KVR Audio

McLilith · Post by **McLilith** » Wed Apr 06, 2005 6:40 am

I've been looking on the internet for accurate and complete musical timing formulas to determine things such as:

The duration (in seconds) of a note, for a given tempo and time signature.

The duration (in seconds) of a measure, for a given tempo and time signature.

All the formulas I've seen, seem to assume 4/4 time signatures, or they assume you are working strictly with 1/4 notes, or some other assumption. I'm looking for formulas that take everything into consideration, and don't make any assumptions.

For example, if I know that I have a tempo of 137 beats-per-minute, and a time signature of 9/8, I want to be able to calculate the length of a 1/16th note (dotted, normal, or triplet), and also the length of a measure based on that same input data.

I'm writing some software to make such calculations, and I think I'm doing things correctly, but I need to check my work against some sort of very trusted, standard formulas. I've tried a few tempo calculator programs, but because some of them make arbitrary assumptions, I get conflicting results from some of them. I just don't know what to trust at the moment.

Thanks,
McLilith

Warmonger · Post by **Warmonger** » Wed Apr 06, 2005 6:56 am

If you think your formulas are right, then what's the problem? It shouldn't be hard to check if everything works. If the units all check out when doing your dimensional analysis, and the most absurd examples give correct results, it should be just fine. It's not like you're using any advanced math; it should be a straightforward 4-operator based formula.

C00kie · Post by **C00kie** » Wed Apr 06, 2005 7:31 am

The time signature does NOT alter the duration of a quarter note. It only changes how the notes/beats are grouped together in bars.

If you have 137 bpm and 9/8 in a bar, that means:
* it takes 137 quarter notes to fill one minute
* it takes 137 quarter notes to fill 60 seconds
* one quarter note takes 60/137= 0.4379 secs
* one eigth note takes half that: 0.2189 secs
* nine eigth notes take 1.3708 secs
* you said it takes nine eigths to fill one bar, so one bar takes 1.3708 secs
* one "dotted" eigth note is 1.5 a normal eigth note, so thats 0.3284 secs

Plain calculations, only divisions and multiplications. Try to recalculate these please...

McLilith · Post by **McLilith** » Wed Apr 06, 2005 8:10 am

C00kie wrote:The time signature does NOT alter the duration of a quarter note. It only changes how the notes/beats are grouped together in bars.

If you have 137 bpm and 9/8 in a bar, that means:
* it takes 137 quarter notes to fill one minute

...

No, I think you're wrong.

It takes 137 beats to fill a minute.

137 BPM = 137 Beats per Minute, correct?

Since your time signature is 9/8, then those beats are equal to 1/8 notes. This is detemined by the second number in the time signature, correct?

So, it should take 137 eighth notes to fill a minute, not 137 quarter notes.

The duration (in seconds) of one beat, is what doesn't change with a change of time signatures. With a tempo of 137, one beat will have a period of roughly 0.43796 seconds.

Since our beat is equal to an eighth note, thanks to the 9/8 time signature, an eighth note will have a duration of roughly 0.43796 seconds.

If I messed something up, please explain where.

thanks,
McLilith

duncanparsons · Post by **duncanparsons** » Wed Apr 06, 2005 8:59 am

first, it's formulae surely!

also bpm refers to crotchets, or what those further west of here seem to call a quarter note. In notation you are normally told how many of what type of note to expect in a bar. There are oddities, such as you may see a dotted crotchet and a figure of 120, but the time sig says 4/4 - so you're going to be swinging those pants abit..

I understand your point, that a bar of 9/8 at 100bpm should be the same length (in time) as a bar of 9/4 at 200bpm (or is it 50bpm? top of head here!). However, most software is tuned to using a standard crothet as the unit of measure (if you'll pardon the pun)

Try a demo of sibelius, and see what that does - that's going to be the most Orchestrally real world. For the most part tho', you're only going to be interested in the 'denominator', and there shouldn't be toooo much need to worry about dotted crotchet tempo declarations..

Don't know if that helps!
DSP

Warmonger · Post by **Warmonger** » Wed Apr 06, 2005 9:17 am

Right, every sequencer I've tried assumes BPM == QNPM, so that's a reasonable convention to stick to, whether that's correct behavior or not.

Dennis DeSantis · Post by **Dennis DeSantis** » Wed Apr 06, 2005 9:19 am

BPM does not, by necessity, refer to crotchets/quarter notes.
It is, in all cases, entirely dependent on the meter. In meters with quarter note denominators, the "beats" in question will then be quarter notes - but this is the only (albeit most common) case in which this is true.

For eighth note denominators, there are two common possibilities, depending on whether or not the numerator is a multiple of 3:

- "simple" meter, in which case the beats in question will be eighth notes, and the tempo indication will indicate this: (eg: eighth = 108)

- "compound" meter, in which the beats in question will be dotted quarters, and the tempo indication will indicate this: (eg: dotted quarter = 108)

An excellent summary of metric notation can be found here:
http://www.music.vt.edu/musicdictionary ... asics.html

McLilith · Post by **McLilith** » Wed Apr 06, 2005 9:21 am

Warmonger wrote:Right, every sequencer I've tried assumes BPM == QNPM, so that's a reasonable convention to stick to, whether that's correct behavior or not.

