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As I understand it, the great bulk of music from the Baroque, Classical, and Romantic eras are at least these days performed on equal temperament instruments. And yet there is still a great deal of discussion of the inherent colour of various keys used for compositions (not merely of the keys in relation to each other within a piece, which I can understand).

While many instruments (and indeed singers) clearly have a natural range and tone changes considerably outside of it, and while very large absolute pitch differences are clearly detectable even by the most tin-eared whereas others are cursed with absolute pitch, as a non-musician of a mathematical bent, I find it hard to understand, from a mechanistic perspective, how different keys in the same scale can continue to be coherently and consistently said to have distinctive colour with pieces composed for, and played with, equal temperament.

I'm somewhat confounded by composers, wishing to use all the forces at their disposal, of course choosing the key they think best supports their piece, such that, for example, a piece of child-like innocence might be composed in C-major as a result of the belief in the inherent colour of keys, such that there are very few examples to suggest that the key have any other character.

Is there some mechanism which I haven't anticipated or, in this context, is it just hokum? I apologise if, in my naivety, I have stepped into controversial territory.

UPDATE: I might clarify my difficulty. If most people only sense relative pitch (and certainly much music theory is based around that idea) and if a key is shifted in equal temperament then all those relative pitches stay the same. So I'm told one thing by these ideas, and then another by the idea that keys -- even keys very close together in absolute pitch of the tonic -- have colour. I understand that there's more to real music than oscillators (such as sympathetic vibration, string tuning, timbre differences etc) and would like to understand if and how this adds up to key differences. I certainly have favourite keys and want to understand what that means.

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    There's nothing special about music -- the human brain is not a digital computer, it interprets and "colors" everything subjectively. Do you view psychology and neuroscience as "hokum"? – Matthew Read May 17 '15 at 7:01
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    I was asking a question, not making an assertion! I find it hard to understand how it cannot be, and am trying to understand. – Dan Sheppard May 17 '15 at 17:17
  • Excellent question Dan. I recently had a discussion on this stackexchange arguing that there is no difference difference, lets say, D major and E major chords from the perspective of harmony (assuming they are played independently and not allowed to create an implicated of a tonal area). The answers to your question confirm my argument. – lobi May 19 '15 at 20:19
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Maybe somewhat controversial. There is definitely some serious hokum going on here, you're right. BUT, I think you're underestimating the color differences a number of keys have on some instruments. The string section is the most dramatic—they generally have three strings that are free to vibrate sympathetically when they are playing a single pitch on the fourth string. When the string player is playing a pitch that includes some of the open string frequencies in its harmonic spectrum, you definitely hear it. D major on a cello, for example, can be a much bigger sound generally speaking than Db major.

Further, all instruments have a lowest possible note, and when a piece is in a key just a little lower than that, it makes less range available on that particular instrument that is useful for the key.

The more specific the description of the color of the key, the more hokum is involved, but there are unequivocally some general differences on different instruments.

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    Interesting about sympathetic vibration. As an erstwhile violinist and a guitarist, often I have to stop open strings vibrating on guitar. Are there times when a violinist/cellist stops other strings vibrating, or leaves them open on purpose? Is there an instruction in the music for either? – Tim May 17 '15 at 6:51
  • Yeah, I play both guitar and cello, and stopping strings is totally normal on guitar and almost never done on cello. Part of the difference is that there are two fewer strings on cello and they're more distant from each other, and part is that it's much easier to stop strings on the flat fretboard than on the curved fingerboard. I've only seen indications to dampen strings when an unpitched effect is being called for or when you're supposed to stop a note rhythmically. An "x" on the strings line or space is used for that, so I suppose you could use that in other situations. – Pat Muchmore May 17 '15 at 11:01
  • How particular frequencies fill particular performance spaces help as well and can make a big difference. Frequency response is different from instrument to instrument, piano to piano, day to day even, much less on how instrument construction has changed over the centuries: Bach's violins were very different from ours. However, if you really want to know for yourself, put down your math books and use your ears. Try finding the same piece in different keys, and listen, listen, listen. The keys ARE different, but in what ways that are entirely up to your own interpretations. – aaaaaaaaaaa May 18 '15 at 5:05
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Yes, and one can go a little bit further. The traditional qualities associated with common keys in the 18th century can be correlated with orchestration, in that different instruments sounded better (or, sometimes, could only really play well) in certain keys. Examples:

  1. A and E major had the reputation of being "fiery" -- probably because both keys would make heavy use of the open E string at the top of the violin, which had a sharp, piercing tone.

  2. C, D major, and E-flat were the "majestic" keys, largely because the brass instruments of the time sounded better crooked (that is, with a crooked piece of tuning inserted into the bore) so that their overtone series was based in C, D, or Eb. Other crooks did exist, but they were rarer, and sounded poorer. So - if you wanted loud and exceptionally bright, you went for D: the strings could use lots of open strings, and the brass and timpani could hammer away. C major would be even better for the brass, but slightly darker from the strings. Eb would be excellent for brass, and also for woodwinds like clarinets, so you could get a mellow, deep richness to the tone. (Compare the late Mozart symphonies here: 35 and 38 (Paris/Linz), in D; 39, in Eb; and 40, in C. They each have a different orchestral sound.)

  3. F and G major were considered "pastoral" keys: good for winds, but not military brass, and resonant but not sharp on string instruments.

  4. The hypothesis is that these key associations still had force, even at the keyboard; and the associations of the keys remained long after it was possible to play pretty much anything in any key.

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Strings are tuned in perfect fifths, brass uses the overtone series and valving compromises in its scales. While instruments with per-note strings, keyholes, tines or whatever can be tuned in equal temperament, quite a bit of the characteristic substance of an orchestra does not belong in that class. This also affects orchestration, further adding to the characteristic colors expected from certain keys.

  • That's a good and interesting point. – Dan Sheppard May 17 '15 at 19:48

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