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Post by reTrEaD on Jun 18, 2023 8:28:36 GMT -5
Piano is a rather visual medium. When learning music theory, I find it convenient to use a piano or other keyboard. One common question is: Why is there no black key between B and C, and between E and F. Here's David Bennett's explanation:
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Post by JohnH on Jun 19, 2023 8:12:07 GMT -5
Well thanks for posting that! I learnt quite a lot there which I'd never grasped before from other explanations. Plus, found out how there can really be a B sharp!
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Post by reTrEaD on Jun 19, 2023 22:07:20 GMT -5
Well thanks for posting that! I learnt quite a lot there which I'd never grasped before from other explanations. Plus, found out how there can really be a B sharp! Indeed! There can be a B-sharp (C) Or a C-flat (B) Or an E-sharp (F) Or an F-flat (E) It's important to know when to use those particular sharps or flats rather than their enharmonic equivalents with natural names. At 13:50, David explains one of many reasons: the avoidance of cluttering up the sheet music with unnecessary accidentals, toggling back and forth between C-sharp and C-natural. In my opinion, it's worth circling back to 10:19 understand another reason. Here, David is repeatedly stacking fourths above flat notes. In each case, the fourth looks like a fourth on the staff. Also, the note names skip two letters. But at 10:44, although we COULD call "B" the perfect fourth above G-flat, we really SHOULDN'T call it B! It looks like a (augmented) third on the staff and we only skipped one letter name (also implying the interval is a third of some sort). It's right and proper to refer to this "B natural" as a C-flat. I fully understand why David chose to call it B. This was a convenient way to show a black key wasn't necessary. But this is one of those instances where a white key should be referred to as its enharmonic equivalent that isn't a natural.
Does that make sense?
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Post by Yogi B on Jun 20, 2023 8:36:19 GMT -5
Piano is a rather visual medium. When learning music theory, I find it convenient to use a piano or other keyboard. Whereas I tend to find a keyboard's misrepresentation of interval spacing actively unhelpful. To someone with no (or very limited) musical knowledge, purely looking at the key layout easily leads to questioning why it isn't perfectly regular. In contrast, the equivalent scenario using a fretboard would be them looking at the frets and spontaneously wondering why they didn't look like the below illustration (and without this observer even knowing the guitar was in standard tuning!): It's important to know when to use those particular sharps or flats rather than their enharmonic equivalents with natural names. At 13:50, David explains one of many reasons: the avoidance of cluttering up the sheet music with unnecessary accidentals, toggling back and forth between C-sharp and C-natural. With the older, looser, definition of enharmonic (where notes are in the vicinity of the same pitch, but not identical in pitch), these would be different pitches. For example, the choice between G♯ or A♭ dictating which of the two split keys (indicated in the video at 12:57) was used. With even temperament producing exact enharmonic equivalents, the duplication of accidentals is effectively redundant except — for the reason given — in the matter of notation. If musical notation (and nomenclature) had kept up with the rise in popularity of 12-TET, we should've ended up with a chromatic stave (with unique note names) similar to Dodeka notation in which all accidentals (and thus key signatures) are unnecessary. This is another issue that chromatic spacing would solve. With each accidental being able to occupy only a single position (and name), it leaves no opportunity for this kind of discrepancy to occur. And it gives each interval a distinct spacing which automatically remains consistent when transposed — this manifests both on a chromatic stave and, in the case of a chromatically spaced keyboard, as consistent chord shapes. |
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Post by reTrEaD on Jun 21, 2023 11:42:41 GMT -5
Piano is a rather visual medium. When learning music theory, I find it convenient to use a piano or other keyboard. Whereas I tend to find a keyboard's misrepresentation of interval spacing actively unhelpful. To someone with no (or very limited) musical knowledge, purely looking at the key layout easily leads to questioning why it isn't perfectly regular. I suppose we can attribute that to point of view and whether one can properly assess what they see. While it's true the white keys only are evenly spaced, we can still observe the black keys. The semitone interval distance between any two white keys can easily be discerned by counting all keys (not just the white ones). It's painfully obvious that since there are NO keys between B and C, this interval is only one semitone. In contrast there is a key between C and D, hence a two semitone distance. The other church modes provide less utility for me but the Ionic (in particular C major) and Aolian (A natural minor) are readily apparent on a keyboard and provide a