5/5 timing..."it doesn't exist"...wait...or does it?

1/4-1/5=x
(15)/(45)-(14)/(54)=x
5/20-4/20=1/20

so, 1/20th should be added to a 1/5 to make a 1/4 note.

lets try to do that up by adding a 1/32 note with a dot.
1/32*3/2=3/64
1/20-3/64=1/320
so we are very very close…

But it seems obvious the conversion is not easy. Probably impossible since both 2 and 5 are primes so their powers never converge. (there might coincidentally be some note that with a dot and a correct number of it enables conversion)

To a mathematician the reason notes in fractions of two are popular is obvious. That way you get the most different lengths in the most intuitive way. Let’s consider the 1/5 note. It’s one fifth of a 1/1 note, of which one fifth is 1/25. So on to 1/125 and then 625 and on to 3125.

With fractions of two, you go 1/1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128, 1/256, 1/512… the numbers remain useable for a long time. If you want to halve any one of these, it’s no problem. From 1/256 you get 1/512 and so on.

Try halving 1/125! You get 1/250. How do you represent that in this system? That’s the same as 1/((5^3)*2). You’re mixing different primes into the system by doing something as simple as halving! It gets muddled very quickly. In the “fractions of two”-system, every note is representable as 1/(2^x) (sometimes with an added *1.5).

However, I’m beginning to see the value of dividing it into fifths… it’s a very different way of seeing music and I can hear the point your going to make that halving is not an intuitive thing to do in this system, but rather dividing it somehow in fractions of 5. This is surely a fun thing to explore. However, there’s a very easy way to accomplish this in the conventional system called tuplets! They also work for thirds and even sevenths: en.wikipedia.org/wiki/Tuplet

So, we can keep the good sides of both systems and do away with the annoying math just by using tuplets. That’s my solution anyway. What do you think?

This might also be of interest: vai.com/LittleBlackDots/tempomental.html

Yeah, Yorick - the reason we use tuplets is that it’s easier than not using them. Part of that is convention, but part of it is that the fewer symbols we use, the easier they are to use.

Not to downplay the obvious musicological import of Stumpy’s suggestion.

But musical notation is full of “cheats”. There are many instances where a meter (and therefore the figures used) can be written more than one way. The simplest way is usually chosen.

But you know, Stumpy - follow your dream.

OK…I redid my math and got it fixed.
I just needed to remove the right amount…and needed to double check to make sure it was making sense.

But here’s the conversion of how much time a 5/5 version of a note takes in relation to how much time a 4/4 note(s) take.

So, for instance, writing a 5th note in 5/5 is like writing an eighth note and a sixteenth note down and tying them together.

(as to the tuplets…close, but many times, those are treated as slurs by many, many people…as well…it’s a messy way to write. It would be far easier to write 5/5 and know the timing of notes inherently.)

5-5 duration conversion.jpg

Oh…and I could still be wrong so I’m going to go back over this some more again later to make sure the half and whole are correct…quarter and below, I’m pretty sure on.

As far as the duration tree…I’m not really sure that form of presentation will end up being an effective way to convey the translation as it doesn’t break down AND convert cleanly.
The 5/5’s break down to each other relatively close to how things break down in that tree above…but not quite…
But it has no bearing on how much time that would be in a 4/4 format…

In short…I’ll get around to a re-do on the tree later.

There’s just no way to convert these…I’ve realized the above conversion is close, but it’s still slightly off…short a fraction of time.

For instance the quarter being made of an eighth and a sixteenth is actually still 1/16th short, which would mean that I would have to go figure out how to shove another 16th into the equation, which would mean tearing apart probably something like 64th or smaller notes to find it…and that’s if I could.

I’m thinking at this point, that there really is no such thing as a conversion.
The timing, sure, it exists, but a conversion…I’m really doubting that.

On a related note…what would relatively come close to the concept, but not really, is just doing 5/4 and telling a whole note to hold an extra quarter, and a half note to hold an extra eighth.
It wouldn’t be a true 5/5, but it would get rid of the annoying 5/4 with whole notes only equaling 4 beats issue.

Or you could just forget about conversion altogether and come up with a new set of symbols for 1/5 notes. Like using triangles or squares instead of circles on the notes. That would be easy and intuitive.

I had a look into it and figured a workable system. Check it out.
fifths.jpg

Beautiful; simply beautiful.

My problem is playing it; that’s why I have been hell-bent on a conversion; translating how long 2/5ths of 5 beats is in what normally would contain 4 beats.

It’s very difficult to get the mind to do.

I think I can train my mind around it if I toy with tempo’s (shoving some faster tempos in calculation to what would normally be slower tempos).

Are those somewhat akin to arpeggios?

What are you referring to by, “those”?

Sorry, never mind. I was thinking of something else.

I think I’ve got a way to translate HOW fast a 1/5 note is…which is REALLY difficult since it’s supposed to take place in the same amount of time as 4 beats, and it can be hard to figure out exactly how fast that is and isn’t.

But…I realized that the trick isn’t in a note conversion, but a tempo conversion.

4/4 Tempo name 5/5 Equivalent 4/4 Tempo name 48 Largo 63 Larghetto 60 Larghetto 79 Adagio 72 Adagio 94 Andante 76 Andante 100 Andante 112 Moderato 148 Allegro 138 Allegro 182 Presto 184 Presto 242 Prestissimo 208 Prestissimo 274 Prestissimo

Loosely, the formula is that a 5 fifth notes are 31.57% faster than a 4 quarter notes, so you increase your tempo of whatever you would have it as by 31.57% and you have your 5th notes timing.

