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At 5/31/11 05:34 PM, Chris-V2 wrote: That's a false arguement, as in any scale that is assymetrical you may have distinct modes. Melodic minor, harmonic minor, hungarian minor etc. etc. Even entatonics have this luxury, and modes of gapped, octo and nanotonic scales can all sound wildly different.

Look at the vector class of the 7-35, to understand what I'm saying (this is outside of the realm of tonality, but applicable).

--2 5 4 3 6 1--

No other septachord set class has this property - you can look all you like, but one doesn't exist. How does this translate? There are mostly 4ths and 5ths in the system (making it ideal for a system that deals especially with those intervals), followed by major seconds, then major and minor thirds (respectively), minor seconds, and finally a single, defining tritone. This prominence of intervals in this particular manner is incredible, in terms of pitch class, because it implies an order of dominant intervals (which, by the way, often helps form the structure of pantonal music).

In the case of other asymmetrical classes, there may be different 'modes', but there is often no dominant interval, and if there is there is certainly no set hierarchy to the other interval classes - there will be overlap (and therefore ambiguity in strength of presence in a piece) that will throw any set structure out of wack.

Also, you're missing what is possibly a much more practical reason for such a setup that I mentioned before - it's the maximally even distribution of seven notes over twelve halfsteps. I didn't go into detail on it, but it perhaps is even more relevant to the discussion because it very well could have been something that they thought up.

In a not-so-mathematical way of putting it, think about it this way - given twelve spaces to fill, how could you best put seven people as far away from each other as possible? After some shuffling you'll find that the best way to do this is to place them in seat 0,1,3,5,6,8 and 10... which is exactly the same as the 7-35 set class (or the diatonic scale). I don't know the exact mathematical formula offhand, but I know it deals with floor functions and such.

So yeah, not only does it's arrival make sense music theoretically, but it makes perfect sense mathematically and perceptually. The theory just helps us figure out the many strengths that the class actually has to offer... I probably should've went into more detail on the maximally even thing earlier :/

While there is nothing wrong with other scales (be they synthetic or generated from our classic model, like the one you propose), your scale does not hold these properties.

Hopefully you'll see that I'm not spouting opinion, here. That's pretty much established in the field, already.

It's not a harmonic construct - it's a contrapuntal one (and since most organized polyphony is a uniquely Western field of musical thought you really won't find too much like it in other world music pre-Paris World Fair, since most world music, particularly India/Indian music was based on monophonic constructs).

Mono and Hetrophonic, to be precise, but yes. And since parallel harmony existed previous to counterpoint I'd forget that. Rounds, Renaissance Music, Parallel Organum, it's all parallel harmony. It existed way before the concious idea of contrary motion and has indeed proved more popular than totaly independant lines of contrary motion.

Mmm... actually Contrary motion has been in existence since at least the 9th century. Again, I point you to the Musica Enchriadis and Socia Enchriadis. Documents in the 9th century that not only maps out how to deal with improvised organum, but also how to improvise true counterpoint (yes, even with some of the classic rules, like not having too much parallel motion as to distinguish between the two lines), and it's dealt with in a fashion that implies that it's already been around for a while. Look it up at a music college library sometime - it's a very short read, but it's absolutely fascinating.

...The V-I's sound is a reason we perceive V-I as good voice leading, not the other way around.

I'm going to have to disagree with that point, actually, simply because the root of the V chord was not considered important enough in a two part counterpoint back in the pre-renaissance era. It was the leading tone and third above/sixth below that got full attention every time (Again, read Zarlino or even J.J. Faux on the topic). When three voices came into play the 5 was one of two places to harmonize from (the other being 4), so it was often used as a result of the counterpoint.

Here's another point to consider - back in the day it was considered better to resolve a piece of work with either 2 or 7 in the bass. If harmony was indeed the reason behind such actions then they would've prioritized 5 in the bass, since that has the most powerful harmonic relationship possible (indeed, post Renaissance it would be unacceptable to end a piece otherwise). There's plenty of documentation from the time that shows their awareness of counterpoint (and a lack of awareness with harmonic theory), so I suspect it's the counterpoint that eventually formed harmonic theory.

No, the leading tone has little to do with the V-I relationship, but the proximity of a m3rd - Unison (a half-step below/above and a whole step below/above).

This is a valid proposal, in one sense, as it does show the tension-release that has become staple to music. But considering the popularity of plagal cadences in alot of this music it comes and it goes.

A plagal cadence is never a cadence. It is an extention of an already completed cadence. Think of it as a series of neighbor tones that occur over the root, and it makes sense.

The leading tone certainly wasn't neccesary in Gregorian Chant with its general focus on whole tone steps.

