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Thread: The Major Second Is Not Dissonant

  1. #46
    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by BabyGiraffe View Post
    Fifths in meantone are flatter than just - 12 equal is actually the sharpest meantone tuning of all of them.
    Fifths are 2 cents flat in ET; ET is not "meantone;" what are you trying to say?

    Here are all octave ratios that are more consonant than 9/8, if we are concerned about beating.

    3/2 perfect fifth
    4/3 perfect fourth
    5/3 major sixth, BP sixth
    5/4 major third
    6/5 minor third
    7/4 harmonic seventh
    7/5 septimal tritone
    7/6 septimal minor third
    8/5 minor sixth
    8/7 septimal whole tone
    9/5 just minor seventh
    9/7 septimal major third (this one sounds to me like a dissonance, honestly)
    9/8 major whole tone !!!

    9/4, 9/2 and 9/1 will blend way better in a harmonic texture than transposed in octave versions of 8/7 or 10/9 - the other choices that million offers for major second.
    I didn't "offer" any particular M2. What are you trying to say I'm saying, or do I not know?
    Last edited by millionrainbows; Nov-15-2019 at 20:07.

  2. #47
    Senior Member Bwv 1080's Avatar
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    Quote Originally Posted by BabyGiraffe View Post
    Here is one great "jazzy" chord that doesn't sound dissonant- 4:5:7:9 = 1-5/4-7/4-9/4 - C-E-Bb*- D(octave higher)
    ok dom 9th chords aren't dissonant?
    Last edited by Bwv 1080; Nov-15-2019 at 20:50.

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    Senior Member Larkenfield's Avatar
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    Quote Originally Posted by millionrainbows View Post
    This proves nothing, harmonically. It's just a CP rule.

    C-D doesn't have to "resolve" up or down, except by academic CP rules. It's perfectly acceptable to the ear as a ninth chord (C-E-G-Bb-D), or as a "major 2" chord (C-D-E-G-C).
    Look. I believe you just don't like the thought of rules, period, because you may not understand the principles behind them, perhaps because you've never taken them seriously to begin with and would rather fly by the seat of your pants. Rules or principles of composition seem academic, inhibiting or restrictive to rebel against even though composers such as Haydn, Mozart, and Beethoven used them—and that's why most theory teachers teach what they used as a starting point and mental discipline in understanding harmony and voice leading... I don't admire that rebellious outlook until there's some genuine understanding of some of the basic principles, including the ability to use them creatively, because I see too much wishful thinking about some of the fundamentals of music. So the subject becomes a mess... I believe it's truly necessary to define what era of music you're talking about because if one is going to talk rules or principles that were followed at the time—what was consider good harmony and voice leading changed from one era to another. In the classical era, the D would not be left hanging or unresolved and under most (all) circumstances would resolve to the tonic, the major or minor third, or the 5th ( C, E or Eb, or G). In the classical era, a work would not be expected to end on a 7th or 9th chord, would it? The example D is not necessary a dissonance but was generally considered to be unstable and in need of being resolved to a consonant tone. But the rules or principles change and evolved when the Romantic and Modern eras came in and there were different thoughts on what the stable and unstable tones were that needed resolution... In modern classical or jazz harmony, all kinds of altered chords are permissible because the ears were ready for a change. Unlike the classical era, one could end a composition on a Major 7th chord with or without a 9th. Modern ears have adjusted and the Major 7th is no longer shocking and didn't need to be resolved to the C, and the D could be used without it being resolved because it added fullness and richness to the chord... But you have to be clear about what era of music you're talking about and that's usually left out and leads to a confusing mess regarding music theory... There's also a difference between a dissonance, sharply clashing tones (such as a minor second C to C# or Db interval) and a major second interval (C-D) where there's a tension that may be considered unstable and simply seeks to be resolved. But it truly depends upon the era one is referring to and I believe that learning some of the fundamental principles that might have been used by Bach, Mozart and Beethoven should, under most normal circumstances,be encouraged because it can sharpen and discipline the lazy mind which thinks that one can essentially rely solely upon his ears rather than learning something that might actually be useful regarding the basic understanding of harmony and voice leading. Not everyone has the ears that Debussy had and can break the rules and have the music work. Yet the understanding of the principles (or rules) is too often dismissed without even knowing the knowledge or talent level of the student who might be struggling or rebelling against them. The learning of such principles might be the best thing in the world for them at this point in their studies and give them something to rebel against knowingly or consciously later. Just because Debussy broke the conventional rules at the time doesn't mean that he didn't know them. It's known that he studied harmony with César Franck though he usually rebelled against those teachings. But then, Debussy was a genius and heard music in his head that didn't match Franck's teachings and so he eventually went his own way.
    Last edited by Larkenfield; Nov-16-2019 at 00:03.
    "That's all Folks!"

