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Piano Keys

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Re: Piano Keys

#31

Post by Nition »

ajuc wrote: post #4

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.

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.

There is the Janko keyboard though: http://en.wikipedia.org/wiki/Janko_keyboard

Re: Piano Keys

#32

Post by moefh »

ofalkaed wrote: post #27
moefh wrote: post #24

Earlier quoted context omitted.

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 Renaiss…

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…

> 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

[2] https://en.wikipedia.org/wiki/12_equal_temperament

Re: Piano Keys

#33

Post by Snarwin »

ajuc wrote: post #4

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's not actually that much to remember. There are 3 shapes that cover most of the major chords, and 3 special cases (F♯, B♭, and B).

Re: Piano Keys

#34

Post by mlochbaum »

bruce343434 wrote: post #2

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.

The point that the article is addressing (but you have to ignore the image and study the equations to see this!) is that this sort of shifting can't equalize everything. In the span of 3 white keys C to E at the front, you have 2 black keys at the back, so if you take r to be the ratio of back-width to white key front-width then you have 3 = 5r. But in the 4 keys F to B, you've got 3 black keys so 4 = 7r. No single ratio works! So the article investigates various compromises. The B/12 solution is what seems to me the most straightforward, divide white keys in each of the sections C to E and F to B equally at the back, and don't expect anyone to notice the difference.

Re: Piano Keys

#35

Post by [deleted] »

Nition wrote: post #31
ajuc wrote: post #4

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.

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 remem…

[deleted]

Re: Piano Keys

#36

Post by ofalkaed »

moefh wrote: post #32
ofalkaed wrote: post #27

Earlier quoted context omitted.

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…

> 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' fre…

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.

[1]https://lsaguitarshop.substack.com/p/gear-27-the-stradivariu...

[2]https://en.wikipedia.org/wiki/Vincenzo_Galilei#Acoustics_and...

[3]https://i0.wp.com/earlymusicmuse.com/wp-content/uploads/2017...

Re: Piano Keys

#37

Post by moefh »

ofalkaed wrote: post #36
moefh wrote: post #32

Earlier quoted context omitted.

> 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' fre…

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 fret…

> I will post it if I remember/find it

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.

Re: Piano Keys

#38

Post by prmph »

I guess I must be dumb or something, but I'm simply not seeing the problem.

Imagine the piano had only white keys, no problem right? Now just place the black keys at the back, between some of the white keys, right in the middle, such that each black key takes like a quarter of the width of the sandwiching white keys.

Now what's the problem with this again? Can someone explain in clearer terms?

If the issue is that we are trying to make the white key all have the same width at the back, well, why should that matter? Pianists don't press the white keys all the way at the back, do they?

Re: Piano Keys

#40

Post by toast0 »

ajuc wrote: post #10
tetraodonpuffer wrote: post #6

Earlier quoted context omitted.

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

Make a dimple on every C key and paint it red.

That's all fine and dandy, except early apple keyboards have the dimples one key over :p
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