Reddit mentions of Structural Functions of Harmony (Revised Edition)

Schoenberg makes a similar observation in Structural Functions of Harmony.

>Structural functions are exerted by root progressions.
>
>There are three kinds of root progressions:
>
>(1) Strong or ascending progressions:
>
> (a) A fourth up, identical with a fifth down
>
> (b) A third down
>
> The term strong is used because great changes in the
>constitution of the chord are produced. When the root
>progresses a fourth up the root note of the first chord is
>degraded, becoming only the fifth of the second chord. In the
>case of the root progression a third down, the root note of the
>first chord is degraded even further, becoming the third of the
>second chord.
>
>(2) Descending progressions:
>
> (a) A fourth down
>
> (b) A third up
>
> They do not posses the conquering power of the ascending
>progressions. On the contrary, they promote the advancement
>of inferior tones. In I-IV, II-VI, III-VII, etc., the fifth of the
>first chord always advances to become the root of the second.
>And in I-III, II-IV, III-V, etc., a tone of inferior importance, the
>third, advances to become the root.
>
>(3) Superstrong progressions:
>
> (a) One step up
>
> (b) One step down
>
> In both cases all the tones of the first chord are "conquered",
>i.e. eliminated entirely.

The text includes examples which point out the roots becoming fifths and thirds in the first case, and fifths and thirds becoming roots in the second case. Schoenberg goes on to suggest guidelines for the implementation of these structures. (edit: formatting)

Yeah... I really don't condone self-teaching for many reasons, but obviously you don't want to hear that right now, so this is just a bit of a disclaimer.

Personally, I think if you're going to study on your own, it's really worth it to get a good background in the "bookwork" elements of singing, like vocal anatomy and pedagogy, as well as language work.

On that end, I would recommend books like Doscher's The Functional Unity of the Singing Voice, McKinney's The Diagnosis and Correction of Vocal Faults, Miller's The Structure of Singing, and McCoy's Your Voice: An Inside View. These are really not easy reads, per se, but they should give you a really good foundation in understanding what's going on physically, and being aware of potential problems in vocal health and hygiene, which is arguably the biggest reason to study with a teacher. (In other words, a good understanding of the physical vocal structure can help prevent unknowingly contorting it in an unhealthy way).

I would also strongly recommend some study in language, diction, and text. Even for non-classical singers, it's worth it to know about how diction and articulation works. Diction for Singers, A Handbook of Diction for Singers, and International Phonetic Alphabet for Singers would be a good start. (And in general, a working understanding of IPA is crucial).

You can also work on text analysis - I'm not really a poetry/text specialist so I can't recommend any specific books, but I'm sure there are many out there.

Marchesi's Bel Canto: A Theoretical and Practical Vocal Method is another resource to look into, as it contains many exercises designed for technical practice - I liken it to the Hanon exercises commonly found in piano curricula. However, I will definitely warn that these exercises can be easily done incorrectly and can lead to the development of very bad habits, so please proceed with caution and be aware that there are many ways to execute the exercises, some of which are not healthy.

In addition, I would recommend a broad study in music theory, music history, and ear training. [Musictheory.net](http://www.musictheory.net] and Teoria.com are well-respected websites that offer lessons and exercises to learn beginner to intermediate level music theory concepts. Good-ear.com is another website I often recommend that focuses more on ear training. I would also recommend checking out the sidebar and FAQs over at /r/musictheory for more details.

In addition to these websites, some books worth mentioning include Berkowitz's A New Approach to Sight Singing, Music for Analysis, Caplin's Classical Form, Taruskin's Oxford History of Western Music, Grout's A History of Western Music, and Schoenberg's Structural Functions of Harmony. While of course you don't need to have a doctorate in music theory to begin singing, I think it can only be helpful to have a really broad basis of understanding in various parts of music, as they directly affect your ability to read, understand, and interpret music.

Anyway, that should give you a pretty decent start. Please feel free to post if you have any additional questions.

Go for old editions. Clendinning/Marvin's The Musician's Guide to Theory and Analysis is respected and tackles a large number of concepts in reasonable depth. Somebody else mentioned the Schoenberg books. Schoenberg was an excellent composer, thinker, and pedagogue. You may find his works to be in a completely different vein from modern harmony textbooks, but they can be incredibly rewarding to a composer.

Structural Functions of Harmony

Fundamentals of Musical Composition

Harmonielehre

Preliminary Exercises in Counterpoint