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Identifying Sense of life of Musical Pieces

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tommyedison
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When I listen to Beethoven's 9th Symphony, 2nd Movement, it makes me think about titanic struggles and the victory of a heroic man over them.

However this meaning I primarly get from my feeling or emotional response to the music. But the emotional response to a particular piece of music depends on the sense of life of the piece and the listener.

My question is, how can we objectively identify the sense of life of a musical piece? On what basis?

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Ayn Rand stated in TRM that no objective criteria for the evaluation of music has been discovered as of yet. She did not say that no objective criteria exists, but that such a study would require the joint efforts of an Aesthetician, a Psychologist, and a Phyisiologist, and that this had not been done yet.

To the best of my knowledge, it still hasn't, although I haven't really been on the lookout for one. I will try to find the area of the book where she discusses this so that you can read her analysis.

Edited to add: It was in the article "Art and Cognition," on page 55.

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Ayn Rand stated in TRM that no objective criteria for the evaluation of music has been discovered as of yet. She did not say that no objective criteria exists, but that such a study would require the joint efforts of an Aesthetician, a Psychologist, and a Phyisiologist, and that this had not been done yet.

To the best of my knowledge, it still hasn't, although I haven't really been on the lookout for one. I will try to find the area of the book where she discusses this so that you can read her analysis.

Edited to add: It was in the article "Art and Cognition," on page 55.

I don't have the Romantic Manifesto currently. From your post I interpret that Miss Rand did not develop such an objective criteria.

What differentiates a symphony with a heroic theme from a cheap peace of music written by a Satanist?

The reason I am so interested in this is that if you know the type of music a person listens to, it can essentially render the character of a man naked before you.

One thing I have noticed about the pieces which have passion in them is the above normal use of high pitch notes.

In Beethoven's especially during his "torture and struggle" phase of music, I have noticed rapid crescendos and diminuendos.

Are these valid criteria to find these themes in a piece of music?

What could be the other criteria by which to judge music?

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Let us first isolate the most essential components of music: melodic/thematic content, harmonic content, rhythmic content. There are of course other elements. Some secondary components to consider could include: sectional/structural form, timbre & dynamics.

Melodic/thematic content

From the Merriam-Webster Online Dictionary definition of melody:

1 : a sweet or agreeable succession or arrangement of sounds

2 : a rhythmic succession of single tones organized as an aesthetic whole

The second definition is more narrow & precise. But still not enough. Let's go a bit further. A melody is a succession of musical notes (pure, properly intonated tones) constructed in such a manner as to be perceivable as a self contained unit. A good melody should have these characteristics & in addition should be goal-directed by implying a harmonic context/framework.

It can also be useful to add further qualities in order to refine our definition. A good melody should also have a healthy variety in vertical dimensions (up & down motion, variety of interval steps & leaps) as well as horizontal dimensions (rhythmic values). It can be helpful to have a single high point & or low point but it is not always necessary. Any number of nursery rhymes & childrens tunes are good examples of bare-bones good melodies (i.e.: "Mary Had a Little Lamb", "Twinkle, Twinkle Little Star", "London Bridge is Falling Down", etc.).

They are good examples because they have clear, direct succession of tones, they imply a harmonic progression (even if only one notes at a time is used!) & as a consequence of implying harmonic content, they are goal-directed. There is a healthy variety in various dimensions. For example, they typically have a "question" phrase that ends on a dominant (half-candence) & then an "answer" phrase. This is usually a variation on the first phrase starting similarly but ending on the tonic (full candence). Harmonic implication as a means of providing a goal is essential.

Sometimes a melody is broken down into smaller parts (or phrases or sections) that are altered, variated, used in different manners. These are typically known as themes, motifs, variations, etc. For example, the melody may be fully stated once, then broken down into smaller components. These smaller components are then used in various ways to create variations, developments, new sections, themes, sometimes whole new melodies.

Harmonic content

From the Merriam-Webster Online Dictionary definition of harmony:

2 a : the combination of simultaneous musical notes in a chord

2 b : the structure of music with respect to the composition and progression of chords

2 c : the science of the structure, relation, and progression of chords

These are all very good! However, they do not specify what that structure is & how it relates (i.e. "with respect to"). I did a whole post on Harmony here

http://forum.ObjectivismOnline.com/index.p...indpost&p=64204

For this post I will summarize. The foundations of Tonal Harmonic Theory are based on voice leading & on triadic harmonies built from diatonic scales. I am going to assume the reader has some knowledge of music at this point. Harmonic structure, per se, has a beginning, a middle (some motion) & an end. The goal is the cadence.

The degree to which any piece (or part of a piece) serves to move toward it's goal (or not) is the degree to which it has successfully integrated it's harmonic content with it's other components.

Side note: if a piece or theme does not have a proper cadence, it does not resolve. It is not necessarily "bad" to not resolve or avoid a proper cadence. Sometimes, if done effectively it can add a great deal of tension/suspense (among other possible effects). But the fact remains that if you are going to use tonal tools (scales, chords, etc.) you are by definition using an integrated system of information with a specific nature (i.e. there is a root note, there is a heirarchy of importance among the notes, the cadence is the goal, etc.).

The premise underlying all of harmony is voice leading. Voice leading is regarding all the notes that comprise a chord as one note of a "voice". As you move to the next chord you regard each note as moving to the next corresponding note in that next chord. "Smooth" voice leading is the "goal" of well-constructed music.

