## Re: [tuning] harmonic/subharmonic

Expand Messages
• ... And... ... hmm... Let s check this out. So, are these formula s right? ... Given: To Calculate: f1 : f2 : f3 - 1/F1 : 1/F2 : 1/F3 F1=
Message 1 of 11 , Jun 1, 2000
• 0 Attachment
Daniel wolf (01.06.2000) wrote:
> ... any collection of tones selected from a harmonic
> series can also be notated as subharmonic and any
> selection from a subharmonic series can also be
> notated as harmonic ...

And...
> The 4 5 6 is easily found by taking the 2 out of 3 set.
> For instance 4x5 4x6 5x6, being 20 24 30 (10 12 15)

hmm... Let's check this out.
So, are these formula's right?
---------------------------------------------------
Given: To Calculate:
f1 : f2 : f3 -> 1/F1 : 1/F2 : 1/F3

F1= f2*f3
______________________
GCD(f1*f2,f1*f3,f2*f3)

Excel Notation: = (f2*f3)/(GCD(f1*f2,f1*f3,f2*f3)

F2= f1*f3
______________________
GCD(f1*f2,f1*f3,f2*f3)

Excel Notation: = (f1*f3)/(GCD(f1*f2,f1*f3,f2*f3)

F3= f1*f2
______________________
GCD(f1*f2,f1*f3,f2*f3)

Excel Notation: = (f1*f2)/(GCD(f1*f2,f1*f3,f2*f3)

----------------------------------------------------

f1*F1 = f2*F2 = f3*F3 =
The distance between harmonic fundamental and subharmonic
fundamental (WOW: between greatest common subharmonic and
is equivalent to complexity n*d for diads?

Peter Mulkers
Nijverheidsstraat 80
B-2840 Rumst
Belgium
P.Mulkers@...
• Peter Mulkers wrote, ... That s right, and many (such as Marion on this list) have come up with this before. However, it s not a great measure of dissonance
Message 2 of 11 , Jun 1, 2000
• 0 Attachment
Peter Mulkers wrote,

>f1*F1 = f2*F2 = f3*F3 =
>The distance between harmonic fundamental and subharmonic
>fundamental (WOW: between greatest common subharmonic and
>is equivalent to complexity n*d for diads?

That's right, and many (such as Marion on this list) have come up with this
before. However, it's not a great measure of dissonance for multiads; e.g.,
the 4:5:6:7:9 and 1/(4:5:6:7:9) chords that Daniel Wolf recently posted
clearly differ in their level of dissonance, but have the same distance
between harmonic fundamental and guide tone (guide tone is Fokker's term for
what you call "subharmonic fundamental").
• Paul! Such things are basic properties behind all the CPS structures. 85% of all post on this list are things that have been said before, even before this list
Message 3 of 11 , Jun 1, 2000
• 0 Attachment
Paul!
Such things are basic properties behind all the CPS structures. 85% of all post on this list are things that have been said before, even before this list existed!

"Paul H. Erlich" wrote:

That's right, and many (such as Marion on this list) have come up with this
before.

North American Embassy of Anaphoria island
www.anaphoria.com

• Yes, I think the guide tone divided by fundamental was a measure used as early as Euler, if not earlier.
Message 4 of 11 , Jun 1, 2000
• 0 Attachment
Yes, I think the guide tone divided by fundamental was a measure used as
early as Euler, if not earlier.
• Paul! Yes! but it was unfortunate that he failed to include 1 in his elements which caused him to overlook the hexany when it was already contained inside one
Message 5 of 11 , Jun 1, 2000
• 0 Attachment
Paul!
Yes! but it was unfortunate that he failed to include 1 in his elements which caused him to overlook the hexany when it was already contained inside one of his structures. By omitting the 1 as a true element of a set, i am not sure how he would have seen the formula I quoted unless he saw the subharmonic version in the 3 5 7 where 1 would not be nessicery.

"Paul H. Erlich" wrote:

Yes, I think the guide tone divided by fundamental was a measure used as
early as Euler, if not earlier.

