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Why do we have sharp and flat notes?
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Jim Opfer
Posts: 1876
Joined: Jul. 19 2003
From: Glasgow, Scotland.
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 Why do we have sharp and flat notes?
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I had a thought this morning that never ocured to me before.
I've never been able to get on top of musical notation with all those sharps and flats, then some notes E and B don't have a sharp. So I wondered why it was this way?
As I said, I have problems understanding notation and for all of you, like me, I just play by ear and have no recognition of when the note I play is a sharp in a scale or flat, to me it's just the sound.
OK! streatching the imagination a bit here, but if you were to be a musical note and in that capacity, if you could ponder things, you would think of yourself as just another note, I mean not 'sharp' or 'flat', just a 'true note' like every other note around you, so why would you have to have the tag: sharp or flat?
So this is all going on in my head then it hit me. 'The whole musical notation system is contrived to make it easier to play the piano'. Think of it, a piano could be made with alternative black/white notes from one end to the other, or just all white notes one end to the other, or just all black notes. That way there would be no sharps or flats.
Problem is that it would be hard to play without the visual recognition of where things are on the key board. So to make it easier, black note groupings were invented but this system ment pairing white notes together and therefore, E and B don't have sharps.
Just imagine how different it would be if we didn't have pianos 
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Date Mar. 1 2008 23:08:49
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Ricardo
Posts: 14828
Joined: Dec. 14 2004
From: Washington DC
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RE: Why do we have sharp and flat notes? (in reply to Jim Opfer)
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Guitarbuddah is right, or at least I agree with all the points he made. Just want to add there is an importance with TUNING systems. Early keyboard instruments were not even equal tempered. So the whole thing was about fine tuning and getting the new 12 note system to work, leaving behind modes and Modal type music/tuning systems. Many musical mined math students have tried to understand "why 12" or how did the early musicians come up with 12? Wouldn't say 16 notes have more acturate intervals? Or perhaps less notes with more pleasing relations? (essential the old modal tuning idea). Well, when it comes to changing keys, the answer always comes back to 12. Wish I understood it, but there is a mathematical reason.
So the REAL question is why does the 7 note scale matter so much? This is a more deep and important way to get at Jim's orginal question. The reason we need sharps or flats is because we need to describe 7 notes in a 12 note tuning system. The indians did the same, 7 main notes but they have 22 note tuning system. Greeks the same, but they had 24 (Indians don't rename imperfect 5ths or octaves as we think of them). Chinese had 60 notes to the octave in their metal pipes or whatever, but yet again describe their scales with 7 main designations.
Wish I could give them but I can't remember. Indian is like "Sa Fa ma pa " or something really sorry, can't remember. But 7. Chinese again, some chinese sounds. Europeans adapt Do re me fa sol la, etc, and others ABCDEFG. In some cases the 7 sounds describe the Ionian or natural major scale (not always litterally because remember the tuning system thing). Oddly, the alphabet system describes natural minor or Aeolian scale, not Ionian. The chinese was really like a "Lydian" scale, but remember chinese modes leave out the tritone, so they deal with only pentatonics. (ACDEG for example, leave out F and B the tritone), but still reserve a name for the extra notes.
So no matter what tuning system you choose, you discover a need for naming the "notes in between". So we use Sharps or flats or with do re mi you say "do bemol" or "sol sustonido". etc.
Once more I point out "Why 7" is so important? I have my own personal "theories" about it. Think about the over tone series (harmonics above a vibrating note), and also that interval the Chinese deliberately omit...I found a connection there.
Ricardo
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Date Mar. 2 2008 20:50:45
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Ricardo
Posts: 14828
Joined: Dec. 14 2004
From: Washington DC
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RE: Why do we have sharp and flat notes? (in reply to guitarbuddha)
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quote:
ORIGINAL: guitarbuddha
Hi Ricardo.
I think that the seven notes are easily explained ( though easy may not be accurate) by the fact that the three major triads which are easily constructed from the harmonic series (I IV and V) generate seven tones. So in C , CEG,FAC,GBD. Also notice the prominance of the two most important tones of the diatonic system, C and G. All strong (primitive) three chord combinations seem to generate seven notes and they seem to get their strength through being easily generated from the harmonic series.
