all about the intervals

[Ogg Vorbis]

Now this is awesome, but I'll have to get back later because I'm too busy- I make my living making what might not incorrectly be called anti-Rameau music, as well as promoting music of "otherness", and right now I've got kind of a legal battle with government mafia (no I won't make my musicians give money to Madonna to play their own damn author's music in public , thanks). So, back ASAP.

Dang! Good luck. I look forward to yakin' it up more with you whenever you are able to un-bury.

[Ogg Vorbis]

This thread got me thinking...

If I were a theorist (which I am not) I might create a system of musical thought which does not take such pains to differentiate between vertical and horizontal intervals or events.

The reason is because intervals between voices act and function exactly the same as intervals between points in the same voice (melodic).

The interval of the perfect fifth from the root note of the scale serves the same function (of re-enforcing the tonality) whether it is a harmonic or a melodic interval.

The interval of an augmented fourth also functions the same regardless of it occuring simultaneously or melodically. In either case, the interval's dissonant stress will give it the same tendencies of resolution, if the context is suitably comparable.

Try this by playing a bit in the key of D Minor. Then just play the notes G and C#, first one after the other and then simultaneously. In the context of D minor, EITHER the simultaneous or the melodic version would have the same quality. Either one would have the exact same tendency to resolve in the same way.

Therefore the function of the interval is identical. And if that's true, then why (other than rhythmic considerations) would we so insist to differentiate between melody and harmony?

What property or properties of the tonal language is illuminated by this distinction?

In the beginning of the slow movement of Beethoven's "Moonlight" sonata for example, the three-note arpeggiation of G# C# and E function to establish the tonal center of C# minor, just as if the notes were played simultaneously. The presence of RHYTHM segments the notes to unfold horizontally, but the intevals have the same function (that to establish C#m-ness) as they would if they were hammered out as "chords."

Some might say that the horizontal "implies" the vertical. That's like saying that flatness implies roundness. Why would this be the case? What is it about roundness that is more fundamental than flatness?

Similarly, why would harmony be more fundamental as to be able to be "implied" by the melodic?

But it also pre-supposes the existance of triads as a distinct atomic building block of music. In order for something with three notes to be implied by two notes, a three-note unit must have some magical preeminance.

But if triads were a magical and preeminant building block of music, then what is the theoretical basis for their being so? Some might say, "Well triads are simply self-evident as atomic structures in music. Two notes can imply a triad, depending on context. Two notes have 'hopes' in fooling your ear into believing that they are actually three."

I would argue that two notes function as two notes. If they have some special ability to re-enforce or establish tonality, it's because they are relatively consonant, not because they are "2/3's of a triad."

C and Eb might re-enforce Cm or Ab major (or it might be used deliberately ambiguously as in the beginning of the Adagio in Mahler's Fifth Symph.). This is NOT saying the same thing as C and Eb "implying" C Eb and G or that the notes might "imply" Ab C and Eb.

Being consonant, they might establish tonality in either one of those areas, but the deciding factor is the context of the rest of the phrase or its cadence (not the hinting at of other "missing" third notes of a major or minor chord.).

Consonance and dissonance has its basis in the overtone series. As it turns out, physics has a lot to do with interval function in tonality. Consonance (whether vertical or horizontal) has a greater ability to establish tonality than its remote relatives, the dissonances. Therefore, to establish a stable cadence, it requires relative dissonance to resolve to relative consonance.

In another thread we discussed what "harmony" is. The result was that no one could really define it satisfactorily. Yet we talk about it all the time as though it is an a priori concept.

If "harmony" cannot be defined soley as the "simultaneous" sounding of pitches (because arpeggios create the sense of the establishment of tonality as well) then the distinction between melody and harmony is meaningless.

Is this faulty thinking on my part?

[psionic]

That's an interesting approach, but rather limited. There are big differences between harmony and melody.

