Twentieth Century Harmony – Chapter 2: Scales

And we march onward into the unknown.

MODES

So, Persichetti starts the chapter with the church modes. I disagree with this approach, so I will instead start with major and minor before going into modal scales harmony. It goes without saying that these scales have a full set of 12 transpositions, and each one has a specific flavour.

Major scales exist. They have chords.
Minor Scales exist. They too, have chords.

Boom, done. Next up, we have modal scales. I will go over these in detail, because of the difference in harmonic materials. I will go over these using the method stated in Ex. 2-9. I took the liberty of rearranging the example to be more condensed.

persichetti 1

Now, in major and minor, there exists primary, namely I, IV, and V in major, and i, iv, and V in minor, alongside secondary chords, which is everything else. The difference in modal harmony is that each mode has different primary and secondary chords both from major/minor, and from each other. The easiest way of determining the different primary chords is determining the different from major/minor, and selecting those chords as the primary chords.* I once again took the liberty of putting it all together in such a way that doesn’t drink paint.

*with the exception of chords containing a tritone – more on that later, mainly because it directly fucks with locrian harmony.

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Now, the reason for the tritone issue is because it REALLY wants to actually resolve. It’ll go either in or out, and it will pull to a tonic chord that isn’t what you actually want it to go to (ie: iv° in lydian does not want to go to anywhere but V, forcing V to sound more like tonic than I will). Now, you might notice that, in locrian, the i chord is actually a diminished triad. That’s a glaring issue, because it will pull to II, and make it sound major instead of locrian. Persichetti suggests a brilliant solution to do this; if you want to use a diminished triad as a secondary triad in modal writing, omit the 5th of the chord. That way, it remains stable, and can still be used in the mode. The same is extended to locrian. It’s fucking genius. Furthermore, it is quite possible to do modal modulations, and can be quite effective if you are working from a single tonal center through drones or melodic circling, as seen here in 2-10.

persichetti 3

Polymodality is also a thing. However, not in the way you might be thinking. “Oh, you arrogant fucking twat you, wouldn’t an example of polymodality be A lydian against D dorian?” Partially, yes. However, it would *also* be polytonal. The reason why is that polymodality refers to the simultaneous occurrence of two different modes, where polytonality involves multiple key centers. D dorian against D lydian would be an example of pure polymodality, because D is the tonal center in either case. D mixolydian against G mixolydian would not be polymodal, due to the commonality of mixolydian, but it would be polytonal due to the two tonal centers. This system is one I do not wholly agree with, and here’s why:

I prefer the Milhaud approach to polytonality, though it also has its own issues in this context. Basically, all flavours of polytonality derived from major and minor can be described using a two-part classification method. For example, polytonality that is written as D major over F minor can be described as VIII-D. It’s significantly abbreviated compared to D major over F minor or D/Fm. It’s also specific and quite easy to understand.

milhaud 1milhaud 2

However, this is only really usable with major/minor polytonalities. The list of different combinations when it comes to writing with the seven modes, much less trying to describe polytonality/modality with other, more exotic modes (ie: Messiaen’s Modes of Limited Transposition) is out of the question. In fact, by my count, which may be vastly incorrect, there are 49 different combinations of this, requiring the use of double letters up to WW to describe them. The next issue would be devising a way of ordering them in such a way that is logically sound and consistent without being arbitrary. Personally, I would start with lydian/lydian, ionian/lydian, mixolydian/lydian, etc., due to it being easy to understand due to the predictability of the movement of the modes as it goes on. Of course, we can also use A-G for the bottom mode, and a numerical designation for the one above, resulting is a beautiful 7×7 grid of this. In this system:

A – lydian
B – ionian
etc.

and

1 – lydian
2 – ionian
etc.

And use it from bottom to top, in terms of register. Seen here as an extrapolation:

milhaudExtrapolation.PNG

Anyway, I digress. This whole mess is a part of the reason why 20th Century Music tends to forgo key signatures in favor of accidentals, because the tonal centers and modes are not necessarily consistent throughout a vertical section of music, and tends to change frequently in a horizontal section of music.

SYNTHETIC SCALE FORMATIONS

Oh god, this one is gonna be broad as hell.

While the overtone series suggests major the strongest, it is not all that can be achieved with scalar formations. The example below is a series of different scales that can be achieved with synthetic formations.

persichetti 4

To fully understand scalar construction, we need to look at the different tetrachords within a specific scale (of course, these only really apply in seven-tone scales). The two tetrachords in a seven-tone scale are not directly linked to one another, and one can be the same, similar, or different than the counterpart of the pairing. In the example below, ignore the part about “Multi-octave.” What I am showing in this example is the way one would go about looking at tetrachords, but Persichetti does not show a visual example of this until Ex. 2-29 in reference to multi-octave scales, but more on that later.

persichetti 5

Of course, the question that immediately springs to everybody’s mind is harmony. “Oh Dr. Theory Slap’d, you curmudgeonly git, how does the harmony work if there are no ways to determine primary chords?” Well, pillock, we can actually define primary chords, even if there are no ways to compare the scale to others to determine characteristic scale steps. But to do that, we need our ears, and a bit of a rule to go by that is highly contextual. And that rules is:

– If there is a major tetrachord within any part of the scale, then the tones bordering that tetrachord are our characteristic tones.

– If that is not the case, the chords that are enharmonic spellings of major or minor chords are primary.

– If those do not exist, the characteristic tones are found in the notes that form augmented or diminished intervals with the tonic.