Good idea, and based on 12 tone tuning system I would tend to agree. But there is flaw with your "I,IV,V" idea. That is, well, you can still get a 7 note scale out of some other 3 chords/triads in the chord scale. I, ii, iii, for example. But also, very important, those "chords" by themselves sound OK in equal temp tunings, but in some modal systems you dont' have those chords as separate entities. You would just have a drone and some intervals above, basically the scale makes ONE fundamental, sweetly tuned 13th chord. But again you have 7 notes to name a mode, like the Greeks. 7 notes, but no chord "progressions" like I,IV,V. (I know the Greek tetra chords imply 8 notes, but one of the notes is an "octave" as we westerns think of it). The thing about V-I in tonal music is you get to modulate, but still the whole thing comes AFTER the concept of a 7 note scale that the chords get derived FROM, not vice versa.
Trying to build chords from the overtone series, I mean the literal pitches, not the equal temp approximations, you get some ugly sounding relations. BUT when heard over a drone, they all sound like the "same" 13th chord, sweet and beautifully tuned.
12 tone music was a nice intellectual game, but really since you no longer deal with the V-I, that music sort of defeats the purpose of the whole equal temp system (finding a pleasing or acceptable tuning that allowed for modulation, from one "mode" or key to another, without having to retune). They could just as easily invent a new tuning system, and indeed some nerds have done just that with their modern atonal music. Honestly I can stomach some atonal stuff, so long as it has rhythm. Opposite to atonal music, hearing an Indian drone and ONE scale improv for 30 minutes, really can bore people.
Again my idea why the prejudice for 7 notes, vs 6,8,9 etc, incorporates both modal concepts AND tonal, and even partially explains the ambiguity for "atonal" music and scales. My idea deals with the tritone's relationship to a key, mode, scale, etc. I could go on for you but I think the point about "why # and b's" has been made clear already.
Ricardo
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Date Mar. 3 2008 4:56:29
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guitarbuddha
Posts: 2970
Joined: Jan. 4 2007
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RE: Why do we have sharp and flat notes? (in reply to Ricardo)
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quote:
ORIGINAL: Ricardo
quote:
ORIGINAL: guitarbuddha
Hi Ricardo.
I think that the seven notes are easily explained ( though easy may not be accurate) by the fact that the three major triads which are easily constructed from the harmonic series (I IV and V) generate seven tones. So in C , CEG,FAC,GBD. Also notice the prominance of the two most important tones of the diatonic system, C and G. All strong (primitive) three chord combinations seem to generate seven notes and they seem to get their strength through being easily generated from the harmonic series.
Good idea, and based on 12 tone tuning system I would tend to agree. But there is flaw with your "I,IV,V" idea. That is, well, you can still get a 7 note scale out of some other 3 chords/triads in the chord scale. I, ii, iii, for example.
Ricardo
Hi Ricardo, that is exaxtly what I meant by 'primitive' chord sequences, ie folkloric and modal (in the western rennaissance sense) sequences.
What would really fascinate me would be some kind of study as to what is percieved by different cultures as 'exotic' in music of a culture to which they have not been exposed. Possibly the time for this is running out.
I suspect that pentatonics (without semitones) sound straightforward to everyone and that scales which contain adjacent minor thirds and semitones, always sound exotic. But I really don't cant verify that. Symmetrical scales are probably always disturbing as they lack a tonal centre ( and all cultures seem to enjoy some concept of a tonal centre ).
Certainly much of the 'comparing' that we in the west do (wether we are aware of it or wish to) with all music to the ionian arrangement is due to a great deal of cultural baggage, but I think that there well be something 'vanillaish' about it intrinsically (tempered or not). Even more vanilla still the Major pentatonic and its imversion the minor pentatonic.
D.
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Date Mar. 3 2008 5:24:14
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a_arnold
Posts: 558
Joined: Jul. 30 2006
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RE: Why do we have sharp and flat notes? (in reply to Jim Opfer)
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F# and Gb aren't the same note, really.
There is an actual frequency difference. Before tempering became common (about the time JS Bach wrote "the Well Tempered Clavier") it was the convention for people to retune their instruments when they changed keys. Modulations (key changes) within a single piece of music were (therefore) rare before that time.
A tempered keyboard (clavier in Bach's parlance) is tuned so that the actual frequency of the black key is a compromise between F# and Gb (and, of course, likewise with other flat/sharp pairs). Most people without perfect pitch (even most with it) aren't bothered by the compromise. Bach wrote the Well Tempered Clavier to demonstrate that the practice of tempering worked; it is a series of pieces in a sequence of keys that would sound horrible on untempered instruments if left untuned.
