Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Piano Keys

mathpages.com

Post reply on HN
Print view View original

11–20 of 75 posts

Re: Piano Keys

#11

Post by ofalkaed »

jng wrote: post #9
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.

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-base…

>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.

Re: Piano Keys

#12

Post by brudgers »

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 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

Re: Piano Keys

#13

Post by moefh »

ofalkaed wrote: post #11
jng wrote: post #9

Earlier quoted context omitted.

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-base…

>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…

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).

Re: Piano Keys

#14

Post by IsTom »

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.

Historically before twelve tone equal temperament playing in another key on a keyboard instrument would sound different.

Re: Piano Keys

#15

Post by brudgers »

jng wrote: post #9
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.

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-base…

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.

Re: Piano Keys

#16

Post by ofalkaed »

moefh wrote: post #13
ofalkaed wrote: post #11

Earlier quoted context omitted.

>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…

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).

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.

Re: Piano Keys

#17

Post by skybrian »

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.

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.

Re: Piano Keys

#18

Post by brudgers »

moefh wrote: post #13
ofalkaed wrote: post #11

Earlier quoted context omitted.

>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…

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).

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

Re: Piano Keys

#19

Post by yayitswei »

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.

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.

Re: Piano Keys

#20

Post by bluGill »

tetraodonpuffer wrote: post #6
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.

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.
Post reply on HN