Music Theory Query Thread!

[Nimble]

Welcome to the Music Theory Query Thread!

This thread is used for the sole purpose of answering questions concerning things of music theory (i.e chord progressions,transposition,scales and modes,all that good stuff) so if you have any questions about music theory,just ask away,and anyone that knows the answer can easily answer it(i can't handle a thread like this by myself.

There are some rules:
1.You can't advertise your music here unless it's giving an example of what you are trying to explain (and i will check the music itself to make sure of this)
2.If you are going to answer a question,answer thoughtfully and specifically to the questioner's situation. if you have no idea what the person asking the question is talking about,you're allowed to ask to specify or let someone else answer the question.
3.Make sure the question you ask is well worded and considerate for the answerers.
4.discussions are allowed too,just make sure they stay on topic/on question.

thats pretty much all i can think of rules right now.will edit when i can think of more.

CREDITS to midimachine for suggesting the idea in the first place!

[Knoxius]

At 5/30/11 12:31 AM, NimblekidX wrote: This thread is used for the sole purpose of answering questions concerning things of music theory (i.e chord progressions,transposition,scales and modes,all that good stuff)

whats transposition
and modes

also teach time signatures thanks

[midimachine]

Pretty dry, Knox.

[BrokenDeck]

THIS THREAD EXISTS ALREADY!

[midimachine]

pfft what kind of nerd uses the thread search

[Nimble]

Transposition is the changing from one key to another (you dont have to change the key signature nessecarily) but usually,it's to a key adjacent to the original key on the circle of fifths. for example:
i want to play a meoldy in G,but it's original key is C. what i have to do is then move up according to the position that G is on in the C scale(thats the simplest way to do it,but there are many more ways to do it) on the C scale,the G is the fifth note(the interval between a C and a G is called an open fifth) [C D E F G] and since it's the fifth note,you go up five notes and you add a sharp to the key signature(again,key changes are optional) you (generally) go up notes if you are going to a "sharper" key signature. For going to a "flatter" key signature,it's a little bit different. instead of going to the fifth note,you go to the fourth(if the keys are adjacent on the circle of fifths,mind you) and you go DOWN,not up. same general idea though. so you go down [C B A G F] add a flat to the key signature

Modes are ancient "scales" because although the regular scales of today sound normal,these sound a bit different,because they essentially move a note up for every mode,but you stay in the key signature.

Ionian-the actual basic scale.(Major Scale)
C D E F G A B C

Dorian-move up a single note from Ionian.
D E F G A B C D

Phrygian-move up 2 notes from Ionian
E F G A B C D E

Lydian-move up 3 notes from Ionian
F G A B C D E F

Mixolydian-move up 4 notes from Ionian
G A B C D E F G

Aeolian-move DOWN 2 notes from Ionian (Minor Scale)
A B C D E F G A

Locrian-move down 1 note from Ionian.
B C D E F G A B

Time signatures are simple.

the top number signifies how many beats there are in a measure,and the bottom note signifies what gets the beat(in 3/8,there are three eighth notes in every measure)

was this detailed enough?

[Knoxius]

At 5/30/11 12:49 AM, midimachine wrote: Pretty dry, Knox.

What do you mean? I don't know what transposition or modes are, and I have trouble with time signatures. Just a kick start to this potentially golden thread.

Also thanks for enlightening me Nimble :3

[Nimble]

you are welcome knox :)

[Chris-V2]

So will this thread be dealing with just the structuralist view of 17th centuary composition or will we be actively discussing how the mind interacts with sound within the context of music?

[Buoy]

At 5/30/11 12:46 PM, Chris-V2 wrote: So will this thread be dealing with just the structuralist view of 17th centuary composition or will we be actively discussing how the mind interacts with sound within the context of music?

no, just the difference between major and minor chords

[Chris-V2]

At 5/30/11 01:08 PM, SBB wrote:

At 5/30/11 12:46 PM, Chris-V2 wrote: So will this thread be dealing with just the structuralist view of 17th centuary composition or will we be actively discussing how the mind interacts with sound within the context of music?

no, just the difference between major and minor chords

Oh. O.k.

