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Old 01-18-2013, 01:46 AM   #1
Unreal T
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septuplets confusion

On the subject of 16th note septuplets. (7 notes played in the time of one quarter note)

How is it possible to split up one beat into 7 EVENLY spaced notes? It is mathematically impossible isn't it? If you had a 60bpm pulse that means there is 1 beat per second...so playing 7 "EVENLY" spaced notes in one second comes out to having to play each note
.1428###### seconds. It seems impossible to do but yet somehow we are able to do it.

What also confuses me more is how it is possible to count septuplets differently. For instance...1212 123..1212 123.....or 123 123 1.......and still manage to play septuplets correctly.

The thing is I think most people understand just to play 7 notes and do whatever tricks other people tell them to do to successfully play septuplets...but I want to understand more deeply and mathematically how it works.
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Old 01-18-2013, 01:59 AM   #2
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Old 01-18-2013, 02:34 AM   #3
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Because measurements of time are man made conveniences that have no effect on our ability to keep a beat?
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Old 01-18-2013, 03:00 AM   #4
shreddymcshred
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Dividing one beat into seven parts

> 3.5 notes must happen per 8th note duration
> Therefore if you are playing 7 septuplet notes in the time of one beat, the midpoint of the beat will fall exactly halfway between septuplet 4 and 5.
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Old 01-18-2013, 03:07 AM   #5
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It seems like you need to take a math class...

1/7 IS mathematically possible. It just has a lot of decimal places. That is the extent of the math behind it. I have no idea what more you want to know.

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Originally Posted by Macabre_Turtle
Because measurements of time are man made conveniences that have no effect on our ability to keep a beat?
This. We don't count music in seconds. Even if you're at 60 bpm, your pulse is every second, but you don't just visualize a stopwatch with multiple decimal points. You subdivide into eighths or sixteenths and anything that falls in between, you just feel it out.

One of the beautiful things about rhythm, especially irregular rhythms, is that it isn't always mathematically precise. That's what defines groove, and that's why computers can never replace real musicians, in my opinion.
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Old 01-18-2013, 03:11 AM   #6
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Lots of times it is just better to think of things as fractions. If you wanted to get more precise with it, just change bases. In base 7, one seventh is simply .1. It all depends on how you look at it. Most people don't think of numbers in more than one base.

If you want to get more complicated, that adds up to 28 notes in a bar with 4/4 timing. You could also have a time signature based around 7 if you wanted, but that's a bit much.

You don't need irrational numbers to make sense of numbers.

Also, hexadecimal/binary (base 2 and base 16) is just better for the vast majority of things when compared to decimal (base 10). They don't teach you that in school, but numbers just make more sense if you can think of them with more than just the same old ten digits.

http://en.wikipedia.org/wiki/Hexadecimal

Seriously, this blew my mind when I figured it out and I will never look at numbers the same way again.
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Old 01-18-2013, 05:33 AM   #7
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They are technically unevenly spaced, but the differences in time are imperceptible.
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Old 01-18-2013, 05:39 AM   #8
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If you cut a piece of fabric 70cm long into seven 10cm strips... that's not mathematically impossible. Each piece is just 1/7. It just happens to be that 1/7 of 70cm is a nicely rounded 10cm. If the fabric was 71cm into seven identical strips, each would still be 1/7 of 71cm. It doesn't suddenly become 'mathematically impossible' just because you tried to convert a fraction into a decimal that isn't nicely rounded. If that's what you're concerned about, instead of using beats-per-minute, use beats-per-seventy-seconds.
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Old 01-18-2013, 06:22 AM   #9
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So by your logic a triplet is impossible because 1/3 of a beat is 0.333333333333333... beat. You don't count the decimals in real life. And septuplets aren't really 7 equally long notes (nobody plays them like that because it would sound like a robot and nobody can play it so accurately). People play them like 4+3 or 3+4 or something like that. So the "first part" of the septuplet is counted in four and the "last part" of the septuplet is counted in three (or vice versa).
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Old 01-18-2013, 06:34 AM   #10
Unreal T
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Ok but If you were to compare a 16nth note septuplet against a sixteenth note pattern is this correct?

The 3rd note of the sept. occurs on the e....the 5th note of the septuplet occurs on the and?

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Old 01-18-2013, 09:48 AM   #11
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Humans don't play in time, like ever. Whether it's straight quarter notes or septuplets, if a human is playing it, it's not in time. We just make (sometimes) good approximations.
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Old 01-18-2013, 12:01 PM   #12
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Or, instead of conjecturing about the mathematics of rhythm, you could set your metronome to 60 and play some septuplets.
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Old 01-18-2013, 06:14 PM   #13
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Quote:
Originally Posted by Unreal T
Ok but If you were to compare a 16nth note septuplet against a sixteenth note pattern is this correct?

The 3rd note of the sept. occurs on the e....the 5th note of the septuplet occurs on the and?

No, you would be playing a polyrhythm and only the first note would be on the same beat in both septuplet and four 16th notes. Same thing goes with a triplet. Only the first note is on the same beat.

But you don't really need to divide the bar in four parts. You could divide it in seven parts as well but four sounds better. I mean, listen to a song with 7/4 time signature. It usually sounds pretty strange unless it's very well done. 4/4 just sounds complete.
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