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.
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.
With the irregular layout we have now, some keys are easy (e.g. C) and some are hard (e.g. B). If you make the layout regular, putting a black note between every white note, then every key becomes the same, but also quite hard, because every major scale is now played like this: https://i.imgur.com/6EmW8eU.gif
It's not a particularly good tradeoff. If you got rid of the black keys entirely instead, you'd have to remember which keys to skip. Harder for beginners than just playing in C.
That regular layout also makes it likely to feel better to the hand to play diminished or augmented chords, while comparatively punishing major/minor chords. It would be an odd choice considering the traditions of western music.
There's also something to be said about each key having a specific motor pattern/spatial layout. Sure, it makes it harder to move knowledge of one key into another, but during playing it also makes it easier to not accidentally completely change the key unless you mean to. It's all tradeoffs.
Can you elaborate on your thinking here? I really feel C is the easiest (in standard major tonality - obviously C minor, blues scale etc are a different story).
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.
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.
>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.
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).
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.
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.
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.
> The western 12TET scale is not actually 12TET or 12EDO, we temper the scale itself and tweak some notes [...]
I think you and I must be using words differently. To me (and to Wikipedia, and everything else I've ever read, including[1] which I just consulted to make sure I'm not crazy), 12TET is a way to specify by how much you have to multiply the frequency of the first note of the scale to get the other notes' frequencies. Wikipedia[2] has a table with the numbers for 12TET (the column "Decimal value in 12-ET"), but it's very simple: you just multiply the value of the preceding note by 2^(1/12). If you take 12TET and adjust/change the notes a bit, then it's not 12TET anymore.
> EDO on fretted instruments goes back to at least the 16th century
I'd love to see a reference for that. I just consulted [1], it has a chapter called "Non-Keyboard Tuning" and it doesn't mention that (although admittedly it spends most of its time talking about violin, with a ton of references to stuff that Mozart said). The book does say that equal temperament was known for centuries before it was used, but the people who first discovered it simply didn't think it sounded good.
[1] "How Equal Temperament Ruined Harmony (and Why You Should Care)" by Ross W. Duffin
Try the wikipedia pages for Equal Temperament and Musical Temperament, they explain all of this.
Here is a 1688 Stradivari[1] guitar with fixed frets and a EDO octave, they were reasonably common by that point. Much of the information regarding this is looking at the fixed frets that many lutes and guitars had applied to their soundboard and comparing that to how composers used those fixed frets, either the tied frets adhere to the scale of the fixed frets or they are out of tune. The history of EDO/ET in fretted instruments goes back to at least Vincenzo Galilei[2] (father of Galileo) who developed the rule of 18 for fret spacing. If memory serves we have a few early steel string instrument (cittern, bandora, orpharion) from around ~1600 with equal spaced frets and this orpharion[3] looks it but it is difficult to tell from that photo. Going back earlier things get more difficult since we have so few intact and unaltered instruments but we do have a fair amount of ingravings and art plus writing on the topic such as Galilei's.
There is a paper going into great depth on all this that is just out of reach in my memory and I can't seem to trick the search engines to give it to me, I will post it if I remember/find it. No time to dig more right now.
If you remember and have the time, please do! (And thank you for the links you already posted).
I see now that everything I read about this was way too focused on keyboard and violin, since I had never heard any of this about fretted instruments. I'm glad I get to correct a bit of my understanding, so thank you. Now I'm left wondering about wind instruments.
Western theory is focused on the keyboard with violin as second fiddle, the rest of the instruments do their own thing unless they are forced to kowtow to a piano or violin. Each instrument is ultimately tuned to the physics which dictate how it makes sound and this is part of why our tempered 12TET works and why we see the rise of the big orchestras of unlike instruments with the move away from meantone, it provides a compromise which works quite well for all instruments with the exception of the brass (with the exception of the trombone) who are forever out of tune (sort of).
Part of the reason beginners sound bad is because most instruments have to bend notes to be "in tune," I can teach anyone to play a chord on the guitar and get them having each note sounding clearly in a couple of minutes but my DMaj will sound better than theirs simply because I have played that DMaj thousands of times and my fingers have learned to adjust the pressure on each string in just the right way to make it sound "right" just as the woodwinds learn to bend certain notes and the brass learns to live with being out of tune.
Also part of why the lute became such a dominant instrument is that it could retune in ways other instruments can not, which was a major advantage for the working musician back in the days when every city had its own idea about tuning; nudge a few frets, retune a few strings and accept that certain notes were now out of bounds and you could play with anyone like you were playing in your native tongue. As tuning became more standard the lute started to die.
Meantone Temperaments on Lutes and Viols might be of interest to you, it is aimed towards lutenists and violists but has some more general stuff as well and I think does a good job of showing the compromises the lute (and viol) had to make in moving away from equal temperament.
I don't really think brass is forever out of tune, I love the brass and used to play trumpet but the brass section is more under the influence of the physics of its instrument than anyone but the pianist but the pianist is "in tune" because western theory is built around the keyboard.
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.
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.
There are such things are Chromatic keyboards (for instance, the Chromatone synth had one), and there was the Janko piano keyboard and there are people that have made keyboards without the spaces in at the B/C and E/F at the back of the keyboard by alternating the white and the black keys such that those spaces just disappear.
The advantages are:
- you need less reach for the same chords
- transposition becomes trivial
The disadvantages are:
- your muscle memory will be invalidated
- the number of instruments set up like that is really small
- no accomplished pianist will want to switch
But if you really wanted to you could adapt an existing instrument to use a different keyboard and it isn't even all that complicated (medium complexity wood working project).
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.
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.
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
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.
That's a bit like complaining that there are six different kinds of chess pieces and you have to memorize how each moves. The truth is, if you have trouble remembering how a knight moves, you can't be that good at Chess anyway.
Remembering twelve different ways of playing a scale is a vastly small part of learning how to play a piano.
> if you have trouble remembering how a knight moves, you can't be that good at Chess anyway.
Non sequitur.
It’s also still a valid question. I play the scales really well on the guitar. And because the frets are all laid out straight, shifting up by one fret means I’m just playing my chords and scales sharp. It makes transposing music incredibly easy.
I still don’t understand why the piano can’t be laid out like that.
Guitar still has the problem of last 2 strings being shifted 1 semitone down for ergonomics reasons, which makes them irregular. But yeah, it's better than piano keyboard.
Except it would render a large swath of the repertoire from the common practice period (“classical music“) more difficult to play because it is written with the presumption that the keyboard is just so and that some future generations won’t try to optimize it.
The organization of the keyboard does necessitate certain fingering choices that are particular; but knowing this, composers have (usually) written in a way that respects that geometry.
The geometric relationship between the note frequencies of a C major chord and a D major chord on the piano is not the same. The key of piece is responsible for some of its “feel”. So it’s not unreasonable that they have different “representations” on the piano although the differences may be subtle.
There aren't 12 shapes. My fingers say C maj, F maj and G maj are the same shape. D maj, E maj, A maj too. And A min is the same shape as C/F/G maj, but would be a different pattern on the proposed "regular" layout. That may not matter when all you want is transposition, but as I said before: transposing is not so important. And there are "shape" based keyboards, as mentioned frequently in the comments. You can even retrofit some on your own keyboard. They're just not popular.
C maj, F maj are the same, but C maj7 and Fmaj7 are not. Ultimately you have to remember which chords are the same and which aren't - which is about the same amount of information as just remembering all the combinations.
It's just an ugly irregular hack. I understand that you can get good at working around it, but eventually it's worth it to fix the underlying problem.
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.