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why half steps between (5 and 6) and (12 and 1) notes?

Posted by despues18 
why half steps between (5 and 6) and (12 and 1) notes?
July 06, 2017 12:28PM
why is there this simple break in the pattern of one whole step between each consecutive note?
Re: why half steps between (5 and 6) and (12 and 1) notes?
July 06, 2017 12:55PM
Uh, I think you're are referring to a chromatic scale with your numbers?

Converting that to a major scale, could I rephrase your question as why half steps between the 3rd & 4th and 7th & 8th (octave) notes? I'm going to suggest it's because that's what sounded good. I don't know the history of musical scales, so probably not the best one to answer.

Anyone?
Re: why half steps between (5 and 6) and (12 and 1) notes?
July 06, 2017 09:33PM
It comes from the ancient Greek diatonic tetrachord - a string tuning arrangement of a four string instrument ("tetra" means 4 and "chord" meant "string"). The intervals between the strings were W W H (or variations of that order) so that the interval between the lowest and highest pitched strings was a perfect 4th. Combining two diatonic tetrachords with the second above the first gives a full scale called the diatonic scale, which we still use, and is the basis of all the modes plus their major and minor key successors. Two other tetrachords were in use in Ancient Greece, called the chromatic and enharmonic tetrachords that used intervals smaller than a half step and larger than a whole step, but they became obsolete. So LowNote is right - they obviously liked the sound of the diatonic scale, just like we do, as 99% of Western music today is still based on it.
Re: why half steps between (5 and 6) and (12 and 1) notes?
July 08, 2017 03:55PM
Okay so it sounds like:

They decided to base a very important progression (diatonic scale) on an instrument they had beforehand. Just because it's convenient I guess.

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

is rep.'d by the progression

W,W,H,W,W,W,H

Which should correspond to the ratios from a youtube class of an interesting teacher trying to explain the pitch progression we use.

Is that about right?
Re: why half steps between (5 and 6) and (12 and 1) notes?
July 08, 2017 04:03PM
Really confused as to why the administrator precludes the images URLs I have to find a workaround with the administrator before I can show you the images that I'm referencing
Re: why half steps between (5 and 6) and (12 and 1) notes?
July 08, 2017 04:06PM
Oh okay that's understandable why he did that.

Here are the links in the format he or she wanted

Rem: just add "h" before each URL so you can use it

ttp://imageshack.com/a/img923/29/ZzFpqB.png
ttp://imageshack.com/a/img923/7158/Bh2U7y.png
ttp://imageshack.com/a/img923/7038/6X6srV.png
ttps://www.youtube.com/watch?v=teSiBdFgDOI&t=227s
Re: why half steps between (5 and 6) and (12 and 1) notes?
July 08, 2017 05:48PM
see very first post in the forum

just remove 'h.t.t.p://' from url to load image to your post so all can see it directly

my answer to your initial question is because the major scale must contain 3 tones in series from one of the whole tone families, followed by 4 tones in series from the other whole tone family, ending in a repeat one octave higher of the initial tone and family

ex: ¦0 0 0¦1 1 1 1¦0
......¦CDE¦FGAB¦C

(just another way of looking at things)
Re: why half steps between (5 and 6) and (12 and 1) notes?
July 09, 2017 03:31AM
despues18 Wrote:
-------------------------------------------------------
> Okay so it sounds like:
>
> They decided to base a very important progression
> (diatonic scale) on an instrument they had
> beforehand. Just because it's convenient I guess.

Yes but nobody 'decided' at first, it was just one of the tuning arrangements they liked the sound of and it became widely adopted - then theorists came along and gave it a name Diatonic tetrachord. Diatonic just means "through the tones" in Greek. They had no idea it would become so successful.
>
> C,D,E,F,G,A,B,C
>
> is rep.'d by the progression
>
> W,W,H,W,W,W,H
>
> Which should correspond to the ratios from a
> youtube class of an interesting teacher trying to
> explain the pitch progression we use.
>
> Is that about right?

Not exactly - because we don't tune instruments that way. What he's showing was a discovery by one of those theorists: Pythagorus (and followers) around 500 BC. He showed how the length and pitch of a vibrating string are directly related. Half the length = double the pitch, etc. Pythagorus went on to devise a standard tuning system that was based on just two divisions of the string length. The 2:1 ratio which was the octave and the 3:2 ratio which was the perfect 5th. He ignored all the other string lengths. To find the pitches for every note, you just take the 5th above and each successive pitch will be 3/2x3/2x3/2 etc, or in our modern terms, C G D A E B F# C# G# D# A# E# B#. The problem is that B# doesn't equate to C, because 3/2x3/2 etc. etc, can never equal 2/1x2/1 etc. etc.