One example: Take a bass guitar, in the key of A minor, riffing on only the 2 notes A and C. In your premises above, there is no fundamental difference between playing low C then low A versus playing low C and high A. In other words, the riffing of a minor 3rd (A, C) is functionally equivalent to riffing of a minor 6th (C, A). Your premise says that they both function to reinforce the key or chord of A minor. To stretch the example, let's say the bass player riffed on low A and a high C two octaves higher; low C and high A two octaves higher; or low A and high C 3 octaves higher. These all have different qualities, surely. Although harmonically there may be some small distinctions, surely it's obvious that melodically each case is very different.

Another example: Take away the restrictions of staying within the confines of chromaticism. Like when a guitar solo bends notes all over the place. Or when a you listen to a foreigner whine or chant or otherwise rant or drone on somewhat melodically. The slight intonations, the inflections, are understood by humans to carry meaning. This is melodic meaning. Linear. Divorced from vertical harmony.

Granted, there are acoustic properties, physical and mathematical definitions or observations that describe consonance and dissonance. But when someone delivers a speech with inspired gusto, and another speaker delivers the same speech but bores the audience to death, that is an analysis of melodic linearity that is needed, not harmony.

Melody borrows concepts from both harmony and linear meaning.

[A.M. Gold]

But the interval of the second is the most common (or second most common) interval in melody, and it certainly doesn't have the same role in harmony.

[jancivil]

This thread got me thinking...

If I were a theorist (which I am not) I might create a system of musical thought which does not take such pains to differentiate between vertical and horizontal intervals or events.

The reason is because intervals between voices act and function exactly the same as intervals between points in the same voice (melodic).

The interval of the perfect fifth from the root note of the scale serves the same function (of re-enforcing the tonality) whether it is a harmonic or a melodic interval.

The interval of an augmented fourth also functions the same regardless of it occuring simultaneously or melodically. In either case, the interval's dissonant stress will give it the same tendencies of resolution, if the context is suitably comparable.

Try this by playing a bit in the key of D Minor. Then just play the notes G and C#, first one after the other and then simultaneously. In the context of D minor, EITHER the simultaneous or the melodic version would have the same quality. Either one would have the exact same tendency to resolve in the same way.

Therefore the function of the interval is identical. And if that's true, then why (other than rhythmic considerations) would we so insist to differentiate between melody and harmony?

What property or properties of the tonal language is illuminated by this distinction?

In the beginning of the slow movement of Beethoven's "Moonlight" sonata for example, the three-note arpeggiation of G# C# and E function to establish the tonal center of C# minor, just as if the notes were played simultaneously. The presence of RHYTHM segments the notes to unfold horizontally, but the intevals have the same function (that to establish C#m-ness) as they would if they were hammered out as "chords."

Some might say that the horizontal "implies" the vertical. That's like saying that flatness implies roundness. Why would this be the case? What is it about roundness that is more fundamental than flatness?

Similarly, why would harmony be more fundamental as to be able to be "implied" by the melodic?

But it also pre-supposes the existance of triads as a distinct atomic building block of music. In order for something with three notes to be implied by two notes, a three-note unit must have some magical preeminance.

But if triads were a magical and preeminant building block of music, then what is the theoretical basis for their being so? Some might say, "Well triads are simply self-evident as atomic structures in music. Two notes can imply a triad, depending on context. Two notes have 'hopes' in fooling your ear into believing that they are actually three."

I would argue that two notes function as two notes. If they have some special ability to re-enforce or establish tonality, it's because they are relatively consonant, not because they are "2/3's of a triad."

C and Eb might re-enforce Cm or Ab major (or it might be used deliberately ambiguously as in the beginning of the Adagio in Mahler's Fifth Symph.). This is NOT saying the same thing as C and Eb "implying" C Eb and G or that the notes might "imply" Ab C and Eb.

Being consonant, they might establish tonality in either one of those areas, but the deciding factor is the context of the rest of the phrase or its cadence (not the hinting at of other "missing" third notes of a major or minor chord.).

Consonance and dissonance has its basis in the overtone series. As it turns out, physics has a lot to do with interval function in tonality. Consonance (whether vertical or horizontal) has a greater ability to establish tonality than its remote relatives, the dissonances. Therefore, to establish a stable cadence, it requires relative dissonance to resolve to relative consonance.

In another thread we discussed what "harmony" is. The result was that no one could really define it satisfactorily. Yet we talk about it all the time as though it is an a priori concept.