Example, if I want to write a piece in Andante 76bpm, then I would write my 5th note version of this in 100bpm.

But you can’t just write 100bpm on the score, because if you wrote 100bpm on the score and wrote it in 5th notes, you would be calling for the notes to played at a tempo around 131-132 bpm since normally, 100 bpm serves 4 beats and not (truly) five.

The way I determined this was simple.

I flipped on a metronome, grabbed a stop watch, counted how long it took for the metronome to hit four beats.
Then I just sped the metronome up until it was doing 5 beats in the same amount of time the previous four beats were accomplished.

That tells me how fast I would play a fifth note.

Kind of screwy, but it’s what it is.

What’s funny about what I just wrote is that I just realized that…in a way…people might have already been playing 5th notes and not realized it.

Since…essentially, if you take 5/4 timing and write your whole notes with a tie to an extra quarter note, and likewise a half note to an extra eighth note, and put it on a speed of moderato when you know for a fact that you want andante, then you have successfully accomplished the same thing as a 5/5 timing structure.

Kind of funny really.

aaaaand another post.

Here I show how 3/4 is converted to 3/5 timing (yes…the mythical non-existent timing of 3/5).

The first is what it would be in 3/5 pure, (pretend those are the 5th note versions that Yorick drew).
The second is what you would normally have in 3/4 at the same tempo.
And the third shows that 3/4 in 100bpm is the same as 3/5 at 76bpm.

Oh…and one last thing…actually looking at things…you don’t even need new notes (eventhough I like Yorick’s notes for clarity’s sake).

Here’s why…

If you write 5/5, then the only mental things that shift are the following:
A whole note now equals 5 “quarter” notes instead of 4.
A half note now equals 2 “quarter” notes and an “eighth” note.
Whatever tempo is listed, it’s actually played roughly 31% faster.

Everything else stays the same.
Why?

Because you are playing 31% faster, which automatically causes the 5th to take place.

When you see, 4/5 as the timing signature, you know that instead of 76bpm listed, you play this at 100bpm and hold the whole notes for 5 quarters and the half for 2 quarters and an eighth.
Which means when you write down a whole note, it will carry for one and a quarter measure.
When you write a half note it will carry for 2 quarters and an eighth of the measure.

So you can’t place a half note and two quarters in 4/5 timing.
You can place a half note, a quarter note, and an eighth note and keep in mind that it will travel at 100bpm instead of 76bpm.

It’s all so terribly simple when looked at this way.

And it doesn’t take any funky conversion for every note in the system…only the whole, the half, and the tempo.

Man…this is better than I had expected!

(edit…now the only thing that’s needed is a notation like a dot, but that represents a quarter of a note’s value added to the notes value…otherwise you end up writing whole+quarter with a tie, and half note + eighth with a tie…unfortunately, there isn’t a notation for doing this…yet)

(edit#2…staccato a dot but not the note? lol…boy…I’m sure that would confuse the heck of people, lol)

Here’s my solution…

Leaving notes just as they are (including half equaling two beats and whole equaling 4)
Adding one simple little concept into music…one quarter value extension…instead of half value extension.
one quarter extension addition.jpg
Mix this with what we know about tempo already, and we can write things in 5/5 just fine by using just regular old X/4 formats.

We can trick the system.
We just keep in mind that if we want someone to play 76bpm 2/5, 3/5, 4/5, or 5/5 then we need to switch our tempo up to 100bpm and write with the additional options of the new one quarter value extension slash mark.

Same goes for 5/4.
We can make it 5/4 and just make our tempo 31% faster, than it would be in 5/4 “normally” and then make our slashes to make whole notes hold for a full measure, and half notes hold for half of the measure.

Also fun though, is that we can now mix things up a bit by having a hold of 1/2 followed by 5/8, and followed by 1/8 all in one measure…

Who cares where the measure bars fall…honestly…in some cases, carry’s will happen, but that’s normal for music anyways…so this is a win/win in my mind.

No?

Win/win indeed! There’s no need to change the system entirely. The notation is just for communicating what you have in your head anyway. Your new quarter-length-addition-symbol augments the system enough.

The problem still is learning to play these notes.

One slash is enough for what you need but you can do all kinds of things with this:
o/ (full note with one quarter added 4/4+1/4) =5/4
o// (full note with one quarter and one quarter of one quarter added 4/4+1/4+1/16) =1 5/16
o///(full note with one quarter and one quarter of one quarter and one quarter of one quarter of one quarter added 4/4+1/4+1/16+1/64) =1 21/64

further experimentation:
o///.=1 127/128
o././=3 33/64
Interestingly, o./=o/.
o./ (4/4+1/2)(5/4)= 1 7/8
o/. (4/4+1/4)
(3/2)= 1 7/8

That’s like the black whole of music, lol…endlessly nightmarish!

Great work expanding on the idea there!

You are both quite insane, you know.

:banana-dance:

I have at this point, plastered this concept up on a google site.

sites.google.com/site/55timing/home

Yorick, if you are still around at some point, I have a special thanks to you for all of your help in this project.
I’m also, at some point, going to place your notation system up as an alternative method of notating X/5 timing as I think it’s a fantastic approach if someone doesn’t mind completely learning a new notation system outright.

But I would rather wait until I have your consent to do that.