------------------------------------------------------------------------
The new secret of how to save 50-90% on CDs and DVDs
....................................................
http://click.egroups.com/1/4756/1/_/239029/_/959894832/
------------------------------------------------------------------------

You do not need web access to participate.  You may subscribe through
email.  Send an empty email to one of these addresses:
tuning-subscribe@egroups.com - join the tuning group.
tuning-unsubscribe@egroups.com - unsubscribe from the tuning group.
tuning-nomail@egroups.com - put your email message delivery on hold for the tuning group.
tuning-digest@egroups.com - change your subscription to daily digest mode.
tuning-normal@egroups.com - change your subscription to individual emails.

North American Embassy of Anaphoria island
www.anaphoria.com

• Paul! I believe his formula was a proof/example of the one I posted to him! ... -- Kraig Grady North American Embassy of Anaphoria island www.anaphoria.com
Message 6 of 11 , Jun 1, 2000
• 0 Attachment
Paul!
I believe his formula was a proof/example of the one I posted to him!

"Paul H. Erlich" wrote:

Kraig,

We're on completely different wavelengths here. I don't know which formula
you're referring to. I was just referring to the formula Peter Mulkers
brought up.

In my opinion, Euler not seeing the hexany was simply an issue of Euler
using the rectangular lattice vs. Wilson using the triangular lattice.

-Paul

------------------------------------------------------------------------
To CD lovers who want 50-90% off every day.
http://click.egroups.com/1/4764/1/_/239029/_/959895931/
------------------------------------------------------------------------

You do not need web access to participate.  You may subscribe through
email.  Send an empty email to one of these addresses:
tuning-subscribe@egroups.com - join the tuning group.
tuning-unsubscribe@egroups.com - unsubscribe from the tuning group.
tuning-nomail@egroups.com - put your email message delivery on hold for the tuning group.
tuning-digest@egroups.com - change your subscription to daily digest mode.
tuning-normal@egroups.com - change your subscription to individual emails.

North American Embassy of Anaphoria island
www.anaphoria.com

• Kraig, We re on completely different wavelengths here. I don t know which formula you re referring to. I was just referring to the formula Peter Mulkers
Message 7 of 11 , Jun 1, 2000
• 0 Attachment
Kraig,

We're on completely different wavelengths here. I don't know which formula
you're referring to. I was just referring to the formula Peter Mulkers
brought up.

In my opinion, Euler not seeing the hexany was simply an issue of Euler
using the rectangular lattice vs. Wilson using the triangular lattice.

-Paul
• Kraig, Well, if it s the same, my comment stands. I d even go further. The formula in itself is extremely favorable to Euler s rectangular orientation, since
Message 8 of 11 , Jun 1, 2000
• 0 Attachment
Kraig,

Well, if it's the same, my comment stands. I'd even go further. The formula
in itself is extremely favorable to Euler's rectangular orientation, since
the formula gives a major seventh chord the same complexity as a major triad
or minor triad. However, on the triangular lattice, on which the hexany
emerges as a very compact region, the major seventh's true dissonance is
better represented

-Paul
• Paul! It is my understanding that the Euler developed the generalized lattice. 5s running vertically, 3s horizontally and the seven diagonally. It was this
Message 9 of 11 , Jun 1, 2000
• 0 Attachment
Paul!
It is my understanding that the Euler developed the generalized lattice. 5s running vertically, 3s horizontally and the seven diagonally. It was this very lattice that Wilson first spotted the hexany which was visible because of the factors. The hexany lattice came afterwards. Wilson development of Lattices is in most cases after the fact of the structure he is illustrating. The lattice is developed to illustrate what he wants the viewer to see or what aspect he wants to bring out. Dallesandro shows many different kind of lattices he has developed.

"Paul H. Erlich" wrote:

In my opinion, Euler not seeing the hexany was simply an issue of Euler
using the rectangular lattice vs. Wilson using the triangular lattice.

-Paul