Since nobody else has directly answered: yes, you have this right.
This is a little trickier. In the link you provided, except the very bottom group, all of the scales are all based on the western 12 note chromatic scale, using instruments that play these 12 notes (or some subset of them). If you play a guitar or accordion, you’re playing in the western 12-note system, because those are the only notes you can play (leaving aside bending notes). You can play using a minor scale or major scale or other scales, but they’re all subsets of the western chromatic scale. So for everything down to and including the “Romanian”, I wouldn’t say it’s forced into the western chromatic scale.
Now the traditional Chinese, Javanese, etc. scales were never part of the western system, and grew out of their own instruments and tunings. I don’t know enough about any of these to say for sure, but I think some of them have only notes that can be matched up to notes in the western chromatic scale (so you could play their scales on a piano), and some have notes that fit in between, so can’t be matched up – you could never play that music on a piano. It’s up to you whether you want to use the word ‘forced’ in any case.
Obviously, which exact frequency corresponds to which note is, as we already said, somewhat arbitrary.
I would say a lot of those are approximations. For example, when I hear Hungarian gypsy music, the tunings, especially on the fiddle, definitely have non-equal temperament going on. While the scales can be approximated to 12-tone equal temperament, they’re not quite right. For the right gypsy feel, you need to hit some of the notes slightly sharp or flat from 12-tone ET.
Same thing with something like a blues scale. The “blue notes” (the minor third, augmented fourth/diminished fifth, and dominant seventh) are generally played a bit sharper or flatter on instruments that allow bending of notes.
The bagpipe scale is often referred to as “A Mixolydian,” but that, too, is only an approximation. Bagpipe intonation is significantly off equal temperament. While you can fudge it with the mixolydian mode, if you want to do convincing bagpipe music on, say, a synth, you have to significantly detune the third and the sixth. (Although I notice that there is no scale on that page specifically referred to as the “bagpipe scale.”)
In my experience, any scale deriving from folk traditions usually strays from 12-tone equal temperament, especially if it involves instruments that are not fixed in pitch.
By the way, I was bored over my lunch break, so I decided to fire up Mathematica and see how close various numbers of fifths are to whole numbers of octaves. In other words, if you made an n-tone scale using Pythagorean tuning, what would the “best” numbers of n be? Here’s what I found:
[ul][li]Five fifths are approximately three octaves, to within 2.5%.[]Twelve fifths are approximately seven octaves, to within 0.28%. This is the “standard” twelve-tone Pythagorean system.[]41 fifths are approximately 24 octaves, to within 0.069%. This would give rise to a 41-tone scale which could then be “tempered”.[]53 fifths are approximately 31 octaves, to within 0.0097%. This would give rise to a 53-tone scale.[]After 53, the next best scale would be a 306-tone scale (306 fifths are approximately 179 octaves, to within one part in 120,000.) This is getting a little silly.[]But we press on. The next best case is a 665-tone scale; 665 fifths are within one part in 6.2 million of 389 octaves.[]If we really want to get ridiculous, we could derive a 15,601-tone scale: 15,601 fifths equal 9,126 octaves to within one part in about 350 million.[/ul] [/li]
At this point, though, adjacent notes of the scale would be indistinguishable to the human ear; in cents, they would be 0.08 cents apart. The trained ear can only usually distinguish notes that are more than 5–6 cents apart, which makes the 306-tone scale and the 665-tone scale dicey propositions too (about 4 cents and 2 cents, respectively.)
There’s a fundamental aspect of all scales that I don’t think has been brought up (although MikeS alluded to it): the fact that any scale is inevitably a compromise, and that there can never be a perfect scale.
The reason is twofold: first, that (as others have said) we like our scales to have small integer ratios between the notes, such as 2/1 (an octave) and 3/2 (a fifth). And second, we like adjacent notes to have the same ratio. But it’s mathematically impossible to have both at once, because that would require an integer solution to 2^a = (3/2)^b. That can’t exist (for a and b > 0), for basically the same reason that all the roots of 2 are irrational.
The various 12-note tunings are basically different ways of approximating 2^(1/12) as integer ratios, while at the same time making the fifths work out as well as possible. It can never really work, but for the most part they can come close enough.
Oh, I was just being especially nitpicky, as I noted. Yes, I agree, in terms of major pentatonics, the 1-2-3-5-6 is the most common in Western music. Minor pentatonic is fairly common, too, which is 1-3-4-5-7 of the natural minor. It’s basically a reduced blues scale. You can play minor pentatonic over any blues and it would work.
