Session 5 February 2000

[Musicinventor]

This is really interesting I think. For a long time I have suspected it may be more about the relationship between whatever place you choose to start your your "tone" and how other tones are added once you decide to start at that same place others can join and adjust to that starting place

With tempered tuning all of the chromatic pitches can be the starting point of 36 uniquely sounding 7 note scales. The attachment shows all 36 in what is called "first expansion of the scale". These are chords and are arranged in the list from brightest to darkest sounding. The first on the list, from bottom up is; C E G B D F# A. To place it back into it’s original setting, rearrange the pitches, starting from C, in alphabetical order; C D E F# G A B C


This is the basis for composition, improvisation, creating melodies and chord progressions. In our current Western music we use maybe ten of these sounds, the most popular being II, and IX.

In the end, our standardization of pitches, I.e. A=440 or 432 is arbitrary. I could call 440hz Cat and 126hz Dog for what it’s worth. It is the actual frequencies that matter most.

And songs or compositions do not even always have to be totally without dissonance to have a positive or healing effect perhaps.

In my opinion, it is the interplay between consonance and dissonance that gives music its overall beauty. What was considered dissonant with Beethoven is today rather mild in comparison with what is now considered dissonant. Without a good balance of the two, the music becomes rather boring or quite annoying. For me, and I speak only for myself, listening to Pop music has become akin to reading those "Dick and Jane" books I was taught from back in the 60’s!

 

[thorbiorn]

A: Remember, you do have cycles but that does not necessarily mean cyclical. 3 Dimensional depiction of loop, seek hexagon for more. Geometric theory provides answers for key. Look to stellar windows. Octagon, hexagon, pentagon.

Stellar windows? A normal window usually has four corners, so that would mean quadrilaterals or tetragons, including squares. However I will look for the last three groups primarily. Octagons was hard, but there were some hexagons and pentagons. Below are screenshots from the program Stellarium.

This octagon from the Crater constellation is not very regular, in fact it is more like a pentagon attached to a tetragon, but it is the only octagon, I have found among the constellation, as they were displayed in the program.

Some hexagons:
Ophiucus

Winter Hexagon, in the Orion direction. Notice tht Rigel in Orion contributes to the Winter Hexagon.

Playing with the settings, there is a Korean and this shows a pentagon and a hexagon. The pentagon is a part of the Auriga constellation

In the modern star system, Auriga constellation makes up a hexagon. The star Capella is also part of the Winter Hexagon.

The stars in Taurus appears as something inbetween a hexagon and a pentagon, but six lines means a hexagon.

Some pentagons
The stars in Cepheus make up a pentagon, but you could say it is a triangle and a tetragon.

Orion has a pentagon:

Orion has cudgel, a pentagon:

Head of Whale in the Cetus constellation is also a pentagon:

There appears to be a pentagon in Bootes, at least if you join the Trapezoid and the adjacent Ptolemy's Triangle

The following appears more as a tetragon, than a pentagon, but there are five stars. It is located in Orion, the three stars at the top is the belt of Orion. It has an interesting name, Venus' Mirror, but one has to wonder how old it is.

Circlet is a heptagon, but a pentagon is also evident. The asterism is located in the Pisces constellation


It would seem the above star groups are little more than manmade construct, but between cultures there are differences, and if one is interested in finding polygons, the traditions passed on by the Greeks appear to be the richer.

It is remarkable that the region of Orion shows up with several identifiable structures, the upper body of Orion is a pentagon, the stars of Orion's Cudgel is pentagon, the star Rigel of Orion makes part of the Winter Hexagon. to which Capella, a part of the hexagon in Auriga, also contributes. If there is a meaning beyond the evident is another question? Would reviewing the properties of stars be of help?