Remember to turn the light off on your way out, guys!

[seel]

At 5/30/11 01:02 AM, NimblekidX wrote: because they essentially move a note up for every mode,but you stay in the key signature.

Wrong. You're still in the key of C major no matter what note you begin with in the scale, unless you're playing say, C major over a D minor vamp, then it's modal and in the mode of D Dorian. It can be hard to wrap your head around, but basically, if you're playing say A major over a chord progression that implies another tonal centre than A or F# (major and minor key) it's modal. Though it's a bit more complicated than that because the major key and relative minor can also be modal. Anyway it's a pretty ancient part of theory and is very rare in modern music, it comes in handy in jazz and classical music though.

[Alchemist94]

I'll help answer any questions asked too, if you'd like?

[Gario]

Alright, here's something for you guys to chew on for a while - why is it that intervals add up to one less than they should, numerically? For example, wouldn't it make sense if combining two octaves made a 16th? Instead, two octaves make up a 15th. Two unisons make another unison, two thirds make a fifth, etc... It makes no arithmetical sense. Who wants to take a stab at answering that?

There is a reason for it, by the way, but I want to see how well y'all know your theory in here (and music history, for that matter), so I'm not gonna tell :P.

[Alchemist94]

At 5/30/11 04:20 PM, Gario wrote: interval stuff

Isn't it because the beginning note isn't counted? Like CDEFGABC contains the same note twice, therefore it would be counted as CDEFGAB? I'm probably wrong but hey, worth a shot haha.

[seel]

At 5/30/11 04:20 PM, Gario wrote: Alright, here's something for you guys to chew on for a while - why is it that intervals add up to one less than they should, numerically? For example, wouldn't it make sense if combining two octaves made a 16th? Instead, two octaves make up a 15th.

No, it wouldn't make sense if two octaves made a 16th because that wouldn't be two octaves.

[Chris-V2]

At 5/30/11 04:41 PM, seel wrote:

No, it wouldn't make sense if two octaves made a 16th because that wouldn't be two octaves.

You've actually made me lol twice now. That said, the question isn't theoretical. By counting through 2 octaves you only count across 15 letters.

Now here's a question. How come the human brain can speed up a peice of music without changing its pitch?

Or why do we use the Major Scale when the Lydian Dominant is the closest equal temperment has to a scale that matches up with the tones of the harmonic series?

Or why is an instrument high in Odd Harmonics considered more consonant than one with alot of Even Harmonics? (Anyone who can do maths and music theory will get this, add 6% to yr base frequency to go up a semitone. Please use 100hz as your lowest tone).

[Nimble]

Chris,i can only (try) to answer the first one,as i am still learning music theory.

The human brain can speed up a song but not change it's pitch because the brain has no reference to the tempo of the song,unless given one,and if given one,the brain gets distracted with the music itself and begins to speed up.

and to alchemist,like i said in the first post,anyone can answer(or attempt to answer if it is trivia,like i did XP)

[Chris-V2]

My point was that music theory doesn't really address perceptual issues. It much prefers to simply state its own law. I'm not here to knock it, asuch, I'm just asking what exactly is and is not music theory?

Lydian Dominant scale is stated in less mathy terms here but essentialy the point remains the same. The Lydian Dominant scale seems to match the overtone series far more strongly than the major scale and most people can not sing a Lydian Dominant scale. Is the issue physical (Does our brain disagree with its construction) is it cultural (It's a rarely heard scale outside of Eastern music and Jazz) ?

It's also interesting to see how the timbre of an instrument can lend itself to certain chord progressions. Ever play a D Sus 2 on a guitar and notice how it shimmers? Ever play it on a piano and notice how more prominant the interval clash is? Or how cool dissonant, detuned beating effects (2 out of tune notes generating a pulsing effect) can be on bass or synthesizers but sound horrible on voice or woodwind?

