Is the space between thoughts an indicator of meditative calmness?

the space between thoughts is a technical term used in yogachara and madhyamika it doesnt refer simply to the stopping of thoughts which happens at the end of the 4th of the 9 stages of shamata (aka access concentration, and which by the end of the 8th results in being able to sustain vivid extended uninterrupted attention on the spacious luminous nonconceptuality that is the mind ie. an ongoing observation of a lack of thoughts)

with good instructions it should not take longer than 2 or 3 months to fully stop thoughts arising and pulling u off ur chosen object of single-pointed fixation (aka end of stage4). quite a while before this happens ur enemy already is not fully formed thoughts arising and pulling u off ur object but rather the beginning processes that eventually lead to full thoughts arising--these are the subtle and brief interruptions arising and pulling u off ur object momentarily which u immediately observe and correct by returning to ur meditation object.

While eating on either form, sound, smell, taste, bodily touch, yet not aware of it, that, what the Sublime Buddha called "household-equanimity" may be present at such time, equanimity which has not gone beyond sensuality. As it is a very dangerous one it's very needed to leave home first before engaging in higher paths, good householder. May he know those "good" in meditation but incapable of leaving home as those caught up there where hardly one could ever trace the path.

When we begin to meditate, we think about our breath and so become more calm. But the aim is for the calmness, and the deep and regular breathing, to come not from 'outside' imposed by attention, but from 'inside', leading the breath rather than following it. Like a mood or an attitude, of serenity & equanimity. I would say just as breathing naturally slows then, thoughts also slow.

In samatha meditation, it's not truly 'thoughtless' intervals that it is about, but meditative absorption. This can be focused on the sensation of breath on the tip of the nose, a candle flame, the bodies energy centre just below the navel, or other objects or sensations. See the Nine Mental Abidings for an example of how to understand progress in this.

With this same kind of absorption, vipassana meditation can be applied the deep matters of Buddhism like suffering and dependent origination, reflecting on them as they relate to our own lives. In ways that allows deep insights into our own nature to rise up, once we no longer rush to 'grab' extraneous thoughts and so get distracted.

I would caution against just equating lack of internal monologue with meditative progress. Some people just naturally have little or no internal monologue, and I can tell you they don't find meditation easier!

Sutta AN9.41 provides a broad overview of immersive progression. In the suttas thoughts are included in senses, so we have six senses rather than the contemporary understanding of five sense. Your "gap between thoughts" might therefore be understood as relatable to "secluded from sensual pleasures".

AN9.41:7.15: And so, quite secluded from sensual pleasures, secluded from unskillful qualities, I entered and remained in the first absorption, which has the rapture and bliss born of seclusion, while placing the mind and keeping it connected.

Your word "calmness" touches on many other terms used in AN9.41. For example, "rapture and bliss" in the above. However, "calmness" is also an attribute of "equanimity", which occurs later in the sutta:

AN9.41:9.2: ‘Why don’t I, with the fading away of rapture, enter and remain in the third absorption, where I will meditate with equanimity, mindful and aware, personally experiencing the bliss of which the noble ones declare, “Equanimous and mindful, one meditates in bliss”?’

It might be helpful to read the sutta carefully to explore the deeper meaning in each of the carefully chosen terms. Day-to-day language doesn't quite express the subtleties involved.

I was thinking about OP today and i figured it might be worth adding that OP is not wrong in not judging thoughts & ignoring. It seems you only read part of the Sutta and missed the rest..

I know it is not advised to judge one's inner experience too much during meditation

Sutta

"There is the case where evil, unskillful thoughts — imbued with desire, aversion, or delusion — arise in a monk while he is referring to and attending to a particular theme. He should attend to another theme, apart from that one, connected with what is skillful... "If evil, unskillful thoughts — imbued with desire, aversion, or delusion — still arise in the monk while he is attending to this other theme, connected with what is skillful, he should scrutinize the drawbacks of those thoughts: 'Truly, these thoughts of mine are unskillful, these thoughts of mine are blameworthy, these thoughts of mine result in stress.' As he is scrutinizing the drawbacks of those thoughts, those evil, unskillful thoughts — imbued with desire, aversion, or delusion — are abandoned and subside. https://www.accesstoinsight.org/tipitaka/mn/mn.020.than.html

OP

and that inhibiting thoughts intentionally is not recommended

Sutta says that sometimes it's appropriate to be without attention to thoughts but at other times one should investigate & direct thinking to abandoning.

"If evil, unskillful thoughts — imbued with desire, aversion or delusion — still arise in the monk while he is scrutinizing the drawbacks of those thoughts, he should pay no mind and pay no attention to those thoughts. As he is paying no mind and paying no attention to them, those evil, unskillful thoughts are abandoned and subside. Just as a man with good eyes, not wanting to see forms that had come into range, would close his eyes or look away; in the same way, if evil, unskillful thoughts — imbued with desire, aversion or delusion — still arise in the monk while he is scrutinizing the drawbacks of those thoughts, he should pay no mind and pay no attention to those thoughts. As he is paying no mind and paying no attention to them, those evil, unskillful thoughts are abandoned and subside. With their abandoning, he steadies his mind right within, settles it, unifies it, and concentrates it... "If evil, unskillful thoughts — imbued with desire, aversion or delusion — still arise in the monk while he is paying no mind and paying no attention to those thoughts, he should attend to the relaxing of thought-fabrication with regard to those thoughts. As he is attending to the relaxing of thought-fabrication with regard to those thoughts, those evil, unskillful thoughts are abandoned and subside. With their abandoning, he steadies his mind right within, settles it, unifies it, and concentrates it. Just as the thought would occur to a man walking quickly, 'Why am I walking quickly? Why don't I walk slowly?' So he walks slowly. The thought occurs to him, 'Why am I walking slowly? Why don't I stand?' So he stands. The thought occurs to him, 'Why am I standing? Why don't I sit down?' So he sits down. The thought occurs to him, 'Why am I sitting? Why don't I lie down?' So he lies down. In this way, giving up the grosser posture, he takes up the more refined one.

OP

would it be right to say that a period wherein thoughts are more infrequent signifies a calmer mind? Does the diminution of thoughts correlate with calmness?

In general yes, if you can still thought it's closer to the stilling of applied & sustained thought/ideation.

Another metric by which one can judge one's ability to concentrate is the strength of one's ability to apply the mind to a theme and keeping it connected without disturbance, this can be thinking about a particular theme without disturbance. This can be a contemplation subject or memorization even.

I think using both metrics is more reliable measure of own's abilities because everybody can keep their mind more or less still and one might fool oneself into thinking it's amazing when it's modicum at best.

“And what, Ānanda, is the perception of abandoning? Here, a bhikkhu does not tolerate an arisen sensual thought; he abandons it, dispels it, terminates it, and obliterates it. He does not tolerate an arisen thought of ill will … an arisen thought of harming … bad unwholesome states whenever they arise; he abandons them, dispels them, terminates them, and obliterates them. This is called the perception of abandoning.

If one didn't develop abandoning then one wouldn't abandon...if one didn't perceive abandoning... if one didn't conceive abandoning... if one didn't feel abandoning... didn't cognize abandoning... didn't experience abandoning then one wouldn't come to having abandoned.

Thoughts are like breath they get more subtle and rare, is perhaps as simple as i can put it.