Diatonic Harmony Nomenclature in the Schillinger System of Musical Composition

[@aryamvarona5488]

you are a musical hero !!! I am reading all your work and its incredible !! this channel deserves more attention !!!!!!!!...blessings from Cuba !!!!!

[@FransAbsil]

@aryam varona Thanks for the positive feedback and kind words. Heroes end as either Achilles or Ulysses; may we all find our Ithaca. I return the greetings to Cuba, country with great music. Ideas about increasing the channel visibility are welcome.

[@lawrencetaylor4101]

This is exactly what I needed at this time as a piano Nooby and 4 months of trying to learn music theory. Merci beaucoup.

[@FransAbsil]

@Lawrence Taylor thank you and welcome to the channel. This is indeed a good video to start with. I hope you will have a pleasant journey. Don't hesitate to ask, in case you have a question.

[@david_lynch]

Your channel is a gem

[@FransAbsil]

You're welcome. Was there any subject you liked in particular? Or any suggestions for future episodes?

[@heinvanmaarschalkerwaart9799]

Indeed, thank you for the explanation, Mr Absil. . Gershwin followed lessons with Schillinger. Benny Goodman also, but BG was more interested in playing the clarinet than in the advanced theory of SCHILLINGER Harmony. The rhythm theoory is even more complicated with si formulas

[@FransAbsil]

Thanks for the comment. Indeed there was a time where several well-known musicians were taking lessons with Joseph Schillinger. These days the System of Musical Composition seems relevant only to a small interest group. Indeed learning techniques from the system is hampered by its quasi-mathematical character. Hopefully my videos will inspire a wider audience to try and experiment with his methods.

[@heinvanmaarschalkerwaart9799]

I am interested as I am an arranger and as such known as Art Marshall. My arr are on You tube and mainly cover Gershwin themes for clarinet or sax quartets, Check out my Oh, Lady be good. The rhythm formulas will make a lot of people shrink back. Anyway I enjoyed your explanation very much. Thank you.

[@danmcgirr4210]

Legend! Thank you for these fantastic videos. Your knowledge is inspiring!

[@FransAbsil]

Hope you're not bothered by the mix of UK and US English in the voiceover, as, with Ira Gershwin, 'I say n-ee-ther and you say n-ay-ther'.

[@danmcgirr4210]

No problem here.

[@amityrockwell5162]

Thank you very much. I just bought these books and they are very dense with information. A second set of eyes, yours in this case, helps clarify things.

[@FransAbsil]

@amityrockwell5162 I am glad to hear that you appreciate this introduction to the notation and nomenclature in the Schillinger System. Did you feel the need to search for online sources after buying the books? In case you have further questions or suggestions for other system aspects that may benefit from clarification, please let me know.

[@amityrockwell5162]

@@FransAbsil At first I did not. I just assumed it would be difficult but the experience would make me better. I just searched KZbin to see if anyone else had followed this path. That's how I found your excellent work.

[@FransAbsil]

@amityrockwell5162 Thanks for elucidating.

[@wasabi1drful]

That was very informative! Thank you!

[@FransAbsil]

@wasabi1ful You're welcome. Does this imply that you are new to the Schillinger System? (I do suggest this video tutorial as an excellent starting point.) Have you been watching other tutorials on this channel and felt the need to go to this video? (Just curious.) Thanks for the positive feedback.

[@wasabi1drful]

@@FransAbsil I heard mention of the Schillinger system but I never looked into him. I want to better understand his pitch scale theory. I have watched quite a few of your Schillinger videos and the Riemmian transformations. Do you think theories and methods are adaptable to “free” improvisation?

[@FransAbsil]

@wasabi1ful Your idea to look into the Schillinger Theory of Pitch-Scales absolutely makes sense when looking for source material to be applied when melodic elements are the primary factor in 'free' improvisation (indeed a somewhat contradictory approach). In particular have a look at Chapter 3, The Evolution of Pitch-Scale Styles. Of course there are many more sources on (modal) scales in modern improvisation. You may also want to consult the Slonimsky Thesaurus of Scales and Melodic Patterns. Riemannian Transformations are useful when writing harmonic framework, less suitable for improvisation in my opinion. The Schillinger Symmetric System of Harmony may be a better source, as such chord progressions occur more frequently in modern jazz improvisation. But it all depends on the level of 'freedom' you would like to achieve and master. Hopefully this response makes sense. Thanks for asking.

[@wasabi1drful]

@@FransAbsil Thank you for the thoughtful suggestions! I look forward to more of your videos.