I think the way overtones interact are probably just, if not more, important than the way the fundamental tones sit together. And again, to reiterate my question, what do you people consider music theory to be?

[Nimble]

well,music theory is really anything "philosophical" about music. tone,chords,style and feel,that kind of stuff. thats the basis of music theory,and it can change slightly from person to person,so don't take my word for it seriously,just take it the way you want to.

[Breed]

Okay so an italian sixth chord is a double diminished triad inverted yes? So that makes it an augmented sixth. Now does it have to built on the IV chord? How off does it sound to use it to set up something besides the dominant?

Has anyone played around much with added sixth chords in their compositions? Any neat progressions or imagery/emotions you got out of your music with it?

I hate learning this stuff off wiki & forums but my college doesnt offer theory over the summer and I'm too eager to jump ahead.

[Nimble]

ok,

i have no idea what the first paragraph said xD

but the second one is simple. i personally love using sixths almost as much as using additive ninths,and i have a pretty neat progression;[G G7 C6 Cm6] it starts on first and resolves on the fourth. it's kind like [C C7 F Fm] BUT it includes the sixth,which makes it sound brighter IMO. plus, G and Cm6 are like twins.

[Gario]

At 5/30/11 04:31 PM, Alchemist94 wrote:

At 5/30/11 04:20 PM, Gario wrote: interval stuff

Isn't it because the beginning note isn't counted? Like CDEFGABC contains the same note twice, therefore it would be counted as CDEFGAB? I'm probably wrong but hey, worth a shot haha.

Hey, I didn't expect to see a correct answer so quickly. Back when the concept of intervals were created, the medieval people didn't understand the concept of 'Zero', so they made the unison count as 'one' nominally, but function as zero. Totally fucks everything up. Thank God Allen Forte clears this up with his system... but most people hate music that uses his system of intervals, so we're still screwed.

No, it wouldn't make sense if two octaves made a 16th because that wouldn't be two octaves.

And here's a man who doesn't understand the question. Though it's a moot point now.

Now here's a question. How come the human brain can speed up a peice of music without changing its pitch?

Humans listen to music from a relative standpoint, not from an absolute one. It's pretty close to the same reason that everybody, with practice, can learn relative pitch, but only a select few people can hear absolute pitch. Our brains are just not wired for that.

Or why do we use the Major Scale when the Lydian Dominant is the closest equal temperment has to a scale that matches up with the tones of the harmonic series?

Simple (and this really is strict music theory) - because one of the most often used predominant chords, the subdominant (and the closest chord to the tonic on the circle of fifths spectrum, as well as the dominant) becomes a diminished triad. Most composers like that chord for it's harmonic relationship with the tonic and the common tone it holds with it, so tonal music gravitated toward the use of the scale that allowed for the use of this chord.

Or why is an instrument high in Odd Harmonics considered more consonant than one with alot of Even Harmonics? (Anyone who can do maths and music theory will get this, add 6% to yr base frequency to go up a semitone. Please use 100hz as your lowest tone).

Dunno. Because... it's more awesomer? Sorry, physical acoustics wasn't my strong point.

[Gario]

At 5/30/11 08:34 PM, LogicalDefiance wrote: Okay so an italian sixth chord is a double diminished triad inverted yes? So that makes it an augmented sixth. Now does it have to built on the IV chord? How off does it sound to use it to set up something besides the dominant?

Has anyone played around much with added sixth chords in their compositions? Any neat progressions or imagery/emotions you got out of your music with it?

I hate learning this stuff off wiki & forums but my college doesnt offer theory over the summer and I'm too eager to jump ahead.

Augmented sixths are the most awesome thing on the planet, though the Italian sixth is pretty wimpy. In essence, it's a chord that has an augmented 6th above the root (along with a minor third above the root). Because of the enharmonic similarity to the m7th (on a keyboard, the A6th and m7th are identical), augmented chords get their flavor with their resolution, not their intervalic layout. As such, the chord ends up strongly leading into the next chord, which often is V, but also can be used as an applied chord of sorts (e.g. in G Major, A-C-F# to G-B-G would be an applied It6+3 / I... hard to type the correct labeling here).

