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Thread: Musicians call the note with frequency "440 vibrations per second" an "A"

  1. #1
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    Musicians call the note with frequency "440 vibrations per second" an "A"

    Hello, my friends

    I just read this:

    The higher the frequency of a note, the higher it sounds. Cientists can measure the frequency of notes, and like most measurements, these will be numbers, like "440 vibrations per second."
    But people have been making music and talking about music since long before we knew that sounds were waves with frequencies. So when musicians talk about how high or low a note sounds, they usually don't talk about frequency; they talk about the note's pitch. And instead of numbers, they give the notes names, like "C". (For example, musicians call the note with frequency "440 vibrations per second" an "A".)

    I always felt some difficulties in understanding why musicians (and all people related with music) give different names to things. Most of the things in music theory have their own names in the science world. Being myself an engineer by formation, and a musician in my heart, I have been "duelling" between these two sides of the same thing since I began to go a little deeper in music theory, maybe 20 years ago.
    But I never went that far because I always felt that things were really confusing. So this made learn just the strictly necessary for my musician needs at the time.

    I wonder what's your oppinion about this. Do you think the same issues happen frequently with other people? Did this happened with you?

    And I'm not talking about the best that could happen: to define the standrad notes name as Dó Re Mi Fa Sol La Si Do instead of C D E F G A and B. That would be asking too much...but would be great.

  2. #2
    Registered User Malcolm's Avatar
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    I do not think most musicians get involved with frequencies, sound engineers, and old ham radio operators involve themselves with frequencies.

    But, back to the question -- theory is IMO a language we speak so we can communicate with other musicians. How much of that language we use depends on how far we have traveled down that theory road. Case in point, I can talk a bunch of theory, but, can not talk to you about music frequencies.

    Now ham bands are another story.

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    I admit it won't be practical to talk about music theory using the scientific nomenclature because:

    1 - Some musicians know the theory but don't know the theory basis (scientifc phenomenons that explain the theory itself).

    2 - It would be really difficult to go against something that is used by everybody and accepted as "the norm".

    For these reasons, if I want to talk about theory with another musician, I will use the musical nomenclature. But to me, use it without knowing the reasons behind, feels like doing something that works, but without knowing why.
    But this how I feel, and that's why I'm studying physics together with music theory.

    For example, how can someone explain why a perfect fifth is considered perfect? Just because it sounds good?
    Well, to me that is not enough....and if we consider the scientific reasons why it sounds good, we will have to study a little bit of accoustic and physiology of the human hearing.

    Obviously I don't want to diminish anyone who doesn't know the scientific explanations for what's behind music...that's just my way of learning things (which, sometimes, gives a lot of headaches).
    Last edited by rbarata; 11-08-2010 at 02:20 PM.

  4. #4
    bitter old fool Jed's Avatar
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    Quote Originally Posted by rbarata View Post
    I admit it won't be practical to talk about music theory using the scientific nomenclature because:
    Agreed

    Quote Originally Posted by rbarata View Post
    1 - Some musicians know the theory but don't know the theory basis (scientific phenomenons that explain the theory itself).
    Musicians will range from those that understand the sounds but know no theory (the majority) to those that understand the sounds and know the theory (the minority) to those that have learned some theory but don't understand the sounds (very few) to those that know the theory, the sounds and the physics (almost none).

    Quote Originally Posted by rbarata View Post
    2 - It would be really difficult to go against something that is used by everybody and accepted as "the norm".
    Remind yourself daily of this sentiment.

    Quote Originally Posted by rbarata View Post
    For these reasons, if I want to talk about theory with another musician, I will use the musical nomenclature. But to me, use it without knowing the reasons behind, feels like doing something that works, but without knowing why. But this how I feel, and that's why I'm studying physics together with music theory.
    As a fellow scientist I can appreciate your dilemma. But as an adult you have seen this before. Whenever non-scientists talk about scientifically based phenomena they invariably "get it wrong". This is how life is. We cannot change it. We cannot force people to use the correct terms. They will always have their own language to describe these things. We can either learn their language and in knowing the science, we can bridge the gap. Or we can accept their language and move on to more important things.

