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Thread: What Does "Harmonic" Mean?

  1. #91
    Senior Member fluteman's Avatar
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    Quote Originally Posted by Luchesi View Post
    Yes, when I tune a piano my goal is 2 to 3 cents, depending upon the instrument and its condition. Customers don't want to pay you to come right back 2 weeks later because the piano has inevitably 'fallen' and you hadn't anticipated it.
    Yes, 2 cents is very good, so you are welcome to tune my piano. If you saw my correction to my original post, you saw that I meant 2 Hz, not two cents. BabyGiraffe gave a good basic summary of human ability to hear differences in pitch above, although I'm sure he'd agree that it was only a summary of a much larger subject.

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    Senior Member millionrainbows's Avatar
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    I was tested, with another guy, and we both could hear a difference of 2 cents, on fairly high-pitched wind chimes, probably A=880. The difference was identifiable, but it really wasn't pitch I was hearing; it was that the higher note sounded ever-so-slightly "brighter."

    I got to do all kinds of experiments when I was working at the chime factory. I cut a 17-note per octave Arabic chime, a 7-note ET chime (which is Thai tuning), A "harmonic" bass tuning which had a harmonic seventh, just fifth and third and some kind of second, a solfeggio tuning, a septimal whole tone scale based on a septimal second, all sorts of stuff.
    It was valuable, because it showed me that sound is linked to physics, arithmetic, and actual materials.
    Last edited by millionrainbows; Oct-26-2019 at 02:12.

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    Quote Originally Posted by fluteman View Post
    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.
    There is a theory that there are so many sequences, arpeggios and ostinatos in a typical Baroque music work, because they were sounding somewhat different, because there are more unique intervals in irregular temperaments (known as well-temperaments). This won't happen in equal or just intonation (where you shouldn't really play the out of tune notes, that's the whole point, at least in theory).
    About Werckmeister 3 - Scala gives this data, comparing it to 12 equal - I compared the most even mode, it's the closest one to 12 equal.
    Standard deviation: 3.7435 c. Maximum deviation: 7.8200 c.


    If we compare 12 equal to:

    55 equal meantone - SD: 6.3420 c. M:-10.9091 c. (Some of the modes of Werkmeister are more uneven than that)

    43 meantone, we get: SD: 8.1118 c. M:-13.9535 c.

    50 equal meantone SP: 7.1181 c. M:-12.0000 c.

    31 equal meantone: SD: 11.2519 c. M:-19.3548 c.

    19 equal meantone: SD: 18.3583 c. M:-31.5789 c.


    Equal 19 meantone is potentially useful for chromatic 12 tone music, because it is not really that close to it, so it can be considered as melodic and harmonic scale on its own - we have small and large semitone ( 63.15789 cents and 126.31579 cents).
    Other useful scales for 12 equal based chromatic tonality are 22 equal (semitone is split as 54.54545 cents and 109.09091 cents, but it's not meantone, so there is different logic in many chord progressions), 17 equal (70, 140, but 17 equal clearly won't work for good triadic harmony on most timbres - some slightly inharmonic instruments like piano can do it, but not flutes or strings, still counterpoint is possible in a medieval style - using fifths, fourths and quartal/quintal stacks.)


    " 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?"

    Not really, 99 % of the listeners won't notice them or the musician will adjust their melodic or harmonic intonation or occasionaly modulate a comma up/down, or just drift away from the initial tonic as the piece progresses, if there are many distant modulations.
    It's more of a compositional and notational problem.
    If you want to compose or perform in a close to optimal 5-limit tuning, you have to basically deal with 53 equal - where the difference of pythagorean and syntonic comma, called schisma, is the only significant interval tempered.
    53 equal is the modern theoretical Turkish system. I was very surprised when read in modern Turkish dissertation that "Rast" - their diatonic is basically the Western major scale. But that is because in 53 equal Pythagorean and just intonation major are different scales. (Another layer of confusion was the naming - "Rast" in Arabic countries is the neutral, not the major tetrachord; but other Arabic tetrachord names are also swapped in their Turkish variants).

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    Senior Member millionrainbows's Avatar
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    One advantage of creating other ET octave divisions on a normal keyboard (by modulating/"stretching" the keyboard voltage) is that you can see some connections with normal tuning. In 19-tone, tune the octave past the "C to C" 12-note ET octave to "C-G", the G past the octave C. If you compose melodies in 19, then convert them back to 12, it gives a diminished tonality.

    !7 note ET is octave on F; 22 tone ET is C-Bb (flat seven).

    You begin to see that these other ETs are based on overtones of the 12 ET, and that is why certain ET tunings are favored, such as 17 (C-F fourth), 19 (C-G fifth), 21 (C-A relative minor), and 22 (C-Bb flat seven).
    Last edited by millionrainbows; Oct-26-2019 at 13:29.

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    Senior Member fluteman's Avatar
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    Well, BabyGiraffe, I guess I and a lot of people I know have exceptional hearing, as we can easily tell the difference between equal temperament and various forms of just intonation in the right contexts. 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?

    Or take a famous traditional Japanese melody such as Sakura (cherry blossoms). This uses a pentatonic scale roughly similar to the Phrygian mode. Compare a recording made with traditional Japanese instruments such as the koto with a westernized recording. This should be very easy to do. The famous French flutist Jean-Pierre Rampal made a series of recordings of traditional Japanese melodies, including Sakura, all in westernized arrangements with equal-tempered tuning. I think in most the flute is accompanied by a western harp, although the koto and other instruments are also used. Listen and compare:

    Last edited by fluteman; Oct-26-2019 at 15:25.

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    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by fluteman View Post
    ...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?
    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.

