I’ve never found the answer to this seemingly straightforward question:
Western music is based on 12 semi-tones, right? 13 notes in the chromatic scale. Now, of these, 7 are called A-B-C-D-E-F-G and another 5 are “Enharmonic”, and named as sharps or flats in relation to the above Major scale.
So–why are A-G the notes they are? I can’t seem to find any rationale for making those 7 of the 13 notes the special ones. Why not simply A-A#-B#-C-C#-D-D#, etc?
Somehow these ended up where they are for a reason.
Based upon past threads, you could get a long explanation.
But, in a nutshell:
The diatonic scale (7 notes) came first.
The intervals in the original scale were common ratios of frequency, i.e. based upon the overtone series.
7 notes is somewhat arbitrary, the Greeks did 7, others did 5, 6, 8, 9, etc.
various orderings of the 7 notes became “church modes”, e.g. Dorian, Mixolydian, etc.
These were “simplified” into our modern Major/Minor scales.
The chromatic notes came along because if you started a scale on something other than “C”, you discovered that you needed note(s) in the gap(s).
rationalizations of the whole frequency thing were attempts to make everything line up better when you shifted into other keys. These tuning systems are Just Temperment, Well Temperment, and many others.
our modern scale is 12 semitones with Equal Temperment, which is a tuning system using one ratio for the semi-tone: the 12th root of 2. In other words, 12 multiples of a semi-tone is 2 which is an octave ratio.
Wow. That’s one of the best concise explanations I’ve ever seen.
(Hopefully) related question: How did the particular frequency 278.4375 Hz get to be middle C? Is this just an accident? After all, one can preserve the relationship between frequencies on the chromatic scale regardless of those absolute frequencies, so it’s tempting to think middle C is an historical accident. But is it?
I’m not sure if I’m reading your question right, but historically A is generally the note one tunes from. Since the early 20th Century, A has been standardized as 440. (A=440). If you work back to C in equal temperament, you get a frequency of 278.4375.
Ah, but then why A440? History. Pitch has fluctuated all around. Since the Baroque era, A could have been anywhere from 350 to around 500. Eventually, the music community startded standardizing and ended up with 440.
This is, of course, the Reader’s Digest condensed version of the story.
That’s the gist of my question, and I just used middle C because I was unaware that A was the customary benchmark of pitch. In any case, the notes that make up the chromatic scale now have completely standardized and universally-recognized frequencies, and I’ve always wondered if there was something deeper than historical accident at work in determining whatever pitch finally ended up being middle C. It would appear no such determinant exists.
Basically, it reasserts my statement that middle C mathematically is 261.63 in equal temperament (although in practice it’s played at 262-264 HZ) and not to believe everything your read on the internet. I’m still trying to figure out how in the hell somebody came up with middle C278.4375.
There is a reason for the standardising of pitches to have happened somewhere around the 440Hz mark described. It happened alongside the standardisation of notation in treble and bass clefs. With pitches somewhere around what we have nowadays, the main range of choral music fits neatly into the two clefs, with little need for multiple ledger lines to take the music much higher than top A or lower than bottom E.
The standard pitch of C or A has varied much over time. According to this site:
If Venice orchestras tuned at A=467, that would give a C of about 278. If so, that would probably be at an historic high. There is even a movement to lower the standard pitch of A to 432, which some claim has richer harmonics, although I suspect that might be more subjective observation than physical property.
The actual intervals between notes is pretty much standardized at the tempered scale. But there are those who think there are better ways to tune. Check out this site on Lucy Tuning.
To try and tackle Sevo’s OP, although it is true that the modern chromatic scale places one-half (tempered) step between adjacent notes in the scale, our ears recognize relationships that are different than pure mathematics. Example: an augmented triad, composed of:[ul][li]Lowest pitch[]2 whole steps up[]Second pitch[]2 whole steps up[]Third pitch[/ul]…sounds a bit odd to our ears. It has been described as “unstable” and is rarely used in modern music. [/li]
Similarly, a whole-tone scale, where the intervals between adjacent notes is one whole step always, has been used in music, but infrequently, and seems to have an “unsettled” feeling, as there is no feeling of “key.”
