Music theory is not logical

Chords, scales, harmony, melody, etc.
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mediumaevum wrote:
Delta Sign wrote:The color of the keys doesn't matter. It's always one semitone from one key to the next.
I'm trying to count to a third (tertian, Latin, Terts, Danish, Third Interval).

It should be a simple task, but I guess not...

1. I have a C. Now, where's the third? According to music theory lessons I've taken and wikipedia and WHAT NOT! - a "Third" is composed of THREE SEMITONES (halfnotes).

2. Question: Do I count C too when counting to a third? Or do I count C#, D, D# (or Eb) - three semitones?
No

3. Question: Which direction? If I have a C, and I go DOWN, my "third" is not a D# (or Eb) - it's instead A.

Summed up my simple questions I have yet to have answered are:

Do you count the root tone (don't know the proper name, I begin with C, so let's call C root tone) when counting to a Third Interval?

Do you go up or down/right or left on the keyboard when counting an interval?
1.Minor third from c = Eb ( e flat ) = 3 semitones above C
Mayor third from c = e = 4 semitones from c


2.Both ways
3. C= root ...counting 7 semitones up ( not starting on c ) gives us G = which is the FIFTH , C-->perfect 5th G
Counting 5 semitones down from c , gives us also a G ---->perfect fourth -->C


Reason why the counting is not intuitive is because you have two half steps in scale , yet we count the scale degrees in 1,2,3,4,5,6,7,
Last edited by gentleclockdivider on Tue Jun 26, 2018 7:32 pm, edited 1 time in total.
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NB: bad typo corrected: '3rd' for '6th.' apologies
mediumaevum wrote:I'm trying to learn music theory, and I am a logical thinking person.

I have a lot of difficulties figuring out the logic in music theory, simply because... it defies all logic.

Let's take a Third Interval as example.

A Third Interval is defined as:

Three halfnotes to and from the root note (we are always counting the root note & interval too).

From A to C there are 2 whole steps + ½ step, which makes 4 half steps.
But Third Interval is described by halfnotes only. Yet when counting the Third Interval (or any other interval) it varies wether or not we count in halfsteps or not, as if one have to remember a whoe bunch of rules of what a Third Interval is, there is no underlying logic behind it. You cannot count mathematically.

If a Third Interval is defined as three (3) half steps/half notes from the root, ie. C, then the Third Interval should be D. But it's not.
One has to remember "as is". It "just is this way", you can't count.
Some of this will likely be redundant to what's been said, but that isn't a bad thing here I don't reckon.

C D E; 1 2 3.

"Third" with no qualification is simply letter names. There is a minor third which is C D E, except the E is modified because the quality minor in certain interval types is a smaller interval than major. <Eb>

Seconds, thirds, sixths and sevenths are, from small to large: diminished, minor, major, and augmented. So: C to Dbb (double flat) is a diminished second. (On a piano this is the same pitch as a unison, use cases comparatively rare, but for purposes of providing the convention (the logic) I'm including it.) C to Db is a minor 2nd; C to D, major 2nd. C to D# is an augmented second.

Compare 3rds: C to Ebb, diminished; C to Eb, minor; C to E, major; C to E#, augmented.
diminished 3rd also comparatively rare in western harmonic music, as is dim 4th. But in Carnatic music it is meaningful, in the basic construction of scales. It's going to exceed the scope of what I'm after here by a lot but there are entirely logical reasons when these odd-seeming ones are used.

Which will not be apparent right away; for instance let's move on to a use case consistent with the logic of these spellings which, according to harmonic music and conventions which arose in the use of that, see more use.
6ths: C to Abb, diminished 6th, don't know if I've even seen that, but we're being consistent and a use of this quality of interval (diminished) is about to reveal itself. C to Ab, minor 6th; C to A, major 6th; C to A#, augmented 6th.
Here was something which arose in promoting tension and movement, harmonically: the augmented 6th chord.
Yes, it sounds like a minor 7th but it functions a certain way. That too exceeds this lesson. But here is the first common use in the convention of this *quality* of interval.

