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Martha Lucia

Forms, Structures, Progressions ?

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For classical era form(beethoven, mozart, haydn) get 'Classical Form' by William Caplin. For baroque era form, search 'sinfonia' and 'suite' on wikipedia (the suite will give you rhythms for each movement). You can check out my suites on score exchange if you have sibelius score, if not I could pm you some pdfs, and that'll show you the basics. There's basically a characterstic rhythm, and an A and B section. The A and B sections are repeated once each, A starts in tonic key and ends in dominant. B starts in dominant and ends in tonic (it's useful to write alternate repeat endings so the ends of each section don't sound as final just yet). I used to put the B section in the dominant mode rather than key (purposefully, I like the harmony produced as I was just starting to study world musics).

Everything else is based off any of the forms you encounter from studying those two things, from tone poems to opera overtures. It's all a matter of just how far the composer deviated from the form for more avante garde pieces like Liszt. free-form is still psychologically restrained by the human mind after all. After a some time studying that it may interest you to study the form of so called free form movements. I recommend How Ravel Orchestrated the Mother Goose Suite by Peter Alexander, this will show you the ropes in doing so (takes all of 2-3 weeks to go through, rather than a lifetime of studying the score. It gives you a process for privately studying other scores that may interest you in the same manner). But again, this free form stuff is all up to you, you might just need to see 2 or 3 different composer's ways of deviating from strict form before you get the lightbulb above your head.

I would, however, start with Tonal Harmony from Kostka. It will have you mastering nearly every aspect of tonal harmony, and gets your feet wet into form. After that you might be interested in baroque stuff, I'd get 'Fundamental Studies in Fugue' from Hugo Norden as well as his 'Technique of Canon' (maybe not, see below). Loverich 'examination fugue' is also tremendously helpful. This is all assuming you have mastered counterpoint, which you only need one book to do so, which is free of charge since there is no copyright on ancient books, it's 'A treatise on counterpoint and fugue' from Luigi Cherubini. Most people say get Fux's counterpoint book, but it's no where near as good as this. It also touches on the basics of fugue and other forms, like the inverse contrary motion form. Should pretty much be it, unless you want to get into jazz, if so get Andy Jaffe's Jazz Harmony and Mark Levine's Jazz Theory (though Levine has a bit of an Allan Holdsworthian modal approach to 'this chord denotes this scale' you'll soon see his logic). Everything else is up to you, but that's easily 2 years of material.

on technique of canon: the books is cheap and worth the money, so still get it. just ignore all his crap about repeat calculations as that's irrelevant. as long as it sounds good in the harmonic idiom of your choice, it's fine. copypasta this somewhere and read it once you get the book (this was a review I submitted to amazon:

I spent about 2 weeks with this book, 1-3 hours a day on a daily basis. His analyses are incredibly deep and enlightening. He explains just enough to where the student must learn the rather more intricate nuances on his own by attempting to write out each kind of canon and when they get stuck, analyze extensively Norden's examples and analyses of real works by Bach and Haydn. That's most of what you will be doing with this book, once you've wrapped a new concept around your head, you'll spend about 2x as much time working out every single little kink you can think of by really digging into the do's/don't's and the how's of his examples. Probably the most helpful thing in this book are the tables of inversions, the main one being page 27 which you will be flipping back to a lot. No trial and error needed if you have it spelled out for you like that, you will instantly see if something is invertible or not.

As mentioned earlier, the analyses of his own examples as well as from Bach and Haydn are incredibly detailed. However, a lot of this just ends up being ways to optionally double check your canon in purely formulaic and mathematical terms, and are useless otherwise, and rather time consuming, albeit intriguing methods of breaking down any canonic passage to the smallest detail. 'Three part canon in vertical alignment' is a section that is supposed to let you map out the melodic movements and their resulting harmonies for multi voiced canons. A simple trial and error note by note approach is much quicker, this section is useless unless you have the working memory of a goldfish.

His method of repeat calculations is made to look like a method to actually write out the last few bars of a canon properly, but in effect it's merely a way to double check your canon. This was the biggest stepping stone for me, so if you get this book copypasta the following write up into a text file, print it out (at least 10 copies) in bold 24 point font, and tape it up all around your house, making sure to reread the write up in it's entirety after every single page you read of this book:

wheereas x=the DC inversion (he refers to it as structural DC inversion, it's the only thing you need to know to write any canon except retrograde and contrary motion as well as augmentation/dimunition to an extent):

If you have a 2 voice canon with the voices separated by one canonic unit, then the canonic unit 1 of Risposta should be an interval of x from the canonic unit one of the Proposta.