Schoenberg was famous for going one step farther and working with a melodic and harmonic concept that treated all chromatic intervals as equal. He wrote his pieces using mathematical constructs in contrast to Mozart, who said he just wrote down what he heard in his head. Quick, now, hum some Mozart…now try some Schoenberg…ha! – thought so.
Modern (western) music is a hybrid of tonal relationships that developed and were expanded over the ages. Perhaps if we developed a scale from scratch with no previous music knowledge or history, it might be different. And, indeed, in non-western societies, it is, encompassing quarter and third-tones in oriental music.
Lowering the pitch of orchestral string instruments by that amount does have a noticeable timbral effect - when playing solo, I’ll often choose to nudge below 440.
You may not like Schoenberg, but making false statements doesn’t help your case. And only a very few composers worked in the way that Mozart did (Britten is the only other that I know of).
Mozart has described equal temperament as an abomination, and said in no uncertain terms that his music should not be played in this modern tuning. It wasn’t really until the late Romantics that equal temperament gained the sort of acceptance it has today. More than one musician has quipped that in equal temperament all scales sound equally bad.
Bach, from almost all accounts, certainly did not intend his music to be played in equal temperament (perhaps you know this, I just want to make it clear to readers out there.) IIRC, it was meant to be played in one of the Werckmeister temperaments, which was well-tempered, but not equal tempered. There is an important distinction here. The space between intervals varied slightly depending on key. The keys were stable enough to be in tune, but not every key sounded the same. Different keys truly had different feels to them, because the relationships between notes varied ever so slightly.
So, over time, we have also lost the true sense of key color. Sure, some people with absolute pitch will say that C# feels different than C (and perhaps it does), but back then C# truly felt different even to the casual listener because the relative pitches changed. Back in the late 1700s or early 1800s, there were treatises about the entire notion of key color. Every key and tonality had a feeling associated with it.
So, anyhow, music up until the mid-to-late-Romantics should not be played in equal temperament, if you want to remain absolutely faithful to the original.
[QUOTE=Musicat]
Example: an augmented triad, composed of: Lowest pitch[li]2 whole steps up[]Second pitch[]2 whole steps upThird pitch …sounds a bit odd to our ears. It has been described as “unstable” and is rarely used in modern music. Similarly, a whole-tone scale, where the intervals between adjacent notes is one whole step always, has been used in music, but infrequently, and seems to have an “unsettled” feeling, as there is no feeling of “key.”[/li][/QUOTE]
“Sounds a bit odd to our ears” - to whose ears? And who says it sounds ‘odd’? And what do you mean by ‘odd’? “Seems to have an unsettled feeling” - in whose opinion? And what do you mean by ‘unsettled’ anyway?
Music aficionados… of whom I have known several… have this strange tendency to take arbitrary, subjective opinions based on nothing empirical whatsoever, and to represent them as some universally agreed or standard point of view that can actually be demonstrated or proved. I had the same trouble with music teachers throughout my formative years. They would say things like, ‘Pieces in a minor key sound sad and mournful’. To present an arbitrary opinion in absolute terms is self-evident rubbish. If you doubt me, go ahead and prove the assertion that minor key = ‘sad’ or ‘doleful’ sound. It can’t be done because there’s no link whatsoever. Music teachers tend to recycle this kind of dreck simply because it’s what they were told by their music teachers… and so the cycle goes on.
There is nothing, nothing whatsoever, intrinsically ‘sad’ or not ‘sad’ about the sound of a minor chord or a piece played in a minor key. If you took a music class, completely new to standard music theory, and told them the opposite (‘major key = sad, minor key = happy’) they would believe it and would convince themselves they could ‘hear’ the difference. But they would be hearing what they were told to hear.
A tune may or may not sound happy or sad to me. It may or may not be in a minor or a major key. My opinion about its sound and corresponding emotional impact is just as real and valid to me as yours is to you.
