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Thread: Is the Perfect Fourth a Dissonance? If So, Why?

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    Senior Member millionrainbows's Avatar
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    Default Is the Perfect Fourth a Dissonance? If So, Why?

    From WIK:
    The perfect fourth may be derived from the harmonic series as the interval between the third and fourth harmonics. The term perfect identifies this interval as belonging to the group of perfect intervals, so called because they are neither major nor minor (unlike thirds, which are either minor or major) but perfect.
    The perfect fourth is a perfect interval like the unison, octave, and perfect fifth, and it is a sensory consonance. In common practice harmony, however, it is considered a stylistic dissonance in certain contexts, namely in two-voice textures and whenever it appears above the bass. If the bass note also happens to be the chord's root, the interval's upper note almost always temporarily displaces the third of any chord, and, in the terminology used in popular music, is then called a suspended fourth.
    In the 13th century, the fourth and fifth together were the concordantiae mediae (middle consonances) after the unison and octave, and before the thirds and sixths. The fourth came in the 15th century to be regarded as dissonant on its own, and was first classed as a dissonance by Johannes Tinctoris in his Terminorum musicae diffinitorium (1473). In practice, however, it continued to be used as a consonance when supported by the interval of a third or fifth in a lower voice.
    Modern acoustic theory supports the medieval interpretation insofar as the intervals of unison, octave, fifth and fourth have particularly simple frequency ratios. The octave has the ratio of 2:1, for example the interval between a' at A440 and a'' at 880 Hz, giving the ratio 880:440, or 2:1. The fifth has a ratio of 3:2, and its complement has the ratio of 3:4. Ancient and medieval music theorists appear to have been familiar with these ratios, see for example their experiments on the monochord.


    It sounds to me like the treatment of the perfect fourth as dissonant is just a stylistic convention, based on harmony in thirds.

    From WIK:
    Suspended Fourth: The term is borrowed from the contrapuntal technique of suspension, where a note from a previous chord is carried over to the next chord, and then resolved down to the third or tonic, suspending a note from the previous chord. However, in modern usage, the term concerns only the notes played at a given time; in a suspended chord, the added tone does not necessarily resolve and is not necessarily "prepared" (i.e., held over) from the prior chord. As such, in C–F–G, F would resolve to E (or E♭), but in rock and popular music, "the term is used to indicate only the harmonic structure, with no implications about what comes before or after," though preparation of the fourth occurs about half the time and traditional resolution of the fourth occurs usually. In modern jazz, a third can be added to the chord voicing, as long as it is above the fourth.

    In Western music, dissonance is the quality of sounds that seems unstable and has an aural need to resolve to a stable consonance. Both consonance and dissonance are words applied to harmony, chords, and intervals and, by extension, to melody, tonality, and even rhythm and metre. Although there are physical and neurological facts important to understanding the idea of dissonance, the precise definition of dissonance is culturally conditioned—definitions of and conventions of usage related to dissonance vary greatly among different musical styles, traditions, and cultures. Nevertheless, the basic ideas of dissonance, consonance, and resolution exist in some form in all musical traditions that have a concept of melody, harmony, or tonality. Dissonance being the complement of consonance it may be defined, as above, as non-coincidence of partials, lack of fusion or pattern matching, or as complexity.

    Understanding a particular musical style's treatment of dissonance—what is considered dissonant and what rules or procedures govern how dissonant intervals, chords, or notes are treated—is key in understanding that particular style. For instance, harmony is generally governed by chords, which are collections of notes defined as tolerably consonant by the style. (There is likely, however, to be a hierarchy of chords, with some considered more consonant and some more dissonant.) Any note that does not fall within the prevailing harmony is considered dissonant. A given style typically pays attention to how its musical structure approaches dissonance (in steps is less jarring, a leap is more jarring), and even more to how they resolve (almost always by step), to how they fit within the meter and rhythm (dissonances on strong beats are more emphatic, those on weaker beats less vital), and to how they lie within the phrase (dissonances tend to resolve at phrase's end).
    Last edited by millionrainbows; Aug-24-2019 at 11:34.
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    Senior Member Woodduck's Avatar
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    In brief: since "dissonance" and "consonance" have more than one definition, since in any definition they are relative to each other, and since talking about sensory phenomena without reference to specific sounds is apt to lock us in a theoretical ivory tower out of touch with reality, the answer is "yes and no."