    Quote Originally Posted by rbarata View Post
    For example, how can someone explain why a perfect fifth is considered perfect? Just because it sounds good?
    Well, to me that is not enough....and if we consider the scientific reasons why it sounds good, we will have to study a little bit of accoustic and physiology of the human hearing.
    And if you decide that you must have a good explanation for the derivation of every musical term, you will drive yourself crazy long before you learn music theory. Better to approach music theory as a language. Learn to speak the language first, then you can formulate your own physical explanation for each of these terms.

    Quote Originally Posted by rbarata View Post
    Obviously I don't want to diminish anyone who doesn't know the scientific explanations for what's behind music...that's just my way of learning things (which, sometimes, gives a lot of headaches).
    Agreed. There are easier ways. Learn the language, strive to understand the concepts separate from the nomenclature - and you will find what you are looking for. But force someone to defend a language designed by non-scientists in scientific terms is a fools errand.

    cheers,

    BTW - It's call a perfect 5th for lot's of good reasons, none of which will make sense to you before you understand the major scale, it's intervallic structure and the harmonic sequence (over tones). All of which requires that you take a leap of faith about some basic nomenclature.

    BTW #2 - It would be easier on the eyes if you used the forum's default font rather than changing the font of your posts to suit your personal tastes. See also the concept of language being about understanding other people rather than trying to get them to understand you.

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    Hi Jed, thanks for the reply

    Better to approach music theory as a language.
    Yes, that's what I'm doing. So far, most of the physical concepts behind music theory are explained by one of my physics favorite chapters so it's not so difficult. I just have to give a quick look at what I've learned.
    That's a way I've found to "integrate" this new language. It's easier this way.

    I just wanted to know if someone else had this dillema.

    BTW #2 - It would be easier on the eyes if you used the forum's default font rather than changing the font of your posts to suit your personal tastes. See also the concept of language being about understanding other people rather than trying to get them to understand you.
    I haven't changed any settings in my account. Are you refering to the italic text?

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    There are tags in some of your posts changing the font, making the text small and hard to read (I inserted the "x"s so the forum software won't interpret the tags and you can see what they look like):

    [xFONT=Helv][xSIZE=2]Hello, my friends[x/SIZE][x/FONT]

    [xSIZE=2][xFONT=Helv]I just read this:[x/FONT][x/SIZE]

    If you aren't manually changing the font every time you post, I don't know if there's something in your account settings that might be causing it or ??
    Last edited by walternewton; 11-08-2010 at 03:54 PM.

  7. #7
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    Quote Originally Posted by rbarata View Post
    For example, how can someone explain why a perfect fifth is considered perfect? Just because it sounds good?
    Well, to me that is not enough....and if we consider the scientific reasons why it sounds good, we will have to study a little bit of accoustic and physiology of the human hearing.
    When these things were decided, there was really no such thing as "science". Our notion of objective science (proving things by experiment, looking for underlying causes) is relatively recent.
    In the days when the concepts behind our scales (and music terminology) were being developed, music and art were all more like kinds of philosophy, with spiritual overtones. And so was science.
    So when Pythagoras laid down the principle of ratio in musical scales, he was thinking both about sound, and about mathematical simplicity or perfection. Ie, he discovered that simple ratios (figures of 2 and 3) produced harmonious sounds, and reasoned that this was because God was a mathematician. It all supported the notion of the "harmony of the spheres" - the idea that heavenly bodies moved in exact circles, whose relatioships were akin to musical sounds (or perhaps actually produced musical sounds, albeit inaudible ones).
    AFAIK, they had no concept of "frequency" back then - certainly no way of determining cycles per second. They just perceived that relationship: of simple ratios (lengths of strings or weights of metal bars) to nice sounds.

    IOW, "perfect" 5ths (and 4ths, unisons and octaves) were so-called for two reasons: simplicity of ratio, and purity of sound. To the Greek mind - as I understand it - these reasons were not separate, but intimately related: essentially both sprang from the same origin: God's design of the cosmos.

    BTW, I'm not saying the Greeks used the word "perfect" - I'm not sure what they called them - but they did regard octave, 4th and 5th as fundamental scale divisions. And the European Catholic church adopted the same basic concepts: God's music was supposed to be "pure", made of sounds which blended as smoothly as possible. In the beginning, church music permitted no harmony at all, and when it did, it began with 4ths and 5ths only.

