[HN Gopher] Piano Keys
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Piano Keys
Author : gametorch
Score : 30 points
Date : 2025-07-15 21:50 UTC (4 days ago)
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(TXT) w3m dump (www.mathpages.com)
| bruce343434 wrote:
| On my (accoustic) piano, the black keys are just as wide as the
| back ends of the white keys. This is achieved by shifting the
| position of the black keys a bit, instead of centering them right
| between the white keys.
| o11c wrote:
| Same, but I had to look. I wonder how badly this affects muscle
| memory?
| madaxe_again wrote:
| In my experience, you fumble for a minute and then you adapt.
| I had a Young Chang that followed this model, and a Yamaha at
| school that didn't.
| blobbers wrote:
| Generally speaking fumbling on a piano doesn't bode well
| for performance... it's a little bit like Olympic
| gymnastics, you only get one chance to stick the landing!
| blobbers wrote:
| This is fascinating! I've never played a YC seriously, but
| I have played several Yamahas and currently play on a Kawai
| and Baldwin. I've often wondered if the Baldwin or Yamaha
| is laid out slightly differently than the Kawai because I
| feel like playing broken 4 note chords the fingering can
| feel off on one piano vs another. It's a slight stretch but
| the 4-5 on the second 4 note chord can be uncomfortable on
| the Kawai and comfortable on the Yamaha. I never play them
| in the same room, one is at my teachers and one at home.
|
| Very interesting! Is there a spec for this? Or a layout
| description? Surely something as precise as piano would
| note this.
| Nition wrote:
| Interesting, my piano is a Yamaha (specifically a 1980
| Yamaha YUA, basically a U3), and it _does_ follow the model
| (black keys shifted to create equal width for the rear of
| all white keys).
|
| Photo: https://i.imgur.com/ulsLUoG.jpeg
|
| I also have a MIDI keyboard (M-Audio Hammer 88) which
| follows the same model, although it's not quite as perfect
| as the Yamaha in maintaining the white key width.
|
| I'd like to see a photo of someone's piano with the black
| keys _not_ offset, I actually thought they were always that
| way. It 's a good system because it lets the black keys be
| spaced a little further apart, while also reducing the jump
| between black key clusters.
| ajuc wrote:
| I never understood why the piano keyboard isn't regular. It
| forces players to remember different positions for the same chord
| transposed to start at different notes.
|
| Like why do I have to remember the shape for C major and D major
| chords? It should be the same shape just starting at C vs D.
|
| It's not even that hard to fix. There's 12 semitones in an
| octave. Just make it 6 white 6 black keys.
| tetraodonpuffer wrote:
| having the keyboard the way it is also allows you to more
| easily orient yourself, you can feel with the sides of your
| fingers if you are next to E/F or B/C and with the corner of
| your eye it's also straightforward to figure it out. I don't
| think it'd be possible (or anyways even more difficult than it
| is now) to play large jumps accurately if the whole keyboard
| looked the same
| paulgerhardt wrote:
| I think both of those concerns were addressed by the Dvorak
| of piano keyboards:
| https://en.wikipedia.org/wiki/Jank%C3%B3_keyboard
|
| Has the symmetry of GP while large jumps are accomplished by
| shifting up a row or two.
|
| I assume it didn't take off for the same reason Dvorak
| didn't.
| ajuc wrote:
| Make a dimple on every C key and paint it red.
| bluGill wrote:
| There are multiple alterative layout that some advocate for.
| they generally do sonething else for orintation. putting a
| bump on middle c and other places.
| krallja wrote:
| https://en.wikipedia.org/wiki/Jank%C3%B3_keyboard available
| since 1882!
| jng wrote:
| The white keys form a sequence of notes (frequencies) that is
| known as the diatonic scale. It's the foundation underlying all
| popular western music. It is not random or arbitrary, it has
| some nice dual mathematical and musical properties: intervals
| between the notes in the scale have special frequency ratios
| that sound pleasing to the ear (read Helmholtz's "On the
| sensations of tone" for a fascinating physically-based take on
| why it is like that -- he is known as "the father of
| acoustics", and that book contains the distillation of 8 years
| of deep, smart research way before we had the means or
| understanding we hav today). A ton, if not most, of popular
| music can be played using only the white keys.
|
| There used to be keyboards with other different arrangements,
| which were actually extremely cumbersome and actually didn't
| allow very rich and interesting musical excursions like
| modulations (look up "microtonal keyboards"). Today's standard
| keyboard and tuning is a compromise between those fundamentally
| mathematical and perceptual acoustic relations (the tonic, the
| fourth, the fifth, the sixth, the major and minor third, the
| "sensible" or subtonic...) and the ability to perform those
| trans-tonality excursions. A fully regular keyboard like you
| propose would lend itself more easily to those excursions, at
| the cost of being less apt at the foundational diatonic model
| and most popular music.