    Wishing to avoid confinement in the ivory tower, I take exception to Wiki's statement that a perfect fourth is a "sensory consonance." From a purely sensory (acoustical) standpoint, the effect of consonance or dissonance depends on the clash of partials. Hence the degree of dissonance audible in an interval can depend on the timbre of the instruments that play it and the register in which it's played. Example: on the piano, intervals played high on the keyboard sound "pure," while those played low are rich in audible partials. In the high register, a perfect fourth and a perfect fifth both sound consonant, but played in the bass register the fifth sounds fairly pure while the fourth sounds muddy and harsh.
    Last edited by Woodduck; Aug-24-2019 at 16:59.

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    Senior Member caters's Avatar
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    I actually answered a question on Stack Exchange about 12TET intervals and how dissonant they are. I don't mind posting it here.

    I don't know if this is the true dissonance ranking but here is my personal ranking:

    Rank -1

    Unison

    This I don't really consider to be an interval because the 2 notes are exactly identical. So, that is why I gave it the negative rank.

    Rank 0

    Octave and Perfect fifth

    These are the 2 most open intervals and so it isn't surprising that these intervals would be the most consonant. I don't consider the seventh to be open because when you invert it, it becomes a second. Octaves technically invert to a unison but practically speaking, they self-invert, meaning that an octave becomes another octave. Fifths invert to fourths so there isn't much difference. Also, these intervals are fundamental to any tuning system. Without them, the entire field of music theory would fall apart.

    Rank 1

    Perfect fourth, Major third, and Major sixth

    Unlike some people who view the perfect fourth as dissonant, I don't, at least outside of contrapuntal contexts. It isn't as consonant as the perfect fifth but it isn't all that dissonant either. Some might argue "If it doesn't appear in the harmonic series, than it is dissonant", basing their argument off of the supposed fact that the note of the perfect fourth never appears, but then that would lead to the tritone being more consonant than the perfect fourth which is just wrong.Thirds and sixths tend to be consonant but the major ones are understandably more consonant than their minor counterparts.

    Rank 2

    Minor third and Minor seventh

    This again isn't agreed upon but I view these 2 intervals as being consonant but not as consonant. This is partly because, when you combine the two intervals, you get a very peaceful sounding minor seventh chord.

    Rank 3

    Major seventh and Major second

    These 2 intervals are both quite dissonant, the second especially. But they still have a lower ranking than the last few intervals.

    Rank 4

    Minor second and Minor sixth

    Now this might seem odd, after all the minor sixth shows up everywhere. But here's the thing. When it shows up as part of a chord, I rank it based on how consonant the chord is in root position. When it is all by itself with no harmonic context, at least to me, it sounds augmented, more specifically like an augmented fifth. And augmented fifths are dissonant.

    Rank 5

    Tritone

    This is the only rank besides the negative rank that has a single interval. To put it simply, the tritone is the most dissonant interval, not just a very dissonant interval. Part of the reason is that it divides the octave cleanly in half. Now you might think that octave symmetry should make it very consonant. But in fact, this usually turns out not to be the case. For example, the whole tone scale, as a scale is relatively consonant. But harmonically, it is extremely dissonant. All the fifths are either diminished or augmented. This makes for some weird harmonic progressions. So actually, symmetry is kind of a guarantee for extreme dissonance. That is, unless you consider Dorian to be symmetric(which most don't, when most people say symmetry in music theory, they mean octave symmetry, not palindrome symmetry).

    But like I said, this is my own personal ranking of the intervals. The objective ranking in 12TET may very well be different. But this personal ranking does all have to do with 12TET since it is the only tuning system I use.

    In conclusion, I would say that outside of counterpoint, the perfect fourth is just as consonant as the major third and major sixth and thus is not just a sensory consonance but a true consonance.

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    Senior Member isorhythm's Avatar
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    I think you answered your own question - it depends which sense of the word dissonance you mean. Nothing mysterious here.

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    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by Woodduck View Post
    Wishing to avoid confinement in the ivory tower, I take exception to Wiki's statement that a perfect fourth is a "sensory consonance." From a purely sensory (acoustical) standpoint, the effect of consonance or dissonance depends on the clash of partials. Hence the degree of dissonance audible in an interval can depend on the timbre of the instruments that play it and the register in which it's played. Example: on the piano, intervals played high on the keyboard sound "pure," while those played low are rich in audible partials. In the high register, a perfect fourth and a perfect fifth both sound consonant, but played in the bass register the fifth sounds fairly pure while the fourth sounds muddy and harsh.
    I have to disagree totally with this. Why? Because I think you are avoiding any scientific or quantitative definition of consonance and are "saving it" for your CP argument that says a perfect fourth above the tonic is a dissonance. It makes little sense to say "played in the bass register the fifth sounds fairly pure while the fourth sounds muddy and harsh" without saying why. After all, there is little qualitative difference between 2:3 and 3:4.