    Of course, your scientist's mind is not satisfied in the same way an ancient Greek or medieval mind would have been. I'm not a scientist, but I'm also curious about the physics underlying music.
    However - from the various books I've read on the subject - the science of physics and acoustics does not help us very much in understanding music, unfortunately. It gives us the harmonic series, which is obviously connected with musical sound on some level. But physical science doesn't explain anything beyond that, esp why we choose not to obey the harmonic series, and choose sounds that disagree with it - often preferring dissonance to consonance. Music can only really be explained in full by cultural anthropology - that kind of science!

    IOW, while it can be fascinating to delve into the world of musical sound (vibration, frequency etc), it's a mistake to think you will discover any secrets there. Certainly not anything that will make music theory easier to comprehend!

    As I've said before, it's like expecting to understand why people speak the way they do, by examining how their vocal cords work, the shapes of their mouths, etc. That's all very fascinating, but it has very little to do with language, still less to do with the meanings of words.

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    Cause discovered!!

    Sorry! When I write a draft of my posts in my e-mail editor, together with the text I past also the case formats. I believe this one now it's ok.

    It won't happen again.

    BTW, anyone knows the default letters of the forum?

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    Hi JonR

    When these things were decided, there was really no such thing as "science".
    Right!! I discovered that a few weeks ago in this forum.
    Maybe it doesn't makes much sense but knowing it made me understand a lot of things in music theory and my learning so much easier.
    This pureness and it's relation with God has, I think, its explanation in the balance we discussed a few weeks ago, about the multiples of 2 in the harmonic series. This is nowadays easily explained and understood by the light that science brought to these issues.

    Of course, your scientist's mind is not satisfied in the same way an ancient Greek or medieval mind would have been. I'm not a scientist, but I'm also curious about the physics underlying music.
    However - from the various books I've read on the subject - the science of physics and acoustics does not help us very much in understanding music, unfortunately. It gives us the harmonic series, which is obviously connected with musical sound on some level. But physical science doesn't explain anything beyond that, esp why we choose not to obey the harmonic series, and choose sounds that disagree with it - often preferring dissonance to consonance. Music can only really be explained in full by cultural anthropology - that kind of science!
    Basically, music is an older language than science. Music is influenced by cultural and anthropological aspects (among many other things) while science is not.
    Sometimes I think that understanding the relationships of music with the factors that gave origin to its differences around the world is far more difficult than music theory itself.
    At least in my country, all the music universities include a discipline called "Music history". I never understood why they included it but, today, I understand why.

    Maybe seeing it by the light of the science is like a refuge from my side.
    Last edited by rbarata; 11-08-2010 at 05:26 PM.

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    Quote Originally Posted by Jed View Post
    And if you decide that you must have a good explanation for the derivation of every musical term, you will drive yourself crazy long before you learn music theory.
    That's certainly true, but I think is is far more so due to the fact that a lot of the nomenclature and other descriptive systems in traditional music theory are *completely meaningless* to the music than the fact that it would actually be a huge job. The names we use today may reveal the way people *used to* think about music, but many times they are not actually relevant to the theory.

    My classic example is the name, and definition of, "The Perfect Fifth", which I've had explained to me this way several times:
    -Why is the fifth note of the major mode called perfect?
    -Well, the fourth is called perfect, and perfect intervals invert to each other. A perfect fourth inverts to a fifth, so that fifth is perfect!
    -And why is the fourth called perfect?
    -Because the fifth is perfect, and it inverts to the fourth!

    A close examination will reveal that this argument uses circular definitions and is not telling us anything about why the fifth (or fourth) is called perfect. An even closer examination of interval naming reveals a pattern for all other intervals:

    If a given generic interval (second, third, sixth, seventh) appears in two sizes in the diatonic scale, the larger is called major and the smaller minor. If the interval naming system were followed, this would apply to the fifth and fourth as well because each of them has a smaller and larger version in the diatonic scale respectively:

    The interval we now call the augmented fourth appears in "Fa" mode, and the interval we now call the diminished fifth appears in "Ti" mode. If we were to be consistent about our naming patterns, they would each be called the major fourth and the minor fifth respectively, the perfect fourth and fifth changing to minor fourth and major fifth respectively. The only intervals that do not exist in two sizes in the diatonic scale are unisons and octaves, so they are the only intervals that should really be called perfect.