Another neat use is to use the enharmonic structure to your advantage when modulating to an odd area. The German Augmented 6+ 5 (which is basically like the Italian except for the fact that there's a perfect 5th above the root, as well) is enharmonically the same as a seventh chord in root position, so one can use it both ways in a single song to mess with the listeners a little bit. For example, one could use G-B-D-F (V7 in the context of C Major) and resolve it to CM (I). Using those same notes, though (G-B-D-E#, in this context) it can resolve to F#M (or F#m) without missing a beat.

Take a look at the French 4+3, which uses both an augmented 4th and 6th. Rearrange it to one of it's inversions you'll notice that it's completely symmetrical, meaning that if you transpose it up six half steps you'll arrive on the exact same four notes. Everything about being symmetrical applies to that chord... which is quite a bit, actually.

Experiment with them and I'm sure you'll discover many neat tricks with them.

[Chris-V2]

At 5/30/11 09:29 PM, Gario wrote:

Humans listen to music from a relative standpoint, not from an absolute one. It's pretty close to the same reason that everybody, with practice, can learn relative pitch, but only a select few people can hear absolute pitch. Our brains are just not wired for that.

This is a good starting point for a difficult question. Human brains are constructivist (According to some!) and rather than remembering everything we merely remember elements and put them together as need be. So while we can remember the original tempo and starting pitch (To a surprising degree of accuracy considering AP is so rare) we don't need to use them. Our brain mainly concentrates on interval distances and rhythms.

Simple (and this really is strict music theory) - because one of the most often used predominant chords, the subdominant (and the closest chord to the tonic on the circle of fifths spectrum, as well as the dominant) becomes a diminished triad. Most composers like that chord for it's harmonic relationship with the tonic and the common tone it holds with it, so tonal music gravitated toward the use of the scale that allowed for the use of this chord.

It's an interesting point ) but well before tonalism took hold, even before Gregorian Chant and other pre-tonal concepts, there seems to have been no real desire to use this scale.

My current theory is simply that the major scale evolved from the major pentatonic due to the lesser amount of dissonance (#4 is pretty dissonant, and considering 3rds were considered dissonant at the time this would have been a startlingly ugly tone). As for the leading tone, who knows? It's not like the Mixolydian or Dorian mode are uncommon in early folk music. As far as I'm aware the question remains unanswered.

Dunno. Because... it's more awesomer? Sorry, physical acoustics wasn't my strong point.

Alright. I'll do this one, though it's not acoustics! I'd meant Odd overtones, btw, so really I meant Even Harmoncs. Anyway, time for a run down.

100 hz = Fundamental
200hz = 1 octave.
300 hz = 1 octave and a 5th.
400 hz = 2 octaves
500 hz = 2 octaves and a 3rd
600 bz = 2 octaves and a 5th
700 hz = 2 octaves and a b7
800 hz = 3 octaves
900 hz = 3 octaves and a 2nd
1000 hz = 3 octaves and a 3rd
1100 hz = 3 octaves and #4

And from here on it gets very out of tune, though by equal temperment we're out of tune by our 8F (800 hz) as octaves aren't strict frequency doubling. It's more like 1.013. However are ears have quantize functions, and this frequency difference can be considered negligible.

The debate has been going for years, especialy amongst distortion pedal enthusiasts as some units produce more even harmonics (Harmonic Perculator by Interfax) or more odd harmonics (Something like a Boss DS-1, most symmetrical clipping distortion). We can see Odd Harmonics have dissonant tones relative to the fundamental, but not to each other, and we can see that we get alot of stacked octaves with Even Harmonics. So in some ways Odd Harmonics can sound a little harsh, as they don't reinforce the fundamental the way Even Harmonics do. It's also very likely the 5th harmonic (Major 3rd) will be audible and could mess with the consonance of a chord progression.

