad nomenclature and
concepts (e.g., "V", "ii", or "vi") if you're not interested in diatonic
harmony!

Yes, you're certainly right that definitions don't make music; they
make models for music. How much heed a composer chooses to give to those
model structures is largely a different matter entirely.

It's easy for students and instructors, composers and performers to get
the impression, after writing their 629th SATB part-writing exercise, that
those annoying voice-leading rules from Freshman and Sophomore Theory
classes aren't meaningful to "real" music. I really disagree. Anybody who
feels that way needs to listen to Mozart's "Ave Verum Corpus", or the
"Agnus Dei" of his Requiem.

I'm certainly not suggesting by any means that that is the only valid or
useful mindset from which to write music. But it's far from useless just
because it doesn't comprehend the idea of a comma.

The ideas of traditional harmony has value applied to certain microtonal
systems - as much or as little value as it has in 12TET. Traditional
theory is based upon triadic harmony, but it's most basic emphasis is
functional harmony:
* Leading tones want to go up,
* Sevenths want to go down,
* Dominant seventh chords want to resolve to tonic chords, etc.

Functional harmony is also the basis behind wandering tonics: If you
can convince an audience that some pitch is the leading tone, and you
resolve it upward by half-step, then they'll believe that the pitch you
land on is the tonic, even if it's not the tonic you started on. Taken out
of the framework of functional harmony, and of tonality, the idea of
wandering tonics is no longer meaningful.

So it's certainly not unreasonable to think that the tonic could wander
down to the original pitch of the leading tone, for example. But if it
does, it's still functionally the tonic, because that's how our ears will
perceive it.

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Charles Lucy wrote:
>
> >Even allowing for some [error] in measurement, this is definitely
> >nowhere near the the series of fourths and fifths you
> >predicted! Will you admit this?
>
> Patience Matt! This is only the first stage.

Yes, but there are already contradictions. shouldn't
we iron them out before proceeding?

> I see that you expect everything to be laid out on a plate
> for you.

Of course! I will not automatically jump to your conclusions,
just because you do. You're the one who claimed he found a
better model for the physics of ghosttones on real strings,
and that ghosttones follow a cycle of pi-derived fourths and
fifths. I expect you to be able to back this up, or stop
making the claims. I have nothing against any tuning system.
I do have a problem with unfounded claims being made about
a tuning system in order to promote its use. I'm requesting
logical exposition of those claims in expectation that
failure to produce such exposition will discredit the claims.

> Let's add the note names to this simple table of results.
>
> The values below are from A2 string (110Hz.)
> !
> Approx Fret's Heard Heard
> Finger Note played Scale Approx. Note heard Scale
> Percent at near fret Position Hz Position
> 50 A3 220 (Hz) VIII 220 A3 VIII * 1
> 41 F#3 184 VI 550 C#5 III * 4
> 33 E3 164 V 330 E4 V * 2
> 25 D3 147 IV 440 A4 VIII * 2
> 20 C#3 137 III 550 C#5 III * 4
> 17 C3 132 bIII 660 E5 V * 4

The second column, approximate notes played on nearby
frets, is irrelevant to the discussion of ghosttones.

BTW, 41 percent is probably is mismeasurement of 40,
40 being twice the distance of 20, both positions
being nodes which divide the string into 5 parts and
produce a pitch near 550 Hz.

> So the notes which we produce produce from this are
> A, C#, and E.

Yes, which are easily explained as falling near the
integer multiples of A, in the series 1 2 3 4 5 6.

> The Spiral of fourths and fifths runs:
>
> A E B F# C# in one direction (Vths)
> A D G C F Bb in the other. (IVths).

You said that the frequencies and volumes of ghosttones
followed this dual series.

The E's you found (330, 660) were in the wrong octaves
to coincide with your ascending fifths series which
predicts E to occur in the octave between 110 and 220.

You didn't find any ghosttones which produced B or F#
in the series of ascending fifths, let alone have them
be louder than the C# you found.

You found no ghosttones which produced D G C F or Bb.
This last fact pretty much destroys the ascending-
fourths half of your proposed dual series.

Notice that the integer-multiple series (1 2 3 4 5 6)
nicely explains your own findings without skipping
any expected pitches. It also predicts that you will
find an additional ghosttone with an approximate
frequency of 770 near the string percentages 14, 29,
43, 57, 71, and 86. Let me know if you find it.

> The figures for metronome readings represent the beat
> frequencies, as beats per minute (i.e. tempo of the beating).

I understand bpm, but what are the beats supposed
to be a measurement of in the first place?

Matt Nathan

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