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Dorian mode symmetry
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Dovdimus Prime



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PostPosted: Wed Oct 13, 2004 5:20 am    Post subject: Dorian mode symmetry Reply with quote  Mark this post and the followings unread

I've just noticed something unusual about the dorian mode - it has a line of symmetry. If you play it from the top or from the bottom you encounter the same sequence of intervals. Is this well-known and a complete yawn or is this not a common observation? Do you think it has any applications?

This means (I think) that if you take any piece of music written in the major scale, and rotate the score 180 degrees around one of the second degree notes (or any music in natural minor scale rotated around a fourth degree note), the resulting melodies will contain the same sequence of intervals, just going the other way. I'm going to be checking this out when I get home.

Also, the chords would be reflected, e.g. major triads would become minor triads and vice versa.

Just thought that was quite interesting. Could have applications in terms of developing melodies and chord progressions and suchlike.

Help a student of music theory. Any comments?

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mosc
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PostPosted: Wed Oct 13, 2004 6:46 am    Post subject: Reply with quote  Mark this post and the followings unread

That never occured to me before, but I think you are onto something. I often play music using harmonies derived by using inversions of the primary voice, usually delayed a few beats, or even measures. If you listen carefully to the music I wrote for your "My name is... " movie, you observe that inverted melodies. http://electro-music.com/forum/topic-3730.html It's a big technique used by the serialists. Retrograde is another good one. I usually pic the inversion point by what sounds the best - not for some intellectural theoretical reason.
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zynthetix



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PostPosted: Wed Oct 13, 2004 2:47 pm    Post subject: Reply with quote  Mark this post and the followings unread

Never really thought of that. I used to use "dorian modes" with raised 6ths or 7ths for modulating key on guitar, but I wasn't really playing in the dorian...I was just thinking of the pattern I was playing as a dorian with raised degrees , the end result was a melodic minor. /tangent

you can get the same symmetry by rasing the sixth degree of a natural minor scale (aeolian mode)....kind of melodic minor, but without the raised 7th.
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aquanaut



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PostPosted: Wed Oct 13, 2004 5:07 pm    Post subject: Reply with quote  Mark this post and the followings unread

Quote:
This means (I think) that if you take any piece of music written in the major scale, and rotate the score 180 degrees around one of the second degree notes (or any music in natural minor scale rotated around a fourth degree note), the resulting melodies will contain the same sequence of intervals, just going the other way. I'm going to be checking this out when I get home.


You now have an understanding of music theory above average because i don't understand what you're saying here. Smile

Never saw the symmetry of the dorian mode. One thing i like about dorian is the capacity you have to take any chromatic note from it, play a minor third from that note and back into the mode and it always sounds good: d,e,ab,b,a,g,a,f...

or dm7 chord + E major scale 2 octave higher melodically and then resolve to D with the melody, when you resolve change the harmony.
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Dovdimus Prime



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PostPosted: Thu Oct 14, 2004 8:12 am    Post subject: Reply with quote  Mark this post and the followings unread

mosc wrote:
I often play music using harmonies derived by using inversions of the primary voice, usually delayed a few beats, or even measures.


Hmm. Could be a semantic mix-up here, I'm not sure I know what you mean. As far as I understand it, a chord is inverted by moving one of the voices up or down an octave, over the other voices. Inverting a major chord produces another major chord. Rotating a chord around a note reverses the order of the notes. Rotating a major triad produces a minor triad, because the minor third is now underneath the major third.

mosc wrote:
If you listen carefully to the music I wrote for your "My name is... " movie, you observe that inverted melodies. http://electro-music.com/forum/topic-3730.html


By the way, thanks for that, it's ace!! Very Happy I will have a closer listen, although I doubt I'd be able to spot it, because I'm crap at that sort of thing...

mosc wrote:
Retrograde is another good one.


I assume this means reversing the order of notes in a melody, i.e. producing a palindrome?

_•°ø wrote:
You now have an understanding of music theory above average because i don't understand what you're saying here.


Well, no, actually I realise just how badly I explained it! Confused

All I'm talking about here is turning a score upside down - just flipping it over, using one of the notes as a pivot - rather like flipping over a game of Connect 4. This turns all the peaks into troughs and vice versa. Chords become changed: e.g. major triads become minor triads and vice versa. The intervals in the melodies (i.e. from one note to the next) are the same size, but go in the opposite direction. This changes the sequence of intervals in the scale, and therefore the scale itself, as I mention below. But if the score is rotated around the tonic of the dorian mode (which is the II of the major scale / ionian and the IV of the pure minor scale / aeolian), then the scale of the upside-down piece remains the same, because the dorian mode is symmetrical - i.e. the same played upwards or downwards from the tonic.