Same goes for all the tired cliches the music luvvies tend to churn out about certain keys being best suited to certain moods or emotions, ‘A minor evokes qualities of blah blah blah’ or ‘D major tends to evoke moods of blah blah blah’. More arbitrary opinion masquerading as absolute or empirically demonstrable fact. Take any piece you like in A minor. Increase every single note by the same amount, from start to finish (easily done using varispeed). It’s now in a different key. Exactly the same darn piece of music. Exactly the same emotional impact in any given listener’s opinion. QED.
Is it fair to say that now, with modern usage of equal temperament over just temperament, the only practical and/or aesthetic value of differing key signature is to accomadate certain vocal and/or instrumental ranges?
People say these things for two other reasons. Firstly, it’s tiresome and unnecessary to use the word ‘subjectively’ every such comment about music - it’s all subjective. And I’d have certainly thought it was kind of obvious that in this discussion, ‘to our ears’ is shorthand for ‘in the cultural environment in which we acquire our aesthetic and subconcious understanding of musical sounds’.
Secondly, in that same cultural environment, the use of a minor key has become associated with ‘sad’ music. It’s an association, not a physical property of the scale. But it exists.
Reread pulykamell’s comments about this, and how recently equal temperament has prevailed. These associations of scales are a hangover from past generations - but they’re still important for understanding what those composers were writing, even if we’re playing it in equal temperament.
Mainly, yes. However, there are particular keys that have particular implications on some instruments, beacuse of particular notes included or omitted - keys such as D and G (major or minor) on orchestral strings give opportunities for many open strings, including their use in double-stopping. G# minor or E major, for example, prevent this. Other instruments have other properties that also affect individual pitches in such ways.
There’s also ease of playing, especially considering keyboards. Certain passages that are easy to do at one key are much harder to play at another key. A good composer (e.g., Chopin) knows this and takes advantage of the eccentricities of the shape of the human hand and the pattern of black and white keys.
[QUOTE=ianzin
There is nothing, nothing whatsoever, intrinsically ‘sad’ or not ‘sad’ about the sound of a minor chord or a piece played in a minor key. If you took a music class, completely new to standard music theory, and told them the opposite (‘major key = sad, minor key = happy’) they would believe it and would convince themselves they could ‘hear’ the difference. But they would be hearing what they were told to hear. [/QUOTE]
Perhaps true, perhaps not. I try to avoid this sort of vocabulary as well, but in Western music tradition, I don’t think it’s unfair to say major sounds “happy” and minor sounds “sad.” These scales don’t exist in a vacuum; they certainly have emotional associations connected with them. Maybe using an emotional word like “sad” to describe the minor scale isn’t accurate, but to me all the modes, played without greater context, have a certain feel to them. Major is bright, happy. Dorian is aggressive, war-like. Phyrigian sounds exotic and middle Eastern. Lydian is a bit exotic, but very bright and happy. Perhaps the brightest of the modes. Mixolydian, not as bright as major Ionian. And so on. I would rank the modes from bright to dark in this order: Lydian, Ionian, Mixolydian, Aeolian, Dorian, Phryigian. Locrian I won’t even place because it’s just plain weird. So maybe sad and happy aren’t the best words, but for me it works in terms of bright and dark.
And augmented chords ARE unstable. That’s their whole nature. I wouldn’t consider them necessarily weird or rare. But the relationship between the three tones: root, major third, augmented fifth is mathematically “tense.” A pure major chord has a 3:2 ratio between the fifth and the root. If you listen to a perfect fifth being played, it will not have any beats to it. (Well, in equal temperament it will beat slightly). However, with an augmented fifth, there’s dissonance. There’s no stable base, like the perfect fifth, for the chord to sit on, so it sounds unstable. There’s a physical reason for why some chords sound more unstable to others.
D’oh! As an amateur guitarist, the configuration of different instruments should have been an obvious reason for choice of key signature. Transposition is often the only remedy for the guitarist attempting some pieces, or use of a capo; but the latter can create an undesirable shift in pitch in some circumstances.
I’m still trying to figure out how in the hell somebody came up with middle C278.4375.