Classifying Tunings

I can see two clear groups of tunings:

A) The ones using fractions as ratios

B) The ones using roots to determine the ratio

Meantone and XVI to XVIII century western tunings (non 12ET)
would be in between I suppose???

I'm still missing out of this two groups Gamelan and Javanese
tunnings. any others???

According to the Maths applied on the tuning, how would you
classify them???

Anyway, I don't think mathematics are always used to calculate
tunings (like specially with Gamelan / African tunings ), so
probably is better to classify tunings historically within
the different cultures.

Tony Salinas

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Charles Lucy wrote:

> Please can we get some definitions of these terms for me,
> and also for others who might like to use them with minimal
> ambiguity.

timbre tone quality, the way a note sounds (as determined by its partials)
simple tone sine wave, also called pure tone, (a timbre with one partial)
complex tone a timbre with multiple partials
partials the simple-tone or sine-wave components of a timbre
harmonic partials partials whose frequencies relate in whole numbers
inharmonic partials partials whose frequencies do not relate in
whole numbers
flageolet tone a sound you get when you lightly touch a string
while exciting it
ghosttones (same as flageolet tone)

> >You're saying that the various tones you get by
> >lightly touching an open string in various places
> >form a continuous series separated by intervals of
> >fourths and fifths.
>
> >Please write out this series of fourths and fifths
>
> It is easiest to do this by posting the guitar fretting
> positions as a start.

Fretting positions say nothing about ghosttones. A
fretted string is effectively an open string with shorter
length. One can place frets at arbitrary positions and
produce equally strong sounds. Please explain the
sequence of ghosttones which occur in a series of fourths
and fifths.

> "Ghosttones" can be found at frets close in the cycle
> of fourths and fifths.
> i.e. Through fifths E, B, F#, C#, G#, etc.
> Through fourths D, G, C, F, Bb, Eb etc.

What are the frequencies of these ghosttones (rather
than the frequencies of the fretted tones at the same
locations (which is what your charts show))?

When you say "at fret...B" do you mean only a single
fret or all the frets which produce B's?

> The volume is lower the further you move away from A.

I'm plucking my violin as I write this. I notice that
the strongest ghosttone is the one I get when I touch
the string near the middle. Does your sequence include
this ghosttone?

Are you saying that there are no ghosttones at places
other than these fret positions?

Are you sure that the volumes of the ghosttones in your
series are in the same order as the series (in other
words that no ghosttone is louder than one earlier
in the series)?

Are you saying that the volume of a ghosttone some
number of fretted-fifths along the series is as
loud as the volume of a ghosttone the same number
of fretted-fourths along the series (for instance
ghosttone at fret for C# as loud as ghosttone at
fret for F)?

Matt Nathan

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