I certainly wouldn't understand what I've just said above, by the way!! Shocked

Here are some more thoughts. If you rotate a score upside-down around one of the notes like I've been describing, the pattern of intervals of the scale changes - in fact, it reverses. It's like playing the scale from the top instead of from the bottom. Each mode is changed by this process into another mode as below:

Ionian <- -> Phrygian
Lydian <- -> Locrian
Mixolydian <- -> Aeolian
Dorian <- -> Dorian (precisely because it's symmetrical)

I didn't realise this relationship existed. I haven't really thought about how it might be used yet. If anyone has come across this sort of thing before, let me know!!

A caveat. Turning a score upside-down would probably change the perceived tonal centre of the piece as well, so the twinning of modes I’ve mentioned above is probably not really the case.

A short rant. There are scales which are described as symmetric scales but they aren't necessarily symmetrical in this way - i.e. that they produce the same pattern of intervals when played up or down from the tonic. I actually think that the type of symmetry I'm describing is a better use of the word than the type represented by symmetric scales - i.e. that they contain small repeated interval sequences that render them tonally ambiguous. (I think 'ambiguous scales' is a better term for them than 'symmetric'.) As an example, diminished scales are described as symmetric but are not symmetrical when played in either direction from the 'tonic'. HW becomes WH and vice versa. Still, it's not up to me to challenge established musical terminology!!

Thank you for reading my thoughts. Sorry if this post is too long, dense or just plain stupid. As you will gather, I've just being doing a lot of thinking about scales and modes recently. If you have any comments, or want to tell me just how wrong I am, please do!!! It's good for my education...

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jksuperstar



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PostPosted: Thu Oct 14, 2004 9:19 am    Post subject: Reply with quote  Mark this post and the followings unread

Lot of legalspeak lately, this topic just triggered an odd thought. If you applied this method to an existing piece of music, would it still be considered remixing/plagerism? Or would the new note structure be defined as a "new" song? In essence, the "seed" of the song is still another peice of work, so is the question becomes-- is applying a cakewalk script to change the score considered the same as applying a delay to an audio sample? worded like this, it seems illegal to me. But having an obscure relationship such as this create a bridge between two pieces of music could also be a "long stretch" in a legal system. I guess one could argue the orignal work was an "inspiration", and just because you used math to create your own work rather than emotion, doesn't make it any less of an arguement.

I'm sorry off topic
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Dovdimus Prime



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PostPosted: Thu Oct 14, 2004 10:53 am    Post subject: Reply with quote  Mark this post and the followings unread

It is a good question. Because you are just applying an algorithm to someone else's work, not really adding anything creatively - I would class it plagiarism.

I'm going to give it a go.

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elektro80
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PostPosted: Thu Oct 14, 2004 12:30 pm    Post subject: Reply with quote  Mark this post and the followings unread

Well yes... there are a lot of systems inside the system and you have all sorts of methods derived from seeing the systems.

You probably already know abou this text..? Symmetry as a Compositional Determinant

Larry Solomon also wrote this nice little text way back : Music Theory & Analysis 

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PostPosted: Thu Oct 14, 2004 1:12 pm    Post subject: Reply with quote  Mark this post and the followings unread

Back to the inversion question. I mean inversion like the serialists did.

Take a tone row: C D E F

If you invert his, you get: C B-Flat A-flat G

Start on the first note and go down the same numbers of semitones you went up in the original row.

I like to do this with midi to automatically generate harmonies.

Often, it also transpose the inversion, or invert around a different note. If you delay the derived melody you get sort of musical canon.

Personally, if you write a melody, I don't think you automatically own every inversion or retrograde melody that is derivable from it. If that were the case, we'd end up with nobody being able to write anything. It is reasonable to speculate that one could take any piece of music, and any other piece of music, plug them into a program and get some algorithm that would generate one from the other.

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aquanaut



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PostPosted: Thu Oct 14, 2004 1:35 pm    Post subject: Reply with quote  Mark this post and the followings unread

First, thanks for bringing this subject up, it answered a couple of question of mine. One of them was why, in C major, switching from a C major chord to a C minor chord works. If you take the same upward interval step of the ionian mode and spell it downward you get this: C,Bb,Ab,G,F,Eb,Db. Ab major scale. C minor triad is chord #3 and is the pivot chord between C and Ab. ex: Fmaj7,Cmaj7,Dm7,Dbmaj7,Cm7,Abmaj7. IV, I, II, IV, III, I


Now, the symmetry of the Dorian mode means you can't create anything new from it.

One weird thing. E phrygian... Downward it creates an E major scale.