Many theorists & composers also regard voice leading as not merely a chordal analysis tool but an essential way of creating independent & yet interweaving melodies. This is very true in Bach (& Beethoven!). For although at any time you can isolate a chord based on all the notes that are sounding at one time, the more important thing is that each voice carries it own melodic thread. So if you have (like Bach did in many of his classic 4 part chorales) a piece that all the way through uses four note chords it is constructed in a way that if you follow say the top note of every chord ("the top voice") you will find a complete melody; & likewise for the other 3 voices.

There has been a great deal of nonsense spread about "the rules of music" (usually in regards to counterpoint & harmony in general) being "arbitrary human conventions". Then, there is a long list of composers that "broke/bent/ignore/re-wrote the rules". It does not help that some of the very specific classical rules of counterpoint voice leading are not essential to the nature of tonality. These exceptions are frequently held up as examples of why throwing out all the rules is a good idea. Most of the rules exist for a reason; some of them exist for very good reasons; some are non-essential. I can get into this in depth later if someone is interested.

Rhythmic content

Musically, Rhythm answers the question "When?" On a small scale, it deals with the length of the melody notes relative to each other (& ultimately to all the other notes in the piece). On a larger scale it encompasses the tempo(s) & meter(s) of a piece. A healthy variety of rhythmic material is usually desirable, as in other components. The specific characteristics of any given meter should be integrated (i.e. work with & not against) the other components (melody, harmony). The tempo should be within a suitable range of human cognition. I know that last sentence seems a bit Over Obvious. Unfortunately, it does need to be said. There are pieces (mostly computer-rendered) that go so fast the human ear & mind literally cannot comprehend what is happening. On the other end of the spectrum (but the same counterfeit coin) there are pieces that are written such that one note is supposed to be played every 50 years. "Modernists" are always up to something irrational.

There has been a great deal written in musical history texts about musical rhythm & dance. There is probably a lot of interesting info from which to learn if it was approached in an objective manner. I don't know much about it from that angle though. I know Rand had interesting things to say in The Romantic Manifesto. Perhaps someone on the forum can contribute.

Sectional/structural form

This relates to the manner in which all the sections (or melodies if more than one) are structured in what particular order. Again, the purpose is to create a satisfyingly integrated whole. For example, in classical music, the "gold-standard" of structural form was Sonata-Allegro. In the widest sense this consisted of an Exposition (statement of themes 1 & 2, or more), Development (variation on themes), Recapitulation (restatement of themes 1 & 2, more). The form was highly plastic, though, allowing many different possibilities for variation & alteration. There were other forms: Rondo, Minuet & Trio, etc. Larger forms were the symphony, the concerto, etc.

There are some modern day musicians who claim to "hate the rules" of all that "stuffy classical" music. First, it is ironic; think about any standard pop song's structure: verse & chorus, optional bridge/solo, repeat verse & chorus. This (on a much smaller scale) exactly mimics sonata-allegro form. Aren't they a rebellous lot? Next, the richness in integrated components (themes, harmonies, rhythms, etc.) of the simplest Haydn piano sonata (for example) is well beyond anything any pop song has ever achieved. Don't get me wrong here. There is some pop music which I think has great value; there is some pop music I personally enjoy. I am not saying it is all useless or evil. By it's nature, I think it has to be more brief & to the point (i.e. use less musical tools & info available to a composer). Finally, consider the vast majority of what exists as pop songs. How much variety in form & structure has been achieved in that genre compared to classical with it's "overbearing & striaght-jacketing rules"? Please, stop, it hurts.

Anyway, there's more structural form variation & integration in ONE Beethoven sonata than in the last 50 years of pop music.

Timbre

Timbre (pronouced "tam-ber") is characteristics of the sounds employed by a piece. For example an oboe has a woody, nasal tone, a violin can have a lyrical, flowing, singing tone (or a hoarse, scratchy tone). The composer's intentions are carried out in this regard by which instrument(s) he of she specifies to play the notes of the piece.

This is a very important issue in ensemble playing. Especially when scoring for orchestral resources.

As usual, the timbres involved in the piece should be (everyone say it together!) integrated with the other components of the piece. So, a delicate melody should be played by an instrument capable of expressing the proper context. A theme (or harmony) of "noble" quality might be best represented by brass (particularly a french horn). The electric guitar is a very interesting case (one that especially fascinates me, I am primarily a guitarist & grew up playing electric guitar). It has the ability to "sing" expressively like a violin, the ability to sound glass-like transparent with a clear ringing bell-tone like a harp. It also has the ability to sound incredibly ugly & noisy like an industrial machine that is disintegrating.

Side note: Timbre & scoring is one aspect of Beethoven that really gets me. Often it is pointed out that Beethoven was "deaf, but still wrote great music". Well, that's true & must have been hard for him to deal with emotionally. But, having said that, I can write music all day long without hearing a note of it, & I know how it will sound. Any decent musician can do this. What I consider amazing is how, years after having gone deaf, he could still imagine, conceptualize & project how to orchestrate. It is easy enough to write down on paper a C major chord. What gets difficult is: which note of the chord do you assign to which instrument to get the proper effect? Without being able to actually hear the possible combinations? Beethoven wrote his last 3 symphonies under those conditions (among other works, like the C-sharp minor quartet). That is mind-boggling!