good starting point for exploring other types of scales. We can immediately discern which notes are in play and the semitone intervals between any two notes are not too difficult to recognize. If musical notation (and nomenclature) had kept up with the rise in popularity of 12-TET, we should've ended up with a chromatic stave (with unique note names) similar to Dodeka notation in which all accidentals (and thus key signatures) are unnecessary. Definitely interesting. With conventional notation, we know the distance between two line is some sort of third. But we don't know what kind of third, without context. With this notation, we immediately know the distance is a major third since there will always be a four semitone distance between the two notes and three chromatic intervals within the space. But there's definitely a cost in terms of vertical real estate. Because there are three notes within the space, the gap between lines must necessarily be greater so we can easily discern whether the note is adjacent to the line below, equal spaced, or adjacent to the line above. This is another issue that chromatic spacing would solve. With each accidental being able to occupy only a single position (and name), it leaves no opportunity for this kind of discrepancy to occur. And it gives each interval a distinct spacing which automatically remains consistent when transposed — this manifests both on a chromatic stave and, in the case of a chromatically spaced keyboard, as consistent chord shapes.I reckon you'll find substantial resistance to a chromatic stave and a TON more resistance to chromatically spaced keyboard. While consistent chord shapes would surely be a benefit, there are only two ways to get there. Decrease the width of each key (not very practical) or have each octave occupy 70% more space from left to right. Where currently a pianist might be able to span an octave from thumb to pinky, they would only be able to span a perfect fifth, with the same stretch. Since this is a family friendly venue, I can't repeat the sort of response you'd be likely to get. Let's just say it would be a definitive no. |
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Post by kitwn on Jun 23, 2023 21:21:50 GMT -5
Exactly why the notes are named as they are is steeped in history starting back in the monasteries of 600 years ago as well as the mathematics of frequencies in simple ratios and the psychoacoustics associated therewith.
One way to understand the way we write this stuff on the modern stave and to see where the key signatures come from is to invent two rules and then write out all the major scales accordingly. I've never seen these stated explicitly but they are implied from the way music is written. Rule 1: Each letter from A to G must be used once and only once. Rule 2: Every scale must contain notes modified either by only sharps or flats, a mixture of both is not permitted. Follow the circle of fifths clockwise writing the notes of the major scale (remember your 'tone, tone, semitone, tone, tone, tone, semitone') scale following Rules 1 & 2 using only sharps: C C D E F G A B C G G A B C D E F# G 1 sharp D D E F# G A B C# D 2 sharps A A B C# D E F# G# A 3 sharps E E F# G# A B C# D# E 4 sharps B B C# D# E F# G# A# B 5 sharps F#/Gb F# G# A# B C# D# E# F# 6 sharps C#/Db C# D# E# F# G# A# B# C# 7 sharps G#/Ab G# A# B# C# D# E# ? Doesn’t work. D#/Eb D# E# ? Doesn’t work. A#/Bb A# B# ? Doesn’t work. F F G A ? Doesn’t work. C Back to the beginning. For as long as it works, each scale contains the same notes as the one before but with one extra note sharpened in the order F, C, G, D, A, E, B. Very logical and a good order to learn your scales in because of that. One sharp is always the key of G, two sharps is always D and so on. You don’t need to examine which sharps they are to work out the key from the key signature. Work anticlockwise round the circle of fifths (or clockwise in fourths if it’s easier) following Rules 1 & 2 using only flats: C C D E F G A B C F F G A Bb C D E F 1 flat A#/Bb Bb C D Eb F G A Bb 2 flats D#/Eb Eb F G Ab Bb C D Eb 3 flats G#/Ab Ab Bb C Db Eb F G Ab 4 flats C#/Db Db Eb F Gb Ab Bb C Db 5 flats (easier or not than 7 sharps?) F#/Gb Gb Ab Bb Cb Db Eb F Gb 6 flats (same as 6 sharps) B B ? Doesn’t work. E E ? Doesn’t work. A A B ? Doesn’t work. D D E ? Doesn’t work. G G A B C D E ? Doesn’t work. C Back to the beginning. For as long as it works, each scale contains the same notes as the one before but with one extra note flattened in the order B, E, A, D, G, C. This is the same order as for the key series using sharps but in reverse and missing the F. Including F, and therefore having 7 flats would put us in the key of Cb. Again this is logical and a good order in which to learn these scales. One flat is always the key of F, two flats is always Bb and so on. You don’t need to check which notes get flattened in the key signature to know which key you are in.
For 10 out of the possible 12 scales there is only one option of key signature. Rule 1 makes you obey Rule 2 anyway, but the existence of rule 2 makes it clear that you don't have to remember a confusing mixture of both sharps and flats when reading the dots.
I'm currently trying to up my music theory knowledge and reading ability. Slogging through this lot has been very useful.
