BPM, beat durations vs frequency

Question

I understand that 60 BPM means 60 Beats Per Minute. And if the "BPM beat note" is a quarter note, it means a quarter note has the duration of 1 second (each quarter note should be held 1 second when playing). But what if I don't want hold each beat 1 second but instead 0.5 seconds, yet still keep the frequency of them (still 60 BPM). Meaning, there will be a gap of 0.5 seconds between the actual beats. So I will actually play 1/8 notes as the beat.

Whats's the correct notation for this so it all fits together? If I haven't missed anything, I can't really use the BPM notation to address this, right? I assume I should notate the beat note as 1/8 notes. Should then the time signature address this? Example: 60 BPM - Quarter note, Time signature 4/8 (the "beat" note of the time signature = 1/8 note). Or maybe it doesn't really matter, and I could simply use 4/4 as the time signature?

I heard that BPM and the time signature are independent of each other, but as they both address the beat note type, I assume they in most cases should always be the same: if the BPM specifies 1/4 note as beat note, the time signature should logical also be x/4. If not, why?

Answer 1

In order to notate 60 BPM where the actual duration of the sounded pitch lasts only 1/2 second, you would notate uses pairs of eighth notes and eight rests.

X: 1
T: 60 BPM Example #1
T: Sounding durations = 1/2 sec.
M: 4/4
K: none
Q: 1/4=60
!tenuto!B z !tenuto!B z !tenuto!B z !tenuto!B z |

The lines above the notes are "tenuto" marks, which mean to be sure to hold the note for its full length.

This could also be notated using staccato markings on quarter notes. A common interpretation for staccato notes is that they take up half the notated length.

X: 1
T: 60 BPM Example #2
T: Sounding durations = 1/2 sec.
M: 4/4
K: none
Q: 1/4=60
L: 1/4
.B .B .B .B |

My personal preference would be the eighth-note/eighth-rest notation. I find it more precise, especially since I don't adhere to the "staccato = 1/2 length" convention.

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The BPM designation and the time signature "beat note" need not be the same. Tempi can be given in terms of BPM (corresponding to the time signature's "beat note") or in terms of a note type.

For example, in 6/8 time, it's common to give the speed in dotted quarter notes, even though the time signature indicates eighth notes as the "beat note". 3/4 time, when the speed is fast, is often given in terms of dotted half notes per minute. 2/2 time is sometimes given in quarter notes or whole notes.

I think the confusion is that there are two somewhat independent notations. 1/4 = 60 means "there are 60 quarter notes per minute." dotted-quarter = 120 means "there are 120 dotted quarter notes per minute." These notations can be independent of the time signature — or rather can be adjusted to the time signature.

BPM is specific to the designated "beat note". So, in 3/4 time, the following notations would all result in exactly the same overall speed:

• dotted half-note = 40
• quarter-note = 120
• 120 BPM