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Why no minor 5ths?

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PsYcHoNIK
(@psychonik)
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this is what deterrs me from learning "theory"...
its all about making no sense ablout a relatively simple concept.

a diminishesd 4th is a 3rd. they are the same tone, they have the same meaning they sound the same they ARE THE SAME IN EVERY ASPECT aside from people who like to make themselves sound smart. we get the point, yes you're all theoretical geniuses, but please DO NOT SAY THAT THE TWO THINGS ARE DIFFERENT IN ANY WAY!!!!! does it even matter what you call them? when does it matter? in what practical application does it mater? in what sense does it matter to a beginner who wont pick it up anyways! it just adds unneccicary jumble to the mix. the two notes are the same, no matter if you call it Fb or E its the same thing there is nothing different about it. it MIGHT be slightly easier to think of it in that context in SOME applications, but it is the SAME THING. if somehow it is not please tell me how because i fail to grasp the concept.


   
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NoteBoat
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You've only got so many 'flavors' of intervals... notes in key will be perfect (unison, fourth, fifth, octave) or major (second, third, sixth, seventh).

Any major interval lowered one half step chromatically will be a minor interval.

After that, any perfect or major interval raised one half step is augmented; raised two steps is doubly-augmented. Any perfect or minor interval lowered one half step is diminished; lowered two steps is doubly-diminished.

Theoretically you could go even farther, but a whole step 'out of key' is the practical limit - usually reached by lowering/raising both notes:

G-C = perfect fourth
Gb-C# = doubly-augmented fourth

G-D = perfect fifth
G#-Db = doubly-diminished fifth

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m07zm4n
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RTB_Chris, yes, I got it completely the other way around...
I meant exactly what you wrote... :)

kingpatzer: thanks, crazy! 8)
I'm still confused...

PsYcHoNIK: AFAIK:
It all boils down to how you determine intervals:

(I take NoteBoat's examples)

G-C = GABC, so it's a fourth, because it goes over four notes. And it's a perfect fourth because it's 5 halfsteps apart.

Gb-C# = GABC, again a fourth, because it goes over four notes. and it's a doubly-augmented fourth because it's seven halfsteps apart.

Now, i really don't know for which cases you'd need doubly-augmented or diminished intervals, but for major, minor, diminished, perfect and augmented, I can see there use in keys.

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um...
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sirN
 sirN
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Now I'm doubly confused

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321Barf
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Now I'm doubly confused

Don't be.The basics are pretty straight-forward.The rare intervals these guys are talking about aren't very common occurrences,they are rare occurrences.It's not worth it to let periferal abstract concepts confuse you or get in the way of the practical,bare-essentials and basics.


   
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321Barf
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n'er mind


   
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PsYcHoNIK
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Gb to C# is not a fourth.. its a fifth. In what application would you call it a fourth? it leads to nothing. its a non functional theoretical device that negates the facts. If i am playing a Gb and a C# on my guitar, i am playing a Gb power chord. Root-5. now if i play a G and a C i am playing fourths. if i move the G to a Gb and the C to a C# i am plaing 5ths once again. I wrote a metal riff in which i do this just to prove to myself that imnot crazy.
please please PLEASE tell me WHY YOU WOULD EVER USE THAT KIND OF NAME! double augmented fourth. you cant say because it would otherwise land it on a non perfet interval... because a 5th is still perfect.
it seems like all this does is confuze people. show me a musical example where it is relevant and i will accept it as a part of musical theory, but if you fail to do so i will continue to rant on why it is not. Does it make something simpler like in a key signature sense?
im again no theory buff.. but i do like to think i have a common sense about what i do know.
if it has something to do with the key signature, is it referred to as that to remind you that your "out of key" as noteboat put it?
I would seriously like someone to explain its practical application because i know i can understand it if it can be applied practically (after al thats what music theory is about... applying your knowledge to help you read/write music) but if not then its pointless and should be avoided.


   
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NoteBoat
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Gb to C# is a fourth. You'd call it a fourth in EVERY application, because that's exactly what it is. It does not 'negate' any facts... and yes, a doubly-augmented fourth sounds exactly like a perfect fifth.

The critical thing in identifying an interval is the space between the note names. Theory has grown up around standard notation (not the guitar, or even the keyboard - music theory preceeds keyboard instruments). If you have notes on the musical staff, fifths are two lines or spaces apart; fourths are smaller than that:

With me so far?