Now, the 7th: C to Bbb is a diminished 7th; here is the first common use of this *quality*. The diminished 7th chord; made of minor thirds ('diminished' first of all due to the dim. 5th created by two min. 3rds): C Eb Gb Bbb.
Tempting to call this Bbb 'A', and we can do literal minor 3rds voila: A C Eb Gb. But spelling is spelling and there are reasons. C to Bb, min. 7th; C to B, maj. 7th; C to B# aug. 7th. Here is another one which conventionally is rare to non-existent. These ones which look like unison or octave have no real point except with instruments which are not fixed like a piano to only 12 tones per octave and here will be exotic anyway. They will, in other words, be microtonal (which only really means 'interval smaller than a semitone'). Just showing the meanings of terms, thoroughly.

So there's a logic of consistency which is never violated here, even as there is less use of certain qualities of interval within this class; then there is the logic of spelling which agrees with consistency and additionally accords to the logic of use cases.

There is of course another class of interval which enjoys a default status basically, known as perfect. Unisons/octaves, fourths, and fifths.
C to C, perfect unison or octave; C to F, perfect 4th; C to G, perfect fifth.
C to C# is an augmented unison or octave; F to F# is an augmented 4th; C to G# an aug. 5th.
C to Cb is a diminished unison or octave; C to Fb a dim. 4th; C to Gb a dim. 5th.
As with the other class of interval, use cases reveal the value of spelling (and are sometimes ignored for simplicity's sake).
Last edited by jancivil on Tue Jun 26, 2018 10:12 pm, edited 4 times in total.

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Thank you, everyone, I think I understand it now.

I appreciate the help that I've got here so far, I'll continue studying.

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Nice :)

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mediumaevum wrote: If a Third Interval is defined as three (3) half steps/half notes from the root, ie. C, then the Third Interval should be D. But it's not.
Keep in mind that neither the number nor the quality of an interval can be determined by counting semitones alone.
For Example: There are 4 semitones between A & C#, A & Db, A# & D, and Ab & B#, but....

the interval A-C# is a major third (as it spans 3 staff positions)
the interval A-Db is a diminished fourth (as it spans 4 staff positions)
the interval A#-D is a diminished fourth (as it spans 4 staff positions)
the interval Ab-B# is a doubly augmented second (as it spans 2 staff positions)

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It's around the point that people start talking about C# and Db as though they're different notes and then talking about a B# when anyone can see that the next note up from B is C and there's no such thing as a B# that you realise that the OP was pretty much right.

Whilst there is some sort of "logic" (or at least system of rules) to note and interval theory it's not the sort of thing that any normal person is likely to regard as logical.

Steve

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Yeah, it all makes sense, but it's certainly convoluted :hihi:

I mean, look at this thread. The question is super simple, yet it spawned a big discussion :hihi:

One of the problems I often see when beginners are asking questions about music theory on the internet, is that the experts often expect them to go full Ligeti on their first day.
In my opinion, and I know I'm alone with this opinion, there is nothing wrong with learning the easy way first, even if it's the wrong way. Throwing advanced theory at a beginner just because something they learned isn't technically 100% right, will only confuse them.

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Delta Sign wrote:Yeah, it all makes sense, but it's certainly convoluted :hihi:
I mean, look at this thread. The question is super simple, yet it spawned a big discussion :hihi:
The question was not super simple because you are searching for logic in something that is fundamentally a cultural construct. I think it has already been pointed out but that question was the starting point of an entirely new direction of composing music in the form of atonal music at the beginning of the 20th century.

Interesting thread. :tu:
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slipstick wrote:It's around the point that people start talking about C# and Db as though they're different notes and then talking about a B# when anyone can see that the next note up from B is C and there's no such thing as a B# that you realise that the OP was pretty much right.
Not at all. First of all, a seven-note scale having seven letter names is normal.

C# D# E# F# G# A# B#.
Same 'logic' as C D E F G A B.
What's your problem with that?

The next note up from B flat is C? There's your logic. It's nonsense. You don't like enharmonics is all. Wouldn't surprise me if, because sharps all you see in the DAW piano roll then F G A A# C D E is a perfectly good representation of F major scale to you. If not, well you're inconsistent.

It's a thing. If you want a flats-oriented key and you want to know best practices as to dealing in it, you go with flats. Same with a sharps-orientation. You don't muck it up with the wrong spelling. You shoot yourself in the foot when you do.
One would tend to have a reason to use key of Db or key of C# and there might be a choice between them, based in context.