Quote:
If you rotate a score upside-down around one of the notes like I've been describing, the pattern of intervals of the scale changes - in fact, it reverses. It's like playing the scale from the top instead of from the bottom. Each mode is changed by this process into another mode as below:

Ionian <- -> Phrygian
Lydian <- -> Locrian
Mixolydian <- -> Aeolian
Dorian <- -> Dorian (precisely because it's symmetrical)


I understand. But if you flip the score upside down, the semantic, the meaning of the score dissapear also. CEG becomes GEC and it can't be seen as a triad. Revoiced it's a C chord inversion on the fifth, Or a Eminor6
chord.
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mosc
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PostPosted: Thu Oct 14, 2004 1:52 pm    Post subject: Reply with quote  Mark this post and the followings unread

Well, if you are using the C clef which puts the C on the middle line, then flipping the score does a pretty good job of inversion around C. Laughing
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Dovdimus Prime



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PostPosted: Thu Oct 14, 2004 2:17 pm    Post subject: Reply with quote  Mark this post and the followings unread

jksuperstar wrote:
If you applied this method to an existing piece of music, would it still be considered remixing/plagerism?


Well, make up your own mind. Is this my work?

http://www.dovdimusprime.com/EKNM.mid

Glad to see this topic has kicked off some discussions. Don't fully understand everything you guys are saying, I'll have to work at it - but it looks interesting and worthwhile.

Elektro - thanks for the resources, I haven't seen them before - I'll check them out.

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PostPosted: Thu Oct 14, 2004 6:09 pm    Post subject: Reply with quote  Mark this post and the followings unread

Dovdimus Prime wrote:

http://www.dovdimusprime.com/EKNM.mid


Well, it sounds like Mozart, but then again, so does Haydn. Shocked

You're on the right track. Keep it up. Try to get 40 symphonies, 23 piano concertos, several operas and major liturgical works in before you are 37. Twisted Evil

Seriously, slow that down and use some more interesting instruments and you might have something pretty nice.

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PostPosted: Fri Oct 15, 2004 12:11 am    Post subject: Reply with quote  Mark this post and the followings unread

Hey.. the mid is cool. But yes, record it with some fat and nice sounds.. and slow it down a bit.
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Dovdimus Prime



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PostPosted: Fri Oct 15, 2004 1:10 am    Post subject: Reply with quote  Mark this post and the followings unread

mosc wrote:
You're on the right track. Keep it up. Try to get 40 symphonies, 23 piano concertos, several operas and major liturgical works in before you are 37. Twisted Evil


Once I write the CAL routine I need to rotate all of Mozart's work, I'll have equalled his body of work in one evening!

mosc wrote:
Seriously, slow that down and use some more interesting instruments and you might have something pretty nice.


Elektro wrote:
Agreeing with what Mosc said.


Ha ha! I really don't think it's my work, but I will be using the technique to generate variations in my own stuff.... thanks! Very Happy

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PostPosted: Sat Mar 26, 2005 2:28 pm    Post subject: Reply with quote  Mark this post and the followings unread

Here's an interesting site to have some visual clearity when you need it!

http://www.looknohands.com/chordhouse/piano

Just click the mode on the right side and look at the 'half-steps'

that reversing of the intervals -that's only what it is- is an interesting thought btw, i like it!

When you're on the site, check out the following: Very Happy

In C > Click on the modes in the following order and look at the keyboard how it changes... Ionian, Mixolydian, Dorian, Aeolian, Prygian, Locrian

That refers to the circle of quints Rolling Eyes
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PostPosted: Wed May 04, 2005 3:57 am    Post subject: Reply with quote  Mark this post and the followings unread

Have you tried compressing the intervals?

For those of you with a little time and a way of producing quarter-tone music try this. Pick a pitch as the center point (if your music has a key center that pitch mid range will do-that pitch will not change). Then take a look at each interval above and below that pitch, and reduce the distance by half. So, an octave becomes an agumented 4th and a fifth becomes a major 3rd one quarter step flat.

It sounds complicated and time consuming, but not too much after you get going and know what the intervals become.

Of course you don't have to compress by 1/2. Different ratios have different effect and placing the center point at the top of the note range, or above, or lower has interesting effects too.

The result may not be the most musically useful (especially if you use a Bach chorale as a source), but you will come away from the experience with a greater understanding of how fifths and octaves work in tonal music.

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mosc
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PostPosted: Wed May 04, 2005 6:31 am    Post subject: Reply with quote  Mark this post and the followings unread

This is easy to do on an analog synth by attenuating the 1 volt/octave signal from the keyboard or sequencer. Of course, you can stretch this too.
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