If you have a 2 voice canon with the voices separated by a bazillion canonic units, then the umpteenth canonic unit of the Risposta should be an interval of x from the corresponding umpeenth canonic unit in the Proposta. Double counterpoint inversions (DC) are calculated by 2 intervals and then subtracting 1, (5+4-1=DC8). If there is a negative number involved (voice crossing) then add 1 (this only happens in augmentation/dimunition, since in other canon types you simply subtract 8 to get things working again (an interval of a 9th while in DC 8 is also 2 in inversion, or the upper voice dips down a 2nd above the lower voice). We can allow this to happen if it's contrapuntally sound, he simply subtracts 8 from the 2 voices involved and pretends 9 is 2).

So if I have a canon in DC 8, with 2 canonic units before the entrance of the Risposta, the first unit in the Risposta (bar 3 assuming whole notes are taken as the CU) should be an octave from the first canonic unit in the Proposta (bar 1). Bar 4, the second canonic unit of the Risposta, should correspond in an 8ve exactly to canonic unit 2 in the Proposta (bar 2). Bar/CU 5 in R is bar 3 in P, 6 in R is 4 in P etc. Every last unit should align in this manner, right on to the very very last notes of the canon mechanism, no repeat calculations are necessary.

In a 3 part canon (or 4 or even more parts, you break it down into the comprising three part canons, P-R1-R2, R1-R2-R3 are the two comprising three part canons that make up an 4 part canon for instance)...it's a bit different as there are two arrangement types:proposta in the middle voice, proposta in an outer voice. even if you have a hundred rispostas, it's basically going to break down to these two (think about that for a moment, the proposta is either in a middle voice or it's not, it's either in an outer voice or it's not). the method of calculating the structural DC inversion is only somewhat different between these two.

If proposta is in the middle, take CU 1 from R1, calculate the interval from CU 1 in the P, and add that to the interval from R1 CU 1 to R2 CU 1. That's your structural DC inversion. From R1 CU1 to P CU1 is 'v1 of CU1'. from R1 CU1 to R2 CU 1 is 'v2 of CU1'. you may also have v1/v2 of CU2/CU3 etc if there is more than one canonic unit. Let's say from R1 CU1 to P1 CU1 is a 5th. From R1 CU1 to R2 CU1 is a 4th. We would have DC 8. You can double check the other canonic units if you have a multi CU canon, but they will all come out to DC 8, so that's just unnecessary double checking imo.

If proposta is in an outmost voice, instead of adding v1 to v2, v2 needs to be inverted by the octave. so if v2 (CU1 R1 to CU1 R2) were a 4th, it's octave inversion is a 5th (just as a 3=6, 2=7 etc, if you don't know that these are off the top of your head stop reading and go finish learning counterpoint). So instead of 5+4=9-1 = DC 8, we would have 5+5=10-1=DC9.

In a 4 voice canon or more, the process has an added step since there are really 2 three part canons (or more if there are more than 4 voices). Basically, R1 will become the P of the second canon, so for a 4 voicer we have P-R1-R2-R3. We split them in two, P-R1-R2, then R1-R2-R3 (which would be P-R1-R2 when calculating this second canon). Let's say the first canon, P-R1-R2, has the P in middle voice. You know what to do. Now the second canon, R1 becomes P. So now our new P, let's say it's in an outer voice. the entire thing may look like :P-Alto, R1-Soprano, R2-Tenor, R3-Bass. You should also know how to calculate the structural DC inversion of a canon with P in an outer voice by now. As you can see, you will have to write the entire 4 part canon while keeping in mind there are really two 3 parters in operation at once. It's best to attempt to make both canons in DC 8, though he does give one where canon one is in DC 12 and the other is in DC 10. P-R3 does not get calculated, R3 should be good harmonically with the P and all other voices automagically. Just make sure to not get lost, v1/v2 of canon one CU1, v1/v2 of canon one CU2, CU3 etc (however many CU you're using) should add up to canon one's DC inversion. as you do this make sure note by note that v1/v2 of canon two CU1 adds up to canon two's structural DC inversion. remember that all canonic units of a given canon all add up to the same DC inversion automagically, so all units in canon one = x and all CU in canon two = y. So if the different canons are in different DC inversions, it becomes trickier, that's why in 4 or more voicer canons it's best to make all canons in DC 8.

In invertible canon, the DC inversion for both R above and R below the P are calculated rather simply. Let's say the R above is a 6th above P (starts on C in the P, A on the R). Now let's say The R below starts on B below that C, so that R in the upper voice is a 7th from R in the lower. That's our DC inversion for both versions, DC 12 (7+6=DC 12). Simply take the interval from R in the upper voice to the P, and add that to the interval from R in the upper voice to R in the lower voice (C-A is 6, A-B is 7, 6+7=DC12). So now you've only to write out both at once, in DC 12.

