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Music theory basics - half vs full step

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Music theory basics - half vs full step

Postby 7enderbender » Tue May 23, 2017 12:56 pm

Hello Everyone,

SOS magazine reader here, first time posting here. Been a guitar player for a long time and I'm a pretty decent player with good ears if I may say so - which leads to the not untypical issue that my music theory knowledge is completely spotty and I'm sure I'm suffering from a bunch of misconceptions.

I undertook several attempts in the past to fix that by reading, watching videos, trying to learn keyboards a bit and taking lessons. I lose interest quickly. Why? Because some of the very basics that everyone immediately skips over make no sense to me. Let me exaggerate a bit:

It starts with music notation. For me as a player of a stringed instrument things don't line up with reality. So historically letters have been assigned. Ok, fine. These letters then are represented by a (rather difficult to read) system of dots on and between lines. A system of how long the note is included - ok, that can be learned though I still don't find it elegant.

Then we include half notes. In notation and on keyboards the kinda skip around (whereas on my guitars I go from one fret to the next). In notation now we end up with nomenclature that indicates two different names for the same note. And then there are straight letter notes (no # or b) that are considered a half step.

See where I'm going with this?

So what's the actual physics here that makes me go from a "B" to a "C" and it's a "half step" while going from "C" to "D" is a "full step"? Who thought it was a good idea to call "C" that instead of, say, B#? Why isn't everything more linear like it is on my guitar neck?

There must be a reason behind it rooted in some kind of physics - or is this really just completely random or for the convenience of keyboard players?
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Re: Music theory basics - half vs full step

Postby Hugh Robjohns » Tue May 23, 2017 2:01 pm

There are plenty of articles online about the origins and development of written music.

It does appear to defy logic in many areas, I agree, but that's just because of the way it developed. There is no 'physics' involved in the naming of notes, it's all much more arcane than that -- and the naming of letters was more for the convenience of monks than anything, as far as I can see. ;-)

But there's no point complaining about it; it is what it is and it just has to be learned -- like the syntax and vocabulary of any language.
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Re: Music theory basics - half vs full step

Postby Ramirez » Tue May 23, 2017 2:23 pm

7enderbender wrote:So what's the actual physics here that makes me go from a "B" to a "C" and it's a "half step" while going from "C" to "D" is a "full step"?

Well, look at your fretboard. Going from B to C involves moving up one fret (i.e. one semitone / half-step). Going from C to D involves moving up two frets (i.e. two semitones / one step). The only difference between guitar and keybard is that you're skipping a fret on the guitar, and skipping a (black, in this instance) key on the keyboard.

Steps/tones/notes/semitones/whatever you want to call them line up on guitar same as a keyboard really - adjacent notes are always a semitone/half-step apart.

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Re: Music theory basics - half vs full step

Postby Hugh Robjohns » Tue May 23, 2017 2:39 pm

I think he understands that R.

The question is why some single letter increments (B-C, or E-F) only incur a semitone change in pitch, while other single letter increments (C-D, D-E, F-G, G-A, A-B) incur a full tone change.

It doesn't appear very logical Captain... :beamup:

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Re: Music theory basics - half vs full step

Postby Ramirez » Tue May 23, 2017 2:55 pm

Hugh Robjohns wrote:I think he understands that R.

The question is why some single letter increments (B-C, or E-F) only incur a semitone change in pitch, while other single letter increments (C-D, D-E, F-G, G-A, A-B) incur a full tone change.

It doesn't appear very logical Captain... :beamup:

H

Ah I see. Thanks Hugh! :oops: :headbang:
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Re: Music theory basics - half vs full step

Postby 7enderbender » Tue May 23, 2017 3:08 pm

Ramirez wrote:
Well, look at your fretboard. Going from B to C involves moving up one fret (i.e. one semitone / half-step). Going from C to D involves moving up two frets (i.e. two semitones / one step). [...] - adjacent notes are always a semitone/half-step apart.

Aled

Thanks. And this is exactly my point. Going from B to C is one fret on my guitar. Yet, per official music theory it's NOT a semitone/half step but a FULL step. As suspected, I don't think anyone could indicate any physics here yet, that would explain this. And yet, even during your first theory lesson they'll throw this at you as fact and almost a natural law - and then quickly derive from this how you use this - rather illogical "fact' - to derive major and minor scales. And that's before I even ask what happens if I tune my guitar up or down a half step - or perhaps a quarter tone just for laughs and giggles. Relative to each other you're still looking at "minor" and "major" scales but per "the rules" it should be something different.
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Re: Music theory basics - half vs full step

Postby Ramirez » Tue May 23, 2017 3:39 pm

7enderbender wrote:Going from B to C is one fret on my guitar. Yet, per official music theory it's NOT a semitone/half step but a FULL step

Hmm.
No - B to C, as per official music theory as you say, is a semitone/half-step, NOT a full step.

