Music theory is not logical

Chords, scales, harmony, melody, etc.
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A semitone isn't a note (e. g. a key on keyboard or a dot on stuff). Semitone is a distance between two neighbor notes. C and C#, C# and D, etc. It's absolutely logical.
Last edited by lobanov on Tue Jun 26, 2018 1:53 pm, edited 2 times in total.

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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).
A third is the third NOTE counting from the base note. As has been said earlier in this thread, you CANNOT have two notes with the same name when defining intervals (e.g. you cannot have C and C# or Db and D, you have either one or the other). So, counting from C upwards a third is ALWAYS an E (being either E or Eb). If the third IN THE TONATLITY YOU ARE WORKING falls in the E, the third is major. If the third falls in Eb the third is minor. If you have an altered note, that note forms a new interval. But since it is AN ALTERED NOTE, it replaces the note it alters, therefore, if you are in C Major, and suddenly appears a Bb, that Bb replaces the B.
mediumaevum wrote: 2. Question: Do I count C too when counting to a third? Or do I count C#, D, D# (or Eb) - three semitones?

You count ALL the notes - the first note up to the last note. That's why a third from C is an E (C-D-E - three notes). And it doesn't matter how many semitones you have. It matters just the note names. You could have C#-D#-E#, or C#-D#-E, or C-Db-Eb, or C-D-Eb, or Cb-Db-Eb. In the first case, the third would be Major, in the second case, it would be minor, in the third case it would be minor, in the fourth case it would minor, and in the fifth case, it would be Major. Note the presence of Cb (which many would name B). In fact Cb and B are two different notes, belonging to different tonalities.
mediumaevum wrote: 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.

You can count a third in either direction. If you count a third UP from C it's an E. If you count a third DOWN from C it's an A. Of course, a third UP from A is also a C. HOWEVER in the case you wrote, an interval from C to D# would NEVER be a third, but an augmented second (again, a D# belongs to a tonality completely different from an Eb). So, from C to D# you have an augmented second, but from C to Eb you have a minor third EVEN IF THEY ARE (APPARENTLY) THE SAME THING ON THE KEYBOARD.
Fernando (FMR)

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Delta Sign wrote:You don't count the C and it doesn't matter in which direction you count. Three semitones are a minor third and four semitones are a major third. You can count those up or down, it doesn't matter. The "third" is only the name of the distance, or interval. The "minor" and "major" is the "quality" of the interval.

If you want to build chords, you have to count up, of course. The root note + a major third + a perfect fifth is a major chord, for example.

Edit: Yeah, what tehlord said.
Thanks, this clears things up. Thanks a lot!

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fmr wrote:
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).
A third is the third NOTE counting from the base note. As has been said earlier in this thread, you CANNOT have two notes with the same name when defining intervals (e.g. you cannot have C and C# or Db and D, you have either one or the other). So, counting from C upwards a third is ALWAYS an E (being either E or Eb). If the third IN THE TONATLITY YOU ARE WORKING falls in the E, the third is major. If the third falls in Eb the third is minor. If you have an altered note, that note forms a new interval. But since it is AN ALTERED NOTE, it replaces the note it alters, therefore, if you are in C Major, and suddenly appears a Bb, that Bb replaces the B.
mediumaevum wrote: 2. Question: Do I count C too when counting to a third? Or do I count C#, D, D# (or Eb) - three semitones?

You count ALL the notes - the first note up to the last note. That's why a third from C is an E (C-D-E - three notes). And it doesn't matter how many semitones you have. It matters just the note names. You could have C#-D#-E#, or C#-D#-E, or C-Db-Eb, or C-D-Eb, or Cb-Db-Eb. In the first case, the third would be Major, in the second case, it would be minor, in the third case it would be minor, in the fourth case it would minor, and in the fifth case, it would be Major. Note the presence of Cb (which many would name B). In fact Cb and B are two different notes, belonging to different tonalities.
mediumaevum wrote: 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.