    My whole point is that you may become very confused by traditional theory, but it is more likely due to the problems and inconsistencies of the system than a lack of understanding of their derivation. Their derivation is often convoluted and not rooted in actual relevant theory.

    I'm definitely not saying that there are not *very cool* results you can get from the view you've taken on. I'm also very interested in the physics and math of music, and it has led me to some discoveries that I would never have reached without it that *are* musically meaningful. It's just that the theory that describes music nowadays is so convoluted that you are more likely confused by it for that reason than for any lack of understanding of psychoacoustics or their derivation.

    John

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    Quote Originally Posted by JlMoriart View Post
    My classic example is the name, and definition of, "The Perfect Fifth", which I've had explained to me this way several times:
    -Why is the fifth note of the major mode called perfect?
    -Well, the fourth is called perfect, and perfect intervals invert to each other. A perfect fourth inverts to a fifth, so that fifth is perfect!
    -And why is the fourth called perfect?
    -Because the fifth is perfect, and it inverts to the fourth!

    A close examination will reveal that this argument uses circular definitions and is not telling us anything about why the fifth (or fourth) is called perfect.
    Well of course that's a circular argument, but there is a perfectly (oops ) good reason for the term, as I described above. The 4th and 5th have the simplest ratios (in just intonation of course), and have the strongest consonances (after the unison and octave, which are also technically "perfect").
    They were also the prime scale divisions. They have quite different characters from the other scale intervals.
    Quote Originally Posted by JlMoriart View Post
    An even closer examination of interval naming reveals a pattern for all other intervals:

    If a given generic interval (second, third, sixth, seventh) appears in two sizes in the diatonic scale, the larger is called major and the smaller minor. If the interval naming system were followed, this would apply to the fifth and fourth as well because each of them has a smaller and larger version in the diatonic scale respectively:
    Yes, but perfect intervals can go two ways.
    IOW, they have a common central position - the "perfect" interval. That can be either raised (augmented) or lowered (diminished).
    (Diminished 4ths and augmented 5ths occur in the harmonic and melodic minor scales, which are by no means uncommon.)
    2nds, 3rds, 6ths and 7ths come in two common sizes, neither more common than the other.

    IOW, the terminology does have a logic, given the different natures of the intervals, and especially given the historical derivation and usage.

    Of course, if we enlarge a major interval by a half-step it becomes augmented, and a minor interval reduced by a half-step is diminished, but that doesn't spoil the logic.
    IOW, the standard sizes of intervals are either perfect, major or minor. Their alterations are augmented or diminished.
    Quote Originally Posted by JlMoriart View Post
    If we were to be consistent about our naming patterns, they would each be called the major fourth and the minor fifth respectively, the perfect fourth and fifth changing to minor fourth and major fifth respectively.
    But that doesn't allow for the others kinds of 4th or 5th - we'd still need the terms augmented and diminished. IOW, it ignores the nature of 4ths and 5ths as commonly used.
    Moreover, the "major 4th" and the "minor 5th" are far less common than their counterparts - so those terms are misleading.
    But mainly it's ignoring the tonal, acoustic quality of perfect 4ths and 5ths. With 2nds, 3rds, 6ths and 7ths, they are comparable in terms of consonance/dissonance (major and minor versions differ, but not by much). The difference between a perfect ("minor") 4th and an augmented ("major") one is stark: strong consonance vs strong dissonance.
    Also, in your system, the "minor 4th" and the "major 5th" are the more consonant ones, which also puts out confusing signals.
    Quote Originally Posted by JlMoriart View Post
    The only intervals that do not exist in two sizes in the diatonic scale are unisons and octaves, so they are the only intervals that should really be called perfect.
    It's not impossible to see augmented and diminished versions of those, but it's certainly rare - and they don't exist in any common scale of course.
    I agree there's a good argument for giving those intervals a different adjective - if only because they are the same pitch class (all other intervals are between two different notes).
    Quote Originally Posted by JlMoriart View Post
    My whole point is that you may become very confused by traditional theory, but it is more likely due to the problems and inconsistencies of the system than a lack of understanding of their derivation. Their derivation is often convoluted and not rooted in actual relevant theory.
    Well, the terms are "music theory", although of course music theory is not "theory" in any scientific sense.
    There are not actually that many inconsistencies in music theory, although much of it depends on context. Terms can change their meaning over time, or have two or more senses. (The eternal problems over definitions of "key" and "mode" are just two notorious examples.)
    But most things that seem crazy on the surface have logic underneath when you understand the usage and derivation.

