Twelvetone Triads and Hexachords: Part 1 Polychord Structures and Properties
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- čas přidán 5. 07. 2024
- This video tutorial is the first in a series about 12-tone triads, that is, sets of four triads that together cover all chromatic pitch-classes. This episode discusses the pairwise combination of triads in thirds into hexachords. These receive a corresponding Pitch-Class Set prime form label and Hindemith Chord Group classification. Triad pairs are stacked as polychords with a Ulehla Chord Tension Level indication, depending on the distribution of dissonant intervals over the chord structure. The video contains polychord voicing, chord progression and two composition examples.
Contents:
00:00 What this video is about
00:28 Section 1. Introduction
01:03 Section 2. Fundamentals
01:19 Section 2.1. Twelve-tone triads
03:09 Section 2.2. Hexachord combinations
05:04 Section 2.3. Chord tension level classification
07:17 Section 2.4. Polychord voicing
14:00 Section 3.1. Chord progression and composition example 1, 4/4, guitar etude
18:05 Section 3.2. Chord progression and composition example 2, 3/4, orchestral suspense cue
21:55 Summary and conclusion
Find the interactive Pitch-Class Set Analysis tool at
www.fransabsil.nl/htm/toneset...
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#TwelvetoneTriads #Polychords #CompositionTechnique
Great channel Frans, brilliant editing, you should have way more subscribers!👍👍👍
@CliffordMartinOnline Thank you for the kind words. Had a brief glimpse at your channel, will return. As to the number of subscribers, still doing my best to present the hidden gems in the Schillinger System (and other) composition techniques. Trying to show practical examples but I may be missing the target after all. Fate, destiny? Or simply not enough humour / online clowning to attract viewers? Who will tell? Stick to the cathedral builder mentality: contribute with your craft although one will never see the end result. Have a nice weekend!
I stumbled upon this video while looking into the ut re hexachord from medieval chant. I’m really enchanted by the rich dissonance that these triad-based hexachords produce. It hadn’t occurred to me that you could have a sense of tension and release in a 12 tone setting. But, of course, it makes perfect sense. Traditional jazz harmony is chalk full of dissonance that our ears are perfectly comfortable with. Also I think that the modern tempered tuning system lends itself quite well to a 12 tone palette, whereas some notes in the diatonic scale suffer from the adjustments that equal temperament makes necessary.
@robbes7rh Thank you for adding the meaning of 'hexachord' in Medieval music, where it refers to scale and melody (as opposed to 2-layer triadic harmony in this video; maybe an omission on my side). And for your view on dissonance control potential in twelvetone structures and progressions. A most valuable contribution to the discussion.
@@FransAbsil - that’s very kind of you, thank you.
Gotta say, I'm a big fan of your exploration of atonality. I used to have a narrow-minded view of atonality, but your videos are helping me dive deeper into this side of music. I came back to your channel in the nick of time since I am composing a piece with atonality in it. (I've never done this before!) Also, I'm a big fan of your clean editing skills. Your videos are extremely well organized and they make learning fun. Cheers!
@Exero, once again, thanks for the continual positive feedback. These crazy days, one needs a bit of encouragement in order to keep producing in-depth tutorials. A discovery of the atonal language through the use of pitch-class sets and their properties might very well enrich your musical vocabulary. And help you escape from the straightjacket of diatonic harmony; good luck on your journey.
@@FransAbsil It's my pleasure to give this kind of feedback. I also can fully understand needing encouragement for producing materials in a niche category. I'm in the same boat with my channel. Fear not though; counting your blessings rather than loses can keep one hopeful.
Also, if some of the atonal content in my music appears on my channel, I'll be sure to share it with you!
Excellent tutorial! Thank you.
You're welcome. Hopefully you'll also like the other episodes.
Great , thank you again. beautifiul presentation1
@Hein van Maarschalkerwaart, pleased to hear that you also enjoyed watching this video, about building modern chord structures and creating atonal harmony.
I stumbled across this idea a couple of years ago, but didn't know what it was called. (I also investigated 3-chord seventh chords that use every pitch class exactly once, as well.) My motivation was transforming one of them into another by swapping the chords that contain two particular pitches; e.g., if you take {C,G#m,Db+,Bb+} and swap where the G and G# occur, you get {C+, G+, Db+, Bb+}. It turns out that you can get from any set of 12-tone triads to any other by repeatedly swapping pairs of pitch classes. The diagram showing these relationships also looks rather interesting.
I haven't seen Part 2 of this video yet, but it sounds like you'll be doing something like this there.
@Christopher Heckman. To be honest with you, it is only recently, after buying the Slonimsky book Thesaurus of Scales and Melodic Patterns, that I found the 12-tone triad overview there as well (p. 177, after #1250). How did the search for the sets of three 7th chords fare? I guess the added value of this video lies in the analysis of pairwise triad combinations into hexachords and their properties as PC-sets with cardinal number 6. I never investigated the 2-pitch swap approach to move to a different 12-tone triad set; I use the PC-set analysis tool from my website and then decide on the number of common pitch-classes for transformations. Thanks for presenting your transformation technique; have you considered creating tutorials yourself?
@@FransAbsil I wrote up a search using Maple, and I looked for various structures.
It found 61 12-tone triads, each of which at least three swaps to another one.
For seventh chords: There are 116 "12-tone seventh chords", each of which has at least 8 swaps to get to another one.
There are 66 ways to swap two pitch classes, swap another two, and swap another two, and get back to the one you started with. There are 16 groups (maybe 16*12) of four 12-tone triads, where you can get from one in the group to any other in the group by swapping two pitch classes.
(My 12-tone triads consisted of four chords whose types were in {major, minor, diminished, augmented}, and I had quite a few types of seventh chords, maj7, dominant 7th, min/major7, minor 7th, both types of diminished sevenths.)
I never really put any of these to any use (i.e., no compositions yet), but it seems like you could create pieces where each part has its own 12-tone triad, and adjacent sections have adjacent 12-tone triads.
A lot of what I do with music is hit and miss, which is one reason why I haven't posted any videos. I teach math at Arizona State for a living, which gets top priority.
@Christopher Heckman Sorry for the late reply, there's been a backlog. How clever to use Maple to find the full solution set. It's been a while since I used Matlab and Maple myself. On the channel there's a video with Lutoslawski 12-tone chords, a subset with 3 stacked 'minimum tension' 7th chords. Maybe somehow you'll find the time to experiment with the full solution set and, more importantly, meaningful transitions between these 12-tone chords.
@@FransAbsil Don't worry about backlog; I understand. I will have a few weekend where I will be grading over 100 exams, and the whole weekend will disappear then. 8-)
@Christopher Heckman. I am sure you will beat me in review and calculus skills, but 100 exams in a weekend; 15 minutes per copy implies 3 working days, 30 minutes leads to mission impossible. Hope this all goes well.