The major scale is made of the intervals Tone, Tone, Semitone, Tone, Tone, Tone, Semitone regardless of key. In C major, with the C-D and B-C as discussed in bold, this would be:

C - tone (step) interval - D
D - tone interval - E
E - semitone interval - F
F - tone interval - G
G - tone interval - A
A - tone interval - B
B - semitone (half-step) interval - C

The other keys are exaclty the same just with different letters.
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Re: Music theory basics - half vs full step

Postby job » Tue May 23, 2017 3:47 pm

I think it's because we've ended up dividing the octave into 12 semi-tones on a 7 note scale, meaning there will necessarily be 2 notes that don't have a fixed sharp or flat. The 12 notes are from some ratio of a vibrating string i think, although we've changed it slightly so it conforms exactly to the circle of fiths.

As an aside, C is only always a C if it's in isolation, it would be a B# in, say, a chord whose previous note was some A (if the mode used called for the necessary interval to land on C). Likewise with any other note since progressions always use the next/previous letter (as far as notation is concerned).

Sharp/flat just means you raise/lower the next note by a half step, they don't 'really mean' the black keys.
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Re: Music theory basics - half vs full step

Postby CS70 » Wed May 24, 2017 9:21 am

7enderbender wrote:Then we include half notes. In notation and on keyboards the kinda skip around (whereas on my guitars I go from one fret to the next). In notation now we end up with nomenclature that indicates two different names for the same note. And then there are straight letter notes (no # or b) that are considered a half step.

See where I'm going with this?

So what's the actual physics here that makes me go from a "B" to a "C" and it's a "half step" while going from "C" to "D" is a "full step"? Who thought it was a good idea to call "C" that instead of, say, B#? Why isn't everything more linear like it is on my guitar neck?

There must be a reason behind it rooted in some kind of physics - or is this really just completely random or for the convenience of keyboard players?

Same here, guitar player here. Very roughly, a note is synonym for pitched sound - a sound that you can hear with your ears by making something vibrate in air at a given frequency. To make it quick, you can say "a note is a particular frequency" which is technically wrong, but a shortcut "a note is the name we give to the sound developed by an object oscillating at that frequency". Since we label certain frequencies in a certain way by convention, we often say that an A "is" 440Hz etc. Given a certain note, the more energy per instant the vibration has, the more air is moved for every vibration, the louder the note (approx). Bass notes need more air, so the heard they need more energy (ever though why bass players lug around 600W amps?) That gives you the connection with the physics. Sort of :D

Btw, the stuff that does the vibrating can be anything - a string, glass, even a building (very, very bass notes and little volume tough!)

So by using that physics you make things vibrate and in the west we figured out that 7+1 particular frequencies stood out as pleasant and we got use to hear them and make music with them. They also have specific mathematical properties (the "+1" is an exacty mulitiplier of the first, for example) so the arithmetically inclined started to do what the arithmetically do - i.e. find new relationships based on multiplication, division etc.

One invention were these "half" notes between the frequencies we call C&D, D&E and F&G, G&A and A&B, (why not between E&F and B&A? There's nothing there that has the arithmetic properties we want and since the properties match what sound good to our ears, there's nothing sounding good to our western ears. Note that to *other* ears there might).

Turns out there are actually two pitches that sound good between each of the couples above: say for C&D, one is C sharp, the other is D flat. They are actually distinct - pretty close, but not the same frequency. Problem is, keeping them distinct makes things very complicated when it comes to transposing tunes that make use of them and to build keyboards (and guitars!) which allow to distinguish them. Since notes are just a name for certain frequencies, people said "why dont we split up the frequencies in a slightly different way, so that these sharps and flat end up being the same?" And so they did. To avoid making these pitches sound sour tough, all the other notes had to be re-arranged slightly, with the result that all the sounds which are not the first frequency and the 12th in our subdivision are slightly off with respect to the "sounding good" ones. Traded simplicity for quality! :D That's the idea that the guitar follows, and a piano keyboard (which has only one black key between two whites) and any instrument where the player can't decided the pitch and that can be played in any key.

