#1

I want to know how many times I would have to stack perfect 5th intervals before I ended up with a note that is an octave of the root note. I would assume it would look something like this:

(3/2)^x = 2^y

That should say perfect fifth interval being stacked x amount of times equals an octave y amount of octaves above the root, does it not? If it doesnt, can you help me out?

This questions stems out of my curiosity of equal temperament tuning. The formula for that is (12root2)^12 = 2. Which says if you add 12 12 root 2/s of an octave you get an octave.

(3/2)^x = 2^y

That should say perfect fifth interval being stacked x amount of times equals an octave y amount of octaves above the root, does it not? If it doesnt, can you help me out?

This questions stems out of my curiosity of equal temperament tuning. The formula for that is (12root2)^12 = 2. Which says if you add 12 12 root 2/s of an octave you get an octave.

#2

C > G > D > A > E > B > F# > C# > G# > D# > A# > E# (F) > B# (C)

12 times

12 times

#3

That wasnt what I was asking.

I think it looks something like this:

(3/2)^x = 2^y

log base 2 ((3/2)^x) = y

(3/2)^x = 2^[(3/2)^x]

Idk how to solve for x at this point. But I assume that there is an answer.

I think it looks something like this:

(3/2)^x = 2^y

log base 2 ((3/2)^x) = y

(3/2)^x = 2^[(3/2)^x]

Idk how to solve for x at this point. But I assume that there is an answer.

#4

If we round a fifth off to 701.55, it would take 140391 octaves. But since that's rounded the real number would be far higher. I don't see what practical application this can serve anyone though.

#5

The perfect root is a square note of 5 so 7 by the power of 12 times the number of chords rounded to the number of octaves is equal to the variant of the equator photosynthesis.

#6

Here's the proper answer.

#7

Use Fibbanarchi's ratio and the natural log of sine ( 90 ) ^2 to solve for tan (Pi) and then use the rule of least squares to determine the coefficient between those two values, in radeons of course.

#8

Set it all on fire and bask in it's cathartic glory.

#9

If we round a fifth off to 701.55, it would take 140391 octaves. But since that's rounded the real number would be far higher. I don't see what practical application this can serve anyone though.

Do I ever have practical applications? Sometimes I just need to know things... How did you reach that answer and where did you get 701.55from?

#10

701.55 is the resonant frequency of a perfect fifth, duh.

#11

701.955 is the approximate value of a perfect fifth in cents. How do you not know that if you are asking this question? The rest is basic arithmetic that anyone else could figure out if they weren't too busy smoking their algebra textbook.

*Last edited by theogonia777 at May 12, 2016,*

#12

I'm starting to think my question is flawed... I'm just really confused right now. Why 12 notes? Why not any other number? If 12 root 2 to the 12th power is 2, we could have used any other number. There are an infinite amount of notes, using 12 bothers me.

in reality, it should be infinity root 2 to the infinity power = 2, which makes sense. Infinite amount of subdivisions, but what if I only want the first? Then use that as the new starting spot and do it again and again. I am aware of the pythagorean comma, which is when you do it 12 times you get almost 7 octaves above, but its slightly off.

in reality, it should be infinity root 2 to the infinity power = 2, which makes sense. Infinite amount of subdivisions, but what if I only want the first? Then use that as the new starting spot and do it again and again. I am aware of the pythagorean comma, which is when you do it 12 times you get almost 7 octaves above, but its slightly off.

*Last edited by jrcsgtpeppers at May 12, 2016,*

#13

Why don't you write your own music theory then if it bothers you so much

#14

You dont understand why it bothers me. The sound of just intonation is amazing and I feel like I am dirty when I listen to music that is equal tempered. I feel like the notes we use arent real, theyre just subjective approximations of real notes. I want to play only real notes. I want an instrument that lets me hit the few few harmonics of a note, n, then the first few harmonics of those first few harmonics, and the first few harmonics of those first few harmonics. Is that too much to ask?

If you were just able to map out the first few harmonics of the first few harmonics and write down the hertz, you could make a guitar fretboard that has those real notes marked off with frets and you could play 1-3-5 chords and they would all be in tune.

If you were just able to map out the first few harmonics of the first few harmonics and write down the hertz, you could make a guitar fretboard that has those real notes marked off with frets and you could play 1-3-5 chords and they would all be in tune.

*Last edited by jrcsgtpeppers at May 12, 2016,*

#15

imagine being this much of a jackass lmao

#16

You're quite helpful.