Key signature of Cb major, 7 flats. Cycle of fifths says so.
Cb Db Eb Fb Gb Ab Bb. (Enharmonic equivalent, B major. 5 sharps.)

Now, say we've modulated here from Gb major. Suddenly a composer, arranger or copyist is consulting you with 'anyone can see that there's no such thing as _'? Six flats, Gb major or six sharps, F# major, eh, what?
Which one isn't real?
Gb Ab Bb Cb Db Eb F
F# G# A# B C# D# E#
:?:

You have no clue, do you. No, you don't really care to go any further than your most facile preconception of it. If you did, you'd only muck it up sticking to what's just so obvious, and thought-free. It's alphabetical. FFS.
Last edited by jancivil on Thu Jun 28, 2018 9:54 am, edited 1 time in total.

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Delta Sign wrote:Yeah, it all makes sense, but it's certainly convoluted :hihi:

I mean, look at this thread. The question is super simple, yet it spawned a big discussion :hihi:

One of the problems I often see when beginners are asking questions about music theory on the internet, is that the experts often expect them to go full Ligeti on their first day.
I read most of it. People tried to sort someone else out who was confused. And once someone trying to sort out the initial confusion needed to be sorted.
Delta Sign wrote:In my opinion, and I know I'm alone with this opinion, there is nothing wrong with learning the easy way first, even if it's the wrong way. Throwing advanced theory at a beginner just because something they learned isn't technically 100% right, will only confuse them.
There is no advanced theory here. This is Intro to Theory at a high school level. I mentioned a couple of things I didn't even begin to go into just to indicate there will be reasons if one goes forward for enharmonic choices.
I don't think that is wrong. There was 'throwing'?

I'm not a fan of learning things the wrong way, since that's going to involve remedies later and will tend to result in poorly formed ideas and a lack of clarity.

The OP had confused himself. :shrug: He said there is no logic to it and I answered that.

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jancivil wrote:
Delta Sign wrote:In my opinion, and I know I'm alone with this opinion, there is nothing wrong with learning the easy way first, even if it's the wrong way. Throwing advanced theory at a beginner just because something they learned isn't technically 100% right, will only confuse them.
There is no advanced theory here. This is Intro to Theory at a high school level. I'm not a fan of learning things the wrong way, since that's going to involve remedies later and will tend to result in poorly formed ideas and a lack of clarity.

The OP had confused himself dealing with counting. :shrug:
He was (is?) confused because he was counting semitones, instead of counting notes. Many people here insist in that mistake. When classifying intervals, you count NOTES, not semitones. And that's it. KEEP IT SIMPLE, STUPID. That's the problem of starting to study things the wrong way (thinking it is an easier way).

Forget the semitones, and forget the keyboard. You count NOTES, and you can't have two notes with the same name. Therefore, FORGET THAT STUPID ASSERTION THAT THERE IS NO B#. What would you call the leading tone of C# Major or C# minor?
Fernando (FMR)

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The OP somehow had the notion that a third was only the one thing. There was no quality of third at all.
I was a little buffaloed that someone didn't see 1, 2, 3; A, B, C as a basis to proceed. A to C is a third, yeah?

If one is going to move forward into an actual consideration of music theory, one is going to have to have a clear foundation. What can be simpler than the alphabetical C D E F G A B? No sharps, looks like that. 7 sharps, same alphabet, looks like that only with sharp signs. You get there adding one at a time (and can do, using a nice picture of a circle): key of C, of G, of D, A, E, B, F#, C#. Go the other way 'round: C, F, Bb, Eb, Ab, Db, Gb, Cb.
The trickiest thing about it is there are 7 containing flats, and 7 containing sharps, so with the set being 12 total there are two overlaps coming from either direction, meeting in the middle with {6} F#/Gb.

It's not that advanced. Even children in primary school can do it, with their tiny child heads!

"What would you call the leading tone of C# Major or C# minor?" I doubt that person cares at all.
I actually went into it from the vantage point of C# major only, to keep this at Intro to Music Theory rather than Music Theory 101.

I did mention the augmented sixth, but it's a sixth because of the alphabet. and as I went into all the qualities of two classes of interval used. It's not even Toy Rocket Surgery.