    ...since "dissonance" and "consonance" have more than one definition...
    Not really. The 5th and the 4th are considered to be "perfect intervals": The perfect fourth is a perfect interval like the unison, octave, and perfect fifth, and it is a sensory consonance.

    The fourth is only considered, not defined to be dissonant in CP harmony.

    In common practice harmony the fourth is considered a stylistic dissonance in certain contexts, namely in two-voice textures and whenever it appears above the bass. If the bass note also happens to be the chord's root, the interval's upper note almost always temporarily displaces the third of any chord, and, in the terminology used in popular music, is then called a suspended fourth.
    Last edited by millionrainbows; Aug-24-2019 at 18:19.
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    Senior Member Becca's Avatar
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    There is no "scientific or quantitative definition of consonance", it is a highly subjective, even socially based concept. Yes you can find some which almost everyone will agree on but, as obvious from this thread, there is a large, fuzzy middle ground with substantial disagreement which is the antithesis of quantitative let alone scientific definition.

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    Quote Originally Posted by caters View Post
    I don't know if this is the true dissonance ranking but here is my personal ranking:

    Rank -1: Unison

    Rank 0: Octave and Perfect fifth

    Rank 1: Perfect fourth, Major third, and Major sixth
    This is somewhat contradictory, since you yourself observed that the fifth and fourth are inversions, with only one step of difference in their size.

    I must reject your "personal" ranking of dissonance. From WIK:


    • Perfect consonances:
      • unisons and octaves
      • perfect fourths and perfect fifths

    • Imperfect consonances:
      • major thirds and minor sixths
      • minor thirds and major sixths
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    Senior Member Woodduck's Avatar
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    Quote Originally Posted by millionrainbows View Post
    I have to disagree totally with this. Why? Because I think you are avoiding any scientific or quantitative definition of consonance and are "saving it" for your CP argument that says a perfect fourth above the tonic is a dissonance. It makes little sense to say "played in the bass register the fifth sounds fairly pure while the fourth sounds muddy and harsh" without saying why. After all, there is little qualitative difference between 2:3 and 3:4.


    Not really. The 5th and the 4th are considered to be "perfect intervals": The perfect fourth is a perfect interval like the unison, octave, and perfect fifth, and it is a sensory consonance.

    The fourth is only considered, not defined to be dissonant in CP harmony.

    In common practice harmony the fourth is considered a stylistic dissonance in certain contexts, namely in two-voice textures and whenever it appears above the bass. If the bass note also happens to be the chord's root, the interval's upper note almost always temporarily displaces the third of any chord, and, in the terminology used in popular music, is then called a suspended fourth.
    Do you seriously intend this as an argument?

    I addressed, with precisely stated intention, the idea of SENSORY dissonance, and you think it's meaningful to respond with "I think you are avoiding any scientific or quantitative definition of consonance"?

    I'm just going to let you think about that howling nonsequitur while I go have some breakfast.
    Last edited by Woodduck; Aug-24-2019 at 18:54.

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    Quote Originally Posted by Becca View Post
    There is no "scientific or quantitative definition of consonance", it is a highly subjective, even socially based concept. Yes you can find some which almost everyone will agree on but, as obvious from this thread, there is a large, fuzzy middle ground with substantial disagreement which is the antithesis of quantitative let alone scientific definition.
    It can be a subjective, socially based concept in CP music, but we must also consider this ranking, using ideas and terminology found in Western CP theory:

    Perfect consonances:

    • unisons and octaves
    • perfect fourths and perfect fifths



    Imperfect consonances:

    • major thirds and minor sixths
    • minor thirds and major sixths


    You're "hedging your bet" just like Woodduck, saving it up for your coming contention that "a perfect fourth is considered a dissonance" retort.

    You're not "defining" anything, either; you're just pointing out that "consonance and dissonance" are merely "concepts" which change in different contexts, while ignoring all points to the contrary: ratios, numbers, vibrations, and physical and neurological facts important to understanding the idea of dissonance.

    I even think WIK takes it too far when it calls these ideas and considerations "definitions":

    WIK: "...the precise definition of dissonance is culturally conditioned—definitions of and conventions of usage related to dissonance vary greatly among different musical styles, traditions, and cultures."

    So how can these be "definitions?"

    definition: A statement of the meaning of a word or word group or a sign or symbol (dictionary definitions); A statement expressing the essential nature of something.
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    Quote Originally Posted by Woodduck View Post
    Do you seriously intend this as an argument?

