What, exactly and completely in all its senses, does the term "harmonic" mean?
Oh, like as in HARMONIC DAMPER:Harmonic? Harmonic what? It's an adjective, isn't it, so it needs a noun to go with it.
So far, MacLeod is the only one to recognize the term "harmonic" as having meaning as something other than a noun.Harmonic? Harmonic what? It's an adjective, isn't it, so it needs a noun to go with it.
Is it? I thought "harmonic progression" described a progression of chords, or a sequence. The "harmonic" adjective refers to "harmony," not any vertical entity such as an upper partial or overtone.A harmonic progression is where the word is used as an adjective instead of a noun. It's a vertical arrangement of notes.
And like the harmonic series, this thread divergesThe harmonic series sums up terms like 1/k, where k is an integer.
So, it appears you are prepared to deviate from the idea of the 'natural' harmonic series, and accept any positive integer multiple as a "harmonic." Some literalists would disapprove, saying that "harmonic" should properly only refer to the natural overtone series.I think Bwv 1080's definition is more than complete enough. "Harmonic" as an adjective should refer in some way to the concept of a frequency or frequencies that are a positive integer multiple of a fundamental frequency. It is the relationship of two or more frequencies that is (or isn't) harmonic.
One of the ways verbal language works is that descriptive terms do extra duty, i.e., are given broader or comparable meanings. Western harmony is an outgrowth or development of the harmonic series, making special use first of the unison and octave, then of the fifth, and finally of the triad. Other scales are possible, of course, but the fifth is very useful because in the twelve-tone equal tempered scale, it corresponds so closely to the natural harmonic. The total "correction" required is pretty small, only about 23 cents. But the true 12-tone equal tempered scale is a very modern development in western music, as each step in the scale is higher than the preceding one by the twelfth root of two, and only relatively recently was it possible to calculate that.So, it appears you are prepared to deviate from the idea of the 'natural' harmonic series, and accept any positive integer multiple as a "harmonic." Some literalists would disapprove, saying that "harmonic" should properly only refer to the natural overtone series.
But that would exclude the commonly and frequently-used terms "harmonic progression" and "harmonic analysis," both of which refer to chord progressions and "harmony".
As I said in post #10, "harmonic" as an adjective in this case refers to "harmony," not any vertical entity such as an upper partial or overtone.
Harmonic progressions, as strictly defined by CP Western harmony, are derived from the major/minor scales. If a modern composer deviated from that, and used other 'exotic' scales, diminished scales, whole tone, and the kind of things you might see in Slonimsky's Thesaurus of Scales, I don't see what's so "innovative" about that, except that it has expanded the possibilities from the limitations of the CP major/minor system. The principles I have outlined would still apply to those scales which lie outside the purview of CP tonality, and that's why I think they're important, since they are harmonic principles which can apply to areas well outside CP harmonic practice.Millionrainbows -- To use your terminology, "key areas" are established in western music not just by "root movement", but also by patterns and repetition. Rhythm, dynamics and timbre are also used by sophisticated composers to reinforce and complement the tonal system and point the way to the tonal center, often with great subtlety. It's true that over a span of six centuries or so, harmonic progressions played an ever-increasing and more dominant role in western music. But in the early 20th century, there was suddenly a bit of a roll back in that area.
Stravinsky was an innovator, without a doubt, and I think there were also many other innovators, like Slonimsky for his work in scales.To me, the most important leader of western music away from its slavish obsession with harmonic progression or what you call root movement was not Schoenberg, as important as he was, but Stravinsky, who was to music what his good friend Picasso was to visual art. He demonstrated that, while it is possible to abandon traditional western harmony entirely in favor of serialism (and later, musique concrete, indeterminacy, and other alternative systems), much could be accomplished by simply reducing, even if only slightly, the dominant role harmonic progressions had reached in western music by the late 19th century in favor of other elements, many of which could be made to work well with, and even enhance, harmonic progressions along the circle of fifths.
That is why so many contemporary composers owe so much, almost everything, really, to Stravinsky. Even composers who quite consciously took Schoenberg's path like Boulez (who was such a disciple he didn't think he could advance his own ideas without first proclaiming "Schoenberg is dead!") very much show the influence of Stravinsky.
I'm going with the ideas of Dr. Bradley Lehman (larips.com) who deciphered Bach's well-tempered tuning from a decorative flourish on the cover page of the original manuscript. It was basically an attempt at ET, in which all keys sounded good.Many scholars argue that the Well-tempered Clavier was not composed with equal temperament in mind. Some suggest Bach intended the use of Werckmeister III, where the Pythagorian comma is equally distributed over four neighboring fifths (rooted on C, G, D and B).
What you say is true, especially in light of key signatures, but Chopin later used distant keys like A flat because of ergonomics: the hand sits naturally on the piano when the middle fingers are covering black keys, and the thumb and pinkies cover white keys. He said that C major was the most difficult scale to play because of the thumb cross-under, and started his students out with other scales like A flat. See book "Natural Fingering."...but the piano is designed to play equal-tempered, diatonic scales, most easily C major and nearby keys.
Yes, I read about that analysis of the cover page of the WTC manuscript. Very interesting. I was really only making a general statement that while equal temperament was around by the early 18th century, by Beethoven's time it was well on its way to becoming standard, and the dominance of the piano from the mid-19th century on helped seal the deal. And all this isn't some amazing new insight by me. Historians know all about it.I'm going with the ideas of Dr. Bradley Lehman (larips.com) who deciphered Bach's well-tempered tuning from a decorative flourish on the cover page of the original manuscript. It was basically an attempt at ET, in which all keys sounded good.
What you say is true, especially in light of key signatures, but Chopin later used distant keys like A flat because of ergonomics: the hand sits naturally on the piano when the middle fingers are covering black keys, and the thumb and pinkies cover white keys. He said that C major was the most difficult scale to play because of the thumb cross-under, and started his students out with other scales like A flat. See book "Natural Fingering."
That's fascinating info about auto-tune.Many developers for Kontakt (and similar engines) absolutely always autotune the samples, because many customers (check vi-control forum for many such threads from the last decade) complain about unplayable keys. And many of these libraries record the best orchestral musicians available (Vienna, London, L.A.).
Thanks, that was a very interesting and useful post. However, these "small intervals" aren't entirely irrelevant once we start playing around with these other scales, especially those that aren't equal tempered, in actual musical compositions, right? That's why I was interested in your opinion of the Well-tempered Clavier played in a non-equal tempered tuning like Werckmeister III.438 to 440 hz is approximately 7.88 cents.
[ .... ]
Still, all this is irrelevant to harmony discussions. Such small intervals are considered useless in actual music compositions, that's why equal and unequal temperaments are used.
In the case of Bach, who used his own "ET"-ish tuning, there may be slight differences in fifths and thirds which influenced the way he actually composed each prelude/fugue for the WTC. For example, if the key had a really good sounding major third, he might emphasize that note more. If it had a bad minor third, he might not linger on that note, etc....In his Well-tempered Clavier, Bach wrote a prelude and fugue for all 24 major and minor keys of the 12-tone scale. As only equal temperament gives you identical intervals and chords in every key, the differences there are especially clear. Have you listened yourself?
Bach's tuning has already been revealed by Dr. Bradley Lehman. See larips.comWouldn't it be wonderful if Bach had told someone how he liked his harpsichord tuned?