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Thread: Why do root movements a fourth away tend to weaken the tonality of the key?

  1. #61
    Senior Member isorhythm's Avatar
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    Respectfully, this is an inordinate amount of attention paid to phenomena that pertain only to some logistical problems in the tuning of a handful of instruments and not to the vast majority of music made by humans, in which players and singers simply find their pitches by ear.

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    Senior Member millionrainbows's Avatar
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    That can be blamed on BabyGiraffe and his inaccurate distortions.
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    Senior Member isorhythm's Avatar
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    Quote Originally Posted by millionrainbows View Post
    That can be blamed on BabyGiraffe and his inaccurate distortions.
    I meant his stuff about tuning specifically, not the whole thread. I don't know if they're inaccurate.

    I still want you to explain whether you think diatonic scales comes from stacking fifths, as you say in this thread, or from the just-intoned ratios (1:1, 9:8, 5:4, 4:3, 3:2, 5:3, 16:15) as you've said in other threads. These two models are of course totally contradictory.

    My personal view, in case I haven't been clear, is that the diatonic scales, like all scales, evolved because people thought they made nice-sounding music, for various reasons including but not limited the physical phenomena you've noted.

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  6. #64
    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by isorhythm View Post
    I meant his stuff about tuning specifically, not the whole thread. I don't know if they're inaccurate.
    I meant the whole thread.

    I still want you to explain whether you think diatonic scales comes from stacking fifths, as you say in this thread, or from the just-intoned ratios (1:1, 9:8, 5:4, 4:3, 3:2, 5:3, 16:15) as you've said in other threads. These two models are of course totally contradictory.
    1:1 is not "incompatible" with any other octave. They are not "contradictory" unless you're looking for reasons to prove me "wrong."
    If diatonic scales came from stacking perfect just 3:2 fifths, the difference was ironed-out long ago. Our present ET fifths are only 2 cents flat. This system favors the fifth, and hurts the major third. That's why mean-tone tunings tried to solve this.

    If you think it was Greek tetrachords, that is also incompatible because we don't use Greek tuning. It's all incompatible and imperfect.

    My personal view, in case I haven't been clear, is that the diatonic scales, like all scales, evolved because people thought they made nice-sounding music, for various reasons including but not limited the physical phenomena you've noted.
    If you "stack" fifths, first you get pentatonics: C-G-D-A E, rearranged in-octave as C-D-E-G-A. Notice that it has no tritone.

    If you keep stacking, you get C-G-D-A-E-B-F#, unless you start from F: F-C-G-D-A-E-B.

    We were "kissing the diatonic keyboard's a**" by starting on C.

    Greek tetrachords? They were used separately, and had nothing to do with scales until later. They don't impress me very much. They are too intertwined with specific history, like the tuning of lyres, and don't have the theoretical elegance of stacked fifths.

    3:2: a fifth is still a fifth. I'm not an advocate of "just" intervals like BabyGiraffe is.
    "The way out is through the door. Why is it that no one will use this method?"
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    Senior Member isorhythm's Avatar
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    I know I should let this go, but...

    This is you, less than three months ago: What did Brahms mean by "true dissonance"?

    So what is a major third, according to you? Is it 5:4, or is it the result of stacking fifths, 81:64?

    Put another way, when two unaccompanied singers sing a major third in harmony, what do you think they sing?

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    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by isorhythm View Post
    I know I should let this go, but...

    This is you, less than three months ago: What did Brahms mean by "true dissonance"?

    So what is a major third, according to you? Is it 5:4, or is it the result of stacking fifths, 81:64?

    Put another way, when two unaccompanied singers sing a major third in harmony, what do you think they sing?
    A major third is a major third, based on a 5:4. In ET, this interval suffers the most from being 'just', at 14 cents flat.

    Singers might adjust it. If they've got good ears, they can sing the ET interval.