    I addressed, with precisely stated intention, the idea of SENSORY dissonance, and you think it's meaningful to respond with "I think you are avoiding any scientific or quantitative definition of consonance"?
    When you make statements like "I take exception to Wiki's statement that a perfect fourth is a "sensory consonance," I can see exactly where you're going with this: down the same academic blind alley.

    If you don't acknowledge the FACT of sensory consonance/dissonance, then why does it even matter that you "addressed" it? You apparently missed breakfast, and are out to lunch.
    Last edited by millionrainbows; Aug-24-2019 at 18:56.
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    Senior Member Woodduck's Avatar
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    Quote Originally Posted by millionrainbows View Post
    When you make statements like "I take exception to Wiki's statement that a perfect fourth is a "sensory consonance," I can see exactly where you're going with this: down the same academic blind alley.

    If you don't acknowledge the FACT of sensory consonance/dissonance, then why does it even matter that you "addressed" it?
    In post #2 I cite, with a specific example, a variable which affects the SENSORY PERCEPTION OF DISSONANCE (determined by the clash of audible partials), yet you say that I "don't acknowledge the fact of sensory dissonance"? Huh? Are you trying to gaslight everyone here?

    From my post:

    "...talking about sensory phenomena without reference to specific sounds is apt to lock us in a theoretical ivory tower...I take exception to Wiki's statement that a perfect fourth is a 'sensory consonance.' From a purely sensory (acoustical) standpoint, the effect of consonance or dissonance depends on the clash of partials. Hence the degree of dissonance audible in an interval can depend on the timbre of the instruments that play it and the register in which it's played."

    (I assumed that it's generally known that the different timbres of instruments are a function of the different patterns of overtones those instruments produce. I also assumed an acquaintance with the fact that lower tones, in general, generate more audible overtones than higher ones.)

    An acoustical fact here explains a fact of SENSORY perception: because the SENSATION of dissonance is influenced by the audibility of clashing overtones, an interval can SOUND more or less dissonant depending on the overtones emitted by the sound source. Therefore, a perfect fourth cannot simply be called a "sensory consonance" or a "sensory dissonance," but will be heard as more or less consonant or dissonant depending, in part, on how much clash can be perceived among the overtones produced by the sound source.

    Obviously, this particular aspect of sensory perception is just one factor influencing our perception of consonance and dissonance. But the concrete specifics governing sensory perception - how a specific instance of sound strikes us - appear not to figure into your thinking, which seems so bound to theory as to exclude obvious auditory factors. This theoretical bias leads you to want to make the question simpler than it is. Whether or nor a perfect fourth should be classified as a consonance according to some scale of dissonance is not what I was addressing, and I made this clear when I said "I take exception to Wiki's statement that a perfect fourth is a SENSORY consonance."

    My point is anything but "academic," and in fact it seems that in your fondness for using that term as a derogation you're engaging in projection. The only "academic blind alley" around here is the one you're apparently stuck in - the one that leads to the ivory tower from which you issue ex cathedra pronouncements while pretending to invite discussion. Do you want your thread title's questions examined from all points of view, or is this thread just a lecture in disguise?
    Last edited by Woodduck; Aug-25-2019 at 06:49.

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    Senior Member Bwv 1080's Avatar
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    Quartal harmony is a staple of modal jazz and not particularly dissonant in that context, but in common practice tonality, yes. So depends on the context

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    Quote Originally Posted by Woodduck View Post
    ...a perfect fourth cannot simply be called a "sensory consonance" or a "sensory dissonance," but will be heard as more or less consonant or dissonant depending, in part, on how much clash can be perceived among the overtones produced by the sound source...
    ...the concrete specifics governing sensory perception - how a specific instance of sound strikes us - appear not to figure into your thinking, which seems so bound to theory as to exclude obvious auditory factors. This theoretical bias leads you to want to make the question simpler than it is.
    These are all subjective hoo-hah. There is nothing "concrete" about "how a sound strikes us."

    "Auditory factors" correspond with vibrations, ratios, in this case 3:4, which is a relatively simple whole-number ratio.

    The perfect fourth, along with the perfect fifth, are birds of a feather, they are each other's inverse, and harmonically, they create strong suggestions of tonal gravity: the fifth is heard as "root" on bottom, and the fourth as "root" on top.

    The fourth and fifth are the Western divisors of the octave, and create the Western triumvirate of I-IV-V.

    Additionally, they are the only two intervals that are not recursive within one octave; i.e., when "stacked" they both produce all 12 chromatic notes; the fifth: (7 X 12 = 84) and the fourth: (5 X 12 = 60). This quality they share with no other intervals. These two "brother" intervals were made to travel outside the octave into new territory, tonally speaking.

