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In the videolecture about mathematics and music ..there is a topic about transformation of a melodic line into a another related melodyline
BACH the musical genius from the past.. uses in his canons all kinds of melodic transformations ( see videolink
http://www.zerospec.com/testmap/TransformationsandSymmetry.mp4 )
I mention here some..
- original melodyline
- inversion --> in Synfire = flip at anchor
- retrograde ---> reverse at anchor
- retrograde inversion ---> ??????????
- more ..see video link
Inversion can be seen as a flip horizontal around the anchor symbol and retograde as a flip vertical around the anchor symbol
It is easy performed the "inversion" and "retograde" transformation in Synfire to use the <CTRL> + <SHIFT> left(cursor) /right/up/down
<CTRL> + <SHIFT> up/down = flip at anchor = inversion- <CTRL> + <SHIFT> left/right = Reverse at anchor = retrograde
With this 2 you can do 2 refelections around the x-axis(anchor) and y-axis (anchor) by starting with the original melody
HOW to do now a retograde inversion ? --->
Exercise: make 4 instruments ..starting with a melodyline ( perhaps you want to use the Goldberg variation from BACH itself ) and add the 3 transformations and listen to them all
The video is explaining the transformations with the aid of group theory ..if gives more oversight what you can do with the original melody by using a grouptable when you are doing more complicated transformations with a melody.
Bu Studying BACH you can learn from his transformations..
At the end of the video reveals more about how BACH composes!
Perhaps a idea to dig up some of the old undergraduate studymaterial about groups ?
===========Bach Goldberg Variations===============
To apply melodic transformation you need to study the book to learn to recognize the transformation : The complete idiot's guide : music composition..chapter 13 : employing repetition and variation
- original melody --> transformations
.....................
-inversion ( melodic, mirror ( exactly ..can add chromatic notes, contour )
-retrograde
-retrograde inversion
-diminution ( shrinking )
-augmentation (expanding )
Fr., 15.03.2013 - 09:30 Permalink
man, thanks so much!
I really enjoyed the video, being a mathematician I really enjoyed all the talk and the way the guy describe things..he is really passionate...plus now I see bach and others in different way..they were just crazy :)
very interesting concepts
well, if we want to do retograde inversion we just need to do a retrograde and then the inversion so:
<CTRL> + <SHIFT> up/down + left/right
and that's it.
thanks a lot
G
Mo., 18.03.2013 - 10:12 Permalink
VARIATION TECHNIQUES
Pitch chance(1):
pitch(inversion,retrograde,etc, [modulation( example : Fmaj to Gmaj )]+ modal mixture(or named also mutation: example major to minor ), Chords only!--> reharmonization( or also named diatonic chord substitution( interesting to do diatonic reharmonization in Synfire( rather easy to perform )] or
Same pitches, different rhythm..
Rhythm chance(2).. study this
Same rhythm, different pitches..
Theme alteration (3): truncation,expension,thinning,ornamentation.
Note: reharmonization (as a variation technique for chords): diatonic substitution ( replacing a chord with a related chord either a third above or third below the original )..is a good starting point to bring variation in your chordpogressions ( use for this a dedicated chord container to listening what chord progression you like the most )
The BACH transformations in General MIdi.. the real instrument as a sample is more realistic..try to reproduce it
I try it again with the VST Halion symphonic orchestra and with HALion 4 again ( has also good sounds , based on samples too )
Basic transformation what are easy to perform in Synfire are:
-start original theme ( melody )
- inversion ( melodic, mirror, contour ) -->
-retrograde
-retograde inversion
- diminition ( shrinking.. rhythm)
-augmentation ( expanding ..rhythm)
- sequenze ( pitch )
Again the book idiots guide : music composition ch 13 explains all and has exercizes with answers ..tough
It is all about repetition and variation of a melodic theme .. repetition can be lasting for a maximum of 2 bars and than you must start to do a variation on the theme.
Example : how about "Ornamentation" a another vaiation technique: embellish the melody with neighboring tones, chancing tones..what else more ..to master this ( embellish structural tones ),see book.
A example of a melody with the inversion and the retograde inversion of it
First the inversion 2 times ( 2 x 3 measures) and than 2 times the retrograde inversion and than together voor 6 measures
As extra fun idea.. a did a reharmonization for the inverted melody and the retograde inverted melody ..
A more realistic sound..than it sounds much better
I am wondering about BACH transformations if there are chords involved ?
Mo., 18.03.2013 - 15:52 Permalink
exploring js bach Goldberg variations http://oregonbachfestival.com/digitalbach/goldberg/
see BWV 1087 ( hoover with mouse) : fourteen canons on the first eight notes of the goldberg ground ( see other video too about the build up of the canons (difficulty degree, importance)
example ( you can listening to the canons !)
canon 1 : the sogetto ( the goldberg ground : the 8 notes of goldberg) is accompanied by its retrograde
:idea: the choice of instruments is important here
canon 2: The soggetto 's inversion is accompanied by its retrograde
......
After canon 4 it becomes interesting ( the same thought has the person in the first video )
After these canons ... to go further ( go wild with the canons ..)
Canons of the Musical Offering
http://www.ams.org/samplings/feature-column/fcarc-canons
A last example how one of BACH's canons work : a crab canon
http://www.openculture.com/2009/09/how_a_bach_canon_works.html
Starting with the end of a existing melodyline and using this a a new start of a second melodyline ..is that a retrograde ?--> NO it is a retrograde inversion as a later see on internet about this subject http://en.wikipedia.org/wiki/Crab_canon and thinking on the geometrical transformation of it ...than you get a moebius strip !
Was BACH modest? (pious)
"The aim and final end of all music should be none other than the glory of God and the refreshment of the soul."
~ JS Bach
Perhaps is this all to use for composing modern music..that is the reason why i study a introduction of BACH
Mo., 18.03.2013 - 20:48 Permalink
Hi Gianpiero,
Makes it easier to understand if you are a mathematician ..
I used already some transformations in my short music pieces made
well, if we want to do retograde inversion we just need to do a retrograde and then the inversion so:
<CTRL> + <SHIFT> up/down + left/right
Yes i left this open ...for the readers :) ( i knew the answer already )
------------------------------------------------
Needed to understand this better is to use the book !!
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The anchor symbol is needed for the inversion and retrograde and suppose if you import a midi melodyline in Synfire, than it is divided in segments--> you can pick out a random lenght of the the imported melodic line and make a phrase out of it and assign a anchor to the phrase ..than you can apply transformations
Note: after reading something more about BACH it seems that he is influenced by the old Greeks
Di., 19.03.2013 - 12:12 Permalink
Hi gianpiero
More food for thoughts : ( a bach guide) http://www.scribd.com/doc/74973110/Johann-Sebastian-Bach
I am interested in reading more about the "musical offering" of BACh to understand more how he composes.
Classical composing has also my interest
Also i read in the Bach guide :
He is now generally regarded as one of the main composers of the Baroque style, and as one of the greatest composers of all time.
Well, the greatest composer all time..that's impressive
The "musical offering" seems to me interesting , because it is not only written for a harpsichord as instrument