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A Model of Consonance for N-TET

 Simply, given a root note R and a harmony note H, let s equal the absolute value of the difference in semitones between the notes R and H, and N be the number of tone classes in the temperament. Then the consonance between R and H, C(R,H), is the square root of the ratio between the octaves per cycle of the interval and its steps to octave. We compute the octaves per cycle, OPC, as s divided by the greatest common divisor between s and N, and the steps to octave STO as N divided by s. Then N = 12, s = |d(R,H)|, OPC = s/GCD(s,N), STO = N/s. C(R,H) = sqrt(OPC/STO). The way we interpret this model is as follows. The greater the resulting number, the greater the consonance between the given notes. Hence, the most consonant interval is the unison. So, its consonance is defined as infinite.
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Last Night in Cairo

Last Night in Cairo   Outline © 2023 G. M. Dávila Andino 1. Dr. Seawell has just arrived in Cairo. He says goodbye to his photographer friend. They were on an expedition through North Africa. The Photographer’s going to Gaza to cover the war. 2. He takes some time to walk around the city, just to get a feel for it. Maybe he buys some food from the local cuisine at a small venue. A snack, or a coffee. 3. Veronica's on vacation with her best friend, trying the local cuisine in Cairo, road trip to Giza, buying textiles for her custom clothes. This year has been good for her. 4. At the café, there’s a missed meet between Alexander and Veronica.  5. He buys a prepaid phone and a phone card, maybe, and a computer, he leases a car, parks it, checks into the Marriot Cairo Hotel, checks his emails. there’s one from Anastasia Radwizill. 6. He calls her, leaves a voice message, looks at his Omega watch and passes out. It’s just late and he’s tired. 7. Dr. Seawell wakes up t...
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Of Surreal Geometry 2

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Now, even oscillating curves have a rate of change. It may not be constant, but it exists. Take, for example, the harmonic series. We know it diverges. If we speed things up, we can ask how “fast” is a task approaching infinity. How fast does the harmonic series diverge? The zeroes of the sine function approach infinity at a constant rate equal to a wavelength per unit. Here, we assume as our standard, the rate of change of the natural numbers, which is one per unit. Definition: A discrete supertask is as sequence of events whose number of elements approach infinity at a rate smaller than that of the natural numbers. If we make a transformation of the natural numbers such that its velocity equals ½, then we have a supertask, and have compressed the whole natural number line between 1 and ω/2. Such a transformation can be a projection which will preserve a constant rate of change in the projected space. You may ask what does it mean to reach or approach infinity. With a normal...
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