Yahoo Tuning Groups Ultimate Backup tuning theoretical tuning system

i do not quite understand what you are after here can you elaborate some more

muenda qwa sahure wrote:

> From: "muenda qwa sahure" <muenda@hotmail.com>
>
> I AM OFFERING THE FOLLOWING TUNING SYSTEM AS A "THEORETICAL TUNING SYSTEM"
> SINCE I HAVE NO WAY OF TESTING THE RESULTS MYSELF, EITHER BY WAY OF
> COMPUTER, OR KEYBOARD.
>
> THE BASIC IDEA OF THIS SYSTEM IS THE EQUAL DIVISION OF THE PURE THIRD.
>
> THE EXTREMELY SHARP THIRD E-G# JUST SO HAPPENS TO BE EQUALLY DIVIDED BY THE
> 12TET TRITONE.
>
> ALL OTHER NON-PURE THIRDS ARE DIVIDED UNEQUALLY.
>
> {N} = THE SQUARE ROOT OF N
>
> C = 1/1 C# = 16/15 D = {5}/2 D# = 8/3{5} E = 5/4 F = 4/3
>
> F# = (32}/4 G = 3/2 G# = 8/5 A = 3{5}/4 A# = 4/{5} B = 15/8
>
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🔗muenda qwa sahure <muenda@xxxxxxx.xxxx>

in response to the following

>From: patrick pagano <ppagano@bellsouth.net>
>Reply-To: tuning@onelist.com
>To: tuning@onelist.com
>Subject: Re: [tuning] theoretical tuning system
>Date: Tue, 13 Jul 1999 16:36:54 +0000
>
>From: patrick pagano <ppagano@bellsouth.net>
>
>i do not quite understand what you are after here can you elaborate some
>more

my original post was as follows,

> > From: "muenda qwa sahure" <muenda@hotmail.com>
> >
> > I AM OFFERING THE FOLLOWING TUNING SYSTEM AS A "THEORETICAL TUNING
>SYSTEM"
> > SINCE I HAVE NO WAY OF TESTING THE RESULTS MYSELF, EITHER BY WAY OF
> > COMPUTER, OR KEYBOARD.
> >
> > THE BASIC IDEA OF THIS SYSTEM IS THE EQUAL DIVISION OF THE PURE THIRD.
> >
> > THE EXTREMELY SHARP THIRD E-G# JUST SO HAPPENS TO BE EQUALLY DIVIDED BY
>THE
> > 12TET TRITONE.
> >
> > ALL OTHER NON-PURE THIRDS ARE DIVIDED UNEQUALLY.
> >
> > {N} = THE SQUARE ROOT OF N
> >
> > C = 1/1 C# = 16/15 D = {5}/2 D# = 8/3{5} E = 5/4 F = 4/3
> >
> > F# = {32}/4 G = 3/2 G# = 8/5 A = 3{5}/4 A# = 4/{5} B = 15/8
> >

notes of further explanation:

the initial idea for this tuning system was based on the concept of equal
temperament. the thought was "what happens if one equally divides the pure
third?" since E = 5/4, D must equal the square root of 5/4. therefore, most
of the whole steps in this tuning system, 8 out of twelve, are equal to the
square root of 5 divided by 2.

this gives the first tetrachord in the key of C as

C = 1/1 D = (THE SQUARE ROOT OF 5)/2 E = 5/4 F = 4/3

the second tetrachord is formed in the same manner

G = 3/2 A = 3(THE SQUARE ROOT OF 5)/4 B = 15/8 C = 2/1

at this point 7 of the twelve notes have been established.

since 1/1 reciprocates to itself, and (3/2, 4/3) are recipricals of each
other, i chose to "turn over" the remaining four notes, bringing the total
to 11. so that:

D = (the square root of 5)/2 becomes 4/(the square root of 5) = A#

E = 5/4 becomes 8/5 = G#

A = 3(THE SQUARE ROOT OF 5)/4 BECOMES 8/3(THE SQUARE ROOT OF 5) = D#

B = 15/8 BECOMES 16/15 = C#

now the third E-G# = 32/25. following the above procedure of equally
dividing the third, in this case a non-pure third, yields each whole step as
(the square root of 32)/5.

5/4 times (the square root of 32)/5 = (the square root of 32)/4, which
equals (the square root of two). the square root of two being the 12tet
tritone.

i would appreciate any, and all, feedback on whether or not this system has
any musical value,

thanks.
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🔗David C Keenan <d.keenan@xx.xxx.xxx>

[muenda qwa sahure TD249.5 wrote]
>I AM OFFERING THE FOLLOWING TUNING SYSTEM...
>{N} = THE SQUARE ROOT OF N
>C = 1/1 C# = 16/15 D = {5}/2 D# = 8/3{5} E = 5/4 F = 4/3
>F# = (32}/4 G = 3/2 G# = 8/5 A = 3{5}/4 A# = 4/{5} B = 15/8

You haven't said why you think it might be useful or interesting. I'm
afraid I can't find anything particularly useful or interesting about it. I
admit I haven't listened to it, but I've looked at the errors in the
available 5-limit triads. It is probably best described as a rather extreme
form of variable meantone (with a twist). The extremeness is in making some
fifths just and others a half-comma flat. The twist is in making the F#/Gb
a half-octave from C. Note that sqrt(32)/4 can be simplified to sqrt(2).