Dynamics

Dynamics relate to issues such as volume, attack, decay, etc. One more time, (all together!) the dynamics involved in the piece should be integrated with the other

components of the piece. This includes elements such as crescendos and diminuendos, as mentioned by tommyedison.

These are what I would consider to be valid criteria by which to objectively identify the characteristics of a piece of music. I am, of course, only a musician/composer. I can offer suggestions & ideas as to how these musical elements are perceived & processed by a human mind. But, ultimately, we may need more specialized help (are there a psychologist & a physiologist in the house?). There are a number of decent texts & sources on the physics of sound & human hearing out there. I have read about 10 such books on this topic. I did read Helmholtz's "On the Sensation of Tone as a Physiological Basis for a Theory of Music" years ago. I may have to find another copy of it & re-read. There are a number of decent websites that summarize & reference it.

Now that we have established some foundation premises about the components of music, perhaps we can use them to delve into why/how/where any specific piece (or one/some of it's components) has a good or bad sense of life.

Christopher Schlegel

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Thank you for the detailed reply

I think we should take this bit by bit.

Melodic/thematic content

A melody is a succession of musical notes (pure, properly intonated tones) constructed in such a manner as to be perceivable as a self contained unit. A good melody should have these characteristics & in addition should be goal-directed by implying a harmonic context/framework.

It can also be useful to add further qualities in order to refine our definition.  A good melody should also have a healthy variety in vertical dimensions (up & down motion, variety of interval steps & leaps) as well as horizontal dimensions (rhythmic values).  It can be helpful to have a single high point & or low point but it is not always necessary.

If I am understanding you correctly, you mean to say that the melody should be such that a self-contained complete story can be written on it - on its theme.

But here is where one runs into trouble. How does one objectively define a self-contained melody?

What are its essential components?

You have mentioned quite a few qualities like the vertical and horizontal dimensions of the melody. But they can all be present and still the melody can be a bad one it they are not properly arranged.

How does one define a "healthy" variety of vertical and horizontal dimensions.

On what are these qualities based?

Any number of nursery rhymes & childrens tunes are good examples of bare-bones good melodies (i.e.: "Mary Had a Little Lamb", "Twinkle, Twinkle Little Star", "London Bridge is Falling Down", etc.).

They are good examples because they have clear, direct succession of tones, they imply a harmonic progression (even if only one notes at a time is used!) & as a consequence of implying harmonic content, they are goal-directed. There is a healthy variety in various dimensions. For example, they typically have a "question" phrase that ends on a dominant (half-candence) & then an "answer" phrase. This is usually a variation on the first phrase starting similarly but ending on the tonic (full candence). Harmonic implication as a means of providing a goal is essential.

From what I am understanding, you are saying that a typical music has the "question" phrase ending on the dominant and the "answer" phrase on the tonic.

Are there any other ways of doing such phrases?

Considering Objectivism

Since pain-pleasure mechanism is fundamental to philosophy of Objectivism, what type of phrases or notes can we associate with pain (i.e. something which is demoting your life) and pleasure (something promoting your life).

Should we associate low pitch notes/phrases solely with pain or can low pitch notes/phrases also express happiness?

P.S. I am not a musician so please excuse my lack of ignorance on this subject :huh:

Edited by tommyedison
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Thank you for the detailed reply.

I think we should take this bit by bit.

You're welcome. I should thank you; I've been meaning to start a thread aimed precisely at this topic. I just wanted to lay down a basic outline/framework from which to precede. So, taking this "bit by bit" is an excellent idea & exactly what I intend to do.

How does one objectively define a self-contained melody?

What are its essential components?

How does one define a "healthy" variety of vertical and horizontal dimensions.

On what are these qualities based?

Are there any other ways of doing such phrases?

Should we associate low pitch notes/phrases solely with pain or can low pitch notes/phrases also express happiness?

Wow. Those are great questions & ones I wish to discuss.

I am not a musician so please excuse my lack of ignorance on this subject

There is nothing to excuse! Since I have already interacted with you on music I look forward to breaking this down and thoroughly discussing it. You seem like an intelligent person, so there should be no problems...& you already like Beethoven!

I intend to put together several musical examples to which we can refer in the course of this discussion. It will take a couple of days for me to get enough free time to pull everything together the way I want to make it effective.

Talk soon.

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I have a comment on the issue of tempo. Is there a tendency for us to perceive faster tempos as lively/happy/spirited (e.g. the last movement of St.Saens' 5th Piano Concerto), and slower tempos as unjoyous? I think so.

But listen to Sibelius's late work for strings, Andante Festivo --"slow and festive" (!) A good illustration of how a great composer at the height of his powers can achieve the seemingly impossible.

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There is nothing to excuse!  Since I have already interacted with you on music I look forward to breaking this down and thoroughly discussing it.  You seem like an intelligent person, so there should be no problems...& you already like Beethoven!

Thank you for the compliments. I look forward too to this discussion.

I have a comment on the issue of tempo. Is there a tendency for us to perceive faster tempos as lively/happy/spirited (e.g. the last movement of St.Saens' 5th Piano Concerto), and slower tempos as unjoyous? I think so.

I think the key issue here is what do fast and slow tempos convey to us.

IMO, A fast tempo does convey that the piece is lively as you have pointed out - a sense of increased action as the notes and phrases (actions) are in a quicker succession.

