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Thread: What Does "Harmonic" Mean?

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    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by BabyGiraffe View Post
    They could... if the fifth was 720 cents, not around 702. It's simple math, just do it.
    (If we play them along the major thirds of 12 equal, of course, in a triadic style - you know, like in every pop song).

    Btw, I have never complained about 12 equal fifths.
    Then quit complaining about ET so much. At least it has good fifths. 720 cents is a wolf fifth. Why don't you explain some of what you're talking about?

    Oh, you must mean IF a fifth was 720 cents.

    Ah
    ha ha ha ha ha.
    Last edited by millionrainbows; Oct-21-2019 at 19:19.

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    Senior Member fluteman's Avatar
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    Quote Originally Posted by BabyGiraffe View Post

    I don't know, it's hard to generalize, even back then we had plenty of diversity. It's just that few, selected composers are considered representative of the musical styles.
    Well, no, that's not an accurate historical description of western classical music before Stravinsky. Charles Rosen discusses this in The Classical Style, where he demonstrates that Beethoven's piano sonatas, for example, were almost certainly written with the equal-tempered scale in mind. (Yes, Rosen considers only a few select composers, e.g., Haydn, Mozart and Beethoven, but in the long term these were by far the most influential of the classical period.) This is a significant evolution from the days of J.S. Bach. 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).

    But what clinched the near-universal adoption of equal temperament was the increasingly dominant role of the piano in western music. Inventions such as Erard's double escapement action and Steinway's overstrung cast iron frame made it powerful and flexible, and before the phonograph and radio came along, the piano was the home music system of the middle class. (I estimate the golden age of the piano as from about 1820 to about 1920.) It could be tuned differently, but the piano is designed to play equal-tempered, diatonic scales, most easily C major and nearby keys. Wind and brass instruments were redesigned to more easily accommodate the 12-tone equal tempered scale. You are naive, and certainly not a musician yourself, if you don't understand the enormous impact of these developments on nearly all western music.

    Yes, a cappella choral singers deviate from equal temperament (been there, sung that), but a cappella singing has long been a relatively small niche in western music, for better or worse.
    Last edited by fluteman; Oct-21-2019 at 22:07.

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    Quote Originally Posted by fluteman View Post
    Charles Rosen discusses this in The Classical Style, where he demonstrates that Beethoven's piano sonatas, for example, were almost certainly written with the equal-tempered scale in mind. (Yes, Rosen considers only a few select composers, e.g., Haydn, Mozart and Beethoven, but in the long term these were by far the most influential of the classical period.) This is a significant evolution from the days of J.S. Bach. Many scholars argue that the Well-tempered Clavier was not composed with equal temperament in mind.

    Wind and brass instruments were redesigned to more easily accommodate the 12-tone equal tempered scale. You are naive, and certainly not a musician yourself, if you don't understand the enormous impact of these developments on nearly all western music.

    Yes, a cappella choral singers deviate from equal temperament (been there, sung that), but a cappella singing has long been a relatively small niche in western music, for better or worse.
    Dude, string and brass instruments rely on harmonics, you are not a musician, if you don't understand how they work. You have to manually adjust the intonation all the time. It's not that easy compared to a fretted guitar for example.

    Unequal temperaments, that some composers like Bach used, is basically a mixture between pythagorean and meantone. There are probably infinite ways to create such systems mathematically. We get some out of tune (in 5-limit) intervals as result, but no wolves. (Mapping was 12 equal's val. I have a friend who works as a tuner that created a special 19 keys unequal temperament for my needs.)

    Beethoven may have used unequal temperament.

    Rosen argues that some of his enharmonic modulations sound awful in just intonation, but we can't know, if he used equal or unequal temperament. His early music is most certainly in meantone. Considering how often he relies on augmented sixths as effect, I am not sure that he used 12-equal temperament at all.

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    Quote Originally Posted by fluteman View Post
    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).
    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.

    ...but the piano is designed to play equal-tempered, diatonic scales, most easily C major and nearby keys.
    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."
    Last edited by millionrainbows; Oct-22-2019 at 13:49.

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    Quote Originally Posted by BabyGiraffe View Post

    Beethoven may have used unequal temperament. Rosen argues that some of his enharmonic modulations sound awful in just intonation, but we can't know, if he used equal or unequal temperament. His early music is most certainly in meantone. Considering how often he relies on augmented sixths as effect, I am not sure that he used 12-equal temperament at all.
    Other sources indicate that Beethoven probably used Thomas Young tuning. Nobody had ET back then, it wasn't achieved until 1919. Many tunings were approaching ET, and that's what things were moving towards, but none achieved it. Nevertheless, Bach's tuning (Lehman/Bach) and other tunings were approximations, by ear & stopwatch, of ET.

    Beethoven Young Tuning 200 dpi .jpeg
    Last edited by millionrainbows; Oct-22-2019 at 14:03.

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    Quote Originally Posted by millionrainbows View Post
    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."
    You still get horrible intervals, there is no such thing as system with just 12 keys that sounds good. What you don't get - unlike any meantone, there is no mistuned fifth (but enjoy other mistuned intervals). The closest to sounding good with just 12 keys per octave is 12 equal, wow, which sounds "bad" (to purists). We need minimum 43 equal for meantone that sounds close to 5-limit just intonation. 31 keys sounds also ok and was used in theory - it is known as 1/4 comma meantone.
    https://en.wikipedia.org/wiki/Quarter-comma_meantone

    The guy that posts in the historical performance thread has quotes from Chopin letters about unequal temperament or it was meantone?... What was the name of the thread - I remember it was in general discussions.

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    I'd like to hear serial music played in 43-tone tuning.