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fmr wrote:
jancivil wrote:
Delta Sign wrote:In my opinion, and I know I'm alone with this opinion, there is nothing wrong with learning the easy way first, even if it's the wrong way. Throwing advanced theory at a beginner just because something they learned isn't technically 100% right, will only confuse them.
There is no advanced theory here. This is Intro to Theory at a high school level. I'm not a fan of learning things the wrong way, since that's going to involve remedies later and will tend to result in poorly formed ideas and a lack of clarity.

The OP had confused himself dealing with counting. :shrug:
He was (is?) confused because he was counting semitones, instead of counting notes. Many people here insist in that mistake. When classifying intervals, you count NOTES, not semitones. And that's it. KEEP IT SIMPLE, STUPID. That's the problem of starting to study things the wrong way (thinking it is an easier way).

Forget the semitones, and forget the keyboard. You count NOTES, and you can't have two notes with the same name. Therefore, FORGET THAT STUPID ASSERTION THAT THERE IS NO B#. What would you call the leading tone of C# Major or C# minor?
That's not simple, to count NOTES instead of semitones.

I bet most people here are not writing music on sheet, but use something like a PianoRoll (FLStudio), with a vertical piano to the left to place your notes. Then you're using a piano/keyboard to write music, not notes.

This, I think, should be clarified for beginners who wish to learn music theory that they can't do it this way and expect any logic.

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mediumaevum wrote: That's not simple, to count NOTES instead of semitones.
The classic internal numbering is based on a scale and this makes a whole lot of sense in a strictly tonal music, because there is always just one "third" note in a scale. If the scale is major, then that third is a "major third" and if the scale is minor then that third is a "minor third" but it turns out that a lot of chord progressions and such actually work equally well in multiple scales.

You CAN map intervals into semitones, if you include the qualifiers:

+0 = prime
+1 = minor second
+2 = major second
+3 = minor third
+4 = major third
+5 = fourth
+6 = tritone (classically to be avoided at all cost, lest you burn in the pits of hell)
+7 = fifth
+8 = minor sixth
+9 = major sixth
+10 = minor seventh
+11 = major seventh
+12 = octave

...however... if you are working on tonal music, then at any given time you have some scale as a reference and thinking about the semitones is not terribly helpful, because only some of the notes are "valid" at any given time. When you only consider the "valid" notes, the seemingly weird numbering suddenly makes a whole lot of sense. The actual key and scale can certainly change throughout a piece (this is known as "modulation"), but as long as we assume that there is always one at a given time this numbering scheme makes a whole lot of sense.
I bet most people here are not writing music on sheet, but use something like a PianoRoll (FLStudio), with a vertical piano to the left to place your notes. Then you're using a piano/keyboard to write music, not notes.
This is why you can pick a scale in FL. Open the piano-roll and from the top-left corner menu choose "helpers -> scale reference" and pick a scale (other than the C-major / A-minor that the white keys of a piano will give you). Now the notes of your chosen scale are drawn as "white" and the "bad" notes are drawn as "black" and you can easily count musical intervals the way they are designed to be counted, simply by ignoring all the "black" notes.

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mediumaevum wrote: That's not simple, to count NOTES instead of semitones.

I bet most people here are not writing music on sheet, but use something like a PianoRoll (FLStudio), with a vertical piano to the left to place your notes. Then you're using a piano/keyboard to write music, not notes.

This, I think, should be clarified for beginners who wish to learn music theory that they can't do it this way and expect any logic.
I showed the logic. You appear to be ignoring it. No such "clarification" should be made just out of your choice to dismiss information given you (generously I might add).

A B C = 1 2 3.
This one happens to be a minor third. Not all thirds are three semitones. It looks like things that exceed your immediate grasp may be dismissed as a failure of logic.

So now, this appears: using a piano roll GUI in our common DAW paradigm means notes are no longer notes but pure music creation. That's your logic? :help:


When a music uses, for instance 12 tones to an 'octave' (an 'octave' is a cultural construct and context-bound, yes, and it's not so intuitive to see 12 fitting into 8 but most of us are already here. I will say that regardless, there are <12 to an octave> in several musical cultures), there will be more_than_one quality of 'third'.
Ever hear of say A major chord, vs A minor chord? Here is a quality of third determination.
So this is: 4 semitones = major 3rd, now 3 semitones = minor 3rd. It's still as basic as A B C = 1 2 3. Any A to any C is a third of some quality. The extreme may look like A# to Cb, a doubly diminished third. The idea of thirds is simply down to letter name.

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