Schillinger's Theory of Pitch-Scales: Second Group Properties and Application Examples

Book 2 from the Schillinger System of Musical Composition Book 2 is about pitch-scales. The Second Group of scales has a single root and a range exceeding the octave. Create expansions from a diatonic scale with six or seven pitch-units. Implement melodic forms and octave adjustment. Create a melodic continuity with rhythm superimposition and a modulation section. These techniques are applied to three short composition examples.
Contents:
00:00 What this video is about
00:28 Section 1 Introduction
00:54 Section 2 Properties of Second Group Pitch-Scales
00:58 Section 2.1 Schillinger System Context. Books 1-5 in the System of Musical Composition.
02:13 Section 2.2 Methods of Tonal Expansion
04:46 Section 2.3 Melodic Forms in the Expansions
08:26 Section 2.4 Melodic Continuity and Modulation. Continuity with rhythm superimposition.
11:17 Section 3 Group 1 Pitch-Scale Examples
11:23 Section 3.1 Orchestral texture from 7-unit scale. Diatonic harmony, Riemannian TF.
18:38 Section 3.2 Synth-Orchestral ambient texture from 6-unit scale. Random arpeggiation.
27:01 Section 3.3 Bossa Nova phrase from 6-unit scale. Free harmony.
28:42 Summary and conclusion
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[@christopherheckman7957]

(1) 4:31: "As a generalization, for a scale with n pitch units, there will be n minus 1 possible tonal expansions." (I was going to say that that is only correct when n was prime, but I forgot that in expansion, if a pitch that has been used is encountered again before the scale is finished, then you go to the next unused pitch; i.e., for a 6-pitch scale, you go 1, 3, 5, 2, 4, 6, not 1, 3, 5, 1, 3, 5, ..., mentioned around 18:52.)
(2) 7:11: Re octave adjustment: It seems that the point of doing the expansion is to produce notes that are in the scale, and excluding the others. If you adjust the octaves, then you don't seem to get anything new; you can get the same MFs by permuting the original Group 1 scale after octave adjustment.
For example, the E2 expansion of the C major scale from C4 to B4 is C4 F4 B4 E5 A5 D6 G6. If you adjust the octaves, you can end up with a Melodic Form like C4 F4 B3 E4 A4 D5 G4, which is just a permutation of the original scale to C4 F4 B4 E4 A4 D4 G4, with additional octave alteration.
((After a few minutes of thought)) It seems that limited octave alteration might be a better rule to use. For instance, if you do an E1 expansion of the C major scale, you get a Group 2 scale which is 2 octaves wide. Now, the only octave alterations would be changing the octave by *an even number* (e.g., 15va instead of 8va). You are essentially putting copies of the Group 2 scale on top of each other, like you put copies of a Group 1 scale on top of each other to reach other octaves; thus, you would be able to play C4, C2, C6, C0, C8, etc., but not C1, C3, C5, C7, etc., and it would retain some of the Group 2 flavor.
(3) 11:05: To my ear, this has the same flavor as 12-tone compositions (so you could call them 7-tone compositions), because you're permuting the notes and (almost) not repeating any notes until you've played all 7.

[@FransAbsil]

@Christopher Heckman (1) Since most Schillinger book examples are for scales with 3, 5 or 7pitch-units, the even-numbered issue is only mentioned briefly, bottom of p 133, without an example (that's why I deliberately presented the later tutorial example). (2) Your observation is correct, octave adjustment is equivalent to pitch-unit order permutation of a lower degree expansion. When preparing this video, I was hesitant to mention the octave adjustment aspect (see the book p. 134 and 136), since it introduces inconsistency in the formal approach. I still puzzle over why Schillinger does this, and my best interpretation is that very wide compass melodies are a) hard/impossible to play on most acoustic instruments, b) lose comprehensible & coherent character for the listener (significantly reduced experience of a scalar basis). But this is speculation, since I cannot ask the man himself. (3) Agreed. Indeed when creating a continuity from the MFs there is similarity with serial music melody writing. The similarity would even be stronger for the higher number expansions (E3, E4, etc) without the octave adjustment (as discussed in the previous point). That is why I keep repeating that this technique does not yield 'beautiful' (traditional) melodies; the latter are subject of a different chapter in the SSoMC. Thanks for sharing your observations!

[@damoon57]

You were supposed to make his book easier not harder .

[@FransAbsil]

@damoon57 Thanks for the comment. Believe me that I am doing my best to simplify Schillinger System subjects by presenting alternative notation and many examples that are not in the books. Apparently I failed in your case. Since it seems that you are familiar with the original books, please be so kind and specify where I am making things overly complicated, so I know where to improve in the future.