[@FlorianPi]

First of all, thanks a lot for all of your amazing videos! The Schillinger system is totally new to me and some things are unclear to me: 1, I suppose the concept of positive and negative root cycles is very similar to the concept of "progressions vs. retrogressions"? 2, What I find interesting is that, at least in pop music, there are various examples of the extensive use of ascending fifth progressions. At least in modal music, it even seems to be the preferred way to approach the circle of fifths clockwise. One progression that comes to my mind is the vi-IV-I-V chord loop that is very commonplace in pop music (although a better notation would be i-bVI-bIII-bVII as it seems to be rather an example of pure Aeolian). --> bVI-bIII-bVII (a.k.a. IV-I-V) would be an example of an ascending fifth progression --> To me this "retrogression" sounds pretty stable nevertheless (otherwise constantly looping over those chords, which happens in a lot of pop songs, would be obnoxious) What do you think about that?

[@FransAbsil]

@FlorianPi thanks for the positive response about the many Schillinger System videos. I hope you will find lots of useful ideas and techniques here. I'll try and answer your questions: Q1. Retrogressions: believe it or not, I had to look up this terminology (not found in my library textbooks). But yes retrogression and negative (diatonic) root cycles are similar concepts. Schillinger comes up with this root cycle category from a scientific approach to diatonic scales in 1st expansion, whereas (I guess) retrogression is the label assigned in music analysis of 'unusual' chord progressions. Q2. Sequences of negative root cycles, such as R-5 (your example), and stability. Where did the association positive root cycles = stable progression originate? In summary: a) In Common Practice period classical music in diatonic major/minor proper handling of leading tones (7-1, 4-3) is relevant, and positive root cycles take care of that. b) Dissonance handling of extended chordal functions requires correct preparation and resolution of the dissonant 7th, 9th, etc (vocal music and counterpoint tradition). This will be achieved through positive root cycles in classical music (you may want to watch my series of Schillinger Diatonic Harmony tutorials). What is different in your examples and pop music considerations? 1) there are diatonic modes other than pure major/minor involved, so leading tones lose some of their 'importance'. 2) the impact and emotional quality of the 'song' is determined by other factors than traditional voice leading. 3) in case of triadic chord progressions there are no dissonant extensions. Were these present the perceived (in)stability would certainly be affected by the root movement. Hopefully this bit of musicological musing makes sense.

[@FlorianPi]

@@FransAbsil That makes sense! Thanks a lot!

[@InLightTone]

Wow, really great, definitely want to learn this system. Thanks!

[@FransAbsil]

@InLight-Tone. Glad to hear that you were inspired by this video, that explains the nomenclature of a specific part of the Schillinger System of Musical Composition. Good luck with your endeavour. If you need guidance, let me know.

[@udomatthiasdrums5322]

still love it!!

[@申翀]

One thing I don't get is the definition of positive and negative root movements. The graph is not symmetric, and positives are drawn as ending on d1 while negatives are drawn as **starting** from d4? And the tonic is ill-defined, since later you showed that c to a on C major is also positive?

[@FransAbsil]

@user-gm5bj9lx7u Sorry to hear that the video is somewhat confusing. Let me try and clarify; I assume you are referring to the root cycle (RC) definition diagram at about 12:06 into the video. I tried to put a lot of information in the staff notation: 1) The fact that diatonic root cycles are based on the 1st expansion (E1) of the scale, i.e., scale written as successive thirds. Thus we obtain E1 = d1-d3-d5-d7-d2-d4-d6-d1 (for a 7-pitch scale). 2) The definition of positive / negative RC is based on the direction of root movement in the E1 expansion: to the left (d1-d6-d4-...-d3-d1-...) is positive, to the right (d5-d7-d2-...-d3-d5-...) is negative. Note that in the negative RC example I start on the degree d5; that is in order to demonstrate the fact that positive/negative RC is only dependent on the root movement between two successive roots (not on the absolute values, so there is no need to define everything relative to the tonic degree d1, here pitch-class C). The later examples for positive cycles at 13:17 and negative at 15:09 are also based on the diatonic scale on root C, but that is irrelevant for the RC classification. That should answer your 2nd question: when the root moves from C to A in the diatonic system, that corresponds to a descending (minor) third and thus is a positive diatonic root cycle R3. Does this answer the question(s)?