This is why your guitar might sound great when you play something in A and then sound like it needs retuning when you change to C, even though it is still in tune in A.
Violinists, vocalists, and other players of unfretted instruments can correct for these infinitesimal differences (like between F# and Gb) without retuning. Guitarists and keyboardists can't. So violinists have to correct and play a little off key to sound right with a guitar or piano.
Ricardo and guitarbuddha reference this history indirectly. One could probably google the Well Tempered Clavier (sometimes spelled Klavier) and find more detail.
The musical scale is such a mathematically internally consistent thing (harmonic-sounding frequencies having integer ratios, etc, all known and mapped out since Plato) it has always puzzled me that F# and Gb AREN'T the same. Seems like they should be.
I just asserted that they aren't the same, and they aren't, but I still don't know why not. Just because my music teacher said so doesn't really explain it. Seems an uncharacteristically inelegant aspect of music, given the mathematical elegance of music otherwise.
Anybody know WHY they aren't the same?
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Date Mar. 3 2008 15:40:36
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guitarbuddha
Posts: 2970
Joined: Jan. 4 2007
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RE: Why do we have sharp and flat notes? (in reply to a_arnold)
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Cycle of fifths does not resolve to a note which is the same as the starting note.
How so, well take a guitar low E string, divide it in three and you get a B one octave and a fith higher (which you can tune your B string to). Take a new string tuned to that note and repeat the procedure, so, E,B,F#,C#,G#,D#,A#,F,C,G,D,A and back to E.
Now when you divide your string in two you get an octave (the same note again higher, exactly twice the frequency) now the E (or any other note) that you get when you go up the cycle of fifth actually has a DIFFERENT frequency (is a slightly different note )than the one that you get by doubling continually. Play the two together and it is pretty appalling. This is fundamentally why tuning on any instrument is a compromise and why it is sometimes a very bad idea to tune your guitar with harmonics.
In Bach's times all of the notes were made slightly out of tune so that they got a cycle which did get back to the original note. Strangely enough we on fretted strings have our instruments perfectly tempered as divingin a string in twelve does exactly what it would take very complicate maths to decide to do.Basically take your open string divide that note in twelve and that is where you put your first fret. Take that length and get the second fret a nd so on.
So the note at you seventh fret (where the harmonic an octave plus a fifth is also found ) is in fact tempered and slightly out of tune with the harmonic of the same string. It is often a very good idea to tune to fretted notes for this reason as it gives you a perfectly tempered instrument (something which is much more difficult and expensive to do on your piano).
Before equal temperament for the keyboard instruments we guitarist were way ahead of keyboard technology. The clavichords and harpsichords were tuned to sound sweet (much sweeter than a modern piano) in one key at a time (using the natural harmonic series) and sounded bloody awful if you moved to some other keys. If you wanted to play a piece in a different key then you had to stop and retune. Some open tunings in the guitar are like this, such as DADGAD, and again although sweet they affect your ability to change key.
In the string orchestra the Cellos,Vialos and violins are tuned in perfect fifths and not tempered. Again this sounds very sweet but can lead to tuning problems. However and advantage is that the high notes on the violin are slightly sharp and sound more brilliant against the flatter bass notes helping them to stand out. A fretless player can choose exactly which note to play and there is a real skill in choosing the ones (INSTINCTIVELY) which are most effective in a particular situation. A good blues or rock gutarist can also do this to great effect with bending, again instinctively. On gut we also have access to this kind of thing with vibrato and smaller bends. Also a great technique which a lot is flattening a note by pushing the string towards the bridge which can add a really accentuate a line and although very subtle can bring a lot of life to the music.
This has however NOTHING AT ALL, yup, NOTHING AT ALL, to do with Jim's original question. However it has EVERYTHING to do with why Ron finds organs jarring.
D.
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Date Mar. 3 2008 16:25:40
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Ricardo
Posts: 14828
Joined: Dec. 14 2004
From: Washington DC
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RE: Why do we have sharp and flat notes? (in reply to guitarbuddha)
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Good stuff Budda. Just want to add. The WELL tempered clavier was not EQUAL tempered, and there were different instruments tempered different, not necessasarily a need to retune for each song. Bach's "well tempered clavier" was specifically designed to go through ALL the keys, avoiding say the harsher out of tune intervals in Certain keys, but for that one special tuning only. Aparently the proper well tempered instrument you can hear the difference, compared to say a modern piano.
