Duration of articulations (e.g. staccato, tenuto) for piano

QUESTION

Staccatissimo, staccato, mezzo-staccato, portato, non-legato, tenuto, legato.*

For piano, what would be a (rough) numerical representation of these articulations' gap duration for note duration of 0.5 and 1 second?

*Of them, staccato, non-legato, and legato are the more critical (as occurring more often in sheet music).

BACKGROUND

What the question is about, or what an answer should look like.

I am looking for an answer that might look like:

note 0.5s : . . staccato (sound 250ms, gap 250ms) . . legato (sound 500ms, gap 0ms)
note 1.0s : . . staccato (sound 750ms, gap 250ms) . . legato (sound 1s, gap 0ms)

where ". ." represents the space for the other articulations (e.g. staccatissimo to the far left).

Please note that there are two elements to this answer: (a) an ordering of the articulations in terms of gap length and (b) an indication of what happens when the note becoming longer.

In the above example, when the note becomes longer, the gap remains constant. But we could imagine answers in which sound and gap are proportional or where the sound duration remains constant:

note 0.5s : . . staccato (sound 250ms, gap 250ms) . . legato (sound 500ms, gap 0ms)
note 1.0s : . . staccato (sound 500ms, gap 500ms) . . legato (sound 1s, gap 0ms)

Sample answer 3 (constant sound duration)
note 0.5s : . . staccato (sound 250ms, gap 250ms) . . legato (sound 500ms, gap 0ms)
note 1.0s : . . staccato (sound 250ms, gap 750ms) . . legato (sound 1s, gap 0ms)

I realize that the precision of numbers like 250ms may be ridiculous and am using them only to illustrate my purpose.

Your answer may therefore simply (a) order the articulations from short sounding to long sounding and (b) indicate whether "sound" or "gap" should tend to remain constant (or whether a proportionality applies).

What I am not looking for, and what an answer should not be made of.

I am not asking what e.g. a staccato is. Therefore if you tell me e.g., "A staccato is not just a matter of duration, but it also involves. . . .," that might be very useful information (and I would appreciate it) but would not be responsive.

I am also not asking how to play e.g. a staccato. So again if you tell me that the finger, the wrist, or the arm should go up or not go up, that too may be very useful but not responsive.

A quick way to contextualize may question, I believe, would be to say that I am entering the articulations into computer in MIDI or some other numerical notation and need a rough guideline on appropriate sound/gap duration.

One final note on non-legato. I have read here and there that non-legato is not a separate articulation, but its absence, or the way articulation is left to the performer. If you are of this opinion, I realize that you could not give any sound/gap duration for non-legato.

Thank you very much.

• Unfortunately, you explicitly ban the answer that reflects human performance best, because, well, "staccato is not just a matter of duration." Aside from various genres or contexts that pursue homogeneity, like maybe some minimalism, most human-performed music values variability for expressive purposes. I could face a measure of staccato notes and quite intentionally make some longer than others. Commented Apr 26, 2022 at 14:32
• (I realized what I'm thinking of: Debussy violin sonata, 2nd mvt. Many measures of repeated 16th notes on one pitch, all marked staccato; my goal would be for no two consecutive notes to be the same duration.) Commented Apr 26, 2022 at 14:36
• @AndyBonner Alas, a beginner has to learn first the unvaried so he'd know what he is varying from. Otherwise his variability will be random rather than thoughtful or instinctive. Thanks for turning me on to the Debussy! Internet had Oistrakh. Commented Apr 27, 2022 at 3:11

TL;DR

In order to have unique durations for each articulation, use a formula along the lines of PerformedDuration = NotatedDuration * ListOrderOfArticulation / NumberOfDistinctArticulations (See General Answer). Or use a variation on MuseScore's default duration percentages (See MuseScore definitions).

Since all articulations are interpretive and contextual, all answers to this question will be arbitrary. However, given the idea that a computer needs a fixed indication of how to "perform" each marking, the primary decision is whether the relationships should be linear (i.e., constant differences between "adjacent" durations) or logarithmic (i.e., adjacent durations differ by, say, a factor of 2).

Given the "computerization" context, I think linear relationships will be most successful, as they give the clearest delineation between one articulation and another.

The shortest (pitched) duration the human ear can discern is about 100ms. (See, for example, What's the shortest sound perceptible to the human ear?) So, let D be the duration in milliseconds of some note such that D > 100ms. Then the following table emerges:

articulation duration (ms)
staccatissimo 100 + (D-100)/7
staccato 100 + 2(D-100)/7
mezzo-staccato 100 + 3(D-100)/7
portato 100 + 4(D-100)/7
non-legato 100 + 5(D-100)/7
tenuto 100 + 6(D-100)/7
legato D

There is also a convention that staccato is 1/2 the notated duration. Going with that definition, I would say:

• staccatissimo = 1/4 of the notated duration
• staccato = 1/2 of the notated duration
• mezzo-staccato = portato = non-legato = tenuto = 3/4 of the notated duration
• legato = exactly the notated duration

MuseScore definitions

These are the default percentages of a note's full duration used for various articulations. They come from MuseScore's master instrument definitions file.

articulation duration percentage
staccatissimo 33
staccato 50
portato 67
tenuto 100
marcato 67
sforzato 100
sforzatoStaccato 50
marcatoStaccato 50
marcatoTenuto 100
• Huh, I always thought that Musescore portatos were 75% instead of 67%. Commented Apr 26, 2022 at 5:02
• Thank you. Exactly what I was looking for (indeed an "Oh my God" answer). I cannot upvote while sub 15. As the site discourages non-substantive comments, I will delete this one after some time. Commented Apr 26, 2022 at 5:27