Music

After trying to squeeze an extra note into the existing scale of seven beautiful notes... and failing, I decided to approach the task of making a new scale - or context of tones - in a way that did not necessarily concern itself with prejudice of comfort for tradition. I decided to just divide the space between the ends of an "octave" mathematically, and just see what tones appear. As mentioned above, I am not a mathematician or scientist of sound, I can't explain how an octave is divided in the twelve note system of Western music. All I could do is observe how each of those twelve notes appeared to be about 105.94% larger than the previous... leading to a scale that was not divided equally, but logarithmically. In music, this is supposed to create a scale that is equal in temperament, with smooth predictable ratios between notes, and thus establish a reasonable compromise between various tuning methods. That sounded like a good approach, so I decided to do the same with my scale. I also decided that my eight notes should all have half notes, so I divided the space between two corresponding "octave" tones into sixteen logarithmically spaced segments of 104.4275% between each ascending note. To help people with a prejudice of comfort originating from the context of the twelve note scale, I decided to start and end my "octave" with the established frequencies of the nearest piano I could find. Knowing, from the Do-Re-Mi song, that "Middle C" is an important starting place, I decided to span the C4 octave. I don't know who decided that "Middle C" should always be exactly 261.63Hz in frequency or why (apparently it comes from starting at "A" with 440.00Hz), but I accepted that as a starting point, and developed my scale from there. The results are seen in the diagram below.

I started with an existing octave, and divided it sixteen times instead of twelve. The result was five tones that were exactly the same as the standard octave, and several others there were very close to existing tones.

I have never taken any piano lessons, but as just mentioned, even I know that finding "Middle C" is very important. Exactly why Middle C is not labeled "A" instead of "C" is a mystery to me. But given the fact that the "Do-Re-Mi" song appears to begin at C, I decided that my scale should do the same. Except... when I started from the tone on my scale that was equivalent to Middle C and jumped every other note from there, the resulting scale utilized two of those tones that were equivalent to the flat keys of a piano. Starting with the note on my scale that was equivalent to Middle C and jumping every other note also meant I would be including all four of the tones that are new in this 16 note system. So to make it possible for my scale to include as many approximations as possible for existing notes from the seven beautiful notes of a regular scale, I decided to begin my scale at a frequency roughly equivalent to the previous B that comes just before Middle C (see diagram below).

The difference between notes from a C4 octave oriented to 440.00Hz and this new octave are slight, but probably noticeable to most people. The question is whether anything played with these new notes would sound any good.

Below is a very mandala-like diagram showing the correlations between this new eight note octave, a new eight color spectrum and the nine numbers of numerology (or eight, if we acknowledge the similarity of 1and 9 as links in a cycle). Low frequency colors are paired up with low tones and high frequency colors are paired up with high tones. This diagram is oriented so that it can be unclasped at Magenta, like a necklace, and unbent back to a flat linear progression that would match the direction of notes found on most piano keyboards - where low notes are on the left and high notes are on the right. However... when the numberline of numerology is also oriented that way, its orientation to colors is opposite to the orientation given in the essay Enjoy The Pretty Colors. In that orientation small, compact, intense wavelengths were paired with a small number and the idea of a point being small, and large or long wavelengths were paired with a large number and the idea of a sphere being large. The orientation given in the diagram below is different. In this orientation, a low number is paired with a low frequency color and a low tone, and a high number is paired with a high frequency color and a high tone. As color and electromagnetic frequencies are themselves ironic, I see both orientations as legitimate. The fact that the most intense energy (Gamma Rays) comes from the end of the visible light spectrum that produces a "cool" color (Violet and Blue) is itself ironic - making any one single orientation of color to anything else impossible. So the orientation given below is completely legitimate, even though it does not match previous orientations.

This diagram is oriented so that it can be unclasped at Magenta, like a necklace, and unbent back to a flat linear progression that would match the direction of notes found on most piano keyboards - where low notes are on the left and high notes are on the right. However, it could be flipped left to right if one chooses.

I have not yet examined all the possibilities of this arrangement to discover all the dissonant and consonant combinations or viable ratios. I would hope that notes that share the same square, like 1, 3, 5 and 7, have some kind of harmonic association. And possibly we might find that notes that are 135 degrees from another, like 1 and 4 or 1 and 6, are also somewhat harmonious.

By creating an eight note scale that ends on a ninth that is in phase with the first, there are many trade-offs. The eight notes do not match the sound and rhythm of the more popular seven note Do-Re-Mi scale. That makes it hard to adjust to. But there are some benefits too. One benefit is the simple addition of more notes to play with. By adding four new notes, tones that used to double as both a flat and a sharp are now only flat or sharp, with the new note being the other. This could make for more subtle transitions. Below is a chart that shows ninety nine new notes to play with. It also lists the approximate equivalent note in a traditional scale, and shows in red, the notes that are an exact match in frequency to that of tradition. Among the new notes, none of them are ever more than 1.45% off of tradition. However, when one note is 1.45% off in one direction and the note after it is 1.45% off in the other direction, the combined amount of 2.9% can make a big difference to the ear that expects a certain amount of transition. I suggest giving these new notes a try anyway.

Ninety nine new notes! Give them a try! Make an instrument that can play them! Then try writing the notes down on a staff that looks like the staff illustrated above. By drawing a staff with 5 bold lines and 4 dotted lines, there is no need to indicate sharps of flats - each and every note has a line where it is welcome to appear. In fact, in this system there wouldn't be any such thing as a sharp or flat, just another note - an inbetween note. We could consider the black keys to be lesser or minor notes, but there is really no need. Just place a note (or perhaps a number) on each line or space to indicate the playing of that note. Which is easier to do, when the lines and spaces hold the same notes, no matter what range is chosen. Which means, no need for clefs either. Identify the range of each staff by its octave range: 1; 2; 3; etc. and add lines as needed.

In addition to connecting the seven Newtonian colors to the seven notes of a traditional Western scale, lots of people like to also connect those two systems to the seven chakras of Hinduism. But given what we've just covered, concerning the necessary participation of Magenta to any cycle of color, we can see how including Magenta would also be required in any attempt to include any kind of idea like chakras. Below is a mandala we can use to visualize a series of chakras... or what this study of consciousness and being would call Wave Nodes (i.e. where incoming waves and outgoing waves of cosmic energy meet and create an interference pattern that defines the four circles and a point upon which we base our visual description of a theoretical model of existence). This mandala also demonstrates how invertible the sequence of colors can be... as a core radiates from warm to cold, or a mind radiates from fast to slow. For a more detailed analysis of this mandala, consult the essay The Inverse Universe elsewhere on this site.

Chakras are cool. Are there seven... linearly... or eight... cyclically? In the system of consciousness and being that is being presented everywhere on this site, chakras would be called Wave Nodes. In this system, they can be described with an entire number line or just the four circles and point upon which we base our theoretical model of existence. In this mandala they are being expressed as nine numbers, or eight colors that cycle like an octave through the color Magenta. The white and black dots at the top and bottom represent the binary aspects of The Absentia, with The Universe of life and death between.