Anyway, in modal music, you have a drone, and the soloist be it a vocalist or string player, flute, whatever, can hit a single pure interval, perfectly in tune, and the "color" relative to the drone has expression. In equal tempered tuning, beyond the "bending" you talked about, VIBRATO is used to smear the "coma" problem to the listener, and there the soloist gives "expression". Vibrato is done on string instruments and with the voice, sometimes very exaggerated and gives the illusion that the note is in "tune' with the other instruments.
About tuning to fretted notes vs harmonics. The only problem is you can not tell for sure the finger or fretted note, is being applied a perfect even pressure. Guitars with high action for example are MUCH more sensitive to this. Always safest to have the OPEN strings in tune relative to each other since you are not afforded the technique of vibrato or bending with those notes. And a fast way is the harmonic method, even better, a digital tuner for the open strings.
One more thing about the difference between Gb and F#. Well, there is not really a difference on equal temp instruments, BUT you can get the idea why what seems to be the same note might be OUT of tune relative to other notes (sort of the same idea). The way to hear it is simple if you can hold a note with your voice and have a good ear. Here is what you do.
Take the D string open and pretend it is perfectly in tune. Now tune the note D an octave above, and use your ear to be sure it is a PERFECT octave, not wavering or beating. YOu can use the 3rd fret B string, or 7th fret G string, I don't care, just make sure you are careful about the pressure you put on the fret, don't push too hard.
OK, for a reference play the 4th fret of the D string, that is equal temp F#, and sing the same pitch. Now just play the D string open and listen to the wavering and beating. Lower the pitch your voice makes JUST A HAIR until the beating stops and you have a perfect sweet Major third with no beats. That is a perfect tuned F#. OK, NOW play D you fret an octave higher and keeping singing the same note. That is supposed to be a minor 6th, but it is a bit wavey so if you raise your pitch up just a hair, close to what it was at eh 4th fret, you notice it gets "sweet" again, not wavering. When you can learn how to distinguish those two different notes, the perfectly tuned major 3d above, and the perfectly tuned minor 6 below, then you are starting to hear the difference between an F# and a Gb...sort of. See in modal music, that difference, as subtle as it seems in this exercise, can actually mean an entirely different note and intervalic relation.
OK if that is too hard to do with the voice, you CAN use your guitar. You just have to fret the D on the 5th fret (make sure your octave D notes are PERFECT), and use the 4th fret D string for the F#. To lower the pitch for a major 3rd above, squeeze harder on the F# TOWARDS the bridge. Be careful to not bend your D on the 5th string when you do that. To hear the minor 6th below your higher D note (either 7th fret G or 3rd frt B string) you pull the F# AWAY From the bridge. You try to do this bending thing just enough to make the beats go away so the intervals are "sweet" sounding.
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Date Mar. 4 2008 16:10:19
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guitarbuddha
Posts: 2970
Joined: Jan. 4 2007
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RE: Why do we have sharp and flat notes? (in reply to Ricardo)
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Hi Ricardo, thanks for the clarification, I kind of assumed that well tempered was equally tempered. I know that there were a lot of different tuning systems around.
The thing that I want to clarify in here is that Jim suggested that music theory throws up more problems than it answers. And I profoundly disagree.
Look at Ron's posts on his heroic struggle with El Tempul (and I am sure he will win in the end). The puzzles that we need to solve ARE IN THE MUSIC, that is the sounds we hear and enjoy and the incredible variety of shadings of pitch and meaning that they can convey.
For me a well produced score is a real big help. This is a fact so I will repeat it A GOOD SCORE IS A FABULOUS AID IN LEARNING MUSIC......IF YOU ARE COMFORTABLE READING A SCORE. Now if you aren't (not you Ricardo of course but my posts are pompous enough without writne 'one' all the time) then, until you conquer this skill, the score may seem like another complication. But if you need the score you were not that clear about the music in the first place were you ?
For you and I and the other experienced readers reading a well presented score is not a problem at all. When we discuss elements of music theory here on the foro then we are discussing ways of understanding (and therefore being able to untergrate into our won playing) ACTUAL MUSICAL SOUNDS, RHYTHMS AND HARMONIES, using the theory to help us communicate and to also using the theory in our own private study.
