While it’s true that there’s physical origins of some fundamental frequencies, what cannot be explained in this way is the importance we give to particular scales and chords, because it does not give any hint of the equivalence we hear between major and minor keys and triads.
That we can take any major-key melody and flatten the thirds, tinker with the 6ths and 7ths, and still hear it as the same melody, suggests the sequence of overtones which have some correspondence to a major scale aren’t the explanation for the latter having become so familiar. There’s also the pesky kind-of-flattened-7th overtone which Chronos doesn’t mention - the preview of track 1 here gives an idea of how un-majorish the natural harmonic series can sound.
Let’s not forget that many wind instruments (brass in particular) operate by being able to create waves of different fractional lengths through a fixed length of tubing.
It happened over a long period of time, with different theories and a battle of minds at times - the concept of equal temperament in itself was around for centuries before it became a common standard, and even Bach wrote the Well-Tempered Clavier (not ‘Equal-Tempered’), at a time when various tuning systems were in use - The Well-Tempered Clavier - Wikipedia gives a summary.
…which are then constantly altered to bring them into tune! (See my link to a horn solo a couple of posts back.)
While I understand exactly what you are trying to illustrate, I wonder if that “tones sound good” statement needs to be modified with “to western ears”. Since my ears (both of them) are more west than east, it’s hard to understand why early eastern music was good to their ears but not ours. After all, we all have access to the same acoustic laws and methods of building instruments (tubes, strings, etc.), yet we came up with different harmonic structures.
There’s not much fundamental difference in how these are structured; it’s just that different subsets of notes became popular in different areas. For example, the Arabic tuning system is actually exactly the same as the western one, but with twice as many notes per octave. (So imagine a piano keyboard with yet another color of key between every white and black key that’s already there.)
They never use all 24 notes in a single song, though; like our diatonic scales, they choose a seven-note subset that has some overlap with the equivalent degrees of a western scale.
Gamelan tunings, such as slendro, can’t be meaningfully described in this way. It will always be possible to vaguely approximate things to one chromatic note or another, but can mean ignoring very different decisions and priorities in another tradition.
Could you go through that again a little more slowly?
Are you talking about the difference between minor and major keys (and the way we perceive, say, A major and A minor to be similar even though they have some important notes quite different) or the difference between the sound of an equal-tempered or non-equal-tempered (I’m sure there’s a technical term for that) scale?
That horn solo is a tune played in a minor key on a non-equal-tempered instrument, correct? So it’s an example of both the differences rolled into one?
I do find it interesting that in a minor key, the very first harmonic to be ditched is the Major Third - the most “obvious” and nice-sounding harmonic in the whole scale (excepting the octave). I’m not sure what that means though.
So if I’m reading this right, pianos can be tuned so that a note on one is slightly different than on another, depending on what ratios you use. What about those with perfect pitch, who can identify a note from just hearing it? Is the difference slight enough that it doesn’t make a difference, or can they be tripped up by a badly tuned piano?
Some monks might disagree with you. In medieval times, church music went thru an evolution of harmony, with most songs sung in unison or octaves, then the next step was parallel 4ths or 5ths (Note that an inverted 4th, where the lower tone is raised an octave, becomes a 5th and vice-versa), which sound a little dissonant to our ears, sounded consonant to theirs.
3rds were considered dissonant to early monk ears, but consonant to ours.
And parallel movements of harmony were the only thing in medieval times, then became forbidden in 17th-19th century harmony, but now are largely ignored.
Am I going too fast for you?
This question sometimes causes controversy among musicians. Some claim that good string players play “pure” scales, not tempered ones, but my position is that if they did, they would clash severly with fixed, tempered tuning of pianos. Since they don’t, they don’t. And I question if perfect pitch really exists – my theory is that very good relative pitch does (I think I have it), but absolute perfect pitch does not. If it did, think how horrible it would be for a string player, used to playing with A=435hz, to be put in an orchestra where A=440 (orchestras like this did exist not long ago, with Europeans using the 435, USA using 440).
Most brass instruments are inherently not equal temperment, unless you constantly fiddle with the tuning valves (one exception, of course, is the trombone, which isn’t inherently any particular temperment). To make a truly equal-tempered horn, you’d need a separate set of tubing for each note, rather than just using various combinations of three sets.
You don’t need perfect pitch to be tripped up by a badly tuned piano. But if you’re just talking about a piano whose pitch is raised or lowered beyond the standard A440, it depends on who you talk to. I’ve heard people with perfect pitch say it drives them nuts when a song is in either a different key or slightly sharper or flatter than usually (although in tune with itself), and others I know it makes no difference to.
Major/minor. This was in response to explanations for the dominance of this system which resort to comparison with the harmonic series.
It’s played entirely on the overtones of a single fundamental, and so is in no key.
It means that an explanation for the ‘rightness’ we hear in our tonal system is not adequately explained by identifying major 3rds in the harmonic series.
You certainly can tune a piano differently, such as in La Monte Young’s Well-Tuned Piano. However, a modern piano is not designed to be retuned as a matter of course, whereas earlier keyboard instruments such as harpsichords need frequent tuning, whether to the same temperament or a different one, and so it was no big problem for baroque musicans to experiment.
As for ‘perfect pitch’, this raises the question of to what degree it’s acquired rather than innate, possibly through being surrounded by major and minor tonalities since birth (or even before!)
This was my initial suspicion (including a gut feeling that perfect pitch can be learned), but I had a lengthy discussion once with a researcher who was working on the question of absolute pitch and the stuff that happens in the brain when processing pitch, and she convinced me that absolute pitch is a real phenomenon, which is distinct from the type of learned pitch memory one can sometimes acquire from playing an instrument for an extended period of time. Her research seemed to point that it’s an innate skill. I’m not sure whether I agree with that yet, but it seems to be a skill that, at the very least, is learned very early on in childhood development.
Just to expand a little on my personal experience, I find that even if I haven’t touched a musical instrument for days, I can walk to a piano and sing the note I am about to play. Maybe that’s more of a long-term memory phenomena.
Sometimes I’m wrong, but only off by a half step. Dunno if that means anything.
People with perfect pitch don’t have this problem with being wrong, from all that I’ve ever experienced, and from what the researcher told me. It’s hard for me to know, though, as I do not have perfect pitch, but – once again, this is how it’s been conveyed to me – even if you’re locked in a black room for a several days, when you come out, you don’t forget what “yellow” is, or mistake “green” for “blue.”
Absolute pitch of this nature wouldn’t, however, be enough to hear whether a particular note was exactly in tune with A440 even temperament, though! There may well be an innate skill which, having heard these pitches, provides an exact recall of them, but nobody until the most recent generations of musicians would have experienced this as a norm, and so would not have developed such a particular memory for one tuning system.
- the preview of track 1 here gives an idea of how un-majorish the natural harmonic series can sound.
