DU Musicians please explain this to me ,

[UndertheOcean]

I am learning the Classical guitar , and this little detail is perplexing me .


Most notes are one pitch tone apart , like A to B , D to E , with the sharp and flat symbols denoting upping or lowering the pitch by half a tone.

The exception is E to F and B to C . each are half pitch tones apart , why the hell is that ?

Anyone knows ?

[China_cat]

1. Check a piano keyboard

it's a better illustrative answer.

[UndertheOcean]

2. I am familiar with the keyboard

I just don't understand the reason

[DarkTirade]

3. That's how the 12 tone scale works.

If you went up by whole steps you'd have a 7 note octave instead of an 8 note one. Try doing a scale by whole steps, see how weird it sounds.

[Silver Swan]

4. I would guess

That it how we learn music.

There are other scales that are different, but they are not the Do re mi that we learn as kids.

From Wikipedia, I found that the seven-note scale starting on middle C is an Ionian scale. Going up the keyboard one gets a Dorian scale by starting on the D, a Phrygian scale by starting on the E, a Lydian scale by starting on the F, a Mixolydian scale starting on the G, an Aeolian scale starting on the A, and a Locrian scale starting on the B.

Some instruments are tuned to different modes, to produce different sounds.

I am not an expert, so I can't say much more.

[harmonicon]

5. it's complicated...

It might help to know that in the German system, the notes are A - H, not A - G. In that system, what they call B is what we would call Bb (B flat). This system of 8 notes actually makes more sense in the harmonic series (the harmonic series is... umm... look it up? can't explain in one sentence), if you take your starting point as the note C instead of A. Take your guitar's open "G", which is the first partial of the harmonic series, there's a harmonic on the 12th fret, which is a G an octave higher - that's the 2nd partial. At the 7th fret is a D (the third partial), another G at the 5th fret, a B at the 4th (4th partial), another D... and so on. Well, if this string was an ideal/theoretical string, you would soon run into a series of partials that would be a G major scale, except that it would also have an F natural. Transpose that to C, and you have some understanding of the German system. It is quasi-scientifically based. If you keep going up the harmonic series, it eventually becomes completely chromatic.

Now, that only really works for the musical system that's been in place for the last few hundred years: harmonic tonality. Ancient Greek and Islamic music theory relied on the harmonic series, but moving the focus to very different areas which I won't get into here. What's funny is that in the Renaissance, there was a real interest in Greek music theory, without much understanding of it, though some of the terms were borrowed, words used to describe the different modes, for instance.

Now, before tonal music came into being, western music was modal. That is, instead of relying on moving from one chord to another, it was all based on melody, like in monastic chanting (some of these chants date back to the middle ages). In a modal system, there was no changing of keys. You know, in a piece now, you can move from the key of C to the key of G. In both of those keys - any key - in a piece of music, they are related to their respective root note, with this same harmonic series that I described as taking place via harmonics on the guitar. See, in medieval music, there wasn't this movement of keys. Different pieces could start on different notes, but there was always a fixed relationship between these notes within a piece - there would never be more than 7 different notes in a piece, so they didn't need to have names for more than 7 notes (maybe I should I have said this at the beginning?). This part I'm not completely sure of, but I think my conjecture is right - what we call the Aeolian mode (then and now) was the most common. It's also now called "natural minor". If you start that mode on A, you have A, B, C, D, E, F, G - since they wouldn't have more notes than that in a piece of music, they're just named in the order they come in that mode. All of the monastic modes also only include this notes, or these note relationships, transposed. For instance, the Dorian mode is just D - C, with the 1/2 steps between B/C and E/F. Once different/more complicated music came into being, a lot of the old terminology was just carried over.

I'm sure that I could have explained this much more clearly if I wasn't just writing off the cuff, but that's why I'm not a music theory or music history expert (I am a composer though - like, a real one - no, one here would have heard my stuff, unless you're one of the few dozen who go to tiny experimental music concerts and festivals).

It doesn't deal with this stuff exactly, but a book that I would very highly recommend is called "A History of Consonance and Dissonance", by James Tenney. There are loads of music theory text books out there, but this one is the only book that I know that explains how thoughts about music making, and the terminology that goes with it, changed from the medieval period to the 20th century.

If you need me to clarify something or have another question, just ask. Good luck with the guitar playing!

[MilesColtrane]

6. Because you can't divide 12 by 7 in whole numbers.

[bbernardini]

7. There's also a scientific element to it.

It has to do with the ratios of the frequencies between two different notes. When instruments were tuned to keep certain intervals pure (for example, C to C, or C to G), other intervals would become less pleasant to the ear. The further away you got from the key of C (assuming that was the base note of the tuning), the more certain intervals would become unpleasant, until you simply could not play in certain keys. Thus the introduction of "well temperament," which was a compromise that allowed for composers and performers to play in any key without unpleasant intervals. So, you end up with the half-steps between the 3rd and 4th and the 7th and 8th steps of a major scale.

This is a very simplified explanation, as I don't remember the complicated one. :) Also, I'm very tired, and it's very late. An interesting side product of this compromise is enharmonics, like F# and Gb being the same note. If you were to be technical about it in scientific terms, the notes are different, but the compromise of well temperament makes them the same.

Sweet jesus, I need to go to bed. :)

[UndertheOcean]

8. I am not sure

but I think that F# and Gb are actually the same note , am I mistaken ? I don't see how?