Both of those happen to be perfect intervals. if you make them a half step smaller, by either raising the lower note or lowering the upper note, you get diminished intervals; if you make them a half step larger, by raising the upper note or lowering the bottom note, you get augmented intervals:

These don't look the same, because they are not the same. Oh, they'll sound the same - because F# sounds the same as Gb. They're enharmonic. What you call it depends on which note has been changed - you've either lowered G or you've raised F.

If you continue, and change both notes in opposite directions, you get doubly-augmented or doubly-diminished intervals. These also have enharmonic intervals - here's a doubly-diminished fifth and an augmented third, which are also enharmonic:

You can't possibly look at those two intervals and say they're the same thing. They're not - the first one contains F and C notes, the second one G and B notes... therefore the first will be some type of fifth, and the second some type of third.

If you are playing Gb-C# you do NOT have a perfect fifth - a perfect interval means that each note is in the key of the other. The key of Gb does not have the note C#. If you write it as Db you'll have a perfect fifth - but it's a fifth because you have a D note; with a C note, you get a fourth.

If you tab them out, they'll look the same. Theory is based on music notation; tab is not music notation - it's pitch notation, and has serious limitations (one of them is that you won't be able to understand theory, harmony, arranging, counterpoint, orchestration, musical form, score analysis....)

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kingpatzer
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The critical thing in identifying an interval is the space between the note names. Theory has grown up around standard notation (not the guitar, or even the keyboard - music theory preceeds keyboard instruments). If you have notes on the musical staff, fifths are two lines or spaces apart; fourths are smaller than that:

Ok, so theory doesn't care about what's played, but about what's written?
If that's the case, it clears up a few confussions, but adds a few more . . .l like the question why on earth NOT bother with what actually is?

I believe this stuff is usefull, that's why I'm trying to learn it. But it seems rather odd to me that the "theory" manages to divorce itself from reality. In every other subject I've ever studied the idea of a good theory was to build a model that more and more closely modelled reality. It seems that music theory is hardly concerned with what the notes actually imply in the world of real things.

You can't possibly look at those two intervals and say they're the same thing. They're not - the first one contains F and C notes, the second one G and B notes... therefore the first will be some type of fifth, and the second some type of third.

Here's a prime example. Why can't I say they're the same thing?
Seriously.

I played both notes and recorded the results. I ran them through an FFT transform spectrum analyzer. I compared waveforms, they're the same. I recorded my Son's Sax playing each interval as two seperate whole notes. Again I compared the frequency analysis, they're identical.
I did a short little midi program to run through ever sample in my sequencer, and gues what -- they're all identical.

Now, they are written differently, I understand that. It implies something about what the AUTHOR of the notes was thinking, I understand that too. But to insist that they aren't the same thing when played suggests a perspective so divorced from reality that I can't wrap my head around it.

If you are playing Gb-C# you do NOT have a perfect fifth - a perfect interval means that each note is in the key of the other. The key of Gb does not have the note C#. If you write it as Db you'll have a perfect fifth - but it's a fifth because you have a D note; with a C note, you get a fourth.

If you tab them out, they'll look the same. Theory is based on music notation; tab is not music notation - it's pitch notation, and has serious limitations (one of them is that you won't be able to understand theory, harmony, arranging, counterpoint, orchestration, musical form, score analysis....)

And this confirms what I have been suspecting .. that theory is based entirely on the staff notation and has nothing to do with what is actually played.

Ok, I can handle that . . . but it kind of makes me wonder how much use theory can really have when it divorces itself intentionally from the very thing it's purporting to describe.

"The music business is a cruel and shallow money trench, a long plastic hallway where thieves and pimps run free, and good men die like dogs. There's also a negative side." -- HST


   
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m07zm4n
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What I don't get: Why the big rant at intervals when the whole "problem" might just be that F# = Gb...
That's where everything escalates in my eyes
:?:

NO MORE THEORY!!
um...
KNOW MORE THEORY!!!!

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<------>


   
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NoteBoat
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Well....

Theory started with the sounds; for about the first 1500 years, everything written about music was concerned with the way things sounded, and that was all that mattered. Intervals were identified in terms of their vibrations - 2:1 was an octave, 3:2 was a fifth... things are still looked at in those terms in the field of acoustics.