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    Quote Originally Posted by BabyGiraffe View Post
    Dude, string and brass instruments rely on harmonics, you are not a musician, if you don't understand how they work. You have to manually adjust the intonation all the time. It's not that easy compared to a fretted guitar for example.

    Unequal temperaments, that some composers like Bach used, is basically a mixture between pythagorean and meantone. There are probably infinite ways to create such systems mathematically. We get some out of tune (in 5-limit) intervals as result, but no wolves. (Mapping was 12 equal's val. I have a friend who works as a tuner that created a special 19 keys unequal temperament for my needs.)

    Beethoven may have used unequal temperament.

    Rosen argues that some of his enharmonic modulations sound awful in just intonation, but we can't know, if he used equal or unequal temperament. His early music is most certainly in meantone. Considering how often he relies on augmented sixths as effect, I am not sure that he used 12-equal temperament at all.
    After playing the flute for 50 years, I do have some idea about how it works, including its use of harmonics. In the case of the flute, there was a dramatic change based on the radical invention of Theobald Boehm in 1847 (which also influenced the development of the other winds). The old system flute consisted of a wood tube with tone holes where the fingers could reach them and sized so the fingers could cover them, with a few keys for additional holes for the chromatic scale, or for the lowest notes where the fingers weren't long enough to reach. Boehm made the flute with tone holes optimally located and sized for the 12-tone equal tempered scale, with optimum venting, regardless of what the fingers could reach or cover, with the holes covered by a system of keys connected by rods, clutches and springs.

    The second octave notes on the Boehm flute are still essentially overblown second harmonics, and the third octave overblown third harmonics, but with adjustments to keep them in equal-tempered tune. It's a highly sophisticated yet practical acoustic system with a few minor compromises, especially in the venting holes, so all 12 tones in 3 octaves can be played without too complicated and heavy a mechanism. As a result, 2 or 3 "problem" notes can be slightly harder to play in tune. But in more recent years, very slight and sophisticated modifications have been made to the scale (tone hole spacing and size), often with the help of computer programs, to get a more uniformly satisfactory result.

    The end result is an acoustic instrument that can play three octaves plus of the 12-tone equal tempered scale, with a surprising degree of intonation accuracy and consistency. This is true even of the older Boehm flutes, made before modern computer-assisted improvements and as far back as the mid-19th century, though alas many of those are tuned to a=435 or a=438, or even as high as a=452, rather than a=440, which didn't become the international standard until 1938.

    Unfretted string instruments are obviously another story, and didn't need to be redesigned for equal temperament. But as I said above, the development and success of the modern piano is probably the biggest single factor in making equal temperament the universal standard of western music. It was ideal for playing diatonic scales and triads in any key with relative ease.
    Last edited by fluteman; Oct-22-2019 at 17:32.

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    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.).


    Something funny:

    " "

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    Quote Originally Posted by millionrainbows View Post
    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."
    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.

    It's appropriate that you mention Chopin. He was a pioneer in expanding piano technique, and that included playing ferocious virtuoso passages and entire pieces in any key. And in fact, one of the most important, if not the most important, features of equal temperament is that every interval is identical in every key. So any or all 12 keys can be used, in the same piece even, with no odd sounding intervals or chords. Again, no special insight by me. I would think it's obvious how this has had a profound impact on western music and how we hear it.

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    Quote Originally Posted by fluteman View Post
    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.

    It's appropriate that you mention Chopin. He was a pioneer in expanding piano technique, and that included playing ferocious virtuoso passages and entire pieces in any key. And in fact, one of the most important, if not the most important, features of equal temperament is that every interval is identical in every key. So any or all 12 keys can be used, in the same piece even, with no odd sounding intervals or chords. Again, no special insight by me. I would think it's obvious how this has had a profound impact on western music and how we hear it.
    Well, I'm so glad that you've been pleased with what I've said here. BabyGiraffe, as usual, always has some fascinating insights as well.

    Is everybody happy?
    Last edited by millionrainbows; Oct-23-2019 at 14:13.

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    Quote Originally Posted by millionrainbows View Post
    Well, I'm so glad that you've been pleased with what I've said here. BabyGiraffe, as usual, always has some fascinating insights as well.

    Is everybody happy?
    I'm happy so long as I can get out of bed in the morning and walk down the street (so far, so good). But I'd be even happier if you discontinued those pre-enlightenment, anti-empiricist philosophy posts. There is no theory that explains what makes good music good, and that includes harmonic theory. Music is a fundamentally practical, empirical art, and imo, the best explanation is that of Duke Ellington: If it sounds good, it [I]is[I] good. ;-)

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    Quote Originally Posted by fluteman View Post
    I'm happy so long as I can get out of bed in the morning and walk down the street (so far, so good). But I'd be even happier if you discontinued those pre-enlightenment, anti-empiricist philosophy posts. There is no theory that explains what makes good music good, and that includes harmonic theory. Music is a fundamentally practical, empirical art, and imo, the best explanation is that of Duke Ellington: If it sounds good, it [I]is[I] good. ;-)
    I'm so glad that you have identified "the enemy," and you seem to feel as if you are in control again. Just remember that "tonality is God" and things will continue as is. Remember, if you get scared, there's always a big trouser-leg you can hide behind.

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    Quote Originally Posted by BabyGiraffe View Post
    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.).
    That's fascinating info about auto-tune.

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    Quote Originally Posted by millionrainbows View Post
    I'm so glad that you have identified "the enemy," and you seem to feel as if you are in control again. Just remember that "tonality is God" and things will continue as is. Remember, if you get scared, there's always a big trouser-leg you can hide behind.
    Especially as I get older, three things (among others) become ever clearer: I am not in control (nor is anyone else), things will not continue as is, and there is nowhere to hide. What scares me is the seemingly increasing number of people worldwide who fail to understand one or more of those things.

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