#17

go learn violin or something then

#18

Here's the proper answer.

I knew that was coming, and then it came, and then I chuckled.

#19

Pfft equal temperament pleb

Vallotti Well temperament/5 and 7 temperament or gtfo

Vallotti Well temperament/5 and 7 temperament or gtfo

nah, I applaud your quest, especially as a piano tuner

#20

You're never going to find a whole number excluding 0, which is a trivial case.

#RealAnalysis101

#RealAnalysis101

#21

#22

Also, twelfth root of 2, or (2)^(1/12). 12 root 2 is almost 17.

#23

Illuminati confirmed.

#24

4/5 joke etc

#25

i think we should blow smoke at the wind sails

#26

I feel like the notes we use arent real, theyre just subjective approximations of real notes.

if it makes you feel better, this is 100% true

I want to play only real notes [...] Is that too much to ask?

yeah

#27

dude what do i look like, some kinda nerd?

#28

dude what do i look like, some kinda nerd?

yeah

#29

You know what... I think my question is initially flawed. What I really want to know is this:

If you play taps on a trumpet, you are hitting open harmonics. the 5 to the 1, 5 1 major 3. Those arent equal tempered intervals, those are real just intervals. So, if you go to the 5 and play taps again using the 5 as the 1, then again and again, how many times would you have to do this before it synched back up and was a perfect octave of the original root note? Or would it never synch back up and would it go on tapping forever?

If you play taps on a trumpet, you are hitting open harmonics. the 5 to the 1, 5 1 major 3. Those arent equal tempered intervals, those are real just intervals. So, if you go to the 5 and play taps again using the 5 as the 1, then again and again, how many times would you have to do this before it synched back up and was a perfect octave of the original root note? Or would it never synch back up and would it go on tapping forever?

#31

You know what... I think my question is initially flawed. What I really want to know is this:

If you play taps on a trumpet, you are hitting open harmonics. the 5 to the 1, 5 1 major 3. Those arent equal tempered intervals, those are real just intervals. So, if you go to the 5 and play taps again using the 5 as the 1, then again and again, how many times would you have to do this before it synched back up and was a perfect octave of the original root note? Or would it never synch back up and would it go on tapping forever?

My money's on forever

However what do you mean they aren't equal tempered intervals?

#32

I feel like the notes we use arent real, theyre just subjective approximations of real notes. I want to play only real notes.

*you need help with music metaphysics.*

*fucking classic.*

#33

My answer still stands:

Everything is tempered.

You're never going to find a whole number excluding 0, which is a trivial case.

#RealAnalysis101

Everything is tempered.

#34

My money's on forever

However what do you mean they aren't equal tempered intervals?

Well. on the piano or guitar, a 5th is off by a few cents. On the trumpet, that open 5th harmonic is a pure harmonic, being exactly 3/2;;s in ratio. You cant tune a piano with all pure harmonics because it becomes offset, which is why we use 12 notes blah blahblah blah blah, the point is, I watched this video

https://www.youtube.com/watch?v=1Hqm0dYKUx4

at 2:50 he says (a/b)^n cant equal 2

#35

*you can't tune a piano but you can tuna fish*

#36

you can't tune a piano but you can tuna fish

Time flies like an arrow, but fruit flies like a banana.

#37

are you going to be using the results of this to make dub music or step music?

#38

Not really. I just like learning about this stuff. The dub music I've been making has been focused on the golden ratio and complex beats and time signatures. Like taking a measure of 21/32 and dividing it into the fibonacci sequence:

21

8 - 13

3 - 5 - 5 -8

1 - 2 - 2 - 3 - 2 - 3 - 3 - 5

Then using that as a stencil for a beat or rhythm idea. Then after I write a chord progression that loosely follows that, I will do something like keep the chords playing but change the drums to 3 sets of 7 or 7 sets of 3 and superimpose that.

Sometimes when I divide the partitions I will go back n fourth. 8 = 3 + 5, or 5 + 3, and you can do it both ways at the same time.