For e.g. I don't think Beethoven's Ode to Joy would have been as effective in conveying its meaning if it had had a slower tempo particularly in the 11th - 15th minutes.

It wouldn't have been as forceful and it would have given the impression of a man totally content with his life calmly retrospecting.

But listen to Sibelius's late work for strings, Andante Festivo --"slow and festive" (!) A good illustration of how a great composer at the height of his powers can achieve the seemingly impossible.

I haven't to the Adante Festivo so I can't comment on that. However based on your description it is festive i.e. joyous. However I don't see how lively equates to festive.

At any rate I haven't listened to it so whatever I say about it wouldn't hold much water anyway.

Edited by tommyedison
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Rhythmic content

Musically, Rhythm answers the question "When?"  On a small scale, it deals with the length of the melody notes relative to each other (& ultimately to all the other notes in the piece).  On a larger scale it encompasses the tempo(s) & meter(s) of a piece.  A healthy variety of rhythmic material is usually desirable, as in other components.  The specific characteristics of any given meter should be integrated (i.e. work with & not against) the other components (melody, harmony).  The tempo should be within a suitable range of human cognition.  I know that last sentence seems a bit Over Obvious.  Unfortunately, it does need to be said.  There are pieces (mostly computer-rendered) that go so fast the human ear & mind literally cannot comprehend what is happening.  On the other end of the spectrum (but the same counterfeit coin) there are pieces that are written such that one note is supposed to be played every 50 years.  "Modernists" are always up to something irrational.

There has been a great deal written in musical history texts about musical rhythm & dance.  There is probably a lot of interesting info from which to learn if it was approached in an objective manner.  I don't know much about it from that angle though.  I know Rand had interesting things to say in The Romantic Manifesto.  Perhaps someone on the forum can contribute.

Christopher Schlegel

I've been curious about the tempo issue for a while. What do you think is an unsuitable tempo? And do you believe it is possible to increase the ability of the mind to handle faster music?

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In reading this thread I recalled a writer who may interest you. His name is George Lansing Raymond. He wrote several books on aesthetics, one titled, I think, "Music as a Representative Art (late 1800's). I have his "Poetry as a Representative Art" Here are two excerpts which may stir your interest, for, although concerned with speech, one can see a connection with music.

In discussing duration he says, "in the degree in which utterances are instinctive (spontaneous ejaculations) they find expression in short duration, or----what is the same thing----in fast time. But when one becomes conscious of surrounding influences to which he must conform his phraseology, these put him into a reflective mood, and under the sway of his impressions, he stops to think of what he has to say, and so uses slow time; or, to look at the subject from a different point of view, a speaker, when not desirous of conveying to others the impression that what he is saying demands their serious attention, may talk rapidly. But when he wishes to convey the opposite impression, he talks slowly. Thus, duration assigns a mental weight or measure to ideas".

In regard to pitch he says, "pitch represents the mental movements, or that which underlies them----the mental motives or aims. When a man is light-hearted, when there is nothing to weigh him down, he generally speaks with a lighter or higher pitch, but if he does feel weighted down, or when regarding serious, grave and dignified matters, he uses low pitch."

Mr. Raymond goes on, dealing thoroughly with loudness, softness, simplicity, complexity, the speed of rhythms, etc., and how these are used to represent the feelings behind expressed ideas. If his book on music is as thorough, it may be stimulating to your investigations at the least. He also quotes Aristotle and Max Muller favorably.

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The defintion of melody I outlined was fairly wide in one sense. It allows for a great deal of leeway in the virtually limitless ways in which concrete elements

(which notes, rhythms, etc.) can be applied in creating a melody. In some ways, the qualification of "perceivable as a self-contained entity" is dependent upon the ability of any given individual to identify it as such on their own. It is very elastic but not infintely so. The parameters would have to be limited by the epistemological limit of the human mind. Thus we may need more specialized help in defining that aspect.

By saying "healthy variety", I mean at a minimum it should have some variety. It should not have only one note, or only step wise motion, or only skip motion. It should not have only one rhythmic element; it should have at least two different rhythmic values present. Again, there must be a limit to amount of variety. Too much would make it disintegrate into unintelligability. I don't know where that limit is, a serious philosopher working with a physiologist might be able to idenfity this.

The central (in my estimation) & thus most important characteristic of a melody would have to be that it implies harmonic motion & as a consequence is goal-directed. The easiest (most direct) way to accomplish this is in the form of the "question/answer phrases". This is where I suggest the use of half-cadence & full candence. A melody does not necessarily have to contain these explicitly; they can be implied. In many of Beethoven's pieces, for example, he presents half-cadence after half-cadence moving from key to key. Thus, he prolongs the resolution only finally providing a full candence at the end of the piece. The point is that there should be at minimum at least two chords. Implying the tonic & the dominant chords is the most direct manner of implying motion.

Since can be difficult to discuss without reference to actual music I have compiled several examples.