[harmonicon]

9. yes, and no

It's the whole tonality/harmonic series thing. There are pure musical ratios, and adjusted ratios, or "equal temperament". In equal temperament, the octave is divided into 12 1/2 steps of equal distance. In that case, F# and Gb are the same pitch, but the "just" tuned notes can be different. Now, here's something that you can try on your guitar to illustrate this: there is an F# harmonic at the 4th (and at the 9th) fret on your D string. There is also an F# harmonic at the 7th fret on your B string. Assuming the guitar is in tune the normal way, these two F#'s will be different notes - the difference will be noticeable. The F# harmonic on the B string with be 2 cents sharp of equal temperament (one equal tempered 1/2 step is 100 cents), and the F# harmonic on the D string will be 14 cents flat of equal temperament. That's because harmonics are just intervals, based on the ratio of where the string is divided.

Now, the way the Gb and F# are different pitches has to do with what key you may have started with, and how you modulate between chords and keys (of course on the guitar, unless you count harmonics, they two notes will always sound the same - this is largely theoretical, though orchestral musicians and string quartets will make these kind of adjustments). Really these note names are just convenient ways of describing music - that's why it's called music theory. In actuality, there are an infinite number of pitches, tuning systems, etc. So, say you're in the key of D, and modulate to the key of G. The F# in the key of D will be a different F# than in the key of G. That's because it's a different partial of the harmonic series from each root tone. It'll be 14 cents flat if you're in D, but ... hmm.. well, I don't remember the cent deviation, but it's a different partial when based off of G. So, not only can Gb and F# be different notes, there can be different F#'s, or Gb's - different anything.

One thing you might want to try is tuning the guitar to a certain key to test this out. If you play a normal G chord and tune it to just intonation (you can probably do this by ear, but there are some tuners that give cent deviations as well), you'll see that when you play another chord, say an A, E or D, with the guitar in that tuning, the other chord will sound a bit off. For the G chord, you'd first make sure that all of the G's you're playing are perfectly in tune (the open one and the 3rd fret ones on the two E strings), the tune the B string to the harmonic on the 4th fret of the G, making the B's 5th fret harmonic in tune with the G's 4th. Then, tune the second fret B on the A string to this open B, and finally, tuning the D to the G - the D's 5th fret harmonic being the same as the G's 7th. In this case all of the B's will be 14 cents flat, and the D will be 2 cents sharp, compared to how the guitar is normally tuned. It should sound right though. If you were to then play an A chord in this tuning, it would sound like crap, because the harmonic ratios will be all mucked up (the open A will be 14 cents lower than the A on the G string, and the C# on the B string will be in equal temperament compared to the open A, etc.).

[cemaphonic]

10. Complicated is right

If you want the quick and dirty answer to your question, if your starting note is C, the E and the F both are strong harmonics of C; the F# that you would get to by going a whole tone past E is not, and as a result has a harsh and jarring characteristic that while very important to later music (Renaissance and on) was considered extremely unpleasant and generally avoided in medieval church music.

Basically, the musical theory underpinning all of Western European music is based on the vocal music of the medieval Catholic Church, which itself is based on the imperfectly understood musical tradition of Classical Greece, which was based in large part on science. For example, the pitch relationship between two notes that are an octave apart is a 2/1 (A above middle C is 440hz, A below middle C is 220hz). The relationship between C-G is 3/2 (more or less - there is a huge sidetrack here into tuning systems we are avoiding here). Any 2 white-note combination, except for B-F can be expressed in these sorts of simple fractional relationships.

Not only did this appeal to the ancient Greeks love of mathematical ideals, but these relationships are actually audible. When you play a C on a guitar string, not only are you hearing the C-pitch, but you are also hearing a number of other pitches, G being the most prominent(this relationship is called a perfect 5th, and as above has a pitch relationship of 3/2). These are the harmonics mentioned upthread, and the presence and relative strengths of these different harmonics are one of the most important reasons why your guitar sounds different than a trumpet or a bell. So, since G is already strongly present in a C note, they sound nice played together. Moreover, if you chain these fifths together, what you get is C-G-D-A-E-B-F#, which can (almost) be reshuffled into the familiar diatonic scale. By the time you chain it that far, however, the F# (and for that matter, the B) are pretty distantly related to the original C, and C-F# does not conform to the simple fractional relationships that all of the other notes do, so the F (which is a 4/3 relationship, and a strong harmonic known as a perfect 4th) is used instead. If you continue the chain all the way back around to C, you get the 12 note chromatic scale.


Back to the Greeks - what they did was to divide the octave into two tetrachords (four note combinations). Each tetrachord spanned a perfect 4th and the second one started a perfect 5th above the first. So starting with C, you have a tetrachord spanning C-F, and a second one spanning G-C. The internal intervals of each tetrachord could vary from mode to mode, but because of the harmonic relationships described above they were always some combination of 2 whole tones and one semitone. The medieval music theorists ditched the notion of the tetrachord as a fundamental unit of musical division in favor of the scale (all 8 notes of the octave inclusive), but they retained the basic interval strucure of the tetrachord system, which became the church modes. The end result of all of this was the diatonic scale we have now - ABCDEFG (the 12 note system with sharps and flats was a later development in Western European musical practice, although the ancient Greeks invented it too) - with each mode being a scale starting on one of the notes, and wrapping around. So the Dorian mode, for example would be DEFGABCD. Two of these modes (the ones starting on B and F) do not conform to the tetrachord structure and were basically only included for theoretical completeness, although the one starting of F was very rarely used as an exotic effect. Over time, the church modes eventually gave way to the major/minor tonality that we have today, but really the major tonality is just one of the church modes (the Ionian - CDEFGABC), while the minor tonality is a variant of one of the others (the Aeolian - ABCDEFGA).

Hopefully, I've somewhat answered your question without being too confusing. I am also years away from any kind of formal music theory study. But music theory, acoustics, notation and so on are really interesting fields, with many oddities that arise that can seem really strange until you begin to understand the reasons that they developed that way.