Kit
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Post by Yogi B on Jun 24, 2023 12:29:14 GMT -5
It's painfully obvious that since there are NO keys between B and C, this interval is only one semitone. Are roughly 40% of the keys on a piano already too narrow? Okay, so black keys should probably be excluded due to being easier to hit because of their elevation. So what is the next limiting factor for key narrowness faced by pre-existing pianos? As far as I know: it's the ability to fit ones fingers on the narrower upper portions of white keys, especially those that lie directly between two black keys. This is (at least partly) why, with the exception of G♯, the black keys are not centred on the gaps between white keys (a fact demonstrated by none of the diagrams used by the video linked in the OP). The best reference image I could find is actually from a DIY all wood pipe organ, but the dimensions appear to be fairly typical of piano keyboards. Here the octave spacing is 164mm (the unlabelled gaps between keys are ~1.28mm) and the narrowest portion of a white key is 12.83mm (F & B keys). Whereas, if we were to divide the octave into equal twelfths (and, again, subtract the small gaps) we'd get a key width of 12.39mm. Only 96.5% of the above, or doing the inverse having 12 keys of 12.83mm leads to an octave of 169.32mm only 3% larger than normal (not 70%!). An additional advantage a chromatic keyboard has is that it (presumably) possesses levelled key heights (it'd make little sense to go to the trouble of regularising everything else about shape of the keys and not that). The lack of having to reach over the raised black keys should make the rest marginally easier to hit. Though I must say I do like the sound of 70% wider keys, if only to send them back through time to Liszt, Rachmaninov, and the like: Oh what? Your C—G span now only covers an octave, now you know what us mere mortals feel like!For as long as it works, each scale contains the same notes as the one before but with one extra note sharpened in the order F, C, G, D, A, E, B. It does theoretically keep working above seven sharps, you just need double sharps. In the below, I've represented those by literal doubling of the ♯ symbol, rather than the double sharp symbol (𝄪) which is pretty high up in Unicode (U+1D12A) and might not display correctly. | R | 2nd | 3rd | 4th | 5th | 6th | 7th | №
Sharps |
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| C | D | E | F | G | A | B | 0 | | G | A | B | C | D | E | F♯ | 1 | | D | E | F♯ | G | A | B | C♯ | 2 | | A | B | C♯ | D | E | F♯ | G♯ | 3 | | E | F♯ | G♯ | A | B | C♯ | D♯ | 4 | | B | C♯ | D♯ | E | F♯ | G♯ | A♯ | 5 | | F♯ | G♯ | A♯ | B | C♯ | D♯ | E♯ | 6 | | C♯ | D♯ | E♯ | F♯ | G♯ | A♯ | B♯ | 7 | | G♯ | A♯ | B♯ | C♯ | D♯ | E♯ | F♯♯ | 8 | | D♯ | E♯ | F♯♯ | G♯ | A♯ | B♯ | C♯♯ | 9 | | A♯ | B♯ | C♯♯ | D♯ | E♯ | F♯♯ | G♯♯ | 10 | | E♯ | F♯♯ | G♯♯ | A♯ | B♯ | C♯♯ | D♯♯ | 11 | | B♯ | C♯♯ | D♯♯ | E♯ | F♯♯ | G♯♯ | A♯♯ | 12 | | F♯♯ | G♯♯ | A♯♯ | B♯ | C♯♯ | D♯♯ | E♯♯ | 13 | | C♯♯ | D♯♯ | E♯♯ | F♯♯ | G♯♯ | A♯♯ | B♯♯ | 14 |
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Post by ashcatlt on Jun 24, 2023 13:39:48 GMT -5
One of the main benefits of the arrangement of the keyboard is that you know what note you’re playing just by feel. We guitarists kind of have to look for the dots at least once in a while. Those poor orchestral string players don’t even get that much help. Keyboardists get it easy that way.
Also, double sharp is silly and would be extremely awkward to notate. Why not just add five letters to the alphabet and be done with the whole thing?
I’m not sure “tilting at windmills” is exactly the right phrase here, but honestly the fact that you disagree with the standard is not going to change it. If you intend to communicate coherently with western trained musicians, you’re gonna have to use their language. You can try to invent your own if you want. Maybe you’ll end up in a position where other people are forced to learn your new language. Nashville did it, why can’t you?
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Post by reTrEaD on Jun 24, 2023 16:33:51 GMT -5
It's painfully obvious that since there are NO keys between B and C, this interval is only one semitone. Not quite that obvious until one receives a one-sentence explanation. Not something that is difficult to grasp, even for the beginner. Are roughly 40% of the keys on a piano already too narrow? Okay, so black keys should probably be excluded due to being easier to hit because of their elevation. So what is the next limiting factor for key narrowness faced by pre-existing pianos? As far as I know: it's the ability to fit ones fingers on the narrower upper portions of white keys, especially those that lie directly between two black keys. This is (at least partly) why, with the exception of G♯, the black keys are not centred on the gaps between white keys (a fact demonstrated by none of the diagrams used by the video linked in the OP). The width of the white keys at the front edge of the keyboard, are right-sized when depending solely on visual cues. We can use physical cues when playing in the region between the black keys. With the B and E, we can literally feel the raised black key immediately to the left. With the C and F, we can literally feel the raised black key immediately to the right. For D, F, and G, we can literally feel the raised black keys on either side. These physical cues are extremely useful in indexing one's fingers into the proper location. On a keyboard where all keys extend to the front edge of the keyboard, perhaps it would be possible to narrow each key ever so slightly. But I doubt you could trim much off without physical cues to indicate where you are on the board. If one of every four notes is simply a different color, to represent the lines on the Dodeka, that's only visual cues.