Consider the first part of Beethoven's "Ode to Joy" theme as a complete unit:

http://www.truthagainsttheworld.com/MusicTheory/odetojoy.mid

Now let's remove all variation of rhythm making all the notes of the same rhythmic value:

http://www.truthagainsttheworld.com/MusicT...joynorhythm.mid

Notice that melodically it still contains harmonic goal-directed motion. But making all the half notes quarter notes results in a kind of loopy effect & makes it less effective. It is still a melody but variation of rhythm enhances one's ability to perceive it as a "unit" that starts, goes somewhere & definitively ends. Without rhythmic variation it is not only monotonous but actually more difficult to "hear" the melody. I have read some things that suggest the evolution of melody is in some ways a result of mimicing speech patterns. Perhaps the book mentioned could help clarify this. If we have a linguist on the forum they may be able to help futher with this line of inquiry.

Next let's remove the goal directed component harmony. In it's bare-bones presentation there are only two chords referenced in the melody - the tonic (the "one" chord being a chord built on the first note of the key/scale) & the dominant (the "five" chord being built on the fifth). Beethoven actually uses more chords than this in harmonizing the melody, but this is a simplified version for easier analysis. What you will hear in the next example is the only the notes of the melody that are part of the tonic chord; if a note was part of the dominant chord I did not include it. By doing this it is possible to hear what I mean about goal-directed motion being provided by harmonic changes & motion. No harmonic variety equals no goal-directed motion.

http://www.truthagainsttheworld.com/MusicT...oynoharmony.mid

It possible for your mind to "insert" (imagine) the necessary harmonic background though even when listening to this example. So, to go a step further, this example simply bangs away on the tonic chord under the melody making it harder to imagine harmonic motion:

http://www.truthagainsttheworld.com/MusicT...armonyatall.mid

Notice this could conceivably be the beginning statement of a melody that then went to another chord. Also, notice this could be considered a "theme" of sorts. It could be a melodic fragment that will be used in various ways throughout a larger composition. On it's own, even though it is pleasant, it doesn't really do much or "go anywhere".

Also consider the idea of the half cadence/full cadence. First the melody with only half cadences:

http://www.truthagainsttheworld.com/MusicT...cadenceonly.mid

Notice that is sounds as if stuck in a loop, endlessly open with no definite end.

Now with only full cadences:

http://www.truthagainsttheworld.com/MusicT...cadenceonly.mid

Notice it definitely ends. But without the half cadence first the ending is not fully prepared (or "set up"). It sounds like a melody on it's own but this is due to the fact that there is some harmonic motion going on in the phrase to begin with.

The important point here is that certain notes of scale/key imply certain chords. Implying the right note (at the right time) is crucial in giving the melody a sense of direction. Obviously, by "right note" I do not mean there is only one option or choice available at any given time. Sometimes the choices are virtually limitless; other times, though, they are. It depends what the composer wants to accomplish. An extreme example would be at the end of a piece; if you want to end a piece definitively your only melodic option is the root note.

On the subject of tempo I have the melody played very fast:

http://www.truthagainsttheworld.com/MusicT...ojoytoofast.mid

Since you know it is supposed to be the "Ode to Joy" you might actually be able to identify it after a few listens. So let's make it absurd:

http://www.truthagainsttheworld.com/MusicT...ywaytoofast.mid

I am not aware of any pieces that move faster than eighth notes at 300 beats per minute (bpm) that are discernable. Most of the faster pieces I have ever heard top out at around 250 bpm. The absurd example is 32nd note triplets at 250bpm. This works out to about 50 notes per second. I can play about 20 notes per second in a linear pattern & about 40 notes per second in arpeggiated patterns (sweeping technique!). But if the info is not relatively simple it gets hard to identify. If I am just repeating a single scale or chord it's easy. If it's more complex harmonically it's harder to discern. For example, listen to any of Coltrane's "sheets of sound" solos, Alan Holdworth or Shawn Lane guitar solos.

What I have tried to show here is that many different elements are responsible for a melody qua melody; not just one. In my estimation the goal-directed harmonic implication of any given musical line is the most important, but even this is still dependent upon the other elements to give a melody substance.

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Should we associate low pitch notes/phrases solely with pain or can low pitch notes/phrases also express happiness?

I don't think it's that simple.

For example, the first time Beethoven presents the "Ode to Joy" theme in the finale of the 9th it is by the cellos - very quietly & very low in pitch.

Alternately, consider the infamous "Psycho" shower scene violins. They are extremely high-pitched but not suggesting pleasure or happiness at all.

I think the characteristics of the scale being used (implicitly or explicitly) are more indicative of pleasure/pain. Major scales (& modes) are generally more pleasurable/happy versus minor scales (& modes) are more painful/sad.

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I have a comment on the issue of tempo.  Is there a tendency for us to perceive faster tempos as lively/happy/spirited (e.g. the last movement of St.Saens' 5th Piano Concerto), and slower tempos as unjoyous?  I think so.

But listen to Sibelius's late work for strings, Andante Festivo --"slow and festive" (!)  A good illustration of how a great composer at the height of his powers can achieve the seemingly impossible.

That is a lovely piece. Sibelius's orchestration skills are frequently breathtaking & this is no exception.

I don't think slower tempos are necessarily unjoyous. Obviously it is one way to imply a sad/mournful mood. But it would have to accompanied by a minor scale/mood in order to be effective. A slow tempo with a major scale/mood might suggest seriousness or solemnness, but in a "happy way". I think this piece is more in that category.

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I've been curious about the tempo issue for a while.  What do you think is an unsuitable tempo?  And do you believe it is possible to increase the ability of the mind to handle faster music?