In contrary motion, it's even easier, I had a lot of fun with these. No DC is involved, just an easier to use series of numbers.

Basically, he shows how to make a series of numbers, once again using his repeat method. Once again it's unnecessary as the series numbers will automagically check out fine no matter where you calculate from. Let's say it's a one CU canon. The interval from the R-P in bar 2 of the composition and the interval from R-P in bar 3 give us our series numbers. That's our replacement for DC inversions for contray motion canons. Let's just say we had an interval of 7 and 8 in bars 2 and 3 respectively. write out the smaller number going to 1, and then to the left a few as well, you may wish to write it out the left a whole lot you may not:

9..8..7..6..5..4..3..2..1.-2

10 9..8..7..6 5..4..3..2..1

......^ origin point

now then, as long it all checks out you're fine. Let me add that you can have a bit of voice expansion and crossing in these numbers. Instead of a 5/6, you could have a 12/6 or 5/13 since 12 is a 5th plus an octave and 13 is 6 plus an octave. -2 is a seventh, -3 is a sixth, so voice crossing works as well as voice expansion, no need to keep the voices with an octave of each other. You can therefore have a fuckton of fun with contrary motion canon, if it sounds good to you it is good, provided the series numbers match (taking into account the awesome fact of octave displacement of course, 2/3 works as well as 2/10 or 9/3 etc). If you have more than one CU then each one gets a separate number series.

You can also have the P in one key and the R in another in contrary motion. They must be a semitone apart, and they typically sound the major key a step below (sometimes the minor). Allegedly 2 minor keys cannot be sounded simultaneously in this manner unless they were all natural/aeolian without a big headache of dissonance and chromatic alterations. Basically, D and Db major will make C or C minor. Start on the 7th of the lower key (Db's is C) and the 4th of the upper key (D's is G) so it's always a canon a 5th a way for these bitonal fusion canons (it's the only way to really get them to work pleasantly). The example from Bach given actually has a fuckton of modulations and is supposed to be C minor, I wrote my first one all in one key, Db-D sounding in F major. all notes were natural except B, which was always flat. Note that I made it to where B never occured in the other voice, so no B natural to Bb screw ups happened so it never even went to the subdominant, C, it stayed in F the entire time, which made it sound more unified and you could hardly tell audibly that it was bitonality. This in my opinion is more pleasant than the route Bach took where it modulates, even if smoothly, every single bar. Sounds too odd unless the tempo is at like 50 bpm). So you can see the possibilities and fun of contrary motion.

For retrograde canon it's trial and error note by note, and almost as fun as contrary motion. You calculate the DC inversion by taking the interval between the voices in bar 1 and the interval of the last notes. So let's say in bar 1 both voices have a C, there's an octave. The very last canonic unit, let's say bar 1337, the voices are both on C. That's an 8ve. so we have DC in 15 (8ve one octave higher). they can also be in unison or whatever. Then just fill in note by note, fill in the lower voice bar 2, then take that and put it in the corresponding upper voice bar 1336 and so on til you get to the middle. For Perfect consance DC intervals (DC 1, 5, 8, 12, 15 etc) you will want to have an odd number of CU notes (1337) in this case. Otherwise you get a repeated interval in the middle, and with these DC inversions it'll probably be contrapuntally horrifying parallels of some sort. Basically an even numbered DC inversion is 'impossible' you'd have to move it an octave, as there are no repeated middle notes if there are an odd number of notes. I then went on to write some anyway. He gives you a table that lists what the middle intervals will be/ DC 8/15 will have a unison followed by an octave or similar. So you'd need an odd number of notes to get rid of this problem of having stagnant middle intervals for 2 units. In the same manner, if you are in an odd numbered DC interval such as DC 11, which has a middle interval of 6, if you were to write them in an odd number of notes, you can skip having a middle interval here as well (although an even amount of notes in DC 11 produce a 6/6 middle intervals, which isn't all that objectionable, but you get the point).

Invertible crab/retrogade canons suck, they are contrapuntally bleh no matter what. The trick is that you don't want to use both the upper R and lower R in your composition, at least not at once. unless the counterpoint is only somewhat objectionable in both of them, then you could have them appear separately (perhaps have violins play the upper R and then when that's done have cellos play the lower R, with violas taking the P). There's really no way of getting good harmony out of having both play simultaneously though, no matter how well you feel the counterpoint isn't all that bad for the two individual canons.