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    Quote Originally Posted by JonR View Post
    Well of course that's a circular argument, but there is a perfectly (oops ) good reason for the term, as I described above. The 4th and 5th have the simplest ratios (in just intonation of course), and have the strongest consonances (after the unison and octave, which are also technically "perfect").
    But who decided we should stop at 2/1, 3/2, and 4/3? 2/1 is arguably the simplest ratio, so if you wanted to call it (and it's octave displacements) perfect and nothing else that would at least be consistent. To say that those three ratios are "simplest", however, calls subjection into the picture. Why not extend the definition of "simplest" it to include 2/1, 3/2, 4/3, 5/4, 8/5, 6/5, and 5/3, and then call those intervals perfect as well? And if you are going to bring primes into the picture then 9/8, which is 3-limit (same as 3/2 and 4/3), should be "more perfect" than 5/4, which doesn't seem right either.


    Quote Originally Posted by JonR View Post
    IOW, they have a common central position - the "perfect" interval. That can be either raised (augmented) or lowered (diminished).
    (Diminished 4ths and augmented 5ths occur in the harmonic and melodic minor scales, which are by no means uncommon.)
    2nds, 3rds, 6ths and 7ths come in two common sizes, neither more common than the other.
    I still see no reason that, given those properties, the fifth and fourth should be singled out to be name differently though. The dramatic differences in usage would just be another trait that characterizes each major/minor fourth/fifth:

    "The major fifth is used very often *harmonically* due to its high degree of consonance, the minor fifth less often due to its lower degree of consonance, and the augmented/diminished fifth even less often due to their uncommon chromatic functions."

    The major seventh is used extremely differently from the minor seventh, but we didn't name the major seventh anything but major and the minor seventh anything but minor. We just then tag all of their respective tendencies on to the character of each interval name.

    Quote Originally Posted by JonR View Post
    But that doesn't allow for the others kinds of 4th or 5th - we'd still need the terms augmented and diminished. IOW, it ignores the nature of 4ths and 5ths as commonly used.
    It does allow for aug and dim fourths and fifths, they just get shifted slightly. The diminished fifth becomes minor and the doubly diminished fifth becomes the diminished fifth, etc. The augmented fourth becomes major and the doubly augmented fourth becomes augmented, etc.

    The "nature" of fourths and fifths, I think, is *better* highlighted by this major minor naming system. For instance, I love the lydian mode, and when I play in it I can naturally hear the major fourth as just that: a major sounding version of the melodic function I usually associate with the minor fourth. The minor fifth can be heard as a melodically functional fifth just as easily. The only problem is that we generally associate so strongly the harmonic connotations of the major fifth with the generic fifth that the minor doesn't sound "fifthy" in *harmonic* contexts. But harmony is not all a scale is. A scale is a structure of melody that may or may not line up with harmony in useful ways.

    Quote Originally Posted by JonR View Post
    But mainly it's ignoring the tonal, acoustic quality of perfect 4ths and 5ths. With 2nds, 3rds, 6ths and 7ths, they are comparable in terms of consonance/dissonance (major and minor versions differ, but not by much). The difference between a perfect ("minor") 4th and an augmented ("major") one is stark: strong consonance vs strong dissonance.
    Well, I'd agree that major and minor thirds are pretty much comparable, but the difference between the major and minor as well as the difference between the major and minor seventh seem equally stark.

    Here I'm going to suggest again that the melodic quality of each fifth and fourth I'm describing is perfectly recognizable melodically, and that harmonic quality of each interval should not cover up their melodic qualities.

    Quote Originally Posted by JonR View Post
    Also, in your system, the "minor 4th" and the "major 5th" are the more consonant ones, which also puts out confusing signals.
    Why is that a confusing signal?

    John M

  13. #13
    Registered User JonR's Avatar
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    Quote Originally Posted by JlMoriart View Post
    But who decided we should stop at 2/1, 3/2, and 4/3?
    Pythagoras.
    Ancient Greek music arranged the other intervals by ear, not by maths. IOW, they began with mathematically "perfect" tetrachords, then built their modes by finding 2 other notes that "sounded good". Some of these may well have coincided with other ratios, but - as I understand it - they weren't "officially" recognised.

