question about the "perfect intervals"

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fn86

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im reading a book on musictheory right now, but this is a part that i cant understand, the example uses the major scale.

"Why is a perfect interval so perfect?" It all has to do with frequencies and multiplies of frequencies. When you double a given frequency (going from 440hz to 880hz for example), you create the octave pitch - a perfect interval."

Now this i understand clearly, its kinda logic, but now this is what i can't grip:

"When you double that frequency, you create a pitch a fifth above the octave - another perfect interval. Double that frequency and you get another octave, but double that and you create a pitch a fourth higer than that - the last perfect interval."

i really dont see any logic in that? could some1 pls explain?
 
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fn86 said:
im reading a book on musictheory right now, but this is a part that i cant understand, the example uses the major scale.

"Why is a perfect interval so perfect?" It all has to do with frequencies and multiplies of frequencies. When you double a given frequency (going from 440hz to 880hz for example), you create the octave pitch - a perfect interval."

Now this i understand clearly, its kinda logic, but now this is what i can't grip:

"When you double that frequency, you create a pitch a fifth above the octave - another perfect interval. Double that frequency and you get another octave, but double that and you create a pitch a fourth higer than that - the last perfect interval."

i really dont see any logic in that? could some1 pls explain?
Click to expand...

Inverted perfect intervals retain their "perfection." (wish I could say that better!)

Remember that this is coming from the Western harmony ideas.

http://en.wikipedia.org/wiki/Interval_(music)
 
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i didint understand **** about what you just said, im on chapter 2 in the book and this is the topic covered in that chapter, so i wish you could explain it in a better way, i understand the logic of an octave step having double the frequency compared to the root of it, but thats where my logic stops to work :)
 
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Akridrot said:
They are called 'perfect' because they have "extremely simple relationships between them resulting in high consonance[pleasure to your ears]". They are the most easiest, pleasing distances between notes in [Western] Music Theory to many people, I suppose.

http://en.wikipedia.org/wiki/Perfect_fifth
http://en.wikipedia.org/wiki/Consonance_and_dissonance
Click to expand...

sure man that also makes sense, but i still havent got the answer to the logic behind it all:

"When you double that frequency, you create a pitch a fifth above the octave - another perfect interval. Double that frequency and you get another octave, but double that and you create a pitch a fourth higer than that - the last perfect interval."
 
Hey man, I think the book means that if you halve the frequency, and then add that on to the original frequency, you get to a perfect fifth. So like, if we have A=440Hz, and A2=880Hz, we can work out the "E" (7 half-tones up from A440, otherwise known as a perfect fifth), as
440 * 2^(7/12) = 660Hz. (440/2 + 440) gives us the same.
 
thanks man, that's the most logical answer ive gotten yet, but is it possible to explain it withouth so much math? i mean music theory should be logic and not a lot of math and such
 
fn86 said:
thanks man, that's the most logical answer ive gotten yet, but is it possible to explain it withouth so much math? i mean music theory should be logic and not a lot of math and such
Click to expand...

You just contradicted yourself. Music is all about math - acoustics, waves, etc. Loads and loads of it. Scientific explanations.

It also has the artistic, aesthetic aspects.
 
ok, well let me rephrase my question with this explanation that also belongs to the specific explanation:

"when you describe intervalls by degree, you still have to deal with those pitches that fall above or below the basic notes - the sharps and flats, or the black keys on a keyboard."

"when meauring by degrees, you see that the second, third, sixth and seventh notes can be easily flattened. When you flatten one of these notes, you create what is called a minor interval. The natural state of these intervals (in a major scale) is called a major."

along with this text this kind of picture is inserted:

treblestaff2keyboard.gif


now my question is, how the HELL can i see that the second, third, sixth and seventh notes can be easily flattened? what makes them difference from the first, fourth, fiftth and octave note? i wold think that every note that has a "black"-key before it is the ones that could be easinly flatten, but that is not the case, now i am on chapter 2 in this book, and this is the topic, so please dont tell me to go and read up on my musictheory, cause i AM doing that.
 