Contrary crab canons are easy, whatever interval appears here, is the same interval over there. If I have a 10 bar tune, bar 1 being a 5th, bar 10 will also be a 5th. This won't work unless I have a separating coda, we'd have parallel fifths. So once again, use an odd number of notes/units for retrogade canon, including contrary motion. For invertible contrary motion crabs, they suck. You are limited to whatever intervals/notes work in whatever DC inversion you chose and they once again cannot be played simultaneously without adding free parts to it to clarify the harmony and 'justify' the bad counterpoint that inevitable results. Remember for inverted canons, take the interval from P-R in the upper voice and add that to R upper to R lower (C-A is a 6th, = A B is a 7 = DC 12 invertible contrary motion crab canon). Dc 12 isn't too bad, but there will be a lot of disjunct movement, so no clarinets or brass.

I'll not even go into double or triple crab canons in contrary motion, harmonically difficult to produce and contrapuntally noncontrapuntal, they are rather pointless and rather florid/vague in tonality, and sound rather bland.

You can see how contrary motion 3 or more voicer canons could be rather difficult, perhaps more so than in similar motion. Unless, like similar motion having both canons involved in a 4 or more voice canon use the same DC inversion, all use the same number series will help. A 3 voice canon in contrary motion is really two canons at once, a 4 voicer will be split into 2 part canons, P-R1 and R2-R3 while making sure it all sounds in good harmony. Sometimes it might help to have R2-R3 in a different number series than P-R1, sometimes not. You could mix it up and have R1 in contrary motion, and R2/3 be in similar motion to the Proposta (they'd therefore be in contrary motion to R1). Then R3 could be in contrary motion to R2, or similar motion. These are very hard, I wouldn't worry about mastering them too much. Just stick to writing 2 voice contrary motion canons and writing free parts to them, either contrapuntal or accompaniment. that's typically what 2 voice canons serve as, either a duet of two ensembles/solo instruments or as a basis/framework/skeleton of harmony to which countless free parts can be added.

Augmentation/dimnution is easy, just trial and error. Don't even worry about so called DC inversions here, just pleasing harmonies and counterpoint (every single unit is in a different DC inversion by his method). Let's take a simple 2:1 ratio. An 8 note theme, so that the longer voice plays once through (8 notes) and the second voice must play twice through (16 notes total). Notes 1 and 2 in the faster voice correspond to notes 1 and 5 in the slower voice, so it must produce good harmony and counterpoint in both. Notes 3 and 4 in the faster voice correspond to notes 2 and 10 in the slower voice, and so on. this is the process for all kinds of ratios, such as 3:1 (note that some ratios such as 3:2 or 4:3 are rather difficult so they aren't canonic/repeated in the vast majority of the musical literature, just imitative/one pass through. You could have different things for the other pass throughs in the faster voice. Perhaps have it repeat at a different pitch (watch out for moving nontertianally, the harmonies will be completely different, move by 3rds/6ths not by 2nd/4ths/7ths and you should be fine). The second time or third time around you might do it in retrograde. So now note 1 and 2 in the faster voice correspond to note 1 and 8 (or whatever the last note is) in the slower voice. Watch the harmony, no DC inversions are needed just acceptable harmony and counterpoint.

Not even going to go into rounds.

He explains a bit about ways to go about embellishing these skeleton canons, and how to use them as harmonic skeletons. You might try different things at this point, such as just making the skeleton notes stay the same, but have completely different embellishments in the different voices so people can hardly even tell visually or audibly that there is a canon in effect at all. You could take entire lines or bits of them and make new canons, or use them as cantus firmi for free counterpoint additions. Countless things. Mastering the technique of canon is the biggest step in mastering counterpoint and imitative writing, fugal writing becomes much funner as does counterpoint in general. Remember that if you intend to use a canon as just a skeleton, there is no need for proper harmony or counterpoint! your embellishments can save parallels, treat dissonances as accented passing notes etc, chromatically alter embellishment notes to make modulations where none originally seemed to appear. Sometimes though, you just wanna make a canon and use it as is. In which case, always remember to pay attention to the harmonies being produced, and if it's all contrapuntally sound.

I highly recommend this book, as well as Norden's "Foundation Studies in Fugue". I'd get Luigi Cherubini's counterpoint book and master that before getting those two, it's from the 1800s so is available for free. Loverich has an excellent book on fugue as well, 'examination fugue'. A lot of his ideas are quite objectionable and strict, but they will really help you in the long run.