Here it is as a chain of fifths. Those marked "x" are a half comma (10.75c)
flat. The others are just.

Db---Ab-x-Eb---Bb-x-F----C----G--x-D----A--x-E----B
|
half-octave
|
F#/Gb

I don't understand the point of the half-octave. While it does make B:F#
and Gb:Db barely acceptable fifths (+9.8c) no major or minor triads can be
formed on them, so it is not a well-temperament. It just wastes potential
harmonies and diatonic modulations compared to if F# was a half-comma flat
fifth from B, making F#:Db a wolf.

I don't really understand the point of the half-comma fifths either. I
should think the triads formed on them would be barely acceptable. It's
nice to have some Just triads but this can be done at less cost to the
others as follows:

Db-*-Ab---Eb-*-Bb-*-F--*-C----G--*-D--*-A--*-E----B--*-F#

where the * fifths are 1/3-comma flat. This gives Just C, Cm, E, Em triads.
All the other triads have Just major thirds except the usual meantone
wolves which are made obvious by the notation.

Paul Erlich pointed out some good web pages on this topic recently.
http://www.hlalapansi.demon.co.uk/Acoustics/MusicMaths/MusicMaths.html
http://smt.ucsb.edu/mto/issues/mto.98.4.4/mto.98.4.4.scholtz_essay.html

Then there's Margo Schulter's definitive
http://www.medieval.org/emfaq/harmony/pyth.html

Regards,
-- Dave Keenan
http://dkeenan.com

🔗muenda qwa sahure <muenda@xxxxxxx.xxxx>

DAVE, THANKS FOR THE ANALYSIS. I WILL MAKE NO FURTHER SUBMISSIONS UNTIL I'VE
DONE MY HOMEWORK. IT IS OBVIOUS THAT I AM LIGHT YEARS BEHIND THE CURVE.
ALSO, I WILL OBTAIN THE NECESSARY HARDWARE TO LISTEN TO THE TUNINGS FIRST.

>From: David C Keenan <d.keenan@uq.net.au>
>Reply-To: tuning@onelist.com
>To: tuning@onelist.com
>Subject: [tuning] Re: theoretical tuning system
>Date: Thu, 15 Jul 1999 14:51:21 +1000
>
>From: David C Keenan <d.keenan@uq.net.au>
>
>[muenda qwa sahure TD249.5 wrote]
> >I AM OFFERING THE FOLLOWING TUNING SYSTEM...
> >{N} = THE SQUARE ROOT OF N
> >C = 1/1 C# = 16/15 D = {5}/2 D# = 8/3{5} E = 5/4 F = 4/3
> >F# = (32}/4 G = 3/2 G# = 8/5 A = 3{5}/4 A# = 4/{5} B = 15/8
>
>You haven't said why you think it might be useful or interesting. I'm
>afraid I can't find anything particularly useful or interesting about it. I
>admit I haven't listened to it, but I've looked at the errors in the
>available 5-limit triads. It is probably best described as a rather extreme
>form of variable meantone (with a twist). The extremeness is in making some
>fifths just and others a half-comma flat. The twist is in making the F#/Gb
>a half-octave from C. Note that sqrt(32)/4 can be simplified to sqrt(2).
>
>Here it is as a chain of fifths. Those marked "x" are a half comma (10.75c)
>flat. The others are just.
>
>Db---Ab-x-Eb---Bb-x-F----C----G--x-D----A--x-E----B
> |
> half-octave
> |
> F#/Gb
>
>I don't understand the point of the half-octave. While it does make B:F#
>and Gb:Db barely acceptable fifths (+9.8c) no major or minor triads can be
>formed on them, so it is not a well-temperament. It just wastes potential
>harmonies and diatonic modulations compared to if F# was a half-comma flat
>fifth from B, making F#:Db a wolf.
>
>I don't really understand the point of the half-comma fifths either. I
>should think the triads formed on them would be barely acceptable. It's
>nice to have some Just triads but this can be done at less cost to the
>others as follows:
>
>Db-*-Ab---Eb-*-Bb-*-F--*-C----G--*-D--*-A--*-E----B--*-F#
>
>where the * fifths are 1/3-comma flat. This gives Just C, Cm, E, Em triads.
>All the other triads have Just major thirds except the usual meantone
>wolves which are made obvious by the notation.
>
>Paul Erlich pointed out some good web pages on this topic recently.
>http://www.hlalapansi.demon.co.uk/Acoustics/MusicMaths/MusicMaths.html
>http://smt.ucsb.edu/mto/issues/mto.98.4.4/mto.98.4.4.scholtz_essay.html
>
>Then there's Margo Schulter's definitive
>http://www.medieval.org/emfaq/harmony/pyth.html
>
>Regards,
>-- Dave Keenan
>http://dkeenan.com
>
>--------------------------- ONElist Sponsor ----------------------------
>
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>

theoretical tuning system

🔗muenda qwa sahure <muenda@xxxxxxx.xxxx>

🔗patrick pagano <ppagano@xxxxxxxxx.xxxx>

🔗muenda qwa sahure <muenda@xxxxxxx.xxxx>

🔗David C Keenan <d.keenan@xx.xxx.xxx>

🔗muenda qwa sahure <muenda@xxxxxxx.xxxx>