You can count a third in either direction. If you count a third UP from C it's an E. If you count a third DOWN from C it's an A. Of course, a third UP from A is also a C. HOWEVER in the case you wrote, an interval from C to D# would NEVER be a third, but an augmented second (again, a D# belongs to a tonality completely different from an Eb). So, from C to D# you have an augmented second, but from C to Eb you have a minor third EVEN IF THEY ARE (APPARENTLY) THE SAME THING ON THE KEYBOARD.
Thanks for the detailed description. But with you saying this:
You count ALL the notes - the first note up to the last note.
And Delta Sign saying this:
You don't count the C
I'm getting a bit confused. What's the right thing?

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We have a semitone and a whole tone ( = two semitones). We use them to define a scale. Major: whole tone, whole tone, semitone, whole tone, whole tone, whole tone, semitone. C-major: C, D, E, F, G, A, H. G-major: G, A, H, C, D, E, F#. Etc. We get 7 notes, 5 notes are excluded.

We have intervals. We can define them in 1) semitones or 2) semitones AND whole tones. We get minor second (C - C#), major second (C - D), minor third (C - D#), major third (C - E) etc. E.g., minor third = three semitones = whole tone + semitone.
One semitone is a distance between two notes, as I've said. (C - C#) - (C# - D) - (D - D#) - we have three semitones.

You can build on a keyboard any interval from every note using 12 notes of one octave.
But we have defined a scale, yes? Not all the intervals are part of a scale. We can build only major third in C-major from C upward (C - E), and only minor third from C downward (C - A). C - Eb and C - Ab aren't part of C-major (they're not diatonic). In major scale the third from the root upward is always major, in minor scale the third from the root upward is always minor. If we go downward, all is vice versa.

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lobanov wrote:We have a semitone and a whole tone ( = two semitones). We use them to define a scale. Major: whole tone, whole tone, semitone, whole tone, whole tone, whole tone, semitone. C-major: C, D, E, F, G, A, H. G-major: G, A, H, C, D, E, F#. Etc. We get 7 notes, 5 notes are excluded.
This explanation is a little confusing, and besides, it isn't historically correct in explaining the origin of Major and minor "modes" (which derive from the eight mode systems used previously). All tonalities have seven notes.

You can't talk about "excluded" notes. Intervals are defined in the tonality system, in which all tonalities have seven notes, and the succession of intervals is as you explained. Therefore, mentioning "excluded" notes is absurd. They aren't "excluded" because they didn't belong there in the first place.
lobanov wrote: We have intervals. We can define them in 1) semitones or 2) semitones AND whole tones. We get minor second (C - C#), major second (C - D), minor third (C - D#), major third (C - E) etc. E.g., minor third = three semitones = whole tone + semitone.
One semitone is a distance between two notes, as I've said. (C - C#) - (C# - D) - (D - D#) - we have three semitones.
WRONG again. There aren't C-C# or D-D# in a tonality. You either have C or C# and D or D#. You can't have BOTH. Intervals sare defined inside the tonality. Actually, if you want to be completely correct, you'd have to differentiate between diatonic semitones (E and F, for example, or D and Eb) and chromatic semitones (C and C#, for example, or D and D#). The second are for altering notes, hence the name "chromatic" (which literally means they change - alter - the color). Apparently, they are all the same, but in what concerns tonal system theory, they are not.
lobanov wrote: You can build on a keyboard any interval from every note using 12 notes of one octave.
But we have defined a scale, yes? Not all the intervals are part of a scale. We can build only major third in C-major from C upward (C - E), and only minor third from C downward (C - A). C - Eb and C - Ab aren't part of C-major (they're not diatonic). In major scale the third from the root upward is always major, in minor scale the third from the root upward is always minor. If we go downward, all is vice versa.
This parte is correct.
Last edited by fmr on Tue Jun 26, 2018 3:05 pm, edited 3 times in total.
Fernando (FMR)

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mediumaevum wrote: Thanks for the detailed description. But with you saying this:
You count ALL the notes - the first note up to the last note.
And Delta Sign saying this:
You don't count the C
I'm getting a bit confused. What's the right thing?
If Delta Sign wrote that, he is wrong :shrug:
Fernando (FMR)

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mediumaevum wrote:Thanks for the detailed description. But with you saying this:
You count ALL the notes - the first note up to the last note.
And Delta Sign saying this:
You don't count the C
I'm getting a bit confused. What's the right thing?
Ok, this can be a bit confusing, I suppose.

