Tell me about the missing black keys on a piano.

[GorillaMan]

@Aspidistra

It seems to me that people do use diminished chords reasonably frequently in guitar tabs (which was what I was thinking of upthread). But I suspect that the guitar is not exactly an equal tempered instrument, so I don’t know if that makes a difference.

In terms of temperament, the guitar is a young whippersnapper. However, diminished chords have a big role in tonal harmony, so they work within keys, or as part of a modulation from one key to another, rather than simply as an alteration of a single chords.

[GorillaMan]

@Fish

Incidentally, I seem to recall that there was an experimental piano made with alternating white and black keys, something like this:

 **C# D#  F  G  A  B**
C  D  E  F# G# A#

I can’t recall whether C was a white note or a black note, but you get the idea.

It had a few advantages: it was much easier to transpose from one key to the next (you just move up to the next white key). There would only be two sets of fingering to learn — white-key and black-key fingering. Your hands wouldn’t need to be as big, because there were more keys per inch.

It never caught on. Without labels on the keys it’d be hard to know where you were, especially if you took your hands off of the instrument to go up a few octaves.

That is the greatest advantage of the current piano system. No, it isn’t symmetrical and it isn’t uniform white-black-white-black. Because of this, it’s much easier to see at a glance where you are.

There were all sorts of experiments with keyboard instruments for different temperaments, too - extra manuals, extra keys, some ridiculously complicated things emerged. Something important to remember is that while we see the equality of every key as good, and with the hindsight we have of Mozart through to Mahler this is understandable, an argument against equal temperament was that individual keys were devoid of individual character.

[pulykamell]

@GorillaMan

There were all sorts of experiments with keyboard instruments for different temperaments, too - extra manuals, extra keys, some ridiculously complicated things emerged. Something important to remember is that while we see the equality of every key as good, and with the hindsight we have of Mozart through to Mahler this is understandable, an argument against equal temperament was that individual keys were devoid of individual character.

Wasn’t it Mozart (or somebody similar) who quipped that equal temperament is one in which all keys sound equally bad?

[fachverwirrt]

@Aspidistra

You’re right, I copied down the wrong column in my notebook. Need more caffeine. 5:6:7 is still a nice mathematical ratio though

It seems to me that people do use diminished chords reasonably frequently in guitar tabs (which was what I was thinking of upthread). But I suspect that the guitar is not exactly an equal tempered instrument, so I don’t know if that makes a difference.

Right. Diminished triads are quite common (the top three notes of the dominant seventh chord, one of the most common and recognizable chords in tonal music, outline a diminished triad). What I meant is that the 7th partial itself is generally considered unplayably flat. In just intonation, the minor seventh is generally obtained by taking the ratio between the ninth partial and the fifth partial, not the seventh and the fourth.

I’m not sure you really can outline an “in tune” diminished triad using the harmonic series. It’s possible that 15:18:21 might do it, but that’s getting into a part of the harmonic series where intervals start becoming a little indistinct.

[GorillaMan]

@pulykamell

Wasn’t it Mozart (or somebody similar) who quipped that equal temperament is one in which all keys sound equally bad?

Dr Crotch, no less. According to my sole research tool right now. However, it’s “render all keys equally imperfect”, which is not necessarily the same thing. (I do suspect it was Helmholtz who caused that line to become well-known.)

[Fish]

@GorillaMan

There were all sorts of experiments with keyboard instruments for different temperaments, too …

Well, yeah. But I wasn’t arguing about tuning or temperament, but of the physical layout of the keys themselves.

[GorillaMan]

@Fish

Well, yeah. But I wasn’t arguing about tuning or temperament, but of the physical layout of the keys themselves.

Sorry, yes, I wasn’t clear on what I was talking about. Not for the first time

[pulykamell]

@GorillaMan

Dr Crotch, no less. According to my sole research tool right now. However, it’s “render all keys equally imperfect”, which is not necessarily the same thing. (I do suspect it was Helmholtz who caused that line to become well-known.)

You know what, I’m starting to wonder whether I’ve been misled this whole time. I found this webpage which states:

Especially, Mozart said that he would kill anyone who plays his composition with the equal temperament.

I know years ago when I researched temperaments, I’ve come across this little tidbit a few times. But now, looking into it and from more annotated scholarly sources, I get the impression that Mozart wasn’t really as anti-equal temperament as the above quote seems to indicate, but his favorite intonation at the time was sixth-comma meantone. Do you have any insight into this?

[Fish]

Here’s an alternative piano layout: The Jankó.

[Aspidistra]

I don’t get that. I mean, I get the “whole tone” layout of the bottom two rows, but what’s the point of having those two rows replicated twice to make six rows? Why three touch points for exactly the same note? As far as I can see the most which you would need for universal-transposition purposes would be three rows.

[Fish]

I’m not sure. I’ve never seen one played in person.

Double-manual harpsichords had a … well, a similar feature. The upper manual plucked only one string, but the lower manual (tied to the upper manual) would pluck both that string, and a string 1 octave below it.

I don’t know if the Jankó is set up the same way, where the notes closet to the player are lower in tone. Maybe?

[Sapo]

@Fish

I can do this.

I used to work in a store that sold digital pianos and organs and each had the ability (which we would occasionally demonstrate) to tune the instrument up or down by 0.1 Hz.

I could always tell by sitting down at the instrument and playing a few notes if it was off, even by the tiniest amount.

Ok, this was going to be my next question. Are there digital pianos where you can change from one temperament to another at the flick of a switch?
Does anyone have a link where I can hear the same piece played in different tunings to compare?
I do have a little keyboard at home (that the kids got as a present at some point). I really don’t have the ear to know that playing all whites I am skipping semitones.

[fachverwirrt]

@Sapo

Ok, this was going to be my next question. Are there digital pianos where you can change from one temperament to another at the flick of a switch?
Does anyone have a link where I can hear the same piece played in different tunings to compare?
I do have a little keyboard at home (that the kids got as a present at some point). I really don’t have the ear to know that playing all whites I am skipping semitones.

Yes. I have both a synthesizer and a digital piano that can do, at the least, equal temperament, pythagorean tuning, mean-tone temperament, and just intonation. Your typical cheap keyboard probably can’t though.

[Fish]

@Sapo

Ok, this was going to be my next question. Are there digital pianos where you can change from one temperament to another at the flick of a switch?

Technics made one. I know only because that was the brand we carried at the time. I don’t know about the other brands, I’m afraid.

[GorillaMan]

@pulykamell

I know years ago when I researched temperaments, I’ve come across this little tidbit a few times. But now, looking into it and from more annotated scholarly sources, I get the impression that Mozart wasn’t really as anti-equal temperament as the above quote seems to indicate, but his favorite intonation at the time was sixth-comma meantone. Do you have any insight into this?

No idea, I’m afraid!

[Johanna]

When young I taught myself to memorize the sound of C5 by recalling the first measure of Mozart’s Piano Sonata #7 in C Major, K. 309. Any time I needed to tune anything or to sing a given note unprompted, I could summon up C5 in my mind and from there derive the needed note.