If it's not correct, then it's not reasonable!

McLilith

Warmonger · Post by **Warmonger** » Wed Apr 06, 2005 9:27 am

Okay, then just add an input parameter to your original description that defines what a beat is, and have it default to a quarter note. Since you can't always assume that the user is specifying the BPM in terms of the "denominator", just ask the user what they mean.

How's that for reasonable?

(uh oh, I sense the Reason jokes are not far off...)

stefancrs · Post by **stefancrs** » Wed Apr 06, 2005 9:35 am

Letting beats be 1/4ths seems weird. What would the result be if a beat is 1/4 and your time sig is 9/8 ? The time sig specifies the beats ffs.

AJay · Post by **AJay** » Wed Apr 06, 2005 9:41 am

Hello McLilith. I have been into this sort of calculation for years and thought I might be able to help.

Any bpm = 60/tempo, time-signature is irrelevant for that.

The relevance comes in with how the beats or notes are spread over a bar. The note lengths are not affected by time signature, bar lengths are though.

Your example is 9/8 at 137 bpm.

How do we calcualte 9/8? Always simplify the data. Basic 9/8 compound timing is 3 dotted crotchet beats to the bar.

So 9/8 at 137bpm,
1 bar = (3 X 1.5) * length of beat
1 bar = 4.5 * (60/137)
1 bar = 4.5 * 0.437956 = 1.970802

Also (4.5 X 2)/(4 X 2) = 9/8

3 dotted crotchet beats could also be 4 crotchets plus a quaver - but the 4.5 beats per bar still add up.

So compared to a bar in 4/4, a bar in 9/8 has an extra quaver to account for.

As for the semi-quaver calculation :

1 quaver = 0.5 * 0.437956
OR 1 quaver = 0.437956 / 2 = 0.218978

1 semi-quaver = 0.25 * 0.437956
OR 1 semi-quaver = 0.437956 / 4
OR 1 semi-quaver = 0.25 * 0.218978
OR 1 semi-quaver = 0.218978 / 2 = 0.109489

As you see, the time-signature is not important, it's how many of these notes that fill up a bar that is.

3 dotted crotchet notes = 9 quavers = 18 semi-quavers

1 bar = 18 * 0.109489 = 1.970802
1 bar = 9 * 0.218978 = 1.970802
1 bar = 4.5 * 0.437956 = 1.970802

You need to understand how the bars and notes work in relation to their timing really.

You're on the right lines though.

Hope I helped and good luck to you.

tkmattson · Post by **tkmattson** » Wed Apr 06, 2005 10:27 am

There is a book I have called "On The Right Track", which includes a 200 page click book for scoring to picture in the back - for those who never had to use a click book before*, it shows all possible time signatures, BPM values, & frame rates arranged into tables....

*And I DO mean "had to use one", it is a pain in the arse!!!

Hope that helps....

McLilith · Post by **McLilith** » Wed Apr 06, 2005 9:35 pm

tkmattson wrote:There is a book I have called "On The Right Track", which includes a 200 page click book for scoring to picture in the back - for those who never had to use a click book before*, it shows all possible time signatures, BPM values, & frame rates arranged into tables....

I don't suppose you would want to quote a few examples from the book, would you?

It would help confirm if I'm approaching things correctly. If you're interested, I could give you some time signatures, along with a common tempo for them, and you could tell me things like the length of a quarter note, the length of a bar, etc for each time signature. I promise not to ask you for all possible time signatures.

I just need a few examples, for my verification needs.

Send me a PM, if you're interested.

thanks,
McLilith

peter01 · Post by **peter01** » Wed Apr 06, 2005 10:09 pm

http://www.forret.com/tools/bpm_tempo.a ... t=9&base=8

don't know if it's accurate, but it's nice anyway

McLilith · Post by **McLilith** » Thu Apr 07, 2005 7:09 pm

I still can't figure out the reason Sonar and Tracktion behave the way they do. If I change either the top or the bottom number in a time signature, then the length of a Bar (measure), as expressed in seconds, will change.

I can understand the reason changing the top number results in a change in the lengh of a Bar, because you are adding beats to the bar. I really do not understand how changing the bottom number should have any effect on the length of a Bar, as measured in seconds.

Here are what I've always understood to be the facts:

Tempo = the number of Beats per MINUTE

Time Sig. Upper Number = Number of Beats per MEASURE

Time Sig. Lower Number = Specifies which note is equal to one beat.

Do I at least have those three "facts" correct?

To calculate a measure's (Bar's) length, in seconds:

Length in seconds = 60 / (Beats per Minute) * (Beats per Measure)

or Length = 60 / BPM * Time Signature "Numerator"

Where are those forumulas incorrect?

Where can I find an authoritative text that explains why these formulas are incorrect?

Either my formulas are incorrect, or Sonar and Tracktion are incorrect.

thanks,
McLilith

Music Timing Formulas Needed