Word for part of a beat

Question

I'm writing an article describing the musical tradition of a particular culture, but I'm at a loss for general terms for durations shorter than a beat. Simple prolation (such as 2/4 or 3/4) divides a beat into two X's. Compound prolation (such as 6/8 or 9/8) divides a beat into three X's. What is X called?

Background: Mensural notation nomenclature

In the mid-13th century, Franco of Cologne published a groundbreaking musical treatise that led to introduction of mensural notation based on note shapes. Codeswitcher's answer to "Why are only even values used for note duration?" defines several terms associated with mensural notation:

• Breve: A brief duration corresponding to a periodic accent phenomenon with a period of about a second or two.
• Time: Division of the breve into two or three semibreves.
• Semibreve: One-half or one-third of a measure, depending on imperfect or perfect time.
• Prolation: Division of the semibreve into two or three minims.
• Minim: One-half or one-third of a semibreve, depending on minor or major prolation.

Modern musical notation is descended from this mensural notation. Apart from rounded note heads and fourfold value inflation, the biggest functional change is the loss of "imperfection", or shortening a perfect-time breve to squeeze in a semibreve or shortening a major-prolation semibreve to fit a following minim. Instead, modern notation assumes fully imperfected values and makes perfection (making a note 50 percent longer) explicit by reinterpreting the separator dot that had blocked imperfection in the mensural notation. The converse "alteration" was also dispensed with. This was made practical by the rise in popularity of simple duple meter.

What have you tried?

I've been trying to come up with modern counterparts to the mensural terms. I was considering repurposing the mensural terms (breve meaning 2 or 3 beats, semibreve meaning beat, and minim meaning a half or third of a beat) for relationship with the beat and the Germanic terms (whole note and binary fractions thereof) for durations as written. I dropped this when I remembered that British English uses the mensural terms with modern notation, with their inflated values; for example, Brits call the 𝅗𝅥 half note a minim. Here's what I have:

• Measure: A brief duration corresponding to a periodic phenomenon with a period of about a second or two.
• Time: Division of the measure into two or three beats. (Common time is two layers of duple time.)
• Beat: One-half or one-third of a measure, depending on duple or triple time.
• Prolation: Division of the beat into two or three X.
• X: One-half or one-third of a beat, depending on simple or compound prolation.

Is there a clear name for this sort of part of a beat? It'd represent a 𝅘𝅥 quarter note in 2/2 (cut time) or an 𝅘𝅥𝅮 eighth note in 2/4, 3/4, 4/4, 6/8, or 9/8.

Answer 1

The closest term for what you are referring to is subdivisions as the beat is divided in into smaller parts. The term subdivision is always used when talking about note values less than the beat:

For example on the Wikipedia article for Counting Music states:

Triple meter, such as 3/4, is often counted 1 2 3, while compound meter, such as 6/8, is often counted in two and subdivided "One-and-ah-Two-and-ah"2 but may be articulated as "One-la-lee-Two-la-lee".2 For each subdivision employed a new syllable is used. For example, sixteenth notes in 4/4 are counted 1 e & a 2 e & a 3 e & a 4 e & a, using numbers for the quarter note, "&" for the eighth note, and "e" and "a" for the sixteenth note level.

Along with with the definition of meter and beat:

Most music in the world has a pulse or beat. Usually, the pulses are organized into groups, usually from 2 to 5 beats in a group, and are usually regular (the same number of beats repeating over and over, and the beats always the same length).This grouping is the general idea of METER. Most music derived from European sources falls into DUPLE (2 or 4 beats) or TRIPLE meters. Beats themselves can be SUBDIVIDED into smaller parts, usually 2, 3, 4, 6 or 8 even parts (duple or triple subdivisions)

If subdivision alone seems like it's not descriptive enough term you could use first subdivision to refer to the next smaller note value.