Which goes back to what I was saying earlier, some instruments don't seem to handle dissonance. Some do, and some only if you play them a certain way!

But again this is subjective and wether a Flue (Odd harmonics) or a Trumpet (Lots of odd and even) sound more pleasant is down to preference. But it's an interesting debate and has led to people like Wendy Carlos building new musical systems built exclusively from odd or even overtones (Such as the Tritave system in the Bohlen-Pierce scale, which repeats when the frequency triples rather than doubles).

[Gario]

At 5/31/11 07:45 AM, Chris-V2 wrote:

Simple (and this really is strict music theory) - because one of the most often used predominant chords, the subdominant (and the closest chord to the tonic on the circle of fifths spectrum, as well as the dominant) becomes a diminished triad. Most composers like that chord for it's harmonic relationship with the tonic and the common tone it holds with it, so tonal music gravitated toward the use of the scale that allowed for the use of this chord.

It's an interesting point ) but well before tonalism took hold, even before Gregorian Chant and other pre-tonal concepts, there seems to have been no real desire to use this scale.

Er... actually Lydian was quite popular among those singing Gregorian Chant (perhaps not as much as Dorian, but certainly moreso than Ionian and Aeolian, since those weren't even a usable church mode until the middle of the Renaissance - they're mostly a secular break off from the original usable modes). You won't find any written examples of it because the practice of the time was to write a very basic line and the singers were expected to transpose the proper lines on the spot (it'd be like a trumpet reading a line either as a 'C' trumpet or a 'Bb' trumpet). Lydian was one of the four primary church modes, whereas Ionian wasn't used until much later.

You'll likely find details on it in the Socia Enchriadis or Musica Enchriadis, but unfortunately it's been a while since I read either of those. I think the topic is brought up, but those are more for identifying the beginnings of written music & polyphony.

BTW, my own point of view on this is a variation of what Webern said in his 'Path to New Music' speeches. You should look them up (they're sold as a collection of speeches in a book of that name) - they're very enlightening.

My current theory is simply that the major scale evolved from the major pentatonic due to the lesser amount of dissonance (#4 is pretty dissonant, and considering 3rds were considered dissonant at the time this would have been a startlingly ugly tone). As for the leading tone, who knows? It's not like the Mixolydian or Dorian mode are uncommon in early folk music. As far as I'm aware the question remains unanswered.

Mmm... not quite - there's more than enough evidence simply by score study that musicians back in the day used a full diatonic scale as far back as Gregorian Chant (and since that's a recording of oral tradition, most likely considerably earlier, as well), though the Greeks certainly did use the Pentatonic scale... for the only written piece we have recorded from a pre-AD era. Again, the Musica Enchriadis expounds on the full scale in detail, so it's easy to see that the full diatonic scale was used as far back as the late 9th century.

As for the leading tone, Mixolydian and Dorian actually raise the seventh when they want to end a song, whereas the good ol' Phrygian used the lowered second as the leadingtone so the seventh remains unchanged during a resolution (THAT usage is certainly covered in detail by Zarlino's 1550 'Treaty on Counterpoint').

Dunno. Because... it's more awesomer? Sorry, physical acoustics wasn't my strong point.

Alright. I'll do this one, though it's not acoustics! I'd meant Odd overtones, btw, so really I meant Even Harmoncs. Anyway, time for a run down.

100 hz = Fundamental
200hz = 1 octave.
300 hz = 1 octave and a 5th.
400 hz = 2 octaves
500 hz = 2 octaves and a 3rd
600 bz = 2 octaves and a 5th
700 hz = 2 octaves and a b7
800 hz = 3 octaves
900 hz = 3 octaves and a 2nd
1000 hz = 3 octaves and a 3rd
1100 hz = 3 octaves and #4

And from here on it gets very out of tune, though by equal temperment we're out of tune by our 8F (800 hz) as octaves aren't strict frequency doubling. It's more like 1.013. However are ears have quantize functions, and this frequency difference can be considered negligible.

