RE: [tuning] Re: Response to George Kahrimanis [tuning experiment s]

>I am having fun surfing the waves in the Tuning List, but I think that
>I should get to the reason of my subscribing, to consult y' all about the
>importance of the 11th harmonic in Western Musical practice, especially
>in relation to the augmented triad.

Presumably you'd like to explain the augmented triad as 7:9:11 or
1/11:1/9:1/7? Certainly these intonations would be completely unacceptable
today in a performance of Western classical music and I doubt they would
would have been acceptable for that purpose at any point in the past. The
11:9 neutral third would not be tolerated unless an intentional microtonal
distortion were desired. The two main paradigms for the intonation of the
augmented triad seem to have been a stack of two mean-tempered (or just)
5:4s and a tempered 9:7 (not necessarily in that order), completing a
perfect octave; or a stack of three well- or equal-tempered 5:4s, completing
a perfect octave. The chord is considered "dissonant" in common practice
harmony.

Dear Paul H. Erlich;
To my ear, these are extremely consonant chords, much more than your western practice
numerals would make you think. I also don't understand your "research" concerning the
subharmonic chords for I have always heard them as consonant. harmonically based chords many
times just blend into a timbre. The problem must be with my ears as it is hard to imagine that
science could be mistaken. Subharmonic chords have to my ear a greater depth. In Anaphoria, it
is considered that these sounds are descending from heaven , as the guide tone is found above.

-- Banaphshu

"Paul H. Erlich" wrote:

> >I am having fun surfing the waves in the Tuning List, but I think that
> >I should get to the reason of my subscribing, to consult y' all about the
> >importance of the 11th harmonic in Western Musical practice, especially
> >in relation to the augmented triad.
>
> Presumably you'd like to explain the augmented triad as 7:9:11 or
> 1/11:1/9:1/7? Certainly these intonations would be completely unacceptable
> today in a performance of Western classical music and I doubt they would
> would have been acceptable for that purpose at any point in the past. The
> 11:9 neutral third would not be tolerated unless an intentional microtonal
> distortion were desired. The two main paradigms for the intonation of the
> augmented triad seem to have been a stack of two mean-tempered (or just)
> 5:4s and a tempered 9:7 (not necessarily in that order), completing a
> perfect octave; or a stack of three well- or equal-tempered 5:4s, completing
> a perfect octave. The chord is considered "dissonant" in common practice
> harmony.
>

-- Banaphshu
North American Embassy of Anaphoria island
www.anaphoria.com