Naming of Intervals

HI guys. I'm having some trouble understanding the naming of intervals. But I know you smart guys will be able to help. :D

Well, smart a$$ is a kind of smart .. let me see what I can do :)
I'm reading Music Theory for Dummies (MT4D), and it describes the naming of intervals in terms of Quantity and Quality and the musical stave as follows: The Quantity (unison, second, third, etc.) is the number of lines and spaces between two notes, including the lines or spaces on which the notes occur. 1 lines/space = unison, 2 = second, etc. So from G to F is one line and one space (or two lines/spaces), and thus a second.

That's correct.

The other way to look at it, apart from the staves is just the distance between the names. A to B for example, count A as "one" and B as "two" so you have some quality of a second with an A note and a B note (provided they're in the same octive range. If they're an octave apart you have some type of 9th as A to A is 8 and then B is 9.)
If I'm understanding it correctly, the occurence of accidentals is irrelevant to the Quantity. In other words, Fb to G# (4 semitones) is as much a second as is B to C (one semitone) or Bb to C (two) or Bb to C# (three).

Correct!
The Quality is the number of halfsteps / semitones between the notes, and can be dim -> m -> M -> Aug, although not all combinations are valid (i.e. no diminished unison).

Correct on the first part, but not so much on the second.

There are combinations that aren't valid. There are no minor or major perfect intervals (unisons, fourths, fifths and octaves), but there are diminished and augmented perfect intervals. Moreover there are intervals that this book doesn't cover, doubly diminished and doubly augmented, which are quite rare and the book can be forgiven for skipping them.
But I've also seen intervals described (as on this site) purely in terms of the number of (semi) tones...0 = unison, 1 = minor second, 2 = major second. (For example, on this site, there's https://www.guitarnoise.com/lessons/hands-on-intervals/ ). But then what happened to augmented first, which MT4D swears exists? And does that mean that Ab to A# (2 semitones) is a minor second?

Talking about intervals in terms of merely the number of semi-tones is an over-simplification that leads to errors.

The interval of B - Cb is a diminished second. It is NOT a unison.

This is one reason why reading music is important, you can discover insights into the compossers intent by looking at the intervals choosen that will miss when just looking at a TAB. This is because you can never be certain what note is being played in a TAB.
Could it be that I should be mixing my accidentals? So Ab to A# is a minor second because it's actually G# to A#.

It depends on what the composer writes. If it is written as Ab to A# then it is a doubly augmented unison. If it's written as G# to A# then it's a major second.
Then G to G# could be an augmented first,

augmented unison, correct!
G to A could be a minor second

G to A is 2 semi-tones, it's a second because of the distance between the letters, or the number of lines and spaces on the stave, and it's a major second because it's 2 semi-tones apart.
, and G to A# could be a major second

G to A# is an augmented second -- 3 semitones!
. But Gb = F# to A# is now a third. (A diminished 3rd, maybe?)

F# to A# is a third: F=1, G=2, A=3.

And it is a major third because of the number of semi-tones (F#-G = 1, G-G#=2, G#-A=3, A-A#=4).
I think I'm going to stop now, before I confuse myself (and you) any more. Clearly I'm missing a trick.

It seems to me that you are very close to getting it. Keep plugging away!

I think what you were trying to look at was something like this progression:

E-E = Unison
E-Fb = diminished second
E-Gbbb = doubly diminished third

They're all the same tones, but the intervals are different.

Heres a tip to make sense of when to call something a dimished 5th and when to call it an augmented 4th. They are the same note but they really sound totally different when used. If there is a perfect fifth, in the scale then you would call the fret right behind it a augmented 4th and there would be no perfect 4th, if you played that perfect 4th then you would ruin your chances of hearing the augmented 4th correctly (at least for a few seconds). Think about the intervals like a slider. If you move the perfect 4th up a half step then there will be no perfect 4th anymore. You would move from the 3rd strait to the augmented 4th. Likewise if it was a dimished 5th, then the 4th would be in the normal spot as a perfect 4th and the 5th will have slid down to the dimished 5th from the perfect 5th. You would move from the dimished 5th strait to the 6th. Try this out and hear the difference.

Kingpatzer did a nice job of summing up the intervals.

What's confusing you is that interval names are derived from notes, and what you hear is derived from tones. You can't hear a note - it's a written representation of a tone.

Music theory applies directly to notes, but only indirectly to sound. That might seem silly - but it's because music is a time-based experience. Without time, you can't hear it.

That's pretty inconvenient for studying something. If you want to see how Ravel passes around the melody of "Bolero", you've got the option of spending nearly 20 minutes listening to it... or less than a minute scanning the score. So the study of musical structures (theory, harmony, counterpoint, form, etc.) grew up from notation rather than the direct sounds.

That might seem silly, but an analogy may help understand why we do it this way. When you read this post, you're mentally imagining the sound of my words. If ewe kin reed know mat her witch weigh eye rite a whirred...

You get the idea. Theory is the grammar and the spelling of music, not the diction.

Nothing much to add except a short note on NoteBoats comment where he noted that "you can't hear a note - it's a written representation of a tone"

This is an American distinction. In British (and other?) English you CAN hear a note. I thought I'd mention it as the Grimm is from S. Africa, and I don't know which definition of 'note' they use there.

In Brit English, "note" has two commonly used musical meanings:
First is as Noteboat said "a written representation of a tone".
Second is synonymous with tone but used in different contexts. We say "note" in a musical context ("She ended the song on a shrill piercing note") and "tone" in a non-musical context ("Leave a message after the tone").

I must admit, though, since joining this forum, I've started saying "chord tones" more often - I like the sound of it. :lol:

Wow, it's really much simpler than I thought (and somehow, more complicated :) ). Thanks guys.

Yes, I use the term "note" interchangeably to apply to a played sound or to a piece of musical notation. But it's good to know the distinction. I hadn't intended to get into the distinction between notes on sheet music and tones played alound, but I see its not arbitrary.

Play two notes and you have an interval (in semitones, perhaps), but it doesn't have a name. Play a few more notes, and you have a better idea of the name of the interval, but you're still not sure. As the context increases, your knowledge of the specific interval names becomes more certain. But on a piece of sheet music, the exact interval name is immediately obvious, and it also tells you a lot about what successive intervals may be.

I'm pretty much working my way to scales and chord progression at the moment because my guitar "doodling" is getting tired. I love to just play (no song in particular, just mess with strumming or picking patterns and varying chord progression), but I basically only feel comfortable with about 4 or 5 basic chord progressions.

I'm struggling to get some more stuff in my head, because now, when someone says "you play the D chord, and then add an F# as a base note" it takes me about half an hour to figure it out. :) And the other day, when another guitarist showed me a progression in C major, and which had something to do with "playing the root as the treble and using the inverted third", well, let's just say I'm still trying to figure it out. :D

Your absolutely right about how each note gives context to the notes before it. And not only does context change the name of the intervals it really changes the way they sound!

Try playing a E major A major E major B major and then go back to E major. Really listen to how that E major sounds, its like going home no tension.

Now play nothing for a few seconds to let your ears reset, play an A minor then a G major then play that same E major again, listen to how much different the exact same notes sound in a different context.

Everything is relative, thats what makes music so varied and fun.

You might want to learn about harmony next, you find that the notes each scale degree harmonizes with, (i.e. the other notes of the scale) completely determine the quality of that particular scale degree. If you change one note in a scale you change the way all of the notes sound.