    Pythagorean intonation was the basis of European medieval scale construction - every note determined by the cycle of 5ths, meaning a major 3rd turned out as 81:64.
    It was many centuries later that 5:4 was accepted as a valid ratio, when major 3rds became more accepted as consonances. (And that resulted in two kinds of tone, 9:8 or 10:9, and eventually temperaments such as "meantone".)
    IOW, it was always felt that any interval ratio beyond 4th and 5th was somehow "imperfect" because it couldn't be so precisely and easily determined. There were various 3rds which sounded "OK", or were justifiable by various mathematical methods, but no central one that seemed ideal - no "perfect" 3rd (even a perfect major 3rd).
    Just as in Greek music, the positioning of 2nds, 3rds, 6ths and 7ths was a somewhat arbitrary science. They could go in many different places and be usable (offer different modal sounds), while 4ths and 5ths had to remain fixed. (Lydian mode did contain a #4 degree but, as a harmony, the tritone - root-#4 or root-b5 - was outlawed at that time.)

    I'm not denying that the word "perfect" is not used here in the absolute sense we generally use it outside of music theory! Obviously in music theory "perfection" is relative.

    You're right that - from our perspective - there's a kind of arbitrariness about stopping at a factor of 3. Is 5-limit that much further? That much less "perfect"? But to medieval minds (and some beyond that) it was a step too far, perhaps because of the complications it threw up, and which dogged musicology until equal temperament finally stomped all over all previous temperaments and intonations.
    There are now arguments for 7-limit intervals, and even 11-limit (which are well out of tune with ET, but which some argue explain "blue notes").
    Quote Originally Posted by JlMoriart View Post
    I still see no reason that, given those properties, the fifth and fourth should be singled out to be name differently though. The dramatic differences in usage would just be another trait that characterizes each major/minor fourth/fifth:

    "The major fifth is used very often *harmonically* due to its high degree of consonance, the minor fifth less often due to its lower degree of consonance, and the augmented/diminished fifth even less often due to their uncommon chromatic functions."
    That sounds persuasive as a justification! But - as I say - it's ignoring history. That might not be a bad thing - we modify jargon all the time - but I still see a fundamental difference in both sound and usage today between the "perfect" intervals and the "major-minor" ones.
    The most common scales and modes in use today all have perfect 4ths and perfect 5ths, while the other intervals are all variable. (Lydian and locrian are very rare in use.)
    IOW, you could say the word "perfect" amounts to "mostly invariable". So I agree "perfect" is not a perfect term (they are not totally invariable), but it still makes sense to distinguish 4ths and 5ths somehow from the others.
    Quote Originally Posted by JlMoriart View Post
    The major seventh is used extremely differently from the minor seventh, but we didn't name the major seventh anything but major and the minor seventh anything but minor. We just then tag all of their respective tendencies on to the character of each interval name.
    True. So you've disposed of that strand of my argument.
    But the 7th is clearly an "imperfect" interval in the sense that it comes in two common kinds, both of which are dissonant to varying degrees. We can't determine anything lke a "perfect" 7th, any more than we can a "perfect" 2nd 3rd or 6th.
    Quote Originally Posted by JlMoriart View Post
    The "nature" of fourths and fifths, I think, is *better* highlighted by this major minor naming system. For instance, I love the lydian mode, and when I play in it I can naturally hear the major fourth as just that: a major sounding version of the melodic function I usually associate with the minor fourth. The minor fifth can be heard as a melodically functional fifth just as easily. The only problem is that we generally associate so strongly the harmonic connotations of the major fifth with the generic fifth that the minor doesn't sound "fifthy" in *harmonic* contexts. But harmony is not all a scale is. A scale is a structure of melody that may or may not line up with harmony in useful ways.
    Well, yes. But it seems the distinctions were originally dependent on how the intervals worked harmonically.
    For me, the #4 of lydian is a "sweet" note, but only in certain melodic and harmonic contexts. Against the root - ie as an actual #4 - it's highly dissonant.

