h a l f b a k e r yWe have a low common denominator: 2
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Pianos are tuned in equal temperament. If they weren't, playing in a key other than C would lead to interesting, unexpected harmonies.
It is fairly easy, electronically, to work out what base key one is playing in.
The instrument I propose is an electric piano that automatically adjusts the tuning
based on what you're playing.
For instance, if I selected just temperament, and played a C-major chord, it would sound the same as a C-major chord in just temperament. However, if I then played a G#-major chord, the system would adjust so that the harmony would have the same frequency ratios as in just temperament with the base note having the same frequency as a G# in equal temperament.
Or another example, if I selected to have a harmonic seventh like a barbershop quartet, I could play any dominant seventh chord and it would adjust the frequency of the seventh on-the-fly to give the correct 7:4 ratio.
I am not sure if this has been done before or what it would quite sound like to play a tune.
Pythagorean tuning
http://en.wikipedia.../Pythagorean_tuning
(Wikipedia, but still accurate) [angel, Apr 05 2012]
Quarter-comma meantone
http://en.wikipedia...rter-comma_meantone
[angel, Apr 05 2012]
And again
http://www.gesualdo...antone-temperament/
[angel, Apr 05 2012]
Temperament generally
http://www.midicode...s/temperament.shtml
The context is MIDI, but the details are still relevant [angel, Apr 05 2012]
Guide to Tuning Musical Instruments
http://www.amazon.c...ffen/dp/0715381695/
[angel, Apr 05 2012]
[link]
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Interesting notion. Unfortunately, I suspect that it would sound worse than equal temperament, which at least warns the ear of what's coming.
Also, in your first example, when you play C E and G, how would the system know that you're playing a C major chord and thus use C major temperament, rather than an Am 6th chord which would require Am temperament, or, more radically, Em dim 6 which would need Em temperament?
Worth thinking about more though. |
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The issue is that the 12-note scale that's the basis of Western music isn't compatible with the mathematics of how frequencies work. The way we do it now is to divide the octave into 12 semitones, all of which are the same distance apart. Historically - that is, up until around 1700 - keyboard instruments were tuned to match one (or possibly two) of the mathematically correct spacings for the key that you were playing in. There would always be an error, but the idea was to distribute the error so that it caused least offence. So if you played a piece in the key of D on an instrument tuned to play in A, the intervals would sound discordant.
The system known as "equal temperament" gets around this by making every semitone interval the same, so, to the trained ear, everything sounds discordant, but to the untrained ear it doesn't. Also, keyboard tuning is greatly simplified. |
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Hello, Herr Bach? I have this new instrument that I would like you to try; and perhaps you could even produce some music which would exhibit its capabilities - I might suggest the title "The Pliantly Tempered Clavier". |
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Firstly, //just temperament// is an oxymoron. If it's just it's not tempered. |
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Yes, this has been done in all sorts of ways. Search for 'adaptive intonation', for example. |
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This is an area I am deeply interested in - not specifically the automatic adjustment part, but the avoision of 12 EDO (Equal Division of the Octave; the more technically correct term for what is popularly called 'equal temperament') is central to basically everything I do musically. |
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[angel] I would disagree with nearly everything you said; not so much because you are 'wrong', but because I look at things differently. |
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When getting into this, you very quickly have to abandon, or at least extend, the ordinary concept of 'notes'. I used the analogy before of trying to describe the metric system in terms of inches and feet - which quickly becomes confusing and unhelpful. For instance, a barbershop seventh chord on C can be written as C E\ G BbL, which unambiguously indicates that the pitches are in a 4:5:6:7 (or octave equivalent) relationship. (The 'b' is supposed to be a 'flat' sign, and the L an upside-down 7, but those are the accepted ASCII equivalents.) |
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Notes held with the damper pedal will shift in pitch when the temperament changes. Chord detection is easy when enough keys are pressed, but may be implied if only one or two keys are pressed at a time. |
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[spidermother], you disagree, but not because I'm wrong? Interesting.
I've added a few links which explain why the Pythagoran scale is unsuitable and some of the ways in which it can be improved.