If you count the steps on your scale, you have to count the first note too, because the third note of the scale is always the third (I know this isn't entirely true, but lets just not make it more confusing that it has to be at the moment.) That's how you figure out the third of your scale.
However, if you want to count intervals, for example major or minor thirds, you don't count the first note, because you are not counting notes, but distance, or intervals.

Lets take the C major scale: CDEFGAB

If you count from C, including the C you land on E, which is your third.

If you want to know the interval, or more precisely which quality your third has, you count C# D D# E, which is four steps, which means it's a major third.

It's really not that complicated, it just sounds like it.

Someone will probably be able to explain it better.

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Delta Sign wrote: Lets take the C major scale: CDEFGAB

If you count from C, including the C you land on E, which is your third.

If you want to know the interval, or more precisely which quality your third has, you count C# D D# E, which is four steps, which means it's a major third.

It's really not that complicated, it just sounds like it.

Someone will probably be able to explain it better.
You are confusing things unnecessarily. You don't have to count the semitones, because they don't belong the scale. Thigs are much easier if you don't consider those (as you shouldn't)

Lets take the tonalities starting in C:

C, D, E, F, G, A, B - C Major

From C to D you have a whole tone, therefore the second is Major. From C to E, you have two whole tones, therefore the third is Major. From C to F you have two whole tones and a half tone - a perfect fourth. All fourths are perfect, with the exception of the fourth between the 4th grade and the 7th of the scale (F and B), wich is augmented, also called the Tritone, because it has three whole tones.

From the fourth onwards, you can classify the intervalks by inversion. If the inversion of that interval forms a minor third. But for the fifth, it isn't necessary - all fifths are perfect except the fifth between the 7th and the 4th degree of the scale (B and F), which is the inversion of the augmented fourth - this is a diminished fifth. Major intervals invert as minor. minor intervals invert as Major. diminished invert as Augmented, and ugmented as diminished.

Now, for the sixths. Each Major sixth inverts as a minor third. So, to determine which interval is it between C and A, you invert it: A to C. A to C is a minor third (a whole tone and half tone). Therefore, the sixth is Major (minor invertsd as Major). A to B -> you invert as B to A. B to A is a half tone, therefore, it is a minor second (a Major second is a whole tone, therefore a half tone is a minor second). Consequentely, the seventh is a Major seventh.

@ mediumaevum:

You should work with the inversions, because being able to quickly invert an iterval is as important as knowing how to classify it. And it makes classifying the intervals much easier.

Now, I'll let you apply this logic to C minor. C minor is C, D, Eb, F, G, Ab, Bb and C (although the Bb can be altered to B to create thew leading tone, and the Dominant function)
Last edited by fmr on Tue Jun 26, 2018 3:24 pm, edited 1 time in total.
Fernando (FMR)

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fmr wrote:
lobanov wrote: We have intervals. We can define them in 1) semitones or 2) semitones AND whole tones. We get minor second (C - C#), major second (C - D), minor third (C - D#), major third (C - E) etc. E.g., minor third = three semitones = whole tone + semitone.
One semitone is a distance between two notes, as I've said. (C - C#) - (C# - D) - (D - D#) - we have three semitones.
WRONG again. There aren't C-C# or D-D# in a tonality. You either have C or C# and D or D#. You can't have BOTH. Intervals sare defined inside the tonality. Actually, if you want to be completely correct, you'd have to differentiate between diatonic semitones (E and F, for example, or D and Eb) and chromatic semitones (C and C#, for example, or D and D#). Apparently, they are all the same, but in what concerns tonal system theory, they are not.
It's not about a tonality. It's about a chromatic scale. Change the order of the first two part of my post and you'll see what I mean. They're interchangeable.
Are intervals in a chromatic scale impossible? Why? If they're possible (they are) how we could name them?

