How do you measure tightness

A metronome is a great feedback device. Developing skill in music is as much about developing perception as manual skill, and comparing your playing to a consistent yardstick allows you to see weaknesses or inconsistencies in your playing more easily.

I want BeatBalance to provide more helpful information to analyse playing and address problem areas. At the moment, the app provides only a relatively simple selection of rhythms. One of my priorities for the next stage of development is to expand the range of rhythms available - different time signatures and rhythmic subdivisions triplets, quintuplets etc as well as some more esoteric non-isochronous rhythmic options which I will discuss in a later post. To help players improve their tightness, I wanted to come up with a simple, accurate but easy-to-understand way of measuring tightness and translating that into a useful, intuitive score.

Scoring tightness. Although the app gives you breakdowns and graphs showing your timing, it can be difficult to get an intuitive grasp on what these mean. To contextualise this information I wanted to break the information on tightness down in a way which is accurate but easy to understand intuitively.

The most common way to quantify tightness in drum apps is to use a percentage system - usually a percentage showing how many hits you got within a certain window of time around the target. This was the system I used in early versions of BeatBalance but there are a couple of problems with it which emerged during testing. Related to this is the fact that I want BeatBalance to be a useful tool for players of all levels, and it may well be possible for even highly skilled players to continue to improve their timing over a long period.

This means that subjectively quite similar performances can end up getting very different percentage scores. As a result the app currently uses a different system. The system scores tightness out of , and works by calculating a measure of the spread of the overall timing performance. The more narrowly grouped the performance around the target time, the higher the score. Very often, the measures in question are probability measures , so the last part can be written as.

This is not necessarily so for non-metrisable compact spaces. The collection. On the other hand, the collection. Consider a collection of Gaussian measures. Tightness is often a necessary criterion for proving the weak convergence of a sequence of probability measures, especially when the measure space has infinite dimension.

A strengthening of tightness is the concept of exponential tightness, which has applications in large deviations theory. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search.

What is the motivation behind the definition of tightness of probabilty measures given below? Wikipedia says:. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more.