#1
I learned my "basic" theory from the crusade articles here on UG. What they told me about intervals is that there are:
Unison
min/maj 2
min/maj 3
perf 4
perf 5
min/maj 6
min/maj 7

So if I were to say okay.. what is the interval between C and G#..
I would have said minor sixth.

So I saw that Piston's Harmony was recommended as a really detailed music theory book, so I'm in the process of going through it.

In the very first chapter it says:
a. interval half step smaller than major interval = minor
b. interval half step larger than major/perfect = augmented
c. interval half step lower than minor/perfect = diminished

And then it says.. If the lower note is preceded by a sharp/flat, the interval can be analyzed without the sharp/flat, and then compared to the original with the above rules.

1 So then it gives an example of Eb to C#. In Eb major C is the major sixth, so going a half step above that follows rule b. above.. this makes sense.

2 Then it gives another example of comparing D# to C. The example takes the # off the D, and says that C is a half tone below the 7th of D major. So adding the # back to D makes the interval another half step smaller.. making it a diminished seventh.

My question:

How come in the first example, the sharp is taken off the higher note (C#) and on the second example the # is taken off the lower note?
#2
What page(s) specifically in the Piston? I'll get out my copy and see if I can help you.
#3
I don't understand. Changing the root note from D# to D changes everything. They were just showing that DMaj is easier to analyze than D#Maj?
#4
Oh, I found it, pp. 8-9. He's just giving you tools to determine an interval that has an accidental. You can look at first as if it had no accidental, then account for the accidental and adjust the interval one semitone. It's just a beginner tool.
#5
Page five in Piston's.

The example says using D# major has nine sharps so that using D major would be easier.
D# to C.. D major is D E F# G A B C# D.
C is said to be a half step lower than the seventh.. so it's a minor seventh away from D.
Sharping the D makes the interval a half step smaller, making a diminished seventh.

I just don't get why the sharp is taken off the second note in the first example and then on the first note in the second example :S.
#6
We must have different editions (mine's the 5th). He's just showing you how to approach it from either way - the high note or the low note in the interval.
#7
Quote by ibz120
So if I were to say okay.. what is the interval between C and G#..
I would have said minor sixth.


then you would have been wrong. it's an augmented fifth.

Quote by ibz120
So I saw that Piston's Harmony was recommended as a really detailed music theory book, so I'm in the process of going through it.

In the very first chapter it says:
a. interval half step smaller than major interval = minor
b. interval half step larger than major/perfect = augmented
c. interval half step lower than minor/perfect = diminished

And then it says.. If the lower note is preceded by a sharp/flat, the interval can be analyzed without the sharp/flat, and then compared to the original with the above rules.

1 So then it gives an example of Eb to C#. In Eb major C is the major sixth, so going a half step above that follows rule b. above.. this makes sense.

2 Then it gives another example of comparing D# to C. The example takes the # off the D, and says that C is a half tone below the 7th of D major. So adding the # back to D makes the interval another half step smaller.. making it a diminished seventh.

My question:

How come in the first example, the sharp is taken off the higher note (C#) and on the second example the # is taken off the lower note?


he's just showing you how it can be approached from either end.

in my opinion, however, this is absolutely ridiculous. you're far better off being functional and knowing that D# to C is a diminished 7th, rather than relying on tricks like altering the notes.

if anything, just see it as Eb to C (M6). if the Eb changes to D#, it has to be some kind of seventh, since a D to a C will never be a sixth. since you know that a major sixth is enharmonic to a diminished seventh...well, you see where i'm going.

let's be honest, though, encountering written music involving a D# and a C natural in a melody or a chord is comparatively rare. unless you're just hacking away randomly at E harmonic minor.
Anfangen ist leicht, Beharren eine Kunst.
#8
Quote by AeolianWolf
then you would have been wrong. it's an augmented fifth.


Yeh, strictly speaking C->G# is an augmented fifth, C->Ab is the flat sixth. Because G is the fifth of C, and A is the sixth...

At the end of the day, it's the same interval will sound the same whatever you call it.

Steve
#9
Quote by StevePigott
Yeh, strictly speaking C->G# is an augmented fifth, C->Ab is the flat sixth. Because G is the fifth of C, and A is the sixth...

At the end of the day, it's the same interval will sound the same whatever you call it.

Steve


strictly nothing. it's an augmented fifth, strictly speaking or regularly speaking.

the issue is not about sound. it's about function.
Anfangen ist leicht, Beharren eine Kunst.
#10
Quote by AeolianWolf
strictly nothing. it's an augmented fifth, strictly speaking or regularly speaking.

the issue is not about sound. it's about function.


Dude, I was agreeing with you
#11
Quote by StevePigott
Dude, I was agreeing with you


oh, i know. but i still pick fights.
Anfangen ist leicht, Beharren eine Kunst.
#13
Quote by StevePigott
*sharpens plectrum menacingly*


i c wut u did thar
Anfangen ist leicht, Beharren eine Kunst.