You can work out the various ratios... perfect fourths are 4:3.

So let's see what happens.... up 3:2 from A=440 gives us E= 660. Down 4:3 from A=880 gives us E=660. So far so good.

But a funny thing happens on the way through in one direction or the other... we get:

A=440
E=660
B=990 (octave at 495)
F# = 742.5
C# = 1113.75 (octave at 556.875)
G# = 835.3125
D# = 1252.96875 (octave at 626.48, roughly)

Now let's go up by fourths from A for the others:

A=440
D=586.67
G=782.22
C=1042.96 (octave at 521.48)
F=695.31
Bb=927.08 (octave at 463.54)

Hold on to your hats, now... we're going to find Eb: 618.05.

Eb is a different note than D#. That's going to be true of ALL the notes - F# is not Gb; C# is not Db, and so on.

This was all fine and dandy when instruments were horns and violins. You want Eb, you play Eb - you want D# instead, you play D#. Try to build a harpischord, though, and you need TWO black keys between each white one, because D# and Eb are different notes.

That's exactly what they did - look at keyboard instruments from the 1500s and you'll find split black keys.

Made it kind of hard to play. They needed a better way.

They eventually decided that the black keys should be one note, that D# and Eb should be the same thing even if it meant the notes would be wrong. That meant taking the octave and dividing it up so the notes would be ROUGHLY in tune - it's called even tempering. The perfect notes we just found for D#=626.48 and Eb=618.05 get replaced by one key roughly splitting the difference - they put it at 622.26.

So you've got it the wrong way round - theory describes the perfect world, and Gb-C# is entirely different from F#-Db... they are four different notes, and the intervals will even sound slightly different. Our instruments are a compromise from the perfect world - it's not theory that's out of whack, its our guitars and pianos. :)

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undercat
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...

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undercat
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So you've got it the wrong way round - theory describes the perfect world, and Gb-C# is entirely different from F#-Db... they are four different notes, and the intervals will even sound slightly different. Our instruments are a compromise from the perfect world - it's not theory that's out of whack, its our guitars and pianos.

While the traditional and scientific value is there, the practical use for a system that doesn't relate to any music created in the last 100 years is suspect at best.

Do modern violin players and horn players learn that C# and Db are different notes? Are they assigned different fingerings on horns?

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kingpatzer
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Bach died in 1750 if I remember my music history class correctly. So really, it's the last 250 years, not the last 100, since Bach pretty much settled the argument over how our instruments should sound with his "Well-Tempered Clavier."

"The music business is a cruel and shallow money trench, a long plastic hallway where thieves and pimps run free, and good men die like dogs. There's also a negative side." -- HST


   
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undercat
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Hmm... this is pretty interesting. Gives weight to both sides of the argument.

http://www.matthewdallman.com/temperament.html

Noteboat, I also wanted to mention that your posts have really made me think today. I've written out a whole bunch of responses, ranging from "You're totally right, now I see the light" all the way to "You're an idiot, pure tuning and standard notation is impractical and antiquated." only to delete them when I got to the end and really thought through the entire idea.

Here's where I am at right now:

Even tempered tuning is practical, useful, and isn't going away any time soon. Theory that doesn't relate to it is going to feel antiquated, it's going to be more difficult to understand since we no longer separate C# and Db in any practical way.

Non-tempered tuning is scientifically, measurably correct, all the overtones add up right, and fundamentally, it's how music should sound. The theory that developed from it is beyond it's prime, but so fundamentally ingrained in the way we understand scales and chords and harmony, that to change it would require a complete overhaul of principles, right down to renaming the notes.

The real disaster then is that we try and understand modern music that's played even-tempered using a system of theory that was designed for something else.

One thing I keep on coming back to is that for most of us, Db is no different than C#, and indeed, they are the same note, there's only one place to play both of them on modern instruments, however, our theory has us using different names for them at different times, and our notation can show them 5 different ways (nat. b, bb, #, ##). Since in tempered tuning C# is no more related to C than it is to D, there's no practical reason to even have it called C#, with all the intervals the same, we might as well call D, "C##".

Anyhow, that's where I am right now. looking forward to many more headache's based on this topic... :wink:

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