All in all, there is mostly a lot of fluff in this book. Mathematical formulae to check your work and nothing more, and he acts as though these formulae (especially the repeat stuff, which I strongly advise you to completely ignore) are how the canons are made when it's really just a matter of producing good harmony and counterpoint in whatever structural DC inversion(s) may be in effect. It is, however, a valueless book that will completely change how you write music forever and is usable in all genres (whether you want to write gagaku, hindustani, carnatic, mande, ewe, zimbabwe, techno or anything in between).

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I got my basics in musical forms and structures through two books. One, 'What to Listen for in Music' by Aaron Copland, and the other one 'How to Appreciate Music' by Sidney Harrison (I read the latter in Spanish, so it's possible you may find it as well). These are intended for non-specialists and beginners. Hope that helps :D ...

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Ok, Connor offers some nice books but waaay too much detail and I don't agree ALL of with them.

First off I do not know what level you are at and whatrare your goals - to write better songs? instrumental works? electronic? Each of these have some specific quirks regarding form. I'll just offer some broad recommendations for reading and studying:

IF the fundamentals are lacking (eg you have trouble discerning A major from F minot or can read only treble clef) then

"Music Theory for Dummies" to start

http://www.amazon.co...26644294&sr=1-1

Now if you are seeking how to write song forms - start again with the Dummies series if you have little background.

What is most important though is to STUDY scores to determine form - you will need a grounding in harmony and elements of music.

If you have the fundamentals down and want a more in depth look: Harmony and Voice Leading Aldwell and Schachter - also the workbooks offer great exercises

http://www.amazon.co...26644810&sr=1-4

If you are new to Keyboard Harmony and Improv here is the order from easiest to hardest

Kenneth Simpson Keyboard Harmony and Imrov

http://www.amazon.co...26645026&sr=1-1

Next the Ferguson and Morris books on Keyboard Harmony and reading figured bass

http://www.amazon.co...26645075&sr=1-1

The next one is difficult to find but there are two books of Boulanger Melodies and Basses to Harmonize. It is really a great way to prep for Jazz studies too.

The William Caplin book is a great resource for the Classical style as written - and goes into the Romantic era. However, you need a solid understanding for Diatonic harmony to benefit from this book

http://www.amazon.co...26645189&sr=1-1

A book which takes a different approach to the study of form but is a great at cataloguing the different forms (the musical examples and their classification by form are well worth the investment)

http://www.amazon.co...26645300&sr=1-1

http://www.amazon.co...26645300&sr=1-2

Finally to understand form prior to the classical era this book offers short summaries and some fine examples:

http://www.amazon.co...26645400&sr=1-1

To understand contemporary classical form this a good intro

http://www.amazon.co...47&sr=1-1-fkmr1

To truly understand a good deal of Baropque, Rennaissance and some contemporary classical music, you got to understand counterpoint:

Three books

Fux's Study of Counterpoint

http://www.amazon.co...26646287&sr=1-1

16th century vocal polyphony

http://www.amazon.co...26646343&sr=1-1

Composition and Counterpoint

http://www.amazon.co...26646388&sr=1-1

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For classical era form(beethoven, mozart, haydn) get 'Classical Form' by William Caplin. For baroque era form, search 'sinfonia' and 'suite' on wikipedia (the suite will give you rhythms for each movement)...

Thanks for all the information! I appreciate it. My music theory level is quite poor at the moment, so I have to start with other basic books first so I can understand well. Also that I'm not aiming to write classical music, so the books that go deeper into the subject of classical forms are not a priority for me because I want to do something else, but I'll definitely check out later the harmony ones, and the ones that can apply to all forms of music in general. Thanks again :)

Buy music theory books.

Brilliant idea! quite helpful tip

Ok, Connor offers some nice books but waaay too much detail and I don't agree with them.

First off I do not know what level you are at and whatr are your goals - to write better songs? instrumental works? electronic? Each of these have some specific quirks reqarding form. I'll just offer some braod recommendations for reading and studying....

Thank you! this is very helpful for me, my level in music theory is quite poor and it's not my intention to go deep into classical forms as I mentioned above, so I'll start from the beginning but will have most of the other books you mentioned in mind when I reach a better level, already have the first one to start with :P

The music I do is basically Minimalism combined with Ambient, as in a calm piano with some atmospheres of strings, chorus, glockenspiel, I just wanted to make the songs better when it comes to structures and forms, because so far it's mostly based on emotions.

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Good enough. I think you would make a wonderful 'classical' composer with your sense of melody and feeling; but keep doing what you want to do, keep growing until you master it. If you eventually want to tackle more 'classical' forms in due time, you'll be able to build from what you have learned before. :thumbsup: ...

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