    I don't see how anything I said previously contradicts or disproves this. I'm flexible. I don't make rigid, inflexible pronouncements like BabyGiraffe. The Western music system is imperfect, and I've always stressed that point.
    Last edited by millionrainbows; Jul-31-2019 at 22:16.
    "The way out is through the door. Why is it that no one will use this method?"
    -Confucious

    "In Spring! In the creation of art it must be as it is in Spring!" -Arnold Schoenberg

    "We only become what we are by the radical and deep-seated refusal of that which others have made us." -Jean-Paul Sartre

    "I don't mind dying, as long as I can still breathe." ---Me

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    Quote Originally Posted by isorhythm View Post
    Respectfully, this is an inordinate amount of attention paid to phenomena that pertain only to some logistical problems in the tuning of a handful of instruments and not to the vast majority of music made by humans, in which players and singers simply find their pitches by ear.
    If you really find pitches by ear, you run into problems like microtonal commas, because we are naturally approximating the best tuning, which is something based on small integers ratios, because these don't beat in a harsh manner, if we are after harmony, of course (it takes a lot of training to become a good singer that doesn't "correct" 12 ET intervals unintentionally - whether this is a good or not is another topic - autotune ruins good vocal performances, quantizing them to 12 equal, despite they were fine before that, despite not being exactly on the 12 pitches grid.).

    (And let's not forget that people do what they know; if someone is really interested in new types of music or different takes on the same old stuff, it's way better to understand what is going on than blind experimentation).

    Musical systems have different topology and paths in compositional spaces - if we represent a musical system/scale as a graph, we will traverse the nodes in variety of ways to reach our destinations; and these optimal graphs or travel path will be different in different tunings even when using the "same" 12 keys.
    Most of the Western music theory is based on the meantone graph, but this graph is useless for Turkish music for example (I find it fascinating that Turkish musicians use "wolf" fifths and other intervals not found in all music out there).




    Isorhythm:
    " So what is a major third, according to you? Is it 5:4, or is it the result of stacking fifths, 81:64?"

    Intervals from around 370 up to 430 cents can function melodically as major thirds.
    Only 5/4 (around 386 cents) will synchronise nicely with 5th harmonic of idealised harmonious instrument (organ, string, electric piano etc).
    (We can even calculate the correct tempo that will synchronise even more the texture. Such beatless texture may sound very unnatural.)

    12 ET M3rd of 400 cents will have minimum beating with pefect fifth of 720 cents. This is found in 15 equal (note, this doesn't take into account any inversion of the chord and minor chord, if we take them into the equation, this fails and we need flatter fifth and third than what is in 15 equal).
    15 equal doesn't work very well on harmonic instuments, but with additive synthesizers we can detune overtone partials, creating new variations of existing instruments that work better for certain less harmonic tunings.

  10. #68
    Senior Member isorhythm's Avatar
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    Quote Originally Posted by BabyGiraffe View Post
    If you really find pitches by ear, you run into problems like microtonal commas, because we are naturally approximating the best tuning, which is something based on small integers ratios, because these don't beat in a harsh manner, if we are after harmony, of course (it takes a lot of training to become a good singer that doesn't "correct" 12 ET intervals unintentionally - whether this is a good or not is another topic - autotune ruins good vocal performances, quantizing them to 12 equal, despite they were fine before that, despite not being exactly on the 12 pitches grid.)
    It's not really an "if," it is in fact how it's done. No one sings 12ET by ear unless they're accompanied by a 12ET instrument. I doubt it's even possible. Maybe if you're singing a chromatic scale spanning an octave you'll come close. All this stuff about different tunings is just about the practical challenges presented by certain instruments. It's not as fundamental to music as you're making it.

    Quote Originally Posted by BabyGiraffe View Post
    Intervals from around 370 up to 430 cents can function melodically as major thirds.
    Yes this is sort of my point.

    I suspect that deviations from "ideal" pitch that arise for expressive reasons are bigger than than the differences between various tuning systems in most cases.

  11. #69
    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by isorhythm View Post
    It's not really an "if," it is in fact how it's done. No one sings 12ET by ear unless they're accompanied by a 12ET instrument. I doubt it's even possible. Maybe if you're singing a chromatic scale spanning an octave you'll come close. All this stuff about different tunings is just about the practical challenges presented by certain instruments. It's not as fundamental to music as you're making it.
    I disagree, Without accompaniment, I sing major thirds in ET. Anybody with a good ear does.
    "The way out is through the door. Why is it that no one will use this method?"
    -Confucious

    "In Spring! In the creation of art it must be as it is in Spring!" -Arnold Schoenberg

    "We only become what we are by the radical and deep-seated refusal of that which others have made us." -Jean-Paul Sartre

    "I don't mind dying, as long as I can still breathe." ---Me

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