  4. #49
    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by Larkenfield View Post
    Look. I believe you just don't like the thought of rules, period, because you may not understand the principles behind them, perhaps because you've...etc.
    Is there any "issue" or idea about music, or an opinion that you have about some aspect of music that compels you to discuss it passionately? You need to focus on that, not me.

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    Quote Originally Posted by millionrainbows View Post
    Fifths are 2 cents flat in ET; ET is not "meantone;" what are you trying to say?

    12 ET is 1/11 meantone.
    Meantone means that 81/80 is tempered. So 12 equal is meantone.
    So, the mapping is something like 7 equal, 12 equal, 19 equal, 26, 31, 43 and many others. Out of these 7 and 26 are very distorted compared to just intonation.
    In non-meantone D 10/9 and D 9/8 are separate pitches.

    Here is 41 equal:
    steps: pitch
    33: 965.854 cents
    34: 995.122 cents
    35: 1024.390 cents


    Here is 46 equal:

    37: 965.217 cents
    38: 991.304 cents
    39: 1017.391 cents

    here is 53 equal:

    43: 973.585 cents
    44: 996.226 cents
    45: 1018.868 cents

    These 3 are non-meantone, but also non-septimal pythagorean (where 16/9 and 7/4 would be mapped to one step), so in practice we have a choice of 3 slightly different "dominant" chords.


    Bwv 1080

    "ok dom 9th chords aren't dissonant? "

    They shouldn't be in close to just (septimal) tuning, but in this case there is no fifth. There is noticeable difference in texture - it is way less tense.
    Last edited by BabyGiraffe; Nov-16-2019 at 09:34.

  6. #51
    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by BabyGiraffe View Post
    12 ET is 1/11 meantone.
    Meantone means that 81/80 is tempered. So 12 equal is meantone.
    So, the mapping is something like 7 equal, 12 equal, 19 equal, 26, 31, 43 and many others. Out of these 7 and 26 are very distorted compared to just intonation.
    In non-meantone D 10/9 and D 9/8 are separate pitches.

    Here is 41 equal:
    steps: pitch
    33: 965.854 cents
    34: 995.122 cents
    35: 1024.390 cents


    Here is 46 equal:

    37: 965.217 cents
    38: 991.304 cents
    39: 1017.391 cents

    here is 53 equal:

    43: 973.585 cents
    44: 996.226 cents
    45: 1018.868 cents

    These 3 are non-meantone, but also non-septimal pythagorean (where 16/9 and 7/4 would be mapped to one step), so in practice we have a choice of 3 slightly different "dominant" chords.


    Bwv 1080

    "ok dom 9th chords aren't dissonant? "

    They shouldn't be in close to just (septimal) tuning, but in this case there is no fifth. There is noticeable difference in texture - it is way less tense.
    I see what you're trying to say, but it's not accurate. According to WIK:

    Meantone temperaments are constructed the same way as Pythagorean tuning, as a stack of equal fifths, but in meantone each fifth is narrow compared to the perfect fifth of ratio 3:2.

    Also,

    Equal temperament, obtained by making all semitones the same size, each equal to one-twelfth of an octave (with ratio the 12th root of 2 to one (12√2:1), narrows the fifths by about 2 cents or 1/12 of a Pythagorean comma, and produces thirds that are only slightly better than in Pythagorean tuning. Equal temperament is roughly the same as 1/11 comma meantone tuning.

    So roughly, you are kind of right...sorta.