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    Senior Member fluteman's Avatar
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    Quote Originally Posted by millionrainbows View Post
    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.
    Yes, excellent point, I've read work by scholars on the subject who have said something similar. I guess there will always be some debate on that topic. After all, musicologists need to get published.

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    Senior Member Luchesi's Avatar
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    Quote Originally Posted by fluteman View Post
    Yes, excellent point, I've read work by scholars on the subject who have said something similar. I guess there will always be some debate on that topic. After all, musicologists need to get published.

    I don't see that. We could ask one of the composers in this forum whether they ever think about that. But I expect that composers will begin composing in the same way that performers will first play a piece from which patterns they see standing out as intriguing and interesting. This is difficult to put into words …but I don't think the exact sound of a major third etc. influences them. I play many pianos that are even somewhat out of tune and your hearing adapts very quickly! because other notes in the constellation you grab (and the accompaniment) wash out the very slight deviations you could pinpoint acoustically.

    I always remember from the man who taught me how to tune pianos, he was legally blind. He was an elderly man of few words and he said to me, “We're not going to tune musically, we're going to tune acoustically. ..And then we go back to make it musical.". I initially only got a sense of what he meant, but now I know it's very important to keep in mind.
    Last edited by Luchesi; Oct-27-2019 at 19:05.
    Tradition is not the worship of ashes - but the preservation of fire!
    Gustav Mahler

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  11. #99
    Senior Member fluteman's Avatar
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    Quote Originally Posted by Luchesi View Post
    I don't see that. We could ask one of the composers in this forum whether they ever think about that. But I expect that composers will begin composing in the same way that performers will first play a piece from which patterns they see standing out as intriguing and interesting. This is difficult to put into words …but I don't think the exact sound of a major third etc. influences them. I play many pianos that are even somewhat out of tune and your hearing adapts very quickly! because other notes in the constellation you grab (and the accompaniment) wash out the very slight deviations you could pinpoint acoustically.

    I always remember from the man who taught me how to tune pianos, he was legally blind. He was an elderly man of few words and he said to me, “We're not going to tune musically, we're going to tune acoustically. ..And then we go back to make it musical.". I initially only got a sense of what he meant, but now I know it's very important to keep in mind.
    Hey, don't shoot the messenger, Luchesi. Musicologists like to argue about exactly what Bach meant by "well-tempered" when he wrote The Well-tempered Clavier. And I wholeheartedly agree with your comment that our hearing adapts to 'slightly' out of tune notes. I made that point above, and my own experience confirms it, as does what I have been told by conductors, etc. But have you ever been to a Chinese or Indian restaurant where they are piping in traditional music? (Less common these days, as many of those restaurants try to become more hip for a younger crowd and pipe in westernized music.) Can't you hear that it sounds a little 'off'?

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    Senior Member JeffD's Avatar
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    Quote Originally Posted by millionrainbows View Post

    Is everybody happy?
    What, exactly and completely in all its senses, does the term "happy" mean?
    How did I become a senior member? I only recently figured out where the restrooms are.

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    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by JeffD View Post
    What, exactly and completely in all its senses, does the term "happy" mean?
    It's what they used to say before they said "Is everybody ready to rock and roll?"

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    Senior Member millionrainbows's Avatar
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    This tome should clear up some questions about the Pythagorean method and scales, and clarify things a bit.

    Construction of Scales 200 dpi .jpg

  15. #103
    Senior Member fluteman's Avatar
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    Quote Originally Posted by millionrainbows View Post
    This tome should clear up some questions about the Pythagorean method and scales, and clarify things a bit.

    Construction of Scales 200 dpi .jpg
    Or this one I just found, which is written in a more non-technical, non-mathematical style, and really only summarizes and simplifies what musicologists have written about with great precision and in great detail, but looks like a fun read for those who don't want to get too technical. He discusses what I was trying to talk about, i.e., the imperfections of equal temperament and why it isn't necessarily the best-sounding scale in all circumstances, but he also gives more general information. I do not go along with the idea that equal temperament "ruined" harmony, and I don't think the author does either. He's just trying to sell books by using a provocative title.

    how equal temperament.jpg

  16. #104
    Senior Member Luchesi's Avatar
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    Quote Originally Posted by fluteman View Post
    Or this one I just found, which is written in a more non-technical, non-mathematical style, and really only summarizes and simplifies what musicologists have written about with great precision and in great detail, but looks like a fun read for those who don't want to get too technical. He discusses what I was trying to talk about, i.e., the imperfections of equal temperament and why it isn't necessarily the best-sounding scale in all circumstances, but he also gives more general information. I do not go along with the idea that equal temperament "ruined" harmony, and I don't think the author does either. He's just trying to sell books by using a provocative title.

    how equal temperament.jpg
    What I always conclude is it depends upon what we want from music. Do we want sweet sounds alone, or do we want the intellectual achievement? Can we have both? Bach decided that we needed something close to ET.
    Tradition is not the worship of ashes - but the preservation of fire!
    Gustav Mahler

  17. #105
    Senior Member fluteman's Avatar
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    Quote Originally Posted by Luchesi View Post
    What I always conclude is it depends upon what we want from music. Do we want sweet sounds alone, or do we want the intellectual achievement? Can we have both? Bach decided that we needed something close to ET.
    I think the point this author is making is that in the right (or wrong) circumstances, the sounds can be as sour with equal temperament as with any other tuning (they are all compromises). And of course, a lot of music, including western music from over 150 or 200 years ago and certainly music from other cultures, was written with other tuning systems in mind. As to what tuning Bach intended, there is a wide range of opinions, even from musicologists who spend most of their time examining such issues.

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