But you're right, it's important to distinguish between a tonality and a chromatic scale. May be I've not distinguished them explicitly. And in modern European music (not historically) there is nothing wrong in regarding tonal scales as constructed from a chromatic scale. I see no reason why it could be wrong.

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fmr wrote:
Delta Sign wrote: Lets take the C major scale: CDEFGAB

If you count from C, including the C you land on E, which is your third.

If you want to know the interval, or more precisely which quality your third has, you count C# D D# E, which is four steps, which means it's a major third.

It's really not that complicated, it just sounds like it.

Someone will probably be able to explain it better.
You are confusing things unnecessarily. You don't have to count the semitones, because they don't belong the scale. Thigs are much easier if you don't consider those (as you shouldn't)

Lets take the tonalities starting in C:

C, D, E, F, G, A, B - C Major

From C to D you have a whole tone, therefore the second is Major. From C to E, you have two whole tones, therefore the third is Major. From C to F you have two whole tones and a half tone - a perfect fourth. All fourths are perfect, with the exception of the fourth between the 4th grade and the 7th of the scale (F and B), wich is augmented, also called the Tritone, because it has three whole tones.

From the fourth onwards, you can classify the intervalks by inversion. If the inversion of that interval forms a minor third. But for the fifth, it isn't necessary - all fifths are perfect except the fifth between the 7th and the 4th degree of the scale (B and F), which is the inversion of the augmented fourth - this is a diminished fifth. Major intervals invert as minor. minor intervals invert as Major. diminished invert as Augmented, and ugmented as diminished.

Now, for the sixths. Each Major sixth inverts as a minor third. So, to determine which interval is it between C and A, you invert it: A to C. A to C is a minor third (a whole tone and half tone). Therefore, the sixth is Major (minor invertsd as Major). A to B -> you invert as B to A. B to A is a half tone, therefore, it is a minor second (a Major second is a whole tone, therefore a half tone is a minor second). Consequentely, the seventh is a Major seventh.

@ mediumaevum:

You should work with the inversions, because being able to quickly invert an iterval is as important as knowing how to classify it. And it makes classifying the intervals much easier.

Now, I'll let you apply this logic to C minor. C minor is C, D, Eb, F, G, Ab, Bb and C (although the Bb can be altered to B to create thew leading tone, and the Dominant function)
Yeah, you are absolutely right. It's sometimes hard to figure out how exactly to explain things to a beginner. Your approach is definitely the right one, but I don't know if it's the easiest to understand for a beginner.

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lobanov wrote:
fmr wrote:
lobanov wrote: We have intervals. We can define them in 1) semitones or 2) semitones AND whole tones. We get minor second (C - C#), major second (C - D), minor third (C - D#), major third (C - E) etc. E.g., minor third = three semitones = whole tone + semitone.
One semitone is a distance between two notes, as I've said. (C - C#) - (C# - D) - (D - D#) - we have three semitones.
WRONG again. There aren't C-C# or D-D# in a tonality. You either have C or C# and D or D#. You can't have BOTH. Intervals sare defined inside the tonality. Actually, if you want to be completely correct, you'd have to differentiate between diatonic semitones (E and F, for example, or D and Eb) and chromatic semitones (C and C#, for example, or D and D#). Apparently, they are all the same, but in what concerns tonal system theory, they are not.
It's not about a tonality. It's about a chromatic scale. Change the order of the first two part of my post and you'll see what I mean. They're interchangeable.
Are intervals in a chromatic scale impossible? Why? If they're possible (they are) how we could name them?