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fn86 said:
ok, well let me rephrase my question with this explanation that also belongs to the specific explanation:

"when you describe intervalls by degree, you still have to deal with those pitches that fall above or below the basic notes - the sharps and flats, or the black keys on a keyboard."

"when meauring by degrees, you see that the second, third, sixth and seventh notes can be easily flattened. When you flatten one of these notes, you create what is called a minor interval. The natural state of these intervals (in a major scale) is called a major."

along with this text this kind of picture is inserted:

treblestaff2keyboard.gif


now my question is, how the HELL can i see that the second, third, sixth and seventh notes can be easily flattened? what makes them difference from the first, fourth, fiftth and octave note? i wold think that every note that has a "black"-key before it is the ones that could be easinly flatten, but that is not the case, now i am on chapter 2 in this book, and this is the topic, so please dont tell me to go and read up on my musictheory, cause i AM doing that.
Click to expand...

I see what confused you: your text is not very well written.

In reference to the link I posted, the first intervals "recognized" in Western music theory/harmony were the octave, the perfect fifth, and the perfect fourth.

These are not messed with when talking about making an interval minor. So the only ones available for that are the second, third, sixth, and seventh.

You can only "diminish" the perfect quality of a perfect interval.
 
MadTiger3000 said:
You can only "diminish" the perfect quality of a perfect interval.
Click to expand...

what exactly do you mean by diminish?

your answer was kinda straight up and im understanding it, but still i would apreciate it if you could do it along with the mathematical explanation why they are "perfect", cause i i really wanna understand it like the answer the tell in the book that i'vre wrote in the first message in this thread
 
Hey man, I'm not too good on the physics of music, but, presumably a fifth is called a perfect fifth, because the frequency it oscillates at is complementary to the oscillations of the tonic. ie, 440, 660, 880, these will all sound "complete" and "perfect" when played together because they vibrate similarly (you can see the ratio between them is 1:1.5). I imagine if you drew these out as wave forms, you'd be able to see it visually. I can't say I understand this stuff well, and tbh I've never really thought about why something sounds good, just accepted it I guess.

The maths behind it comes from the fact that all the frequencies are derived from equal temperament tuning. The formula I used simply shows how to find the frequency of any note, given a root note, and how many half steps above, or below the unknown note is.
Unknown Freq = Known Frequency * 2^(#half steps/12)

If the note is below the known note, then the number of half steps will be negative, leading to a negative fraction. Conversely it'll be positive if it's above the known note. Funnily enough, this method of tuning is actually slightly imperfect, if you do the maths you'll find it's like A=440, E=659.1 or something. I got most of this info from here :

http://www.physlink.com/education/askexperts/ae165.cfm

I can't really explain what that book is on about, lol, sounds confusing as hell. If you're just starting to learn music theory, I don't think it's essential for you to understand all the whys and wherefores of all the concepts presented. An understanding of the different threads will develop as your knowledge of the whole picture grows.

But there are plenty of good internet sites on music theory, here are some that I've personally found quite useful. If you find you don't understand something, it's good to check a variety of sources, more often than not, someone will explain it in a way that'll be easier for you to understad.

www.musictheory.net (downloadable resource)
http://www.dolmetsch.com/theoryintro.htm (quite comprehensive)
www.chordmaps.com (explanations are good here)
www.petethomas.co.uk (check the jazz section -personal fav of mine)

Needless to say, absorbing some or all of the music theory on those four sites will probably suffice as a very, very solid foundation.

Hope this helps.
 
all I know is that two notes an octave apart have a frequency ratio of 2:1, this means one is twice the frequency of the other. This means your book is wrong, an interval of a fifth has a frequency ratio of 3:2 and a fourth interval gives a frquency ratio of 2:3. The intervals of a fourth and fifth have an inverse relationship - together they make an octave.
If you double a notes' frequency you get an octave, if you double it again you get another octave.

sorry, that's wrong, a fourth has a ratio of 3:4.
I do have a book that explains this very simply but it's not at hand right now - I will dig it out 2morrow
 
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