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Thread: The Major Second Is Not Dissonant

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    Quote Originally Posted by Bwv 1080 View Post
    11 intervals excluding octave/unison and >octave

    7 is P5th, 8 is minor 6th etc
    Okay, you're going by semitones. Still, there are only 6 intervals if you exclude inversions: m2, M2, m3. M3, P4 and tritone. The inversion of the tritone, which remains the same, is obvious proof of the redundancy of inversion in a tonal system.

    Those translate to semitones as 1, 2, 3, 4, 5, and 6.

    In tonality, each note is an interval in relation to the key note (C), and this can be reached from the "bottom" as in C-D, C-E, C-F, etc., or to the "top" C, as in G-C, A-C, or B-C.
    Last edited by millionrainbows; Nov-11-2019 at 15:07.

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    Quote Originally Posted by Woodduck View Post
    Your "scientific" standard of acoustic consonance and dissonance is not a necessary standard, but merely the one you prefer.
    My "scientific" method corresponds exactly to what I hear. I'm only interested in intervals as they sound.

    Using a different, obvious, and common standard, we find that the M3 not only occurs lower, and thus more audibly, in the overtone series than does the M2, but it predictably creates less beating (is "cleaner") when sounded, especially noticeable when the intervals are played in the lower register of the piano. Obviously the tuning system used will affect somewhat the sound of these intervals when played, but this doesn't change the relative consonance or dissonance of the pure intervals, which equal temperament approaches closely enough.

    I disagree; the ET major third, which is ideally 4:5 (386.31 cents), is off by 13.69 cents from the ET M3 of 400 cents. My view is reinforced because all the mean-tone tuning schemes throughout history were attempts to correct this discrepancy.

    Your justification using pure ratio comparisons is ironically a "platonic" attempt, something you criticized me for earlier.

    The real "problem" is the Pythagorean method of dividing the octave into 12 notes by "stacking" fifths, which is the favored interval in this 12-division.

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    I'm like Debussy in this regard.
    Last edited by millionrainbows; Nov-12-2019 at 00:04.

  4. #34
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    Quote Originally Posted by millionrainbows View Post
    My "scientific" method corresponds exactly to what I hear. I'm only interested in intervals as they sound.
    You say you hear a major 2nd as more consonant than a major 3rd. I hear the opposite. You think you're justifying your judgment by talking about "cents." I think I'm justifying my judgment by talking about the greater audibility of the major third in the overtones of a sounded pitch, and about the less audible beating, the greater clarity of the sound, when the intervals are sounded.

    Obviously, my sole interest here is in "intervals as they sound." If this is also your perspective (which I doubt), you have no monopoly on it.

    the ET major third, which is ideally 4:5 (386.31 cents), is off by 13.69 cents from the ET M3 of 400 cents. My view is reinforced because all the mean-tone tuning schemes throughout history were attempts to correct this discrepancy.
    The impurity of the ET major 3rd is slight enough that the sense of the interval as relatively consonant is not undermined. I think it's safe to assume that most people will hear it as corresponding to the interval clearly audible in the overtone series. Strike a bass C on the piano, listen to the Overtone E, then strike the E. The discrepancy will not be heard by most people.

    Your justification using pure ratio comparisons is ironically a "platonic" attempt, something you criticized me for earlier.
    There's nothing "platonic" about it. You're the one talking about "ideal" or "perfect" quantities that most listeners' ears either can't hear or are indifferent to. Most listeners' ears easily identify the equal temperament major third as the satisfying consonance audible in the harmonic series. Would people prefer the pure third if they heard it? Not unlikely, but in practice it generally doesn't matter. I found your characterization of the ET M3 as "ugly, ugly" simply ridiculous. The sound of an organ or an orchestra playing a major triad in equal temperament - let's take the final B major chord of Tristan und Isolde, which Richard Strauss found particularly beautiful - is satisfying and moving in itself, and not merely because it constitutes a resolution of foregoing harmonies. It's as if the whole harmonic series, an audible cosmos of sound generated by the root B, is resonating in our bodies. The effect of a similar chord using the second rather than the third above the root would not be the same, although it might afford its own sort of pleasure.

    The real "problem" is the Pythagorean method of dividing the octave into 12 notes by "stacking" fifths, which is the favored interval in this 12-division.
    Talk about "platonic" - or "academic"! I think it's safe to say that no one listening to music experiences that "real problem."
    Last edited by Woodduck; Nov-11-2019 at 23:44.

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    OK millionrainbows and Woodduck - I may have been a bit harsh putting the two of you in a room together.

    Forgive the tangent, but I don't visit TC very often, partly because I'm a working musician and partly because I can't stand the posturing of some of the posts on here. There's a subset of people who know very little about music but enjoy pretending that they're smart and, perhaps unkindly, I assumed you belonged to this set of polemicists.