Gregorian Chant is monophonic, so... yeah. It doesn't apply to counterpoint (unless you want to talk about line writing, which was derived from it. Also, it does have half-steps in it, and performance practice would dictate that they end with a raised 7th (people didn't write that in the score - it was always implied). Most people don't sing it like that today, but they did, back in the day.

Not true, as I said plagal cadences were common. Actually, most folk and alot of Church music uses the IV-I. The "Amen Cadence", you know. Fairly bland, really. But effective! Why?

Because, again, it's not a cadence in the literal sense of the word. It's a decoration after an actual cadence occurs.

I dunno, I think you'll find this Classical Era emphasis on form and symmetry stuff abit of a false truth. The Lydian Chromatic Concept goes some way to explaining the modern systems (And indeed is the start of the Scalic model of improvisition, as previously it was a chordal approach!) but it still doesn't really reach into the guys of why we perceive these things the way we do. Why does V-I work? Because it leads to good voice leading and it sits in the major scale! Why is it good voicing? Because it agrees with the V-I and it creates tension-release motion. Why is that a good thing, why is the major scale a usable model? Because!

The Classical era heavily focuses on harmonic theory, so it goes past the realm of this discussion (Remember, it was codified in 1722). V-I works so well because of the combination of the harmonic strength and contrapuntal power. In short runs it's the counterpoint that gives it so much leway, but over long stretches of time (only really possible, by the way, starting from this era on) the harmonic relationship is what really gives it it's bond. There's a reason why pre-Classical music wasn't organized at nearly the same multi-layered level as post-Classical music was - Harmony finally set in, and allowed people to form new, cohesive structures not possible with Counterpoint.

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Sorry if this discussion is taking up so much room, by the way. I don't have too many chances to splurge my music theory nerd-dom anywhere. We'll all help anyone who has legitimate questions on the subject, as well.

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At 5/31/11 06:39 PM, Gario wrote:

No other septachord set class has this property - you can look all you like, but one doesn't exist. How does this translate? There are mostly 4ths and 5ths in the system (making it ideal for a system that deals especially with those intervals), followed by major seconds, then major and minor thirds (respectively), minor seconds, and finally a single, defining tritone.

O.k, this is interesting and more what I was looking for. I can't say I can quite read this class list system straight off the bat as it's half 12 and I'm on my third beer. But I can see what you're getting at. I had previously looked at tetrachords and was aware that most common scales are invariably constructed from them. Actually part of my point was any and all common scales are the Major Pentatonic Scale + 2 buddies. I'm interested in why these 2 are its favourites.

In the case of other asymmetrical classes, there may be different 'modes', but there is often no dominant interval, and if there is there is certainly no set hierarchy to the other interval classes - there will be overlap (and therefore ambiguity in strength of presence in a piece) that will throw any set structure out of wack.

Well actually the Lydian Dominant has mostly 5ths, #4/b5's and minor 3rds. There is a dominant interval set, but the frequency ratios are decidedly more complex. The Simpsons Theme is the most oft cited example, though parts are just Lydian, but give it a listen and decide!

Also, you're missing what is possibly a much more practical reason for such a setup that I mentioned before - it's the maximally even distribution of seven notes over twelve halfsteps. I didn't go into detail on it, but it perhaps is even more relevant to the discussion because it very well could have been something that they thought up.

Yes, but then question of "Why 7?" comes up. That would make the Whole Tone scale king of the hill!

So yeah, not only does it's arrival make sense music theoretically, but it makes perfect sense mathematically and perceptually. The theory just helps us figure out the many strengths that the class actually has to offer... I probably should've went into more detail on the maximally even thing earlier :/

It does, by the laws of theory. My arguement is purely that it's fairly paradoxical to the psychoacoustic laws of consonance. And I'm not even siding with one or the other, I'm just interested in hacking out this as a discourse.

While there is nothing wrong with other scales (be they synthetic or generated from our classic model, like the one you propose), your scale does not hold these properties.

While it does undoubtedly have unique properties, I still can't fully see why this exclusive fleshing out of the pentatonic scale is our favourite. But I've a feeling this is well outside the scope out this, or even an MA!

Hopefully you'll see that I'm not spouting opinion, here. That's pretty much established in the field, already.

I don't doubt that you're sourced, I'm just disputing the sources. They came from their particular frame of mind and I think, considering how much music has changed, revising these concepts can't hurt.

actually Contrary motion has been in existence since at least the 9th century... and it's dealt with in a fashion that implies that it's already been around for a while. Look it up at a music college library sometime - it's a very short read, but it's absolutely fascinating.