Otherwise we would have to have a specific guitar for every key you want to play in (the original GAS I suppose). So that's why flat and sharps are "the same" even if they aren't, and there's two different names for them.
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Re: Music theory basics - half vs full step

Postby CS70 » Wed May 24, 2017 9:46 am

7enderbender wrote:Going from B to C is one fret on my guitar. Yet, per official music theory it's NOT a semitone/half step but a FULL step. As suspected, I don't think anyone could indicate any physics here yet, that would explain this. And yet, even during your first theory lesson they'll throw this at you as fact and almost a natural law

Say you look at the frequencies which sound good starting from 440Hz and name them A, B, C, D, E, F, G. Then you look at the numbers and you discover that these sound have an interesting arithmetic property - the ratios between the corresponding frequencies are made by small integer numbers: 1/1, 2/1, 3/2, 4/3, 5/4, 6/5.
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Re: Music theory basics - half vs full step

Postby BJG145 » Wed May 24, 2017 10:25 am

CS70 wrote:Say you look at the frequencies which sound good starting from 440Hz and name them A, B, C, D, E, F, G. Then you look at the numbers and you discover that these sound have an interesting arithmetic property - the ratios between the corresponding frequencies are made by small integer numbers: 1/1, 2/1, 3/2, 4/3, 5/4, 6/5.

I haven't read up on this, but I'd have thought it was more likely that the scale started with the maths, and it only "sounds good" because we're used to it. Would someone who'd never heard music before find something inherently attractive about those frequencies...? Dunno.

*edit*

On the other hand, maybe you're right...

https://golem.ph.utexas.edu/category/20 ... l_ori.html
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Re: Music theory basics - half vs full step

Postby Hugh Robjohns » Wed May 24, 2017 11:39 am

7enderbender wrote:Going from B to C is one fret on my guitar. Yet, per official music theory it's NOT a semitone/half step but a FULL step.

Er... I think your 'official theory' book is a fake! ;-) The B-C interval has always been a semitone...

And yet, even during your first theory lesson they'll throw this at you as fact...

Not in any of my music theory classes I've had (though they were long, long ago...)

...and then quickly derive from this how you use this - rather illogical "fact' - to derive major and minor scales.

It is certainly true that adjacent notes in major and minor scales vary between full (tone) and half (semi-tone) steps in a prescribed sequence. But that same sequence applies whatever the key.

It is only for the C-major scale that all the note letters happen to be used in order... but that's more coincidence than careful planning I think.
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Re: Music theory basics - half vs full step

Postby artzmusic » Wed May 24, 2017 11:40 am

You might think it would be easier with numbers. But no! If the root is G and everything above it is numbers (which is my approach) then everything relative to G would be 2, 3, 4, 5 etc. But No, now there's a flat 3 and a sharp nine, and augmented this and diminished that. I protest! :protest:

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Re: Music theory basics - half vs full step

Postby Temp » Wed May 24, 2017 12:40 pm

Why isn't everything more linear like it is on my guitar neck?

I have the exact opposite opinion! Interesting how musical perceptions can differ.

I've been a guitar player for 25 years, but when teaching basic theory to other guitarists I always advise them to get a cheap keyboard, stick numbers on all the white keys for one octave (e.g. C3-C4) and then tinker around with it. I've found that this approach can often unravel the crazy up-down-up-down of a guitar fretboard, which, to someone with a flakey knowledge of intervals, might appear to have no underlying logic (I come across a lot of guitarists that are very good with patterns and licks, but don't necessarily know what intervals they're playing).

By demonstrating the simple intervals and degrees that make up the C Major scale (using TTSTTTS, 12345678, solfa etc.), folks can also see how major and minor triads are made up, providing a nice simple entrée into flats, sharps and chord structure. For me, by being visually linear and having chromatic, contiguous notes, the keyboard allows intervals to adopt a more obvious numerical significance, along with other useful stuff like how relative minors work etc.

Cheers.
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Re: Music theory basics - half vs full step

Postby CS70 » Wed May 24, 2017 12:51 pm

BJG145 wrote:
I haven't read up on this, but I'd have thought it was more likely that the scale started with the maths, and it only "sounds good" because we're used to it. Would someone who'd never heard music before find something inherently attractive about those frequencies...? Dunno.

Yeah, probably a combination; real discovery is generally a quite messy affair unless it's seen from far away.

However, there is a fundamental physical relationship (vibrating objects producing air waves with common component frequencies) which is picked by our brains regardless of any math knowledge - or the very existence of mathematical structures to describe it. Same way as, say, symmetric structures, which catch attention and stand out whether you know anything of geometry or not. We're just wired like that.