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    Quote Originally Posted by millionrainbows View Post
    I see what you're trying to say, but it's not accurate. According to WIK:

    Meantone temperaments are constructed the same way as Pythagorean tuning, as a stack of equal fifths, but in meantone each fifth is narrow compared to the perfect fifth of ratio 3:2.

    Also,

    Equal temperament, obtained by making all semitones the same size, each equal to one-twelfth of an octave (with ratio the 12th root of 2 to one (12√2:1), narrows the fifths by about 2 cents or 1/12 of a Pythagorean comma, and produces thirds that are only slightly better than in Pythagorean tuning. Equal temperament is roughly the same as 1/11 comma meantone tuning.

    So roughly, you are kind of right...sorta.
    Man, meantone means (forgive me this pun, wow) that instead of the two types of simple "D" that exist in 5-limit just intonation we use their average.
    None of equal temperaments is exactly x/y comma meantone/pythagorean/diaschismic/septimal or whatever, because these also have infinite pitches, but in practice they are, because the difference is super small.
    Noone cares if you use 699.(and something) for 1/11 meantone or 697.(and something) for 1/4 meantone, because in practice these two sound and give respectively 12 and 31 equal and the small difference is a fraction of the cent. Noone cares about irrational numbers that give infinite pitch gamuts, because if we wanted infinite number of pitches, we would have been sticking to just intonationl!!!
    Last edited by BabyGiraffe; Nov-17-2019 at 09:36.

  8. #53
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    31 equal (aka 1/4 comma meantone) is maybe important, because the geometric mean of 5/4 (major third) is for all practical purposes the "D" note in 31.
    Here is the approximation of it:
    " 31: 5 5 21 N M DE S SD: 0.5055 c. M:-0.7831 c.
    56: 9 9 38 N M DE S SD: 0.3869 c. M: 0.5994 c.
    87: 14 14 59 N M DE S SD: 0.0690 c. M: 0.1068 c.
    205: 33 33 139 N M DE S SD: 0.0179 c. M:-0.0277 c.
    292: 47 47 198 N M DE S SD: 0.0080 c. M: 0.0123 c.
    497: 80 80 337 N M DE S SD: 0.0027 c. M:-0.0042 c.
    789: 127 127 535 N M DE S SD: 0.0012 c. M: 0.0019 c.
    1286: 207 207 872 N M DE S SD: 0.0003 c. M:-0.0004 c.
    "

  9. #54
    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by BabyGiraffe View Post
    Man, meantone means (forgive me this pun, wow) that instead of the two types of simple "D" that exist in 5-limit just intonation we use their average.
    None of equal temperaments is exactly x/y comma meantone/pythagorean/diaschismic/septimal or whatever, because these also have infinite pitches, but in practice they are, because the difference is super small.
    Then I think it is misleading to say that our 12-note ET is a "meantone" temperament; it is an "equal" temperament, especially now that we have frequency meters which can ensure that our ET is spot-on accurate.

    No one cares if you use 699.(and something) for 1/11 meantone or 697.(and something) for 1/4 meantone, because in practice these two sound and give respectively 12 and 31 equal and the small difference is a fraction of the cent. No one cares about irrational numbers that give infinite pitch gamuts, because if we wanted infinite number of pitches, we would have been sticking to just intonation.
    In practical terms, probably not; but let's get our terms correct, at least.

    I'm just saying that you are using this inexactitude for your own license in calling our 12-note ET a "meantone" temperament. This is inaccurate, and misleading.
    Last edited by millionrainbows; Nov-17-2019 at 14:59.

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    Quote Originally Posted by BabyGiraffe View Post
    31 equal (aka 1/4 comma meantone) is maybe important, because the geometric mean of 5/4 (major third) is for all practical purposes the "D" note in 31.
    Here is the approximation of it:
    " 31: 5 5 21 N M DE S SD: 0.5055 c. M:-0.7831 c.
    56: 9 9 38 N M DE S SD: 0.3869 c. M: 0.5994 c.
    87: 14 14 59 N M DE S SD: 0.0690 c. M: 0.1068 c.
    205: 33 33 139 N M DE S SD: 0.0179 c. M:-0.0277 c.
    292: 47 47 198 N M DE S SD: 0.0080 c. M: 0.0123 c.
    497: 80 80 337 N M DE S SD: 0.0027 c. M:-0.0042 c.
    789: 127 127 535 N M DE S SD: 0.0012 c. M: 0.0019 c.
    1286: 207 207 872 N M DE S SD: 0.0003 c. M:-0.0004 c.
    "
    If you want anyone to really get what you are trying to say, you need to take more time with your posts and identify some of these numbers. Are the numbers on the far left equal octave divisions?