It wasn't a problem with simple music at the time but later it became a problem when sharps and flats and keys were gradually introduced and it was found that some keys didn't sound good. Nowadays pitched Western instruments are based on the system called equal temperament, where only the octave is an exact 2:1 ratio. All others are tweaked so that one semitone now equals exactly one twelfth of an octave and all notes like A# and Bb, etc, which used to be slightly different, are made to sound exactly the same.
Re: why half steps between (5 and 6) and (12 and 1) notes?
July 09, 2017 03:10PM
Ok, that actually makes a lot of sense. Thank you. Could you elaborate on what you meant by the problem is that you can't equate B sharp to C? I know that they aren't equally the same, but by what reasoning would you attempt to have them be?

(Unless I guess the B sharp place in that progression should stand for C which would indicate the initial point of the next octave. (because the progression behaves as a circle does i.e. self-repeating))

So if what I just said was true, is it implied that the B Sharp is the only note in error in that progression? Or is there more notes that are incorrect by going by 3/2x3/2?

Now I know why the circle of 5ths is an important tool because for whatever key you're on, the fifths belonging to whatever scale belonging to that key, will sound harmonious with each other. therefore you can build songs and chords that way.
Re: why half steps between (5 and 6) and (12 and 1) notes?
July 09, 2017 11:03PM
despues18 Wrote:
-------------------------------------------------------

>
> (Unless I guess the B sharp place in that
> progression should stand for C which would
> indicate the initial point of the next octave.
> (because the progression behaves as a circle does
> i.e. self-repeating))

Yes, ideally, B# would equal C and the circle would be complete, but it doesn't and if we try to use it as a C, we hear it's out of tune. The annoying pitch difference between B# (arrived at by 3/2x3/2 etc) and C (arrived at by 2/1) is called the 'Pythagorean comma' and for centuries instrument makers have tried to overcome it. Some solutions have included adding extra keys, but that makes the instrument impractical to play. Guitar and other fretted instrument makers used moveable frets to solve the problem, but that only works for simple music that doesn't change key. More complex music changes key mid stream, but a player can't adjust the frets while playing.

>
> So if what I just said was true, is it implied
> that the B Sharp is the only note in error in that
> progression? Or is there more notes that are
> incorrect by going by 3/2x3/2?

Yes there are more - it's just that B#, being the last, is the most noticeably different. The others are also 'out' by lesser amounts. - Notice that there's no F in that 'circle of 5ths', I wrote. Look at the note before B#, which is E#. . As you know, E# isnt the same as F. In our modern key of C major, for example, the note F is very important, and by string length division it should be 4/3 like your pics show, but by Pythagorean tuning the nearest available note is E#.

Now you have to think of it from an instrument makers point of view - say a harpsichord. He starts with one string (say, C), and then tunes the others in fifths as per Pythagorean tuning. But how does he tune the note F? If he uses Pythagorean' tuning, his F will really be E# and will sound crap in the key of C. So let's say he tunes his F to 4/3. Now F sounds perfect in the key of C. But when he tries to play the harmonic minor scale of F# minor (F# G# A B C# D E# F#) he's stuck. He needs E#, but doesn't have it. The best he can do is F. It sounded great in the key of C but will sound out of tune in the key of F# minor.

Tuning the whole instrument using string length divisions instead of Pythagorean tuning would be equally problematic. You could have F no problem, it's just 4:3 but what string division would correspond to E#? Some weird complex ratio, and anyway, there's no room for it if you've already tuned that key to F.

The answer to the problem was found by slightly altering certain notes to make them fit. Instead of basing everything on the 3:2 perfect 5th, a system called mean-tone tuning based everything on the 5:4 major 3rd. That helped but still sounded out in certain contexts. Then came 'Well temperament' which worked very well, and J.S. Bach celebrated its arrival by composing 48 preludes and fugues for the well-tempered clavier' in every key, all of which could be played on the same keyboard - a major musical breakthrough.

What we have now is called equal temperament which is a slight refinement of well temperament. The only true interval is the 2:1 octave. The perfect 5th is no longer 3:2. It's slightly adjusted so that as we go around the circle, we will arrive back at C - not B#. That's why the circle of 5ths changes at the 6 o'clock position. F# is now exactly the same as Gb and it then goes Db Ab Eb Bb F C - and the circle is complete.

The reason equal temperament works so well is that even though all intervals are adjusted except the octave, the difference is too small to hear, or, at least too small to sound bad. That annoying difference between B# and C has been equally spread out among all the intervals.



Edited 1 time(s). Last edit at 07/09/2017 11:26PM by Fretsource. (view changes)
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