I would but my college's section on theory is mainly that Roger Kamien book (With its appauling cover of World Music). But thankfully I'm an electronics nerd and I can pick apart old books on circuits. The idea of contrary motion being firsties is hard to imagine, I was fairly convinved the earliest forms of multiple voice music were things like rounds, which are homophonic.

I'm going to have to disagree with that point, actually, simply because the root of the V chord was not considered important enough in a two part counterpoint back in the pre-renaissance era. It was the leading tone and third above/sixth below that got full attention every time (Again, read Zarlino or even J.J. Faux on the topic). When three voices came into play the 5 was one of two places to harmonize from (the other being 4), so it was often used as a result of the counterpoint.

Yes, but that could just be a cultural thing. We would double the root nowadays and while it'd have been bad form in Mozart's time they'd have doubled the 3rd. Cultural tendencies such as that don't come from any factual point, really, jazz players will happily drop the root or 5th of a dominant chord. Or the 3rd. You might actually only have 1 note that isn't in the upper extensions, but it'll be there. That's just our brains understand that a Cadence should be here and us stretching it. It may have sounded wild at one point but it's sort of integral, I wouldn't say there's much more too it than we learned to contextualize it.

Here's another point to consider - back in the day it was considered better to resolve a piece of work with either 2 or 7 in the bass. If harmony was indeed the reason behind such actions then they would've prioritized 5 in the bass, since that has the most powerful harmonic relationship possible (indeed, post Renaissance it would be unacceptable to end a piece otherwise). There's plenty of documentation from the time that shows their awareness of counterpoint (and a lack of awareness with harmonic theory), so I suspect it's the counterpoint that eventually formed harmonic theory.

Maybe, maybe not! That's supposition, unfortunately. I think the issue is essential that the idea of harmony was a discourse that they simply hadn't discovered. Much like some tribes have no 2 seperate words for singing and talking they had no seperate terms for counterpoint and harmony. They had basic, dualist princaples at this stage (Colour = mix of light and darkness. Life and death, good and bad, God and the devil etc. etc.) and they thought in this binary sense. Voice goes up? Other goes down. Everything must reflect the duality of life and the cohesive unity of nature and the universe.

So to me it's a cultural thing, the concept of Harmony came from Counterpoint but they'd been dealing with it all along but in ignorance. They began to seperate out different bits into new concepts and argueing the same issues in different ways.

A plagal cadence is never a cadence. It is an extention of an already completed cadence. Think of it as a series of neighbor tones that occur over the root, and it makes sense.

We can think of it like that, as a 6 4 suspension. But I don't hear it that way and it doesn't interact that way. The Vc-I can be considered a resolving suspension rather than a cadence but because we hear it to be 2 distinct chords we don't. Likewise I hear 2 distinct chords in a IV-I.

Gregorian Chant is monophonic, so... yeah. It doesn't apply to counterpoint (unless you want to talk about line writing, which was derived from it. Also, it does have half-steps in it, and performance practice would dictate that they end with a raised 7th (people didn't write that in the score - it was always implied). Most people don't sing it like that today, but they did, back in the day.

It's a general rule and it really did depend on the situation. If I wasn't so tired I'd dredge up the old chants we did in a module and alot of them end in a IV-I. I'm aware you call that an extended cadence but there was no preceding leading tone in any of the voices. 2 static voices a 4th apart. I know the rule is made by the exception but I don't think it was that involved, the leading tone is a Tonalist concept.

Again, folk music has little to no reliance on the leading tone. Irish traditional music beats the crap out of b7. I mean it really milks it. Major mode, minor mode. It's rare to find a leading tone. Actually I can't name a trad peice with one. Same of any bulgarian or greek music, the Spanish peice Romanza is one of the few I can think of with a leading tone (And a little chromatic run!).

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I think we can both rest comfortably on most of that - there is a point where we're going to go all fanboy over counterpoint (that's me) vs harmony (that's you). ... sort of a strange way to put it, but there ya go.

Just a quick notice, when I say things get 'knocked out of wack' I just mean that using traditional means to make your music tend to lead to... strange results. Many songs have experimented with other tonal structures, motions, etc., and still manage to sound great (bless the Simpsons).

Alright, I think we've pretty much tired each other out.

Join us next week when we discuss: Tonnetz - Did your music get caught in them?

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At 5/31/11 09:18 PM, Gario wrote: I think we can both rest comfortably on most of that - there is a point where we're going to go all fanboy over counterpoint (that's me) vs harmony (that's you). ... sort of a strange way to put it, but there ya go.