[@申翀]

@@FransAbsil Thanks for explanation. I kind of get it, but I'm still a bit unsure about what really distinguishes positive from negative. Like what makes d1-d7 negative instead of a positive 9th down (going d1-d6-d4-d2-d7)? Is it because the interval must be confined within an octave? Or is it that only the nearest distance on the expansion are taken?

[@FransAbsil]

@user-gm5bj9lx7u Within the octave range any diatonic scale degree can be reached from a starting pitch with one of the root cycle classes {R-7, R-5, R-3, R0, R3, R5, R7}. These 7 unique interval classes are sufficient to describe any diatonic root movement. Your assumption is correct: for classifying interval leaps of more than an octave these should be reduced to the single octave transposition equivalent (not the actual notated music, only for the interpretation in terms of root cycles). With this reasoning you should be able to do exercises with labelling any diatonic harmony system root progression.

[@申翀]

@@FransAbsil Very helpful. Many thanks.

[@ivanmamede]

Does it follow the fundamental bass or rule of octaves?

[@FransAbsil]

@ivanmamede To be honest, I had to look this one up, in order to (hopefully) understand the question (my difficulty lies in the word 'follow'). The video you are referring to is about the Schillinger Diatonic System Harmony terminology (an introduction); the Rule of the Octave is a system for harmonising a stepwise bass with a series of inverted position chord structures, mostly S63, or S43, S2 (a method). There I see more equivalence with the technique of creating 4-part settings with voice leading as the result from the application of a pattern of root cycles and chord inversion positions. That is part of his Book 5 General Theory of Harmony, and on this channel there are many tutorials that present specific techniques from that book. However, for you the best would be to study Chapters 6, 7, 9, and then write your own progressions. That would provide the best evidence of an equivalence with the Rule of Octaves. If you meant to ask something different, please help me by clarifying the question. Thanks for asking.

[@ivanmamede]

@@FransAbsil My question was like "how do you know the chord you're going to use only looking for the bass?". All the chords used so far in the video used the tonic as the bass, so I thought that Schillinger inherit it from old classical. But I think I understood more o r less what you said. Studying music in english a challange.

[@FransAbsil]

@ivanmamede Ah, now I get the question. Since the video focus is on how to create chord structures in 3rds from the 1st expansion of the pitch-scale and the root cycle concept, all single layer, 4-part chord progression examples are in root position. I left other Schillinger diatonic harmony system aspects until later videos (such as doublings and inversions). So, in short, the system does definitely incorporate all 'classical' plus more sophisticated harmony writing. Thank for clarifying!

[@pookibear89]

Hello everyone, maybe someone of you can help me out? Around 11:30 f# is introduced as 11. I am probably missing something basic: why is it f# an not f? Thanks in advance!

[@FransAbsil]

@pookibear89 Thanks for asking. I'll try and answer the question. The example around 11:30 into the tutorial explains the concept of Schillinger System diatonic chordal functions. These are the set of 7 numbers {1=root,3,5,7,9,11,13}, not using any alteration symbols. The example then demonstrates this principle for the extended CMaj7 chord. The regular extension for this chord type is the #11 (here f#), not the f natural (which would create a minor 9th interval with chordal function 3=e in the lower octave). If I had built this example around the Cm extended chord in thirds, the chordal function 11 would indeed have been f natural. So I guess the confusion is caused by the mix of introducing the Schillinger chordal function concept with an illustration based on the extended major diatonic chord. Does this answer the question?

[@pookibear89]

@@FransAbsil Hello FransAbsil, thanks for your reply. I needed to look up extended chords. Those were not part of my repertoire. Shouldn't the extended CMaj7 chord (e.g. CMaj11) have an f? However the example is specificly telling us CMaj#11, and i guess that is why we are seeing the f#. I am wondering if the #11 is a stylistic choice, or a consequence of Schillingers theory.

[@FransAbsil]

@pookibear89 Extending the Cmaj chord in thirds may include the chordal function 11. The chordal function number labeling for harmony tension control in diatonic harmony is part of the Schillinger System approach. And this is irrespective of the specific diatonic 7-pitch scale. So indeed one could construct a CMaj11 chord with either 11=f natural (diatonic 4th degree in C Ionian and other modes) or #11=f# (diatonic 4th degree in Lydian scale). However as a static (sustained) extended chord, the regular/standard solution is with #11, the f#. With the higher chordal functions voiced in upper parts, you would obtain a maj9 (e-f#) and a M7 (g-f#) interval. This chord structure is more 'pleasant', less dissonant than the min9 (e-f) alternative structure. That is why you find the 'regular' structure Smaj7#11 in jazz and popular music.