For those interested, if you have a piano or keyboard at hand, your black keys are basically a pentatonic scale. If you start your scale on the F#/Gb (the first black key in the group of three), you have a major pentatonic scale. If you start your scale on the D#/Eb (the second black key in the group of two), you have a minor pentatonic. If you start with the G#/Ab (the middle key in the group of three), you have a suspended pentatonic, which sounds very East Asian.
This is completely untrue, I’m afraid. Indian classical music simply has no concept of fixed frequencies denoting certain musical notes. Nearly everything in Indian classical music is based on relative frequencies, from an arbitrary starting point that is adjusted to suit the singer or instrument.
I might choose my Sa (or base note) at 523 (or 523.3, or 523.002998) Hz when I sing, because it’s comfortable for me, while my sitar will be tuned to, say 654 Hz, but that’s still Sa on the sitar.
Indian classical music also makes extensive use of microtones - subtle shifts in the frequency of a note to bring about a change of mood or emphasis. These will still have the same name, but sound different enough to be perceptible. While playing the sitar, for example, the frets are moved slightly up or down the neck of the instrument to produce exactly the right “variation” on the note that is required for the raga, or mode, that is being played. I’ve never played a fretless instrument, so I assume this is much harder on something like the violin, involving subtle shifts in finger placement.
The emphasis on fixed frequencies and an equally tempered or chromatic scale in Western classical music is driven by the need to have pleasant sounding harmonies and ensure that a large collection of instruments can be played at the same time. Indian classical music relies much less heavily on harmony, and does not have orchestral music on nearly the same scale, and is therefore less constrained by absolute frequencies.
So the link I provided earlier with scales for various cultures just shows approximations. The Phrygian scale below isn’t an exact Indian scale, is an Indian-ish sounding scale?
Modal Pentatonics
Name -from- F# G G# A A# B C C# D D# E F F# Semitone Jumps
pC Ionian 1 2 3 - 4 5 - 1 2 2 3 2 3
pD Dorian 1 2 3 - 4 5 - 1 2 1 4 2 3
pE Phrygian 1 2 3 - 4 5 - 1 1 2 4 1 4
I suppose the thing I am trying to work out is - is there a fundamental quality of musical tones that cuts across cultures?
Reading posts above shows there is only a **relative **relationship between notes based on the physical interaction one sound wave has with another. And any attempt to compare one culture’s scales with another culture is just an approximation.
I once saw a public television show that claimed that the portability of the accordion popularized a particular tuning—the one we primarily use—across much of Middle and Western Europe.
I’m going to say no, because very few people have perfect pitch (the ability to distinguish different frequencies absolutely). So to most people, it doesn’t matter if you play a song in C major or D major, not to mention different base tunings (415 Hz, 440 Hz, 442 Hz, 443 Hz). Was this what you were looking for?
In fact, there are some orchestras that use different frequencies (sometimes even different depending on their show!). I’ve heard the London Orchestra actually tunes to A=442Hz.
That’s covered upthread. Orchestras tune anywhere from A=440 to A=445, and there is a tendency for the pitch standard to rise over time.
Actually, according to this NYTimes article, some symphonies tune as high as A=450. There used to be a chart online of the major orchestras and their A tunings, but I can’t find it anymore. I believe A=442 was the most usual tuning. Boston Symphony was A=444, although that depended on who was conducting and their preference for the pitch standard.
I wonder how nuts that drives people with perfect pitch. Especially if they learned perfect pitch with a piano tuned to something non-standard like A=443.
Triange is usually treated as atonal percussion for purposes of tuning I think. Marimbas (not sure about xylophones) can be retuned, but it’s as much (if not more) of a pain as a piano. All in all, Marimbas aren’t used in every piece, so I suspect if the show in question required a Marimba they’d either:
A. Special order a Marimba tuned to their preferred frequency (say they always tune to A=442, order a Marimba tuned to that)
or
B. Bite the bullet and tune to the Marimba even though it’s slightly sharper/flatter than the ususal tone they tune to.
Actually, a lot of xylphones are tuned to A=442. Google “xylophone 442,” for example. Here’s a brochure from Vancore xylophones, and 442 is their standard A tuning, with 438, 440, and 444 also being options.