I'm not a harmony fanboy asuch, as again elements of that can be considered social constructs. I'm just approaching Music Theory from a psychoacoustic perspective atm to see what's what. I'm finding it interesting, though it does show alot of what we perceive to be cultural constructs rather than "laws".

Sorry if this has come across as hostile or anything, it's just an interesting debate to me!

Join us next week when we discuss: Tonnetz - Did your music get caught in them?

Followed by Chinchillas, how loud can you blast their ears with white noise before it kills them?

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hey stop the mindless theory wank and discuss something else.

And hey Chris-V2 why don't you marry lydian dominant if you like it so much

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At 6/1/11 10:25 AM, SBB wrote:

And hey Chris-V2 why don't you marry lydian dominant if you like it so much

Maybe I will! Though I was more interested in discussing how it relates to the overtone series (It's why its also known as the Acoustic Scale) and is yet a far less common scale than the major scale.

But yeah. How doez I makes d triangle of 5ths maek my muzic gewd!?

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At 6/1/11 10:25 AM, SBB wrote: hey stop the mindless theory wank and discuss something else.

it's not mindless youre mindless...

... alright, maybe it is a little bit...

I think we've both mutually agreed to stop, so don't worry. Besides, I thought that's what this thread was for? Where else can I wank my theory?!

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Can someone help me figure out the chords/harmony in this. I've figured out that it's probably based around a C minor key and has an E7#9 / E7b9 occasionally. Any leads would be greatly appreciated

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Is there any way that the very absolute basics can be made even more basic?

I've had a hard time understanding theory since I started playing music and it's still most the most elusive part.

Basically what I'm asking is what is the first thing one should know before they can even begin to grasp the concept of music theory.

I'm sorry if this has been asked in another context.

If someone could relate this to guitar that would be excellent!

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At 12/20/11 12:05 AM, ChimeraNoise wrote: Is there any way that the very absolute basics can be made even more basic?

I've had a hard time understanding theory since I started playing music and it's still most the most elusive part.

Basically what I'm asking is what is the first thing one should know before they can even begin to grasp the concept of music theory.

I'm sorry if this has been asked in another context.

If someone could relate this to guitar that would be excellent!

Start with relationships - notes and chords. G-C-D is accessible because it's a I-IV-V progression. Find all the I-IV-V's on your guitar, starting with a different 'I' chord every time.
Then look at individual notes. G-A-B-C-D-E-F#-G is a major scale that starts on the third fret. Learn the pattern and then apply it to the other eleven notes. Find the half-steps (neighboring fret), they're always between the 3-4 and 7-8 in major (note Arabic numerals for notes, Roman numerals were for chords).
Start reading sheet music (grand staff) and learning your major and minor key signatures. Once you're comfortable with key signatures, you can use the numbering system to refer to chords and notes in a universal context.

That should get you started, hopefully. Let me know if something is still unclear.

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At 12/20/11 12:24 AM, Adam-Beilgard wrote:

Start with relationships - notes and chords. G-C-D is accessible because it's a I-IV-V progression. Find all the I-IV-V's on your guitar, starting with a different 'I' chord every time.
Then look at individual notes. G-A-B-C-D-E-F#-G is a major scale that starts on the third fret. Learn the pattern and then apply it to the other eleven notes. Find the half-steps (neighboring fret), they're always between the 3-4 and 7-8 in major (note Arabic numerals for notes, Roman numerals were for chords).
Start reading sheet music (grand staff) and learning your major and minor key signatures. Once you're comfortable with key signatures, you can use the numbering system to refer to chords and notes in a universal context.

That should get you started, hopefully. Let me know if something is still unclear.

Thank you very much for the quick reply!
I kind of understand key signatures. I know that wherever the dot on the treble clef lands is the key the song is in. And I understand that # is sharp and b is flat. That was pretty simple to understand really.

It's always been the I-IV-V and all that that I never really caught on to. But what I understand from what you said: I would be G. IV would be C. And V would be D. Right?

So if someone were to say: Play I-IV-V, they would really just be referring to the chords G, C, and D?

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At 12/20/11 12:33 AM, ChimeraNoise wrote:

At 12/20/11 12:24 AM, Adam-Beilgard wrote:

Start with relationships - notes and chords. G-C-D is accessible because it's a I-IV-V progression. Find all the I-IV-V's on your guitar, starting with a different 'I' chord every time.
Then look at individual notes. G-A-B-C-D-E-F#-G is a major scale that starts on the third fret. Learn the pattern and then apply it to the other eleven notes. Find the half-steps (neighboring fret), they're always between the 3-4 and 7-8 in major (note Arabic numerals for notes, Roman numerals were for chords).
Start reading sheet music (grand staff) and learning your major and minor key signatures. Once you're comfortable with key signatures, you can use the numbering system to refer to chords and notes in a universal context.