    I think we're going to have to agree to disagree on the "nature" of the 4ths and 5ths in comparison with other intervals. I see your logic, but then I also see (and hear) a substantial difference in sound between perfect intervals and the others.
    Quote Originally Posted by JlMoriart View Post
    Why is that a confusing signal?
    Well, I'm still thinking of what I regard as fundamental differences in sound quality.
    It's a narrow point, admittedly: the minor and major 2nd - while being both dissonant - are as different from each other in character as their inversions the 7ths are. If not quite as different as a #4 is from a P4 - IMO .

    I come back to my central point, that I see the conventional terminology as explaining not only perceptible differences in sound, but also how scales are constructed and used: not just historically but today. IOW, I regard the old jargon as useful, while changing the definition of 4ths and 5ths to minor/major is less clear, less revealing. It gets rid of a useful distinction, IMO.

    As I say, it looks like we'll have to agree to disagree.

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    Quote Originally Posted by JonR View Post
    Looks like we'll have to agree to disagree.
    I think the major disagreement is between whether or not the historical treatment of an interval should be reflected in the name: I think not, you think so.
    Another disagreement is whether or not the special case of fourths and fifths, being commonly used in only one of two sizes, justifies a differentiation in nomenclature. "Perfect" covers up that the fourth and fifth have *two* diatonic sizes, but "reveals" that they are unique somehow.

    At this basic a level it comes down to personal preference I supposed, so agree to disagree it is

  15. #15
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    Quote Originally Posted by JlMoriart View Post
    I think the major disagreement is between whether or not the historical treatment of an interval should be reflected in the name: I think not, you think so.
    That's not my main reason. The main one is sound and current usage - that still reflects historical usage, but the history is not the point. They are still very different in character from the major-minor intervals. IMO, that is.
    Quote Originally Posted by JlMoriart View Post
    Another disagreement is whether or not the special case of fourths and fifths, being commonly used in only one of two sizes, justifies a differentiation in nomenclature. "Perfect" covers up that the fourth and fifth have *two* diatonic sizes, but "reveals" that they are unique somehow.
    They are commonly used in one of three sizes, that's my (other) point.

    Perfect intervals:

    Augmented = rare (#4 in major scale; #5 in harmonic/melodic minor)
    Perfect = common
    Diminished = rare (b5 in major scale; b4 in harmonic/melodic minor)

    Major/minor intervals:

    Augmented = rare (#2 in harmonic minor)
    Major = common
    Minor = common
    Diminished = rare (bb7 in harmonic minor)

    That's the way I see it.

    Of course, looking at specific intervals, as used in common scales, things are not quite so symmetrical (as I'd suspect you'd point out). So a #4 is more common than a b4; and a b5 is more common than a #5.

    The same logic suggests that 2nds and 7ths are of a different nature to 3rds and 6ths.
    An augmented 2nd does occur, and is quite a familiar sound (in harmonic minor); a bb2 (diminished 2nd, enharmonic with a unison) doesn't occur in any scale ; likewise its inversion, the augmented 7th (enharmonic with an octave).
    Augmented 6ths do occur in classical music (although not in any common scale), but their inversions - diminished 3rds - don't seem to. (There is an augmented 6th and diminished 3rd in the byzantine or double harmonic scale, which is not part of western theory.)

    IOW, 2nds occur mostly in 3 sizes - major, minor and augmented - and 7ths in 3 sizes - major, minor and diminished.
    3rds and 6ths, OTOH, only occur (in practice) in two sizes, major and minor - except for the rare occurrence of the augmented 6th in classical theory (jazz theory ignores it, or calls it a minor 7th) - and the special instance of the byzantine scale mentioned.

    (I realise this argument can support your viewpoint probably as well as mine! The 3 common sizes of 4ths and 5ths are very like the 3 common sizes of 2nds and 7ths.)

    There's an additional observation about perfect intervals (not critical but some people like to cite it as a reason for the name) - when you invert one, it becomes another perfect interval. When you invert a major interval it becomes a minor one, and vice versa.
    That is, of course, only because 4ths and 5ths are the central intervals in an octave. And as I understand your proposal, that would still work with major and minor 4ths and 5ths; a minor 4th, inverted, becomes a major 5th - yes?
    Quote Originally Posted by JlMoriart View Post
    At this basic a level it comes down to personal preference I supposed, so agree to disagree it is
    Agreed. (Unless you want to dispute any of the above of course )
    Last edited by JonR; 11-10-2010 at 06:24 PM.

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