But you're right, it's important to distinguish between a tonality and a chromatic scale. May be I've not distinguished them explicitly. And in modern European music (not historically) there is nothing wrong in regarding tonal scales as constructed from a chromatic scale. I see no reason why it could be wrong.
In Music Theory, intervals and their classification is about the Tonal System, of which the chromatic scale isn't part of. All intervals, chords, etc. are born out of the Tonal System. If you introduce the twelve notes, you no longer have tonality, so, what's the use of intervals? And how would you define them, anyway? Why would you consider a C# instead of a Db, for example? And a G# insteads of Ab?

You can still classify the intervals, of course, but that would be a useless exercize, since it would serve no purpose in terms of music theory for the twelve tone system. Atonality and the twelve tone system is a completely different thing, which we should take apart of this, for the time being, since it would confuse notions unnecessarily.
Fernando (FMR)

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:)
Last edited by woggle on Fri Mar 01, 2019 7:18 am, edited 1 time in total.

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fmr wrote:
lobanov wrote:
fmr wrote:
lobanov wrote: We have intervals. We can define them in 1) semitones or 2) semitones AND whole tones. We get minor second (C - C#), major second (C - D), minor third (C - D#), major third (C - E) etc. E.g., minor third = three semitones = whole tone + semitone.
One semitone is a distance between two notes, as I've said. (C - C#) - (C# - D) - (D - D#) - we have three semitones.
WRONG again. There aren't C-C# or D-D# in a tonality. You either have C or C# and D or D#. You can't have BOTH. Intervals sare defined inside the tonality. Actually, if you want to be completely correct, you'd have to differentiate between diatonic semitones (E and F, for example, or D and Eb) and chromatic semitones (C and C#, for example, or D and D#). Apparently, they are all the same, but in what concerns tonal system theory, they are not.
It's not about a tonality. It's about a chromatic scale. Change the order of the first two part of my post and you'll see what I mean. They're interchangeable.
Are intervals in a chromatic scale impossible? Why? If they're possible (they are) how we could name them?

But you're right, it's important to distinguish between a tonality and a chromatic scale. May be I've not distinguished them explicitly. And in modern European music (not historically) there is nothing wrong in regarding tonal scales as constructed from a chromatic scale. I see no reason why it could be wrong.
In Music Theory, intervals and their classification is about the Tonal System, of which the chromatic scale isn't part of. All intervals, chords, etc. are born out of the Tonal System. If you introduce the twelve notes, you no longer have tonality, so, what's the use of intervals? And how would you define them, anyway? Why would you consider a C# instead of a Db, for example? And a G# insteads of Ab?

You can still classify the intervals, of course, but that would be a useless exercize, since it would serve no purpose in terms of music theory for the twelve tone system. Atonality and the twelve tone system is a completely different thing, which we should take apart of this, for the time being, since it would confuse notions unnecessarily.
When we use all 12 notes of a chromatic scale in a context of an atonal music C# = Db. No difference. In a tonal scale the names of the notes are ordered. In G-major Gb means something absolutely different than F#. F# is a note of the scale, Gb is a tonic lowered by one semitone.
But C# and Db have the same pitch. Acoustically and visually (on a keyboard) they are identical. Their names depends on a tonal context. In one tonal context it's C# (D-major), in another tonal context it's Db (Ab-major).

And we must distinguish between an atonality and a chromatic scale. The latter is "materialized" in our instruments, in their black and white keys, in their tuning. Chromatic scale in Western music makes all music easily transposable. G-magor is C-major "transposed" by fifth upward, F-major is C-major "transposed" by fifth downward, etc. etc. '#' and 'b' are also signs of a direction of moving in the circle of fifths. And it's a convention to simplify things a bit, put them in order.

:tu:

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woggle wrote:There is no need for music theory to be logical, it just needs to be consistent. A lotof what is being talked about here is descriptive, the definitions prescriptions could be otherwise, they are the result of historic agreement rather than some application of formal logic. Although that doesntpreclude the use of logical systems in elaborating a particular theory, it's just not a necessary aspect of a descriptivetheory.
Well said. Music theory need not be necessarily logical but Just, Well-Tempered...

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