I worry that when people get confused by our discussions they assume that we are as confused and lost as them. Generally we are not, we do not always agree but the theoretical is another USEFUL (although NOT ESSENTIAL) layer in our understanding of music and also in our ability to discuss and share ideas.
I worry that this discussion seems to have boiled down to just you and I and we are preaching to the converted. The majority of posters seem to deny that music reading is any use. They seem to confuse useful with essential, reading music for some styles is not essential but bloody hell is it useful.
I just wish that people would accept that. There are new generations of players composers transcribers and improvisers who will be working on flameco and flamenco type music. I feel sure that the Oral tradition is alive and well in flamenco perhaps more so than in any other guitar based music and that really is a wonderful thing. I agree that the new generations must and will continue with this skill. But we are doing them a tremendous disservice if we by our comments and prejudices encourage them to reject learning to read music. Reading music is bloody great fun, I could never go back to playing from tab or solely from ear, there is too much I want to play (some of it only once at sight and just for a moments entertainment) to abandon this the most useful of the things that I have learned since I started learning.
There is another worry that I have as well (although more for the guitar in general and not particularly for flamenco) when kids were learning from the record they were getting great ear training and really needed to understand what they were playing (on some level) to play along with the recording. Now I notice lots and lots of pupils who are playing from TAB and they don't really understand a bloody thing about what they are playing because they haven't listened to the recording often enough or carefully and actively enough, they are not playing by ear at all. You ask them to 'dum de dum' how they think it goes and what they vocalise has 1)No relationship with the recording 2)Little in common with what they played.
Now we are getting instead of scores with TAB added TAB with scores added. Often the scores are useless (music capoed at the second fret written in the key af F# rather than E, Eb instead of C at the third fret ) no fingerings in the music or pisition indications, no actual FINGERINGS for either hand. Even worse we get a tune with around 12 bars of actual guitar music written over like 20 pages. Ten page turns for five minutes of five chord rock ?
Now I know that the age of defference with snooty 'only classical is worthy' musicians turning off kids with their snooty opinions and zero understanding of anything written since Schuber.... is over. And good riddance to it. But now kids seem to be sold the idea in the media that they know everything before they have even started looking. In the guitar magazines they get the idea that TAB is an advance on standard notation and that ingorance is they key to success in music and in showbiz.
To sum up.
Playing by ear =Great !!!!!!!!!!
Playing from a score with understanding and style= Great !!!!!!!!
Being able to do both= Super great.
Murdering music from TAB= Dull Dull Dull Bu##****.
TAB and ear works too but seems more open to abuse.
I propose that we as a body adopt the above position when we welcome new members and when we influence them by our discussions.
Another thing. Many of the old school classical teachers discouraged playing by ear (since they couldn't do it and didn't understand it) do the ear only players here really want to adopt the same position towards reading ?
D.
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Date Mar. 5 2008 7:18:24
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XXX
Posts: 4400
Joined: Apr. 14 2005
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RE: Why do we have sharp and flat notes? (in reply to guitarbuddha)
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quote:
ORIGINAL: guitarbuddha
TAB and ear works too but seems more open to abuse.
That is not a malfunction of TABs. Its the students choice what to do with it. For example, somebody who is not really interested in learning this stuff seriously, will choose TABs over notes, because they are easier to learn. So, with his attitude he starts to read TABs with half interest, and in the end, doesnt "get" the music behind that. Imagine there wouldnt be TABs.. surely you could also "murder" music from notes. It would just take more time lol.
Further you always generalize from bad TABs to all TABs. Even if there was no accurate TAB on earth, still, that wouldnt mean that TABs are bad, but more that TABs are made poorly. Anyways, not so much important imo. It depends on what suits you more, what type of learner you are. Learning by ear, or TABs/Notes. I never could play something from the paper without first hearing and memory it. I admire people who can do that, but i dont think its neccessary, especially not in flamenco. Regarding TABs or Notes... TABs just make life a bit easier. Its just a luck, a nice coincidence for guitarrists that the guitar has frets and that there is this easy way of notation that everybody understands. And its more accurate than notes, because it shows the fret. You can have also rythmical notation (with the necks). Disadvantage is you have to know that the 5th fret on the A string is a D, and so on, but that should be no problem, since you can take the C chord at first position, and shift it until you have your note at a higher fret.
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Фламенко
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Date Mar. 7 2008 6:32:47
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