If "harmony" cannot be defined soley as the "simultaneous" sounding of pitches (because arpeggios create the sense of the establishment of tonality as well) then the distinction between melody and harmony is meaningless.

Is this faulty thinking on my part?

There is one whole thing I have a BIG problem with here (though it appears well-thought out as a whole): I don't see, and disagree strongly with, the analogy of 'horizontal' IN MUSIC with 'flat', and 'vertical', ie., *polyphony* with 'round'. That, seems very tied to a cultural concept of music, in Western Europe, where to be frank the tunes are quite paltry, the intonation system quite deficient in terms of giving you a satisfying fat resonant OM or tonic (you know, where the intervals coincide better with the way things vibrate in acoustical anything, in 'air'), and y'all has to always be stacking things to make up for these basic lacks. It isn't so round to these ears, just... a major triad on a piano. Inferior, owing to certain compromises... I spend a lot of time balancing and adjusting, *retuning* to get something less... *thin* out of these instruments when I am restricted to...
(My own main axe is electric guitar, gots strings what bend, so I'm equipped for this torture.)

To give you some idea of music which does not stack vertical sonorities, but is practically pure "horizon" where what you said doesn't necessarily apply, go hear, I mean really try to hear a raga (or like form in Hindustani or Karnatak music) played by a master. The lines aren't tied to a concept of a chord, at all. Thus, you don't get a lot of arpeggios in the line. The line isn't made to pay attention to anything but how it vibrates against the Sadja, the tonic, the ONE, OM. It requires no elaboration in 'other parts' to acheive what it does; to think of an interval which equates to say 'minor 7' in the concept of such, pure line, as something harmonic, isn't right, it's beside the point utterly. The guidelines for composition do not consider resolution to a tonic, or movement to this or that area. The tonic is always present, and the line should not lack for interest in movement owing to such an idea, irrelevant to the context and conception.

A 'harmony' is a device which isn't universal in music, in other words. It's made to do something different, and I think in many cases Apart From melody qua melody. I don't think it's a flatness which implies a roundness, not at all. I might suggest you qualify 'music' in this kind of case, as 'western european art music since such and such a date', really, as what you said seems to apply well enough to that, but not so much to 'music' in the larger sense. What it appears to reduce to is: "intervals mean chords; melody implies harmony". Harmony isn't a universal concept in music; to formulate something as universal according to a conception which isn't, doesn't work without qualification.

[synthgeek]

To give you some idea of music which does not stack vertical sonorities, but is practically pure "horizon" where what you said doesn't necessarily apply, go hear, I mean really try to hear a raga (or like form in Hindustani or Karnatak music) played by a master.

I don't want to interrupt here, but can you recommend some stuff in this area? I'm pretty much completely ignorant when it comes to non-western music, and I would like to change that.

[Ogg Vorbis]

Melody borrows concepts from both harmony and linear meaning.

I think that you've said it very well. In many ways BOTH are inherent in the unfolding of intervals over time (melody).

I have thought about your pitch order example with the bass guitar. I am still considering your point because it's really a good question.

If I think about a bass player playing a C1 and then an A above that, I think I would experience it tonally the same as if they were played simultaneously (not musically, mind you - but tonally).

Similarly, if the bassist played them sequentially, but the A is lower, this would be experienced the same as playing THOSE SAME notes simlutaneously.

So my premise does not say that it doesn't matter which octave you play.

But I owe some more thought to this.

Thanks for posting that!

[Ogg Vorbis]

To give you some idea of music which does not stack vertical sonorities, but is practically pure "horizon" where what you said doesn't necessarily apply, go hear, I mean really try to hear a raga (or like form in Hindustani or Karnatak music) played by a master.

I don't want to interrupt here, but can you recommend some stuff in this area? I'm pretty much completely ignorant when it comes to non-western music, and I would like to change that.

This one knocked my tube socks off...

[A.M. Gold]

One thing to consider as an important distinction is the directionality of linearity. There is no directionality to a single chord (though there is order of voicing). Melody inherently contains ascending and descending directional components. The interval is the same but it has a different feel when going up vs. going down. Furthermore, the interplay of upness and downness within a melodic line significantly shapes its character. Of course, the same could be said for a chord progression, but not for a single chord.