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    " I'm just saying that you are using this inexactitude for your own license in calling our 12-note ET a "meantone" temperament. This is inaccurate, and misleading. "

    If it follow meantone mapping, IT IS MEANTONE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

    You obviously have a problem with accepting that 12 edo is meantone - if it wasn't, standard chord progressions wouldn't work at all, requiring enharmonic modulation aside from the few basic chord chord changes in the 5-limit tonality diamond (like most neo-riemannian chord changes which work only because of tempered commas, of course, in other equal temperaments we have other neo-riemannian progressions)...
    Idk, man, I wrote a long post, explaining plenty of stuff but the damn forum/server crashed and all is lost now. I can recommend you Barbour/xenharmonic wikipedia/tonalsoft encylopedia/even reading more carefully standard wikipedia or taking private lessons by someone versed in tuning theory. I have no energy anymore for forums.
    Farewell.

  12. #57
    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by BabyGiraffe View Post
    " I'm just saying that you are using this inexactitude for your own license in calling our 12-note ET a "meantone" temperament. This is inaccurate, and misleading. "

    If it follow meantone mapping, IT IS MEANTONE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    It doesn't follow meantone mapping exactly, so don't place ET, an "equal temperament," in the "meantone" category.

    You obviously have a problem with accepting that 12 edo is meantone - if it wasn't, standard chord progressions wouldn't work at all, requiring enharmonic modulation aside from the few basic chord chord changes in the 5-limit tonality diamond (like most neo-riemannian chord changes which work only because of tempered commas, of course, in other equal temperaments we have other neo-riemannian progressions)...
    Idk, man, I wrote a long post, explaining plenty of stuff but the damn forum/server crashed and all is lost now. I can recommend you Barbour/xenharmonic wikipedia/tonalsoft encylopedia/even reading more carefully standard wikipedia or taking private lessons by someone versed in tuning theory. I have no energy anymore for forums.
    Farewell.
    You should get with a really good editor, and write a book.
    Last edited by millionrainbows; Nov-17-2019 at 22:17.

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    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by BabyGiraffe View Post
    Idk, man, I wrote a long post, explaining plenty of stuff but the damn forum/server crashed and all is lost now.
    Some advice: always copy your writing before you post it. As long as you're at it, paste it into your e-mail and save it as a draft.

    Sometimes a post will take a long time to write, and the server will "time out," making it necessary to re-log-in.

    Also, it may be possible that a lengthy post might raise some sort of a red flag to the mods, who may try to make it impossible to post. Just make sure you copy all your work, or it may vanish.
    Last edited by millionrainbows; Nov-17-2019 at 22:42.

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    Senior Member hammeredklavier's Avatar
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    The drama in this thread is actually funny

    Quote Originally Posted by millionrainbows View Post
    then they are more academic than I realized, and I am very disappointed.
    Quote Originally Posted by Woodduck View Post
    why would you condemn me to a room with millionrainbows?
    The choice of words in the context is funny
    not just "put", but "condemn".

    Quote Originally Posted by Woodduck View Post
    What did I ever do to you?
    "What did I ever do to you??? Why would you condemn me to such misery???"

    Quote Originally Posted by mikeh375 View Post
    oh c'mon MR.
    I mistakenly read it at first as "oh come on, MISTER."

    Quote Originally Posted by mikeh375 View Post
    what you can't seem to do is live in the real world of music making and have a pleasant tone in your posts, instead posting damming assumptions that goad.
    MR sure is skillful in frustrating people with constant unpleasant dissonances in his posts
    Last edited by hammeredklavier; Nov-27-2019 at 23:55.

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    Senior Member EdwardBast's Avatar
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    Quote Originally Posted by hammeredklavier View Post

    MR sure is skillful in frustrating people with constant unpleasant dissonances in his posts
    Talk about the rabbit yelling big-ears!

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