The debate has been going for years, especialy amongst distortion pedal enthusiasts as some units produce more even harmonics (Harmonic Perculator by Interfax) or more odd harmonics (Something like a Boss DS-1, most symmetrical clipping distortion). We can see Odd Harmonics have dissonant tones relative to the fundamental, but not to each other, and we can see that we get alot of stacked octaves with Even Harmonics. So in some ways Odd Harmonics can sound a little harsh, as they don't reinforce the fundamental the way Even Harmonics do. It's also very likely the 5th harmonic (Major 3rd) will be audible and could mess with the consonance of a chord progression.

Which goes back to what I was saying earlier, some instruments don't seem to handle dissonance. Some do, and some only if you play them a certain way!

But again this is subjective and wether a Flue (Odd harmonics) or a Trumpet (Lots of odd and even) sound more pleasant is down to preference. But it's an interesting debate and has led to people like Wendy Carlos building new musical systems built exclusively from odd or even overtones (Such as the Tritave system in the Bohlen-Pierce scale, which repeats when the frequency triples rather than doubles).

Interesting. Though I think it goes out of tune by 700hz (that 7b is more like a note between 7b - 7n) It is an interesting way to approach timbre theory. Mmm... makes sense to me.

[Chris-V2]

While you seem to know alot about Gregorian Chant and Diatonic Theory I'm referring to the Lydian Dominant scale, NOT the Lydian mode. Lydian Dominant = 1 2 3 #4 5 6 b7, Lydian = 1 2 3 #4 5 6 7. So the scale I'm referring to is not Diatonic, it's a mode of the melodic minor or a scale in its own right.

And my question goes further into WHY did the leading tone come to exist? What perceptual or physical structures creates the sensation that V - I is stronger than v -I ? Why have we even generated that as a concept when alot of music styles don't even use chordal structures and prefer drones and complex rhythmic motifs to our concepts of "Harmonic progression". Indian Classical Music has a tonal hierarchy as to where notes should go but despite having cadence-like concepts it has no chordal structures. There's no emphasis on the need for a leading tone, it's contextual to the scale and type of raga as far as I'm aware.

[Gario]

At 5/31/11 01:50 PM, Chris-V2 wrote: While you seem to know alot about Gregorian Chant and Diatonic Theory I'm referring to the Lydian Dominant scale, NOT the Lydian mode. Lydian Dominant = 1 2 3 #4 5 6 b7, Lydian = 1 2 3 #4 5 6 7. So the scale I'm referring to is not Diatonic, it's a mode of the melodic minor or a scale in its own right.

Oh. Well then, that has a completely different answer - because it's not diatonic. See, the Diatonic set class is unique among all set classes in that it is the only one with a hierarchy of interval classes. Not only is this the maximally even set of seven tones against twelve (which is a very important reason for the Diatonic system's existence, in it's own right), the way the interval are set up uniquely allow for every single combination of intervals and chords to have syntactic strength in comparison to any other interval, and this uniquely allows every mode to have a very distinctive sound compared to every other mode.

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. Thus it doesn't work nearly as well in long-term organization as the traditional diatonic scales do... Is this the stuff that the people of the day were thinking about? Probably not, but it's a fairly decent explanation as to why they preferred one scale over another.

And my question goes further into WHY did the leading tone come to exist? What perceptual or physical structures creates the sensation that V - I is stronger than v -I ? Why have we even generated that as a concept when alot of music styles don't even use chordal structures and prefer drones and complex rhythmic motifs to our concepts of "Harmonic progression". Indian Classical Music has a tonal hierarchy as to where notes should go but despite having cadence-like concepts it has no chordal structures. There's no emphasis on the need for a leading tone, it's contextual to the scale and type of raga as far as I'm aware.