Math is usually borne out of the urge of describing something interesting, and then of course it leads to the discovery of other interesting stuff, and then we get used to them and start giving them names :)
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Re: Music theory basics - half vs full step

Postby Guest » Wed May 24, 2017 9:11 pm

How do you view E to F then?

Is that not the same thing?

It’s to do wiv da Key, it/they has/have a dual role.

You work it out.

Use them excellent ears of yourn.

That’s all music is, ears, they tell you everything you need to know, you got good un’s? use ‘em, ‘ow ‘ard’s dat mate.

Simples innit.

Or else, 'ow could i be so capable?

Or not.

Eh.
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Re: Music theory basics - half vs full step

Postby CS70 » Wed May 24, 2017 11:16 pm

LdashD wrote:It’s to do wiv da Key, it/they has/have a dual role.

That'd be the key of the drawer where you keep the real good stuff, innit? :mrgreen:
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Re: Music theory basics - half vs full step

Postby Dynamic Mike » Wed May 24, 2017 11:32 pm

7enderbender wrote:There must be a reason behind it rooted in some kind of physics - or is this really just completely random or for the convenience of keyboard players?

Personally I suspect it's actually the other way around. The scale is most likely derived from a string instrument, rather than a keyboard instrument (which originally only played strings anyway). The mathematics you're looking for is explained pretty well here https://tinyurl.com/l52ql6e which gave rise to the rule of 18 (or 17.817 if you're being pedantic) for determining fret markers. The ratio for determining the n'th fret ensures all steps are the same, so there no need for black frets.

12 full size keys would be a challenging spread for any keyboard player, which possibly gives rise to the need for black keys? Why they chose the notes they chose I've no idea, maybe they were just less commonly used, or maybe it was down to the physical construction of the first keyboards.
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Re: Music theory basics - half vs full step

Postby CS70 » Wed May 24, 2017 11:59 pm

Dynamic Mike wrote:Personally I suspect it's actually the other way around. The scale is most likely derived from a string instrument, rather than a keyboard instrument (which originally only played strings anyway).

The earliest instruments we know of (voices aside) are actually flutes. And that's also where the keyboard comes from - I vaguely remember reading that the chain is pan pipes - organs - harpsichord - fortepiano - pianoforte. An organ had a keyboard to select the playing pipes.
But of course things may have been invented/discovered independently and more than once.

By the way, here's a pic of a harpsichord keyboard in just temperament, with sharps different than flats and accidents between B&C and E&F. The simplification of western subdivision of the octave seems rather modern, as these instrument had a number of intervals available which would satisfy any indian musician...

Image
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Re: Music theory basics - half vs full step

Postby Guest271017 » Thu May 25, 2017 12:46 am

Look, there's only one way to learn guitar. I wish I had had a good teacher instead of a jazz/blues shredder who just ran through scales every lesson showing off. I stopped after 6 months and went on my own. With my drive and the right teacher, who knows...

Learn every note on the fret board. Start in open position and go up and down chromatically, using all fingers, naming all the notes out loud as you go. Move it up to the first fret and do the same. Up and down the neck, don't think about scales, just notes.

Once you've done that so you can just look at the fretboard and pick out all the notes, start with CM scale. Again open position to start and then up and down the neck in every position. Get it so no matter which string/ fret C falls on, try starting on whatever note falls on the low/high E string, in that position. You can name all the notes, so start recognizing the patterns in each position. Do the same for the Am scale after C so you see how minor relates to major. Once you have this much down, you can play in any key, in any position.

Once you have major and natural minor down, work on the different flavors of minor scales, same way as above. After that it's modes. No reason to fear them by this point, it's like playing for instance a C scale, but your treating the other notes as the root.

In 6 months you'll have mastered the fretboard and simple theory will be cake.

Don't try to learn from the keyboard, you'll be translating the rest of your days. People who learn a second language translate through the native one as a matter of course. It slows you down in the end. It's an extra layer of processing. If you want to play guitar, learn guitar.

During this time, make some simple backing tracks of drum, rhythm and bass in the key you're working on and solo over it. This is the practical side of education. Theory in class then real world practice.

Hardest part is staying on task, especially for intermediate players and up. You'll be practicing and something will remind you of something and you'll be in Jam Land in the wink of the eye. Beginners know naught else so they're limited in the wander dept. You have to put at least an hour at a sitting to strict practice. It's better if you practice even when in front of the TV. I sit there for hours at a time, not plugged in and just running through scales. If there's music, I just match the tempo if I'm half paying attention to what's on. If not, I'll match the key on the fly, also.

B-C a whole step??? :headbang:
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