    If the fourth is "singled out" and separated from the fifth as "dissonant," just because the fourth above the root creates a tendency to reinforce another key, then this is an artificial distinction, made necessary by the instability of the major scale, with its fourth above the root.

    The fourth is not "dissonant;" this is an artificial convenience of Western tonality and the harmonic deficiencies of its chosen scale, the major scale, which is designed for instability and harmonic root movement.
    Last edited by millionrainbows; Aug-25-2019 at 11:19.

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    Quote Originally Posted by Bwv 1080 View Post
    Quartal harmony is a staple of modal jazz and not particularly dissonant in that context, but in common practice tonality, yes. So depends on the context
    Are you talking about how fourths sound, or how they are considered? That's two different things. Woodduck seems to be focussed on how the fourth is considered in a Western CP context.

    To me, and to any physicist, consonance and dissonance are based on auditory factors which BTW happen to perfectly correspond with interval ratios. Your "context" is totally subjective and means essentially nothing. It is part of a "belief system" which originated in Christian religion, and still persists.
    Last edited by millionrainbows; Aug-25-2019 at 14:10.
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    Senior Member Woodduck's Avatar
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    Quote Originally Posted by millionrainbows View Post
    These are all subjective hoo-hah. There is nothing "concrete" about "how a sound strikes us."

    "Auditory factors" correspond with vibrations, ratios, in this case 3:4, which is a relatively simple whole-number ratio.

    The perfect fourth, along with the perfect fifth, are birds of a feather, they are each other's inverse, and harmonically, they create strong suggestions of tonal gravity: the fifth is heard as "root" on bottom, and the fourth as "root" on top.

    The fourth and fifth are the Western divisors of the octave, and create the Western triumvirate of I-IV-V.

    Additionally, they are the only two intervals that are not recursive within one octave; i.e., when "stacked" they both produce all 12 chromatic notes; the fifth: (7 X 12 = 84) and the fourth: (5 X 12 = 60). This quality they share with no other intervals. These two "brother" intervals were made to travel outside the octave into new territory, tonally speaking.

    If the fourth is "singled out" and separated from the fifth as "dissonant," just because the fourth above the root creates a tendency to reinforce another key, then this is an artificial distinction, made necessary by the instability of the major scale, with its fourth above the root.

    The fourth is not "dissonant;" this is an artificial convenience of Western tonality and the harmonic deficiencies of its chosen scale, the major scale, which is designed for instability and harmonic root movement.
    "Subjective hoo-hah," huh? Ha!

    In fact, how sound "strikes us" and why it does so - perception and the external factors that shape it - is the thing that ultimately matters in music. Theory that doesn't take the full range of perceptual factors into consideration might as well be called "academic hoo-hah," and is of no more than curiosity value to anyone who doesn't spend his time flooding the pages of music forums with endless repetitions of his pet conceits in order to impress himself and prospective admirers with his superior understanding.

    The truly comprehensive answer to the question posed in the title of your thread is "yes and no." You may not like that, it may not fit with your personal slant on the subject, it may not be what you set out to prove to a doting audience, but there it is, obvious to anyone with a modicum of knowledge - or, more importantly, the ability to HEAR.

    I've mentioned only one factor that determines how consonant or dissonant a perfect fourth can sound. It may be considered an esoteric or peripheral factor, but there's no rational objection to that; I assumed that others would bring up other, more obvious, factors. The elephant in the room, of course, is that in actual music - oh dear, here I go talking about actual music again! - intervals assume functions which determine how we hear them, including whether we hear them as consonant or dissonant, and to what degree we do. Who knew, in 1800, that jazz would come along and turn a major seventh into a consonance? But damned if it didn't happen, and as we listen to jazz we're perfectly at peace with those sevenths - and ninths, and thirteenths, and whatever - lingering in the air, having no sense at all that we're hearing "dissonances."

    The fact that a perfect fourth is the inversion of a perfect fifth and, taken out of context, "borrows" consonance from that interval, is perhaps the most obvious and least interesting thing about it. But if you've set out with the assumption that the subject should end there - that there's nothing else worth saying about the interval, and no other meaning to "consonance" or "dissonance" worth mentioning - then your entire thread is nothing but an exercise in pedantry, designed to have the rest of us seated behind our desks glassy-eyed, taking notes and preparing for the exam.

    Go ahead and roll out all the "objective" numbers and ratios you want from here to eternity. But in the end, music and its elements will be, as they've always been, defined by what human beings compose, hear and feel. A perfect fourth played by an ensemble of tuning forks isn't something I need to listen to or think about. I'd rather see a purple cow.
    Last edited by Woodduck; Aug-25-2019 at 21:51.

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