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). If you think about leading tones in terms to the harmonic relationship you're bound to fail, since it's grandfathered in through a system that didn't even think about harmonic relationships (alright, they DID understand the overtone series and whatnot, but they didn't apply this in what we call a 'harmonic relationship' until much later, officially by Jean-Philippe Rameau in 1722 with his Treatise on Harmony). 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). It's far more powerful than the M3rd - Unison motion (whole step both ways). Since the d3rd was considered too dissonant for use, the m3rd was the closest proximity possible to the unison, so that was the interval of choice when it came to 'cadencing' a song (in the context of counterpoint, a cadence doesn't need the dominant on the bottom). This same logic applies to the M6th - Octave resolution, as well (in comparison to the m6th - Octave). It's not such a big deal nowadays, but back then a song wouldn't sound complete without such a strong resolution.

So really, it's as simple as what is closer to your goal. In counterpoint, the closer a note is physically to the next note, the more powerful the drive to it. And yes... you can also find all this in Zarlino. It's really a great read when it comes to counterpoint, as long as you can stomach the old style philosophy and translation.

[Chris-V2]

At 5/31/11 02:52 PM, Gario wrote:
Oh. Well then, that has a completely different answer - because it's not diatonic. See, the Diatonic set class is unique among all set classes in that it is the only one with a hierarchy of interval classes. Not only is this the maximally even set of seven tones against twelve (which is a very important reason for the Diatonic system's existence, in it's own right), the way the interval are set up uniquely allow for every single combination of intervals and chords to have syntactic strength in comparison to any other interval, and this uniquely allows every mode to have a very distinctive sound compared to every other mode.

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.

So I don't feel that really explains the existence of the diatonic system, really. It existed before these justifications existed, so the issues are going to be either mathematical, perceptual or (more likely) a mixture of both!

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.

Why not? Lydian Dominant, Melodic Minor, Dorian b2nd and the Altered Scale all come from the same framework of steps and half steps and all sound very different. If they were off no use then styles such as Jazz wouldn't work. And while we can argue some of these scales are difficult in static situations, such as the altered scale, then we can also see the Locrian mode doesn't function well for extended periods either.

Thus it doesn't work nearly as well in long-term organization as the traditional diatonic scales do... Is this the stuff that the people of the day were thinking about? Probably not, but it's a fairly decent explanation as to why they preferred one scale over another.

I think I've already said I'm dissatisfied with this approach. Why diatonics? Why not another asymetrical scale?

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.

If you think about leading tones in terms to the harmonic relationship you're bound to fail, since it's grandfathered in through a system that didn't even think about harmonic relationships (alright, they DID understand the overtone series and whatnot, but they didn't apply this in what we call a 'harmonic relationship' until much later, officially by Jean-Philippe Rameau in 1722 with his Treatise on Harmony).

Well for counter point to have existed then harmony had to be the construct they worried about, even if they weren't giving the concept a name. The Picardi Third and the leading tone are things that were generated by something innate to the Western ear. The picardi third can be described by the apparant dissonance of 3rds in any sense, if possibly the voices avoided moving to them! We still don't know, after this, really why we have a perfect cadence. The V-I's sound is a reason we perceive V-I as good voice leading, not the other way around. Though neither statement ever argueably tackles the issue! Semitones weren't even considered easy intervals to sing, going from ti to doh had to have some underlying cause.

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

It's far more powerful than the M3rd - Unison motion (whole step both ways). Since the d3rd was considered too dissonant for use, the m3rd was the closest proximity possible to the unison, so that was the interval of choice when it came to 'cadencing' a song (in the context of counterpoint, a cadence doesn't need the dominant on the bottom). This same logic applies to the M6th - Octave resolution, as well (in comparison to the m6th - Octave). It's not such a big deal nowadays, but back then a song wouldn't sound complete without such a strong resolution.

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?

So really, it's as simple as what is closer to your goal. In counterpoint, the closer a note is physically to the next note, the more powerful the drive to it. And yes... you can also find all this in Zarlino. It's really a great read when it comes to counterpoint, as long as you can stomach the old style philosophy and translation.

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!

Why Music?

[jpbear]

I just use a soundgoodizer.

Thats my favorite scale.