|
| Interestingly also, the notes used by modern keyboards and all
| modern instruments, and to which we are all so accustomed that
| we thing it "just is", is an imperfect compromise that needed a
| lot of selling back in the day, much of which was done by Bach
| (the compromise scale is called the "tempered scale", and Bach
| authored the arch-famous "Well-tempered clavier" pieces to show
| it off -- impossible to perform on keyboards with other
| tunings).
|
| And of course, there is a tradition factor. English isn't
| written like this because it's optimizing for any easily
| describable or measurable optimization metric, more like it
| minimized a socio-perceptual function covering many centuries
| of UX.
|
| Finally, if you want an instrument where all keys are equal,
| you can always move to a fretboard based one like the guitar.
| Funnily, it has a one-semitone-short jump between strings 3 and
| 2 that will throw off the desire of full regularity... again
| due to diatonic leanings. A bass guitar is fully regular, even
| when they add a 5th and 6th string, so that may fulfill your
| wish of a fully regular instrument... and it sounds awesome!
| Just can't do the same things as a piano or a guitar.
| ofalkaed wrote:
| >Interestingly also, the notes used by modern keyboards and
| all modern instruments
|
| Vast majority of fretted instruments since the death of the
| lute are untempered.
|
| Edit: Which is not to suggest that lutes were tempered. Lutes
| and other tied fret instruments allow for unequal fret
| spacing so you can temper one string at the cost of more
| notes being more off from the temperament on other strings,
| or the frets being at an angle so you could find a bit of a
| compromise. But often they were EDO or in the ancient
| tradition of fretted instruments, close enough for rock and
| roll.
| moefh wrote:
| Do you mean equal-tempered?
|
| I never heard someone describe a tuning system as
| "untempered", but I guess it would mean something like just
| intonation -- which sounds really great for playing
| anything in a specific key but falls horribly apart if you
| try to change the key (which is why it has seen very little
| use since the renaissance).
| ofalkaed wrote:
| Equally divided octave (EDO) with no tempering which is
| distinct from Equal temperament. Tempered scales are
| generally EDO with tempering. Other methods like just
| intonation don't really need to be tempered and generally
| are not in my experience, but it has been years since I
| was into just intonation and may just not remember.
| Historically speaking, the advantage of justly tuned
| scales is there is no need to temper it because it is
| already just and perfect, things may have changed in 20th
| century as far as just intonation is concerned and
| tempering, don't recall.
|
| Edit: ET and EDO are essentially the same in the case of
| most fretted instruments, I am dredging long forgotten
| stuff from memory here and somewhat off above.
|
| Edit2: Refreshing my memory some and seeing how much
| things have become muddled in my head over the years.
| Clearly I did not even consider what came out of my
| memory and just regurgitated it verbatim. ET scales are
| not tempered but do not mean EDO. Guitar and the like are
| both ET and EDO. ET and EDO are untempered in the sense
| that notes are not shifted slightly away from the EDO/ET
| as they are on the piano and many instruments.
| moefh wrote:
| I don't see how you can divide the octave equally and not
| end up with equal temperament: that's exactly what equal
| temperament is!
|
| > Tempered scales are generally EDO with tempering.
|
| That's not historically accurate. EDO wasn't used until
| very recently (about the middle of the 19th century I
| think), tempering was used way before that.
|
| For example, the first widely used temperament (which
| became popular in the Renaissance) was the quarter-comma
| meantone, which shrinks each fifth (from the natural 3/2)
| so that the major thirds are perfectly 5/4. The name
| "quarter-comma" means that the amount of shrinkage is 1/4
| of the "syntonic comma", which is the difference you get
| beteween going up 4 fifths (e.g. C->G->D->A->E) and a
| major third plus 2 octaves (C->E->E->E). Those final Es
| can only be the same if you shrink the fifth or stretch
| the third (or both). What this tempering does is shrink
| each fifth by 1/4 of the difference (so that going up 4
| fifths closes it) and doesn't touch the major third. That
| means the major thirds are beautiful, and the fifths are
| a little off. For a chosen key, that is -- everything
| sounds horrible as soon as you try to change the key too
| far away from the chosen key.
|
| In the Baroque period a lot of other temperaments were
| invented, the Werckmeister temperaments were very widely
| used in (what is today) Germany for example (a lot of
| people believe Bach had one of these in mind when writing
| the Well-Tempered Clavier). Those temperaments were also
| defined by how much each fifth is changed from the
| "normal" 3/2, but each fifth was to be changed by some
| different amount in some complicated way.
|
| It was only much later that EDO (12-TET, or "equal
| temperament") started to be widely used. You can think of
| it (and people do!) as a "temperament" because it just
| means you shrink the fifth from the "normal" 3/2 = 1.5 to
| be instead 2^(7/12) =~ 1.4983, so that going up 12 fifths
| lands you exactly 7 octaves above (since 2^(7/12)^12 =
| 2^7). That also means that the octave is divided exactly
| equally, because going up 12 fifths goes through every
| one of the 12 notes before going back to the original
| note.