I do think it is possible to increase that ability to a degree. But there has to be an upper limit. In my post earlier today I addressed what I think of as upper limits.

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In reading this thread I recalled a writer who may interest you.  His name is George Lansing Raymond.  He wrote several books on aesthetics, one titled, I think, "Music as a Representative Art (late 1800's)".

Great! Thanks for the heads up.

    In discussing duration he says, "in the degree in which utterances are instinctive (spontaneous ejaculations) they find expression in short duration...

    In regard to pitch he says, "pitch represents the mental movements, or that which underlies them----the mental motives or aims...

This is an excellent source of potential help aimed right at what I do not yet know. Thanks.

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I want to address the characteristics of various scales & modes. These can be the determining factoring in the emotional quality of a melody.

The characteristics of any given scale is determined by the intervals between the notes of the scale. The primary scales (major & natural minor) as well as the natural modes are a result of various mixtures of 5 whole step & 2 half step.

The major scale is identified by this formula:

1 - whole step - 2 - whole step - 3 - half step - 4 - whole step - 5 - whole step - 6 - whole step - 7 - half step - 1

In the scale (or key) C major this results in all white keys on the piano; or only the letters of the musical alphabet:

c-d-e-f-g-a-b-c

It sounds like this:

http://www.truthagainsttheworld.com/MusicT...cmajorscale.mid

The major scale is identified by this formula:

1 - whole step - 2 - half step - 3 - whole step - 4 - whole step - 5 - half step - 6 - whole step - 7 - whole step - 1

In the scale (or key) C minor this results in a mixture of white & black keys on the piano.

c-d-e flat-f-g-a flat-b flat-c

It sounds like this:

http://www.truthagainsttheworld.com/MusicT...cminorscale.mid

Minor is actually a derivitive scale of major. It is achieved by starting on the 6th note of the major scale. For example if you start in C major:

c-d-e-f-g-a-b-c

Then regard it's 6th note (a) as the first note of a scle (actually it's 6th "mode"), you will get the A Minor scale:

a-b-c-d-e-f-g-a

Modes are a means of achiveing a different scale formula by giving each note of the major scale a chance to be regarded as the beginning note:

Major is also called Ionian: c-d-e-f-g-a-b-c

2nd mode is Dorian: d-e-f-g-a-b-c-d

3rd mode is Phyrgian: e-f-g-a-b-c-d-e

4th mode is Lydian: f-g-a-b-c-d-e-f

5th mode is Mixolydian: g-a-b-c-d-e-f-g

6th mode is Aeolian: a-b-c-d-e-f-g-a (also, the "relative" minor; as in relative to major)

7th mode is Locrian: b-c-d-e-f-g-a-b

Thus each mode has it's own unique sound because the whole steps & half steps are shifted.

The reason Helmholtz (& others going back to the Greeks that correctly identified these intervals) regarded the major as the most stable scale formation is due to acoustical properties (i.e. the physics of sound & the physiology of the ear). In between two octaves (a C note & the next highest C note) the ratio in wave frequency is always 2 to 1 (2:1). Thus if a given C is identified by being a periodic wave at 526 Hertz; the next highest C is exactly double this at 1052 Hz. It is always 2:1 because this corresponds to human hearing physiology. The curvature of the cochlea (the snail shell shaped part of the inner ear) is the reason humans can identify two pitches at a ratio of 2:1 as a strong unison sound and thus called the octave and furthermore the reason that both pitches have the same letter name in scales. This is a crucial fact in the intervallic structure of music. If the cochlea was a straight tube we couldn’t identify the octave as a unison sound and the musical alphabet would have to be organized differently (possibly with no repetition of letters).

In order to get the degrees of the scale to "fill out the octave" the Greeks relied on basic ratios. After the 2:1 ratio of the octave, we cut it in half (split the octave in half) by a ratio of 1.5:1. This results in the fifth. Next is 1.25:1, which results in the major third, etc. This occurs because of the logarithmic nature of the major scale on a frequency scale. Human hearing is of course also very logarithmic in structure. Remember that the cochlea is not only curved but also a pattern of circular diminishing tubular shape (thus the snail shell analogy). The placement of the little hairs (cilia) on the tube walls is crucial because sound waves move these little objects and this movement is what triggers the nervous tissue that gets translated into electrically impulses that the brain identifies as “hearing sounds”. The overtone series is also logarithmic in nature with wider intervals at the bottom and with the intervals becoming progressively smaller as the pitches climb higher.

The Greek system with it's ratios was called Just Intonation. It was found to be limited it that one could not transpose from one key to the next. Those familar with the history of equal temperament tuning already know this story. The point is that even though the ratio theory had to be "fine tuned" it is still the basis for our tonal musical systems. Also, in equal temperament the ratios that still maintain the closest relationship to basic ratios the Greeks identified is of course the octave, fifth & third.

One of the basic applications of frequency ratio analysis of intervals is verification of the fact that the more consonant or “solid” sounding ratios are the lowest numerically or simplest. For example as ratios between notes in a melody & chord progressions get more complex, dissonance tension is built. As the ratios fall in complexity back to the more stable sounding consonant, simpler ratios tension is released into more consonant sounds.

