Tick = Transaction = varying number of contracts per transaction. There is nothing atomic about a transaction that is made up of a varying number of contracts or shares traded. Ticks charts are as inconsistent as minute charts because it is giving as much weight to a single lot trader as it is a trader that moves 100 lots. Again markets are traded in contracts and shares not transactions. What is arbitrary is creating a chart where there is no symmetry in the natural flow of price. The only natural part of the process is the price paid for the instrument and the instument (share or contract) itself.
Regarding your concern for an as natural as possible arrangement of a chart, what do you think about Gann's squaring of time and price? In other words, Gann set a specific scale of a unit of price to a unit of time (or vice-versa), and constructed the price and time axes of the chart according to that scale. If the price of the instrument had an average range of 10 points a day, he would set the price/time axes at a scale of 10 to 1. Supposedly, that reveals patterns and relationships in the chart that are otherwise not possible to be seen in a regular non-scaled chart. However, if that was the case, then every pre-90s trader who used hand-drawn charts, which naturally require a scale, would be able to see these relationships and supposedly be profitable, which we know is not true. IMHO, Gann made more money marketing and selling his courses and books than he actually made trading, and Wyckoff was his partner-in-crime, an "affiliate" of sort, to borrow from modern-day marketing concepts, who had a piece of that pie, for marketing Gann's supposed ability to predict the markets. $5000 a course was no peanuts back in the 1920's. It doesn't help the fact that the time period that Gann's prime years fell on was the most fertile breeding ground of all sorts of mystical ideas and concepts. To this day, not one person has been able to replicate Gann's results, and yet there's hundreds of Gann "experts" who every other day claim to have cracked the "secret" to Gann's method, and yet they need to sell a book or course on how they did it, rather than actually trade it and make money from it! LOL.
I try to keep things as natural as possible and to me that is price and it's naturally created oscillations.
Not totally sure I want to get into this but I disagree. Hence probability theory, stochastic process, discreet time, Bernoulli process, Brownian motion, and on and on. Time interval might be the single most important factor in taking advantage of random process.
There isn't? Say you're hosting a party and need to go get some beer. Are you really going to patronize the store again if the clerk tells you that you need to make ten separate purchases for the 20 cases of beer you want? The size of your purchase is immaterial, it's a single transaction. It's atomic. Same with a tick. If you're plugging those ticks into relational database how do you reference the same tick across two different rows because of some arbitrary size limit? You don't, because the tick is atomic. It's a tuple consisting of three inviolate elements, time, price and quantity. There's no way to know that each single lot transaction is a separate trader. They could all be coming from someone who's hiding size behind a show-only order. No chart is better than any other. Any attempt to say otherwise is just a rationalization because any two dimensional chart will always be a visual approximation for the three vectors of price, volume and time.