    I was fortunate that my conducting professor when I was at music college introduced me to Gesualdo. Through him, I learnt that even the context of dissonance has little meaning. In order to come to this realisation, you need to get in a choir and SING his music. Only then do you really understand (this is partly because pitches shift with his harmony - i.e. a Bb in one chord may be sung sharper than a Bb in the next chord). Fortunately, the human voice isn't tied to keys, valves or frets.

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    Senior Member Woodduck's Avatar
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    Quote Originally Posted by Johann Sebastian Bach View Post
    OK millionrainbows and Woodduck - I may have been a bit harsh putting the two of you in a room together.
    In a way, we're ALL in a room together. Oh, that it should come to this! What WAS it all for?

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    What WAS it all for?
    It was for that major second that Billy Gibbons played in his solo on "Sharp Dressed Man."
    That is a magical sound, especially through a Marshall 4x12 cabinet, which is known to produce "undertones" or difference tones, due to its resonant characteristics. Now, there's a context I can heartily endorse.

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    Senior Member Bwv 1080's Avatar
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    Quote Originally Posted by millionrainbows View Post
    [COLOR=#333333]
    That is a magical sound, especially through a Marshall 4x12 cabinet, which is known to produce "undertones" or difference tones, due to its resonant characteristics. Now, there's a context I can heartily endorse.
    yes, magical because its dissonant, would be boring if it wasnt

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    Quote Originally Posted by Bwv 1080 View Post
    yes, magical because its dissonant, would be boring if it wasnt
    It's dissonant? Compared to what? Not a minor second.

    Yes, it's dissonant compared to a unison. Unless the unison is more than 6 cents off....but a major second has much more leeway than a unison. It can be a 9:8 (203.9 cents) or a 10:9 (182.4 cents).
    The major second was historically considered one of the most dissonant intervals of the diatonic scale, although much 20th-century music saw it reimagined as a consonance.

    Phhhtt!
    Last edited by millionrainbows; Nov-15-2019 at 00:53.

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    Quote Originally Posted by millionrainbows View Post
    Yes, it's dissonant compared to a unison. Unless the unison is more than 6 cents off....but a major second has much more leeway than a unison. It can be a 9:8 (203.9 cents) or a 10:9 (182.4 cents).
    The major second was historically considered one of the most dissonant intervals of the diatonic scale, although much 20th-century music saw it reimagined as a consonance.
    Back in post #32 you made a point of saying that "the ET major third, which is ideally 4:5 (386.31 cents), is off by 13.69 cents from the ET M3 of 400 cents." Here you say that a major second can vary by as much as 21.5 cents. I don't know what any of this is intended to prove, though it might suggest that the second has a greater chance of sounding dissonant than the third. It seems to me that approaching the question of consonance and dissonance through the vagaries of tuning systems is basically unhelpful. And now, when you add to the above that the major second is dissonant relative to something else, and that it was considered one of the most dissonant intervals until it was "reimagined", aren't you undercutting any argument for the interval as being definitely consonant, and aren't you supporting the views advanced by others that its consonance or dissonance are contextual? Given all these variables, what sense is left in the proposition, "the major second is not dissonant"? Is it consonant only because you've "reimagined" it that way?

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    Quote Originally Posted by Woodduck View Post
    Back in post #32 you made a point of saying that "the ET major third, which is ideally 4:5 (386.31 cents), is off by 13.69 cents from the ET M3 of 400 cents." Here you say that a major second can vary by as much as 21.5 cents. I don't know what any of this is intended to prove, though it might suggest that the second has a greater chance of sounding dissonant than the third. It seems to me that approaching the question of consonance and dissonance through the vagaries of tuning systems is basically unhelpful. And now, when you add to the above that the major second is dissonant relative to something else, and that it was considered one of the most dissonant intervals until it was "reimagined", aren't you undercutting any argument for the interval as being definitely consonant, and aren't you supporting the views advanced by others that its consonance or dissonance are contextual? Given all these variables, what sense is left in the proposition, "the major second is not dissonant"? Is it consonant only because you've "reimagined" it that way?
    I'm interested in intervals as harmonic entities, which does not have to "tie" them to being consonant or dissonant.

    It might be helpful to refer to the flatted seventh, or minor seventh (C-Bb), the inversion of the major second, which can also appear as a major second (Bb-C) using the upper C. It's used ubiquitously in dominant seventh chords. In Western CP music, the seventh is tension-producing, and this tension needs resolution.

    However, there is also a septimal (7:4) "harmonic seventh" which is flatter (969 cents) than the ET minor seventh (1000 cents) by a good 30 cents, which is quite noticeable.

    Our ET seventh is derived from the "just" minor seventh (9:5 or 1018 cents).