As as example, this is "Ode to Joy" in major with basic chords:

http://www.truthagainsttheworld.com/MusicT...ojoyinmajor.mid

Since the melody only contains the first through fifth notes of the scale the only note we have to alter is the third if we want to change the meldoy from major to minor. But what a difference that one note makes:

http://www.truthagainsttheworld.com/MusicT...ojoyinminor.mid

Hopefully by listening to these examples one can clearly hear the difference between the "joyful" effect the major scale creates & the "sorrowful" effect the minor scale creates.

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So, according to you, generally, minor scales are more "dim" while major ones are more "bright".

I would like to post my analysis of the Beethoven's 9th Symphony 2nd Movement First Part.

IMO, Beethoven starts with a declaration of some sort either as a declaration of rebellion or an expression of a turbulent state of affairs. He then continues on a dim but rising note to denote the torture and that it is increasing; not going too fast to emphasize the torture phase nor too slow to not make the piece lose its "energy", its strength. Then he switches to a strong high pitch perhaps as a declaration of rebellion.

Am I going in the right direction?

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The easiest (most direct) way to accomplish this is in the form of the "question/answer phrases". This is where I suggest the use of half-cadence & full candence. A melody does not necessarily have to contain these explicitly; they can be implied.

I take it then that generally Half-cadence suggests a question and full-cadence an answer. Do you know any exceptions to this?

Since each half cadence represents a change in frequency by 2 raised to root 12, this would mean that human ear regards a frequency change by 2 raised to 12 times a question and a frequency change of 2 raised to 6 times an answer as a rule.

link

So, Does the human ear automatically regard a certain frequency as a black note or is it because we are so used to hearing C at 435~440 Hz that we automatically assign a white note to it?

I think this is a crucial question because the answer would establish whether only the change in frequency is regarded as meaningful or the frequencies which we hear themselves have a meaning to them. I am inclined towards the former view.

If the former view is correct it means that the black notes and the minor scale give a grave picture only because it is a 12root2 change from the white notes. And this would lead to the conclusion that a 12root2 change represents uncertainty/graveness and a 6root2 change represents a finality.

Wouldn't this mean that if the conclusion of the piece is at a black/grave note, then the piece has a malevolent/uncertain sense of life?

And if this is correct, then would it lead to the conclusion that minor scales having an excess of grave notes allow much less scope for making a happy piece?

Edited by tommyedison
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So, according to you, generally, minor scales are more "dim" while major ones are more "bright".

In a way, yes. If you play a WHOLE scale you will hear "happy" from major & "sad" from minor. Of course it gets more detailed than that because any given melody does not necessarily use all the notes from a scale; some melodies use notes from each scale. But, depending upon which scale a melody (or part of a melody) is BASED will result in this effect.

Just as importantly, the harmonies (resultant chords) formed/implied by the use of various scales give a more complete picture.

Major chords are more consonant (lower ratios=pleasant) & minor chords more dissonant (higher ratios=unpleasant). Unisons (octaves, C to next higher C) are the most consonant interval (1:2), the fifth (C to G) is the next (1:1.5), the MAJOR (C to E) third next (1:1.25). The MINOR third (C to E flat) is (5:6). So the notes of a MAJOR chord (C-E-G) form a combined ratio of (4:5:6) & a MINOR chord (5:6:7). Dominant 7 chords, diminished chords, & contain a lot of dissonance, so they are typically used to build tension toward the end of a phrase. Then comes a major chord (or even minor) to release the tension because they are more consonant (or conversely, less dissonant).

Here's a way of symbolizing it:

1. consonance-solid sound

2. less consonance-less solid sounding

3. dissonant sound-tension builds

4. more dissonant-MORE tension

5. consonance returns-tension released

I take it then that generally Half-cadence suggests a question and full-cadence an answer. Do you know any exceptions to this?

When HC & FC are used their function is to provide the Q&A phrasing. One w/o the other is also widely used. For example, some melodies are based on modes & therefore do not necessarily contain "traditional" cadences. But there can still be a sense of direction to the melody. When a five chord happens without resolving to a one chord it is not necessarily "bad"; it can provide tension that is not resolved.

Since each half cadence represents a change in frequency by 2 raised to root 12, this would mean that human ear regards a frequency change by 2 raised to 12 times a question and a frequency change of 2 raised to 6 times an answer as a rule.

I think you are confusing half-cadence with half-step & full-cadence with whole-step. Half- & whole-steps are interval distances between notes. Cadences are musical chord sequences (involving at least two voices) moving to a harmonic close or point of rest, thereby providing a sense of harmonic direction or completion. The ratio between the frequencies of any two notes a half step apart is 1.05946309436. Using the musical alphabet, if C is 435Hz then:

435 times 12th root of 2 (1.05946309436) = approx. 460Hz (or the note C sharp)

HC is ending a phrase on the five chord (using scale notes 5, 7, 2) (& 4 if it is a full dominant 7 chord) meaning that the melody notes should be one of those scale notes. FC is ending a phrase on the one chord (using scale notes 1, 3, 5) meaning that the melody should be one of those scale notes.

This site is good at describing/playing cadences:

http://www.music.vt.edu/musicdictionary/ap...ce/cadence.html

So, Does the human ear automatically regard a certain frequency as a black note or is it because we are so used to hearing C at 435~440 Hz that we automatically assign a white note to it? I think this is a crucial question because the answer would establish whether only the change in frequency is regarded as meaningful or the frequencies which we hear themselves have a meaning to them. I am inclined towards the former view.