With this whole just intonation thing, I am just looking for harmony ideas. I know bach was aware of how well in tune his notes were and tried to make melodies consist of the basic building blocks to keep it pure. AKA a well tempered clavier.

edit:

with the fibonacci subdivision thing, you kind of have to stop once you hit a 1, because you cant divide any further, but what i might do is poke out all the 1's and just keep going like this:

1 - 2 - 2 - 3 - 2 - 3 - 3 - 5

|0| 1 - 1 | 1 - 1 | 1 - 2 | 1 - 1 | 1 - 2 | 1 - 2 | 2 - 3 |

that way it gives those little metal core stops. It works better when you use 34, because 34 naturally subdivides into more 1's that poke out nicely. Every other fibonacci number works like that.

21

8 - 13

3 - 5 - 5 -8

1 - 2 - 2 - 3 - 2 - 3 - 3 - 5

Then using that as a stencil for a beat or rhythm idea. Then after I write a chord progression that loosely follows that, I will do something like keep the chords playing but change the drums to 3 sets of 7 or 7 sets of 3 and superimpose that.

Sometimes when I divide the partitions I will go back n fourth. 8 = 3 + 5, or 5 + 3, and you can do it both ways at the same time.

With this whole just intonation thing, I am just looking for harmony ideas. I know bach was aware of how well in tune his notes were and tried to make melodies consist of the basic building blocks to keep it pure. AKA a well tempered clavier.

edit:

with the fibonacci subdivision thing, you kind of have to stop once you hit a 1, because you cant divide any further, but what i might do is poke out all the 1's and just keep going like this:

1 - 2 - 2 - 3 - 2 - 3 - 3 - 5

|0| 1 - 1 | 1 - 1 | 1 - 2 | 1 - 1 | 1 - 2 | 1 - 2 | 2 - 3 |

that way it gives those little metal core stops. It works better when you use 34, because 34 naturally subdivides into more 1's that poke out nicely. Every other fibonacci number works like that.

*Last edited by jrcsgtpeppers at May 12, 2016,*

#39

They are all "off" compared to natural harmonics, but theyWell. on the piano or guitar, a 5th is off by a few cents. On the trumpet, that open 5th harmonic is a pure harmonic, being exactly 3/2;;s in ratio. You cant tune a piano with all pure harmonics because it becomes offset, which is why we use 12 notes blah blahblah blah blah, the point is, I watched this video

(VIDEO)

at 2:50 he says (a/b)^n cant equal 2

__are__equally tempered - adjusted so that the exponential ratio is pretty much the same. (there are a few offsets on piano tuning for other considerations, I believe, but overall, the modern system conforms roughly to 12ET.)

I've told you twice, and I'll tell you a third time because you've ignored it, he's right, and asking for perfect music sounds like a good pipe dream.

Octaves and perfect fifths proof:

(3/2)^n = 2^m

3^n=2^k (k=m+n, but k can be anything, just like m and n)

3 is

**odd**. Odd numbers, when multiplied by other odd numbers, make odd numbers.

2 is

**even**. Even numbers, when multiplied by other numbers, make even numbers.

Suppose the two sides are equal for some non-zero counting numbers n and k.

Let 3^n = 2a-1 for some counting number a. 2a-1 is odd by definition.

Let 2^k = 2b for some counting number b. 2b is even by definition.

2a-1 = 2b

2a = 2b + 1

a = b + 1/2

The distance between any counting number is another counting number. But this says that a and b are 1/2 apart, which is a contradiction.

--> the two sides cannot be equal for any counting numbers n and k. QED.

#40

They are all "off" compared to natural harmonics, but theyareequally tempered - adjusted so that the exponential ratio is pretty much the same. (there are a few offsets on piano tuning for other considerations, I believe, but overall, the modern system conforms roughly to 12ET.)

I've told you twice, and I'll tell you a third time because you've ignored it, he's right, and asking for perfect music sounds like a good pipe dream.

Octaves and perfect fifths proof:

(3/2)^n = 2^m

3^n=2^k (k=m+n, but k can be anything, just like m and n)

3 isodd. Odd numbers, when multiplied by other odd numbers, make odd numbers.

2 iseven. Even numbers, when multiplied by other numbers, make even numbers.

Suppose the two sides are equal for some non-zero counting numbers n and k.

Let 3^n = 2a-1 for some counting number a. 2a-1 is odd by definition.

Let 2^k = 2b for some counting number b. 2b is even by definition.

2a-1 = 2b

2a = 2b + 1

a = b + 1/2

The distance between any counting number is another counting number. But this says that a and b are 1/2 apart, which is a contradiction.

--> the two sides cannot be equal for any counting numbers n and k. QED.

that kinda sounds like my proof the magic square is impossible. thanks