While you could narrow the keys such that an octave still spans the same distance as on a conventional keyboard, it would be extremely difficult to play with any speed. Without the physical cues that aid in indexing, sacrificing the room for error built into the standard white key width will result in mistakes when playing at speed. |
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Post by reTrEaD on Jun 24, 2023 16:51:03 GMT -5
One of the main benefits of the arrangement of the keyboard is that you know what note you’re playing just by feel.  |
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Post by Yogi B on Jun 26, 2023 21:19:37 GMT -5
Also, double sharp is silly and would be extremely awkward to notate. I agree it's pretty silly, but it's a silliness that mainly exists as a consequence of trying to ease the awkwardness traditional notation. The double sharp is useful as it enables a transcriber to utilise a staff position that's already been sharpened by a key signature for an even sharper note. For example, say we had a key signature of A (3 sharps: C♯, F♯, G♯) and we want a bar containing both G & G♯. If we didn't have a double sharp the only (and rather weird) option to try to avoid alternating accidentals (like those shown in the example from the video) is to write the G♯ as an A♭. Whereas, the double sharp gives us another alternative: moving the G down to the F♯ line — plus, this would be the only accidental, the other way requires two (G♮ & A♭). Well Dodeka does as explained below: That's pretty horrid. To me C/K is somewhat reasonable as soft/hard variations of the same consonant; D/T kinda work — the Old English letter eth (Ð, ð) was first replaced by the thorn (Þ, þ) but ultimately became "th" (at least, when not mistranscribed as "y"), this why we get things like feather = Feder (in German); speaking of which, H is just awful but doubly so if you happen to follow German language music notion in which B flat is just "B" & B natural is "H"; P, not a clue; and, finally, V is kinda like an upside down A, I guess? If I were designing a new system I'd probably throw out letters altogether and use some sort of pictographic system instead — ideally something with an easily followable pattern modulo important intervals. The best I currently have is something like the following: Λ > V < Λ > V < Λ > V <I don't necessarily wish to change/replace the standard, but I do think being locked into only a single mindset of how music should be visualised is counterproductive. Imagine if the only option for a DAW's piano roll was traditional notation, how much more cumbersome would it be to edit? Plus, from a programming perspective, it's much more complex/difficult to implement (correctly). For example, TuxGuitar's score editor doesn't handle accidentals particularly well, but most notably it will not let you place any 'accidental-free' notes on C♭, E♯, B♯, or F♭ staff lines (e.g. an E♯ will only display in the space above, as an F♮), causing unnecessary accidentals in key signatures of C♭, G♭/F♯ & C♯. I think you need to rewind six months, and stop underestimating the guy's skill. |
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Post by JohnH on Jun 27, 2023 16:50:17 GMT -5
it's 500 years too late to change what a keyboard looks like!
But if we did, I've sometimes wondered about a fretboard inspired keyboard All equal-spaced keys, some with one or two marker dots like we have on a fret board.
But, there are practical advantages with a standard keyboard, where black keys fit in between white. It condenses the physical width of an octave, allowing more chords to be played with one hand. On a fretboard, we have multiple strings so that we can range over many tones within a hand-span.
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Post by unreg on Jun 28, 2023 17:03:37 GMT -5
It's painfully obvious that since there are NO keys between B and C, this interval is only one semitone. It’s painfully obvious to those familiar with a piano/keyboard. At the same time, that common question is easily solved by a small education of music theory. AND then, the piano has acquired one more happy fan. (I’m under the impression that no piano fan can be truly happy without understanding this small bit of music theory.) Why change the keyboard?! It’s fun to learn with its uniqueness AND we also get to look up to keyboard greats such as Radiohead.  |
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Post by ashcatlt on Jun 28, 2023 18:27:42 GMT -5
Honestly, if you change the keyboard, it suddenly becomes much more difficult to teach western music theory. One of the first lessons is often intimately tied to this whole question of where the black keys are and why. It’s a clear and easy illustration of the intervals in standard scales that we can build off of with new students. Yes, that’s kind of a backwards reason to keep it like that, but it sure is nice that we do have it.
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