    From WIK, we read:

    The harmonic seventh arises from the harmonic series as the interval between the fourth harmonic (second octave of the fundamental) and the seventh harmonic; in that octave, harmonics 4, 5, 6, and 7 constitute a purely consonant major chord with added seventh (root position)...

    The harmonic seventh is also expected from barbershop quartet singers when they tune dominant seventh chords (harmonic seventh chord), and is considered an essential aspect of the barbershop style.

    It was used in organs as well:

    In ¼ comma meantone tuning, standard in the Baroque and earlier, the augmented sixth is 965.78 cents – only 3 cents below 7:4, well within normal tuning error and vibrato. Pipe organs were the last fixed-tuning instrument to adopt equal temperament. With the transition of organ tuning from meantone to equal-temperament in the late 19th and early 20th centuries the formerly harmonic Gmaj7♭ and B♭maj7♭ became “lost chords” (among other chords).
    The harmonic seventh differs from the Pythagorean augmented sixth by 225/224 (7.71 cents), or about ⅓ comma. The harmonic seventh note is about ⅓ semitone (≈ 31 cents) flatter than an equal-tempered minor seventh. When this flatter seventh is used, the dominant seventh chord's "need to resolve" down a fifth is weak or non-existent. This chord is often used on the tonic (written as I7) and functions as a "fully resolved" final chord.

    So this flatter seventh, which is used in barbershop quartet harmony, has no need to "resolve" and renders t
    he dominant seventh chord's "need to resolve" down a fifth to become weak or non-existent. That's because it is heard as a consonance.

    This is where the I7-IV7-V7 of blues music came from; Africans originally used instruments tuned this way. Thus, the WIK reference to a I chord makes obvious sense: This chord is often used on the tonic (written as I7) and functions as a "fully resolved" final chord.

    The minor seventh, appearing as its inversion, a major second, is indeed a consonance, especially when it is functioning as a flatted seventh against an upper root. This is not context; this is the harmonic truth of intervals.

    This also considerably weakens the "context" argument that a major second, as a C-D in the lower range (not as a
    flatted seventh) is a "dissonance" in any harmonic sense, if in this context the D is not a chord tone. It can only be considered as "needing to resolve" for contrapuntal reasons, as a stepwise melodic movement, not harmonic in nature.

    This "need to resolve" is based on movement of a line as a logical expectation of melodic movement in time; NOT as an instantaneous "harmonic" phenomenon.

    This "need to resolve" is thus based on expectation (through time) of the expected or predicted movement of a melody line. That's because we are designed to predict the movement of prey.

    If in C-D the chord is a D minor seventh (ii 7), then the harmonic factor kicks in, and the C-D is no longer dissonant.

    Of course, we need to remember that a major second or its inversion, the minor seventh, is used in ET Western music based on a "just" seventh.
    A "just" minor seventh, has an intonation ratio of 9:5 (about 1018 cents).

    That large, sharp seventh needs resolving, down, towards harmonic truth, towards the harmonic stability of the harmonic seventh.

    Is my idea flawed? No; the system is flawed.

    Thus, we see in our 12-division Pythagorean system the fifth as the favored interval, with thirds and sevenths both suffering, forcing us to simply ignore the major third, and to conflate the harmonic seventh with a sharp, ugly "just" seventh derived from Pythagorean procedures.
    Last edited by millionrainbows; Nov-15-2019 at 19:01.

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    Senior Member Bwv 1080's Avatar
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    Is this 'spicy'?


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    16/9 - Pythagorean minor seventh
    9/5 - just minor seventh
    and 7/4 - octave reduced seventh harmonic
    are clearly distinct ratios - meantone temperament maps together in different equal temperaments that support meantone pythagorean and just minor version. Fifths in meantone are flatter than just - 12 equal is actually the sharpest meantone tuning of all of them.
    In non-meantone systems we can find mapping of 16/9 and 7/4 together, this is a septimal pythagorean tuning - 22 and 27 equal are decent for it - we get sharper than just intonation perfect fifths. (One strangeness of any pythagorean tuning - close to just intonation major thirds are actually diminished fourths, wow. The difference between JI major third and pythagorean diminished fourth is called schisma - it's a comma that even 53 equal - the most accurate small 5 and 3 limit system - gets rid of and closes the circle of 53 fifths. The next more accurate fifth comes after we go into equal temperaments where schisma becomes a step, that's too accurate to be even theoretically useful.)

    12 equal's version is closest to 16/9, which is a characteristic dissonance used in dominant seventh chords even when playing in just intonation.

    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.

    All this is facts from basic acoustics.
    Being exposed to these and culturally accepting their sound is another fact.

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    Is this dissonant?

    Last edited by millionrainbows; Nov-15-2019 at 19:43.

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    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)

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