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Could Wagner and Mahler infer a meantone like this?

🔗Ozan Yarman <ozanyarman@superonline.com>

4/29/2005 5:18:22 AM

I think it is time to introduce a diversion in regards to all the controversy on consonance and dissonance that Gene, Monz and others argued over so far. In conjuction, I wonder if Wagner, Schönberg, Mahler and other "please, not 12EQ again!" advocates could have anything to do with what I have to propose below.

Whilst exploring Mr. Serge Cordier's 1975 stretched 12-tone octave temperament with pure fifths at every key, I wondered if an attempt could be made to acquire a meantone temperament of 12 equal divisions where a fundamental consonant interval is achieved at every key. The following is the result I obtained by splicing the pure fourth into 5 equal semi-tones and using 99.609 cents as the generator interval:

Ozan's 12 tone perfect 4ths temperament
|
0: 1/1 0.000 unison, perfect prime
1: 99.609 cents 99.609
2: 199.218 cents 199.218
3: 298.827 cents 298.827
4: 398.436 cents 398.436
5: 4/3 498.045 perfect fourth
6: 597.654 cents 597.654
7: 697.263 cents 697.263
8: 796.872 cents 796.872
9: 896.481 cents 896.481
10: 16/9 996.090 Pythagorean minor seventh
11: 1095.699 cents 1095.699
12: 1195.308 cents 1195.308

This temperament where the syntonic comma vanishes to begin with, is both a 12-tone equal division of a period that is an octave narrowed by 4.692 cents and also a perfect 4ths meantone at every key, which is a tuning that I suspect is unique and unexplored as yet.

Cordially,
Ozan

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 28 Nisan 2005 Perşembe 21:16
Subject: [tuning] Re: Digest Number 3496

--- In tuning@yahoogroups.com, Christopher John Smith
<christopherjohn_smith@y...> wrote:

> Mr. Dent is using the standard terminology of traditional
theory/harmony. His usage is not in any way eccentric, incorrect or
confusing to anyone familiar with pre-20th c. music theory.

The usage conflates different notions, which I think Dent was clearly
doing. It is not only inherently coinfusing, it had both of us, and
certainly Dent is included in this, confused. I mentioned The German
sixth as an example of what can only be interpreted as a septimal
chord from the common practice period. Dent responded that it was a
strong dissonance, and the French sixth even stronger. In context,
since we were talking about *psychoacoustical* dissonance, and since
the French sixth is indeed a harsher chord, this clearly carried an
implication that the French sixth was psychoacoustically rather
dissonant (which is true) and the German sixth somewhat less so (at
best confusing; the chords are not really comperable
psychoacoustically, only in terms of functional harmony and
nomenclature.)

>A chord which in a traditional tonal context needs to be resolved is
a dissonance.

I know that, dammit. I've known that for years. This is not helpful.

> Sorry for butting in, but it gets really tedious wading through
endless arguments based on willful misunderstandings, or refusals to
understand, of what people say.

Which, it seems to me, you are in danger of adding to. Could you do me
the courtesy of trying to figure out what I was saying, and why, and
not merely assume I must be ignorant?