More academic-sounding term for high-variance The goal is to find a term to describe a distribution that fits with the other "lofty"-sounding words like:

*

*Skewness: mode!=mean / symmetry

*Kurtosis: How "fat" the tail is

*???: how much spread is contained within one standard deviation

I guess it's just variance but if "variance" is the most "lofty" sounding word I will be vary disappointed. Ideally I want something that sounds more illustrious.
Question
Are there more technical/uber-statistical terms that could be used to refer to whether 1 standard deviation has "a lot" or "a little" spread?
Thanks

Some intuitive re-expression of the problem:
You could regard the quantile function of the standardized squared difference $\chi = \left(\frac{|X-\mu|}{\sigma}\right)^2$ from the mean
Let
$$F(\chi) = P\left(\left(\frac{|X-\mu|}{\sigma}\right)^2 < \chi \right)$$
Then the quantile function that we speak about is the inverse
$$Q(p) = \lbrace \chi: F(\chi) = p \rbrace$$
This needs to be a monotonically increasing function that integrates to 1.
An example of this function for the normal distribution is:

Taken from here: https://math.stackexchange.com/a/3781761/466748
From this view the kurtosis is equal to
$$ kurtosis = \int_0^1 Q(p)^2 dp$$
And your concept is the point $p$ where $Q(p) = 1$ or differently
$$ Z = \int_0^1 \mathbb{1}_{Q(p)\leq 1} dp$$
Where $\mathbb{1}$ is the indicator function.
Your measure is computing how often standardized values are close to 0, or spread out and away from 1, In some way similar as kurtosis, but kurtosis is assigning more weight to extreme values.
Your measure is similar to kurtosis (from Greek for bulging). But to come up with a term might be difficult since many different shapes can correspond to high/low values of your statistic. Like kurtosis it has a similar relationships with peakedness, but it is also not exactly the same as peakedness and only correlates with it.
Maybe you shouldn't try to condense this in a particular name and you could describe it with a few more words. Because of the binary nature, how you count values below and above $1\sigma$ as either 0 or 1, you might call this measure 'the degree of probability division around $1\sigma$' or (my favorite) 'bulge/tail ratio', a measure for how much probability mass is in the tails and how much in the bulge. Firebug's suggestion in the comments is also nice 'probability concentration'.
Distributions that have a high $Z$ will have most of the distribution being determined by a central part with the tails possibly having large influence on the kurtosis or other values, but in terms of amount of probability the tails will be small.