"Black & white notes" are merely results of the way a standard piano is layed out. The ear/mind does not care if a black key or white is played. What matters are the intervals between the notes (sequentially in a melody, concurrently in a harmony)regardless of whether or not they are accidentals (sharps, flats, black keys). The "change in frequency" is definitely where the meaning comes in (along with how consonant versus dissonant, dynamic level, timbre, etc.).

If the former view is correct it means that the black notes and the minor scale give a grave picture only because it is a 12root2 change from the white notes. And this would lead to the conclusion that a 12root2 change represents uncertainty/graveness and a 6root2 change represents a finality.

Again, I think you are confusing half-cadence with half-step & full-cadence with whole-step. The 12th root of 2 is a half-step interval & the 6th root of 2 is a whole-step interval. But both scales have EQUAL amounts of half-step & whole-step intervals. The crucial difference is WHERE in the scale they occur.

Listen to the scales again & keep these formulas in mind (WS=whole step, HS=half step):

Major scale formula:

1 - WS - 2 - WS - 3 - HS - 4 - WS - 5 - WS - 6 - WS - 7 - HS - 1

Minor scale formula:

1 - WS - 2 - HS - 3 - WS - 4 - WS - 5 - HS - 6 - WS - 7 - WS - 1

Major has a WS between scale degrees 2 & 3; minor has a HS. This is part of the reason they are perceived respectively as happy/sad, pleasure/pain.

Wouldn't this mean that if the conclusion of the piece is at a black/grave note, then the piece has a malevolent/uncertain sense of life?

In some cases that might be possible, but I don't think it is that simple. I think it has more to do with how well (or not) all of the elements are integrated. To use an extreme example, a piece that had ONLY dissonant intervals (melodically & harmonically) would more likely have a malevolent sense of life. It would also help in classifying it this way if it had screetching timbres, too!

And if this is correct, then would it lead to the conclusion that minor scales having an excess of grave notes allow much less scope for making a happy piece?

The intervals in the scale & their resultant harmonies definitely make minor sadder sounding than major.

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  • 1 year later...

Hello All,

Very interesting thread. My regards to Christopher for providing such detailed and well-organized information. Chris, I very much appreciate your approach to defining music. I will need to study what you wrote in more depth and listen to all the music samples you provided.

In the realm of visual arts, I note a difference between true "art" and "design." All art exhibits elements of design, but not everything exhibiting design is art. I can enjoy some forms of non-representational "modern" art as interesting design, but I do not consider it art. I'm thinking of approaching music in the same way, differentiating music from sound design. I enjoy some techno and rap (particularly for dancing), but I think of it more as sound design than music.

I'll respond futher when I've had time to listen to the music samples.

--Dan Edge

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Hello All,

Very interesting thread. My regards to Christopher for providing such detailed and well-organized information. Chris, I very much appreciate your approach to defining music. I will need to study what you wrote in more depth and listen to all the music samples you provided.

In the realm of visual arts, I note a difference between true "art" and "design." All art exhibits elements of design, but not everything exhibiting design is art. I can enjoy some forms of non-representational "modern" art as interesting design, but I do not consider it art. I'm thinking of approaching music in the same way, differentiating music from sound design. I enjoy some techno and rap (particularly for dancing), but I think of it more as sound design than music.

I'll respond futher when I've had time to listen to the music samples.

--Dan Edge

In the same way that cubism or impressionism are in most cases "bad art," inasmuch as they do represent reality, but not in the way reality is actually percieved, I think there is music (some techno and rap, but not necessarily all, and many if not all other genres contain some examples) that would fall in the category of "bad music," if it is periodic (ie, contains what is percieved as melodic, harmonic, and/or rhythmical elements), yet in such a way that it tends toward either sensory-deprivating monotony or unintegratable randomness.

There is also some noise which is compiled by "musicians" or engineers which I think could be described as "sound design," as you say.

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  • 2 weeks later...
Here's a way of symbolizing it:

1. consonance-solid sound

2. less consonance-less solid sounding

3. dissonant sound-tension builds

4. more dissonant-MORE tension

5. consonance returns-tension released

Christopher,

This might muddy the water a bit, but I'd like to bring up a couple things. (Now, it's been a few years since I've really been in theory, so my memory might be faulty). When we're dealing with the Major and Minor scales the two notes we're really focusing on are the third (in the major - two whole steps up from the root, in the minor - 1.5 whole steps up from the root) and the seventh (Major - a half step below the root, minor - whole step below). I was taught in class, that it's that nice little half step to the Octave that gives you that happy feel (resolution). Which is why we start getting fuzzy when we deal with the Harmonic and melodic minor.

For reference (since I didn't see it before)

Major Scale - C-D-E-F-G-A-B

Natural Minor- A-B-C-D-E-F-G

Harmonic Minor (raised seventh to emulate a Major ending) - A-B-C-D-E-F-G#

Melodic Minor (Raised sixth AND seventh for a full Major ending, though play Natural minor when descending) A-B-C-D-E-F#-G#

Some of these "confuse" the cadence by making the IV (Melodic) and V(Harmonic and Melodic) chord MAJOR within a minor scale (which they aren't in the Natural scale). This affects the motion that a melody would have (going minor to major, instead of minor to minor), and certainly the emotional drop (i.e. a larger "emotional" drop from Major to minor, in the resolution, than a minor to minor).

Do we simply percieve these as modes?

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