Once we determine the characteristic tones of a scale, then the process of determining primary and secondary chords is identical to the process used in finding the primary and secondary chords of the modes somewhere above this, and the chords function in the same way; secondary chords function as gravitational forces towards the primary chords. Here is example 2-23 of a thing.

persichetti 6

The wrench that is very rapidly thrown into the metaphorical gearbox of harmony is that the primary chords are frequently augmented, diminished, or some other bizarre fucking combination that will be referenced in like, chapter not-this-one. This is easy to fix; don’t play the primaries as augmented or diminished. Instead, alter the harmony in some way. “But Dr. Theory Slap’d, you blooming nutter, won’t that cause the scalar formation to stop functioning as a synthetic scale and start pushing it somewhere else?” And there you have glanced off of, if not directly hit the nail on the head of why I disagree with Persichetti here. I would personally advise you to use the chords as they appear in the scale (unless you’re modulating or shifting modes of course), as it would retain the characteristic flavour of the tone as whole. Sure, you might get stupidly unstable primary chords, but don’t lead them resolve. Hell, I don’t let things resolve even in conventional keys, much less so in these ones.

Also, this is only considering the harmony of the prime form of the scale (I mean, it’s not necessarily in correct prime form, but you know what I mean). We can also utilize the harmonic possibilities of the inverse of the original scale. That’s right, we can do literal-black-fucking-magic to get around the constraints stated above. Relevant:

relevant

In all seriousness, we can use the inverse because the it has a very similar, if not identical, to the prime form. Kind of due to them being inversions of each other. Like I said, black magic. Some of them are even inversionally symmetrical. Meaning, if you invert it, it will be the same, examples being the below, as well as scales like the whole tone scale and I’m fairly certain that some of the Messiaen mode also possess this characteristic (I know the second mode of V does it. The set is 0-1-5-6-7-11). Which is a bit of a mindfuck sometimes.

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And this whole thing can also be polytonal and polymodal. And this does not end here. In fact, there are scales that are multi-octave in scope. Meaning, if you miss tonic on the way up on accident-but-probably-not-because-you-are-a-sadist, you can continue the scale with new, different tetrachords until you hit tonic. Even if you don’t hit tonic for eight more octaves.

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The most interesting part, I think, of multi-octave scales are the harmony. Unfortunately, due to the harmony getting to the point of being ridiculously stupid thick, the harmonic options become more limited with this scales. The primary chords in these scales are massive, and encompass the multioctave nature of the scale (meaning; twelve-tone chords are a bit of a thing generally), and can go upwards of fifteenths, seventeenths, and even twenty-firsts. Here is a taste of multi-octave scales in use:

persichetti 10

While you can go into polytonality and polymodal textures with this, don’t. It becomes increasingly complicated to retain the different characters of both scales in a polytonal texture. But I will challenge you all to do this anyway. I might even do it later.

PENTATONIC AND HEXATONIC SCALES

I have no fucking clue why Persichetti put these after synthetic scales. The only reason I’m leaving them here is to be faithful to the source material.

persichetti 11

Pentatonic scales, as the name implies, are scales with six two seven five tones. Due to this, the harmony tends to be more or less the complete opposite of multioctave scales, though with a similar outcome; they are quite limited in scope and don’t have a whole lot of options for harmonization. In order to counteract monotony, I recommend either A. not using pentatonic scales or B. changing mode or key often (shouldn’t be too hard, considering the subject of Twentieth Century Harmony). Beyond that, as Persichetti writes, “lavish use of ornamental tones, pedal points, and frequent modal interchanges or modulations to other pentatonics will also help prevent harmonic monotony.” Furthermore, pure pentatonic music is best used in short bursts because it gets very dull, very quickly. To this end, they either tend to melodize or harmonize, but rarely both at once.

And hexatonic scales are scales with nine five thirteen six tones.

persichetti 12.PNG

Copy+paste the entire pentatonic section to the hexatonic section because they tend to be quite similar with each other. However, due to the extra tone in hexatonic scales, there are more harmonic possibilities to be utilized, and therefore, can be much more lively when it comes to harmonization and melodization.

CHROMATIC SCALE

This fucking thing. It’s easy to cover, until it comes to harmonization. When you have all the tones, you have all the chords. It gets a bit difficult.

Of all the applications, it is best utilized with what I would personally define as non-functional harmony. The chromatic scale has no characteristic tones, and therefore, no primary and secondary harmony. The construction of these chords is not discussed until a later-not-this-one chapter. But we can cover the different flavours of chromatic writing:

Diatonic harmony and chromatic melody:

persichetti 13

Diatonic melody with chromatic harmony:

persichetti 14

Chromatic melody with chromatic harmony:

persichetti 15

Mixed chordal structures formed by chromatic motion:

persichetti 16

And finally, chromatic harmony generated by chromatic melody:

persichetti 17

All of these may be used. It’s important to mention that you can also generate harmony from a melody by taking the melody and crushing it into a vertical set. Serial harmony also tends to function in this manner, though with a few more rules.

APPLICATIONS

Oh thank God. This fucking chapter was tedious as hell.

This weeks questions were chosen by two good friends of mine: Amanda, who is practically my older sister because we (quite literally) grew up together, and Heather, who I did not grow up with, but has recently left on her mission (best of luck!). The questions selected were 4, 5, 13, 17, 18, and 21, and because this chapter has 25 questions, the 25% rule is getting an amendment: I will personally select another question arbitrarily to do that is not one of the prior numbers. And this number, after some deliberation, will be #7. As with the last chapter, I will post all 25 questions, and I will highly recommend you do all of them. This time, I hope to be able to put actually-good examples down for the questions selected.

questions 1questions 2questions 3

As for an update on Tymoczko, I’m up to 2,300 words and I’m probably halfway or so through the chapter. It will be a bit, and won’t be as I intended both of these series to work (originally, I intended for alternations between Tymoczko and Persichetti; at this point, every third will be Tymoczko, and hopefully it will work that way). Anyway, I’ll post the examples selected sometime this week, and I’ll yell at all of you next week.

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