That should get you started, hopefully. Let me know if something is still unclear.

Thank you very much for the quick reply!
I kind of understand key signatures. I know that wherever the dot on the treble clef lands is the key the song is in. And I understand that # is sharp and b is flat. That was pretty simple to understand really.

It's always been the I-IV-V and all that that I never really caught on to. But what I understand from what you said: I would be G. IV would be C. And V would be D. Right?

yes

So if someone were to say: Play I-IV-V, they would really just be referring to the chords G, C, and D?

No. In the key of G, it would mean exactly that. But only in the key of G.

I-IV-V become like variables in algebra - you have to do a little math to figure each one out.
For example: in the key of A, I-IV-V becomes A-D-E. In the key of F it becomes F-Bb-C and so on, around the circle of fifths. This is where understanding of all twelve key signatures is important so you don't accidentally end up with the tritone in this progression.

What I would suggest is looking for an online tutorial of key signatures, circle of fifths, scales and common chord progressions - in that order. The last two you should already have a grasp on, being a guitarist, it's just putting them in context with the first two concepts.

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I kind of understand key signatures. I know that wherever the dot on the treble clef lands is the key the song is in. And I understand that # is sharp and b is flat. That was pretty simple to understand really.

After re-reading this, I missed the most important part. The dot on the treble clef doesn't tell us anything. Really, it's just a curly flourish at the bottom that becomes a dot when people (even some publishers) are lazy. In jazz notation, it's just a straight line, no dot, no curl or anything. The sharps and flats at the beginning of a piece tell us the key.

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At 12/20/11 01:27 AM, Adam-Beilgard wrote: Lots of great info

Well I learned key signatures partly incorrectly then. Thank you for correcting that!

As for the rest, I'll have to do just that now that I finally understand what the heck the roman numerals meant.

Thanks again! I appreciate the help!

I can almost promise I'll be back..

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At 12/20/11 01:34 AM, ChimeraNoise wrote:

At 12/20/11 01:27 AM, Adam-Beilgard wrote: Lots of great info

Well I learned key signatures partly incorrectly then. Thank you for correcting that!

As for the rest, I'll have to do just that now that I finally understand what the heck the roman numerals meant.

Thanks again! I appreciate the help!

I can almost promise I'll be back..

Well, even if you don't come back to this thread, PM me any more questions and I'd be happy to help.

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I want to look into serialism more this coming year. More specifically the 12 tone method.

Any suggestions on good articles or books on the subject?

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At 12/20/11 03:31 AM, LogicalDefiance wrote: I want to look into serialism more this coming year. More specifically the 12 tone method.

Any suggestions on good articles or books on the subject?

In all honesty, I can't imagine that being something that a textbook would easily mess up - it's so mathematical in it's presentation that it leaves little room for interpretation (and thus little room for error). If you're just starting take a good look at some reviews for some textbooks, then buy what best fits your needs.

If you're looking to advance serialism as someone who is already familiar with the subject, try checking out Milton Babbit's 'Twelve Tone Invariants as Compositional Determinants'. It's a little tough to read, but it's basically where twelve tone music got it's start, in the theory world.

If you can get a hold of Robert Morris' "Composition with Pitch-Classes: A Theory of Compositional Design", it's a truly amazing piece of work that deals in great detail on twelve tone systems, serial treatment of non-pitched elements, multiplicity... and a shitload of other things. It assumes that you're comfortable with basic discrete mathematics (as do most more advanced atonal/serial theory articles and books I'm presenting), so be prepared for the heavy mathematical language. Unfortunately it's a bit tricky to get a hold of, nowadays - it's been out of print for a while. Best bet is to find that one in a college library or something, but it's still worth mentioning because it's really worth looking for, if you're serious.

David Lewin's "Music Theory, Phenomenology, and Modes of Perception" is also considered one of the great atonal studies, and unlike the other book mentioned I believe this one has returned to print... but I'm not 100% sure if it addresses serial music like the other book, since I haven't read it myself. I need to get a hold of that one...

Morris has another book series, 'Advanced Class Notes for Atonal Theory', that I'd love to buy myself sometime soon (it's available for 35$) that has a chapter dedicated to 12-tone music (you can actually read the overview of it here) that might be the best of both worlds - availability and detail showing that it discuses the 12-tone method in detail. I'd certainly check that one out.

These are not places to start learning about serialism and atonal theory, so if you're shaky on the basics I insist you get your hands on an introductory level book, as well. Also, be prepared for a bit of interesting math. I hope this helps you out a bit.