what are isoharmonic chords?

On Tuesday, July 2, 2002, at 05:44 , tuning@yahoogroups.com wrote:

> My examples of isoharmonic chords don't require rich timbres (or even
> *any* harmonic partials at all) in the tones to make apparent
> whatever consonance those chords may have, so I would consider the
> coinciding combinational tones to be a much better justification for
> consonance at higher harmonic limits than coinciding harmonics.

Hello again George, when you say 'isoharmonic chords', are you referring to this ? :

'Fokker also liked chords whose harmonic numbers had constant
differences such as 3 in the case of the triad 4:7:10:13, etc. He
generated progessions of such chords so that the common difference tone
made a bass drone. I think he called these "isoharmonic progressions."
See his book New Music with 31 Notes (the English translation of "Neue
Musik mit 31 Tonen"), IIRC.' (John Chalmers, March 2001, TD1167)

- Joel

--- In tuning@y..., Joel Rodrigues <joelrodrigues@m...> wrote:
>
> On Tuesday, July 2, 2002, at 05:44 , tuning@y... wrote:
>
> > My examples of isoharmonic chords don't require rich timbres (or
even
> > *any* harmonic partials at all) in the tones to make apparent
> > whatever consonance those chords may have, so I would consider the
> > coinciding combinational tones to be a much better justification
for
> > consonance at higher harmonic limits than coinciding harmonics.
>
> Hello again George, when you say 'isoharmonic chords', are you
> referring to this ? :
>
> 'Fokker also liked chords whose harmonic numbers had constant
> differences such as 3 in the case of the triad 4:7:10:13, etc. He
> generated progessions of such chords so that the common difference
tone
> made a bass drone. I think he called these "isoharmonic
progressions."
> See his book New Music with 31 Notes (the English translation
of "Neue
> Musik mit 31 Tonen"), IIRC.' (John Chalmers, March 2001, TD1167)
>
>
> - Joel

That's exactly what I'm referring to. The term appears on page 79
and is followed by a couple of pages of examples. Even though this
is a book about 31-ET, the numbers in some of the ratios go higher
than you might expect -- up into the 20's in places.

The translation was done by Leigh Gerdine (from German, I believe),
so "isoharmonic" is evidently the translator's term. I don't know
what German and Dutch terms Fokker used, so I have no idea whether
this is a transliteration.

--George