[synthgeek]

@ Ogg Vorbis: Thanks for those. Both good, but I see what you mean about the second one. Wow.

[jancivil]

To give you some idea of music which does not stack vertical sonorities, but is practically pure "horizon" where what you said doesn't necessarily apply, go hear, I mean really try to hear a raga (or like form in Hindustani or Karnatak music) played by a master.

I don't want to interrupt here, but can you recommend some stuff in this area? I'm pretty much completely ignorant when it comes to non-western music, and I would like to change that.

L Shankar, also known as simply Shankar (Lakshminarayana Shankar. Zappa called him 'Larry'); L Subramaniam (same 'first' name, father (V. Lakshminarayan)'s last name, his brother), both violinists. Ravi Shankar, no relation, sitar. "Larry" made some records on ECM with some jazzers, and a rock and roll record if not more than one, but is sort of the ultimate prodigy in music.

There's a lot more but my mind only holds so many names just now... Many have really long first names so you just get, L and V instead. There was someone at the big jazz festival this year... AHA: http://www.prasantmusic.com/concerts_archive.html
Prasant Radakrishnan. That's some band he's got there.

For a good time, google TRIKALA.
Your licks come in three sizes (three 'times', time zones), and that includes all three (or more if you're with L) at the same time. You get L Shankar's group (incl dad, big ol V; Ravi Shankar's drummer Alla Rakha Khan's kid, Zakir Hussein, and Vikku Vinayakram on ghatam (a very similiar lineup to SHAKTI which was a John McLaughlin project in ca. 1978...) Raga Aberi is a great workout of this idea in the Ragam Tanam Pallavi form in 6 3/4 beats tala. 51 minutes, goes by in a flash.

[leggie]

Who was it said 'Music is the space between the notes' ?

Besides me and maybe someone earlier in the thread

[jancivil]

Melody borrows concepts from both harmony and linear meaning.

I think that you've said it very well. In many ways BOTH are inherent in the unfolding of intervals over time (melody).

I have thought about your pitch order example with the bass guitar. I am still considering your point because it's really a good question.

If I think about a bass player playing a C1 and then an A above that, I think I would experience it tonally the same as if they were played simultaneously (not musically, mind you - but tonally).

Similarly, if the bassist played them sequentially, but the A is lower, this would be experienced the same as playing THOSE SAME notes simlutaneously.

So my premise does not say that it doesn't matter which octave you play.

But I owe some more thought to this.

Thanks for posting that!

Melody does not depend necessarily on, to borrow from or be influenced by harmony or <one's> concept of harmony.

Let me give an EZ example: your bass player playing that A after a C below: it may be that the intent of 'A' is to move *directly* to G. Which isn't to say A minor first inversion, unless your mind is tethered to that as the main function of the interval of a major sixth. It's an interval, not a harmony, until it is USED as one. Which is contextual.

Linear meaning, AM Gold just nailed it, has direction. A musical line *can be* contained in the envelope you call a chord or progression of chords, it can imply that, it might in some cases be, not more than these contexts. There is nothing <necessary> to the concept of 'musical' line to tie it in all cases to chords or 'harmony'. There is ONLY context. 'All contexts that are possible' is not the same as 'the context I am familiar with'. There is nothing innate per se to harmony, to say that 'harmony exists where there are tones in a row', is incorrrect.

[synthgeek]

Thanks, jancivil. Between these & Ogg Vorbis' suggestions, I think I'll be kept busy for awhile. I'm currently listening to the lady from Ogg's second suggestion on Lala, they have quite a bit of stuff from her I see.

I haven't been this excited since I was shown industrial music, thanks again guys!

[jancivil]

actually it seems like there's a fair amount of Karnataka on youtube and a general following by its adherents. Some of whom are purists, so watch out.

But, totally buy the record, it's on CD called Raga Aberi by L Shankar.

Melody/Rhythm. And, you rarely get a tala like 6 3/4. Sometimes they do stuff like delay the last three of 27 until the 9th cycle... Everyone knows where ONE is somehow. It might be religion.