As [lurch] has suggested, the entire point of Das Wohltemperierte Klavier was to show that it was not necessary to retune a keyboard instrument in order to be able to play in different keys. |
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Here I go again... I have to take issue with both those statements. |
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The question is, suitable for what? There is much medieval music in which the combination of the perfect consonance of the pure fifths (and even seconds), and the muddy, but brief, "out of tune" thirds, with the pure latin vowels, is like a glorious, crystalline stained glass window, and would only be spoiled by any form of temperament. |
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The practice where pure thirds are added to a harmonic backbone of pure fifths (as exemplified by Dunstable et al., and adored by me) is usually neglected in these accounts, which instead tend to tell a simplified story of an 'improvement' leading from medieval pythagorian to the final glories of equal temperament. |
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And the principle of dividing the octave into 12 equal parts was widely known at least in the early 16th century. It's a myth that Bach invented the tuning, spurious that he even used it, and ludicrous that he would feel the need to prove that it was possible to play in all 12 keys in it. |
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ooh, it's always weird on the Halfbakery when someone annotates an idea and appears to know what they're talking about. |
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Having now (re)read angel's fourth link, I see that it puts my last point a little more mildly than I did: |
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"It is open to debate whether J. S. Bach (1685 - 1750) in Well-tempered Clavier was seeking to demonstrate the freedom of key modulation afforded by equal temperament or the contrasting key characters offered by well temperament." |
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But yes, on this subject, I mostly know what I'm talking about. |
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(C'mon, we're talking about Bach. There's a big difference between excelling in the expressive potential of something (writing a work in all major and minor keys) and merely proving that it can be done. It's like saying Picasso set out to prove that you can draw a face with both eyes on one side.) |
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//The question is, suitable for what?//
Suitable as a way of tuning a keyboard instrument to be played in all keys.
(I partly know what I'm talking about.) |
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Quite, for certain values of 'all'. It's a little circular - the very idea that there are 12 major and minor keys is linked to the development of the instruments and scales that they are played on. It's not by any means a natural law, but more of a convention. |
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In fact, medieval Pythagorian tuning had fewer than 12 notes - typically about 9, Bb to F#. So an inability to play in 'all' 12 keys didn't really matter. |
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I partly know what [spidermother]'s talking about. Composers back-in-the-day fully embraced the wolf chords as well, ie: passages were out-of(-perfect)-tune on purpose. |
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The major exceptions were a capella vocal polyphony (and I assume string quartets, both of) which could pull off perfect tuning given enough attention to detail on the part of the composers (akin to playing with a Rubik's cube), and enough threats of physical punishment directed towards the performers. |
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I've linked to an excellent book on the various temperaments and how best to realise them.
(I have a signed copy; the author, John Meffen, who died recently, was an acquaintance of mine . His daughter played keyboards in my old band.) |
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[+] At least mitxela is trying to do something new, not just repeat history ad nauseam. |
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[ ] yes but it's rather akin to a computer program that "does all your spelling, grammar, punctuation and layout work for you". |
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[sq] //repeat history ad nauseum// huh ? (western) music tuning development isn't like improvements in pure mathematics or improving the understanding of the laws of physics: it's an artform based on mathematical ratios. I know people that work in other tunings: they use the more/less tuned chords the same way, and with much the same result, as an artist shading or bringing out the colours in a painting. |
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From working mostly with either equal or perfect tuning (choral with/without piano or organ): equal tuning is a bit dull but consistent; constant perfect tuning sounds brilliant all the time and can make your brain leak out your ears after awhile. For instance... |
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A chamber choir sings a 15c polyphonic piece along with, and tuning to, the piano: you can hear all the parts distinctly all the way through. When it's finished it takes 15 seconds for the echos to die out. |
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Same song, same volume, but acapella: now throughout the piece there's extra notes coming in from nowhere and during some portions you can't distinguish the individual parts at all. When it's finished it takes over half a minute to fade away (I've clocked it). |
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... And it's not new. As I said, it even has a name: adaptive intonation. |
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[flying screensaver] and [spidermother] of course you are both right. I still want to give a [+] to mitxela for 'effort.' |
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just [screensaver] will do fine :) |
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I wanted to use your 'formal' name. |
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Of course we're right :-). But it's an interesting topic, and not WKTE. |
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Would be more interesting if it were implemented by a mechanical interlock actuated by the combined keypresses of each chord, which move little shifting bridges under each string. |
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