| ofalkaed wrote:
| EDO on fretted instruments goes back to at least the 16th
| century and was essentially the standard well before the
| mid 19th. Equal temperament is an EDO scale whose
| divisions approximate justly tuned scales. The western
| 12TET scale is not actually 12TET or 12EDO, we temper the
| scale itself and tweak some notes to make it work better
| unless you play fretted instruments and then it is up to
| the guitarist to make small adjustments in their playing
| technique so their untempered 12TET is in tune with the
| pianos tempered 12TET.
|
| I admitted to making a mess in that post.
| ofalkaed wrote:
| To offer something better than this mess and correct.
| Fretted instruments are tehnically unequally tempered do
| to the physics the string, the fret board is EDO but in
| fretting the string we stretch it and raise its pitch.
| Fretted instruments use various compensation tricks to
| lessen this effect but most notes are off from both 12EDO
| and 12TET, we get the open string and the 12th fret but
| the rest are off by varying amounts.
| brudgers wrote:
| An untempered instrument would be one that is tuned to
| maintain the perfect intervals of a specific root tone.
|
| Temperament is adjusting tuning for musical practicality.
| 12 TET is simply one set of compromises/benefits in a
| constellation of alternatives.
|
| https://en.m.wikipedia.org/wiki/Musical_temperament
| ofalkaed wrote:
| Thank you for offering something clearer than the mess I
| made. Been 25 years since I studied this stuff and
| finally learned to just accept (and love) the modern
| standard.
| brudgers wrote:
| I agree, the white keys on a piano represent a diatonic
| scale, but because today's pianos are rarely tuned to
| anything other than 12TET, there are few interesting
| mathematical relationships between notes in practice (and
| pianos are normally tuned with high notes sharp and low notes
| flat because that's how piano strings tend to produce their
| partials anyway).
|
| Also worth noting the black keys represent a major pentatonic
| scale and the major pentatonic scale is how many of the
| earliest bone flutes are tuned.
| brudgers wrote:
| _It forces players to remember different positions for the same
| chord transposed to start at different notes._
|
| The piano was developed well before equal temperament came to
| dominate tuning. [1] So each musical key would have different
| harmonic relationships between the intervals within it. And
| musical keys were not thought of as equal.
|
| Generally, the musical keys based on "black keys"/"sharps and
| flats" would be farther from an ideal tuning and there were
| better and worse sounding keys depending on which musical keys
| a piano was tuned for.
|
| Historically in Western European music, there were preferred
| keys and intervals inherited from Plain Chant (roughly C,G, & F
| and octave, perfect 4th, perfect 5th, and the 6th).
|
| Of course using an electronic instrument that can be
| electronically transposed up and down by half steps might be an
| easy way to avoid learning lots of fingerings.
|
| [1] https://www.math.uwaterloo.ca/~mrubinst/tuning/tuning.html
| IsTom wrote:
| Historically before twelve tone equal temperament playing in
| another key on a keyboard instrument _would_ sound different.
| skybrian wrote:
| Chromatic button accordions have each octave in three rows of
| four instead of two rows of five and seven like a piano. It's
| very regular, but doesn't match up with major or minor scales
| or with sheet music. A major scale is a zig-zag.
|
| I play both piano and button accordion and they're just
| different. Neither one has a compelling advantage.
| yayitswei wrote:
| I'm picky about layouts - I type in Dvorak, learned Janko via
| Chromatone, currently playing harpejji.
|
| Coming from a classical piano background, there was definitely
| a learning curve, but I feel like it was worth it. Every chord
| shape is identical across all keys (C major and D major would
| be played the same way), which makes it much easier to learn
| jazz voicings or modulate a song.
|
| If anyone ever builds a quality grand piano with Janko layout,
| I'm buying! Hacks on hacks become unnecessary if you start with
| the right design.
| ncake wrote:
| Same. I recently tried to find a MIDI keyboard like that for
| sale and got nothing. Apparently this is what it's called:
|
| https://en.m.wikipedia.org/wiki/Dodeka_keyboard
| moefh wrote:
| I always thought the canonical way to place the black keys was to
| divide the octave in the two parts that have the sequential black
| keys (C-D-E and F-G-A-B), and then simply place the black keys so
| they're the same distance away from each other and the edge of
| the parts.
|
| That means that the white keys in each of the groups have
| "mirrors": for example, C is a mirror of E, D is a mirror of
| itself (it's the only key like that), F is a mirror of B, and G
| is a mirror of A.
|
| I just looked at the keyboards I have around me (a slightly-
| above-low-end digital piano, a small midi controller, and a small
| 90s synth), and they all seem to fit that description.
|
| ETA: note that the image in the article doesn't fit this
| description: for example the D is way too narrow (the black keys
| around it should be much further apart).
|
| ETA2: I just noticed that this seems to be the "B/12 solution"
| described in the article.
| ralfd wrote:
| I didn't understand this post? More pictures needed?
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