Hey all, I've completed the table of contents and chapter 1 of the first book of Schillinger System. As always, I appreciate the feedback you guys give. I'd be happy to answer any questions you guys have on this thread.

Chapter 1: http://schillinger-system.wikispaces.com/TOR+1+-+Notation+System
pretty cool bra
Looks very good man. I'm still trying to get my head around the rhythmic variables but maybe if I go over it again, it will click. You've done a good job of explaining the material in a clear way.
Thanks for you effort man.

Mind if I ask a question.
Does studying this system require thorough knowledge of conventional music theory (Harmony, Counterpoint) or only the basics?

Also, I'm thinking of getting the 2 volumes of the original book and studying from them by myself, and maybe revise off your wiki. Do you I can do it alone, or does this need some guidance?

Thanks again man and good job. I'm keeping a close eye on this.
Thanks mate. I came across this system a few weeks ago and it interested me. Heading out just now to get some graph paper and give it a bash!
Andy
This is really good stuff, thanks for doing these lessons!
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I'm going to be somewhat critical I'm afraid.

At first sight the graph notation doesn't make a lot of sense.

The terminology is outdated from a current scientific perspective.

The link between the physical form of sound waves and this notation is tenuous. Sound travels as longitudinal waves, the notation is transverse. Many other details don't survive the analogy either: the 'periodicity' of true sound waves is orders of magnitude higher than the graph shows, and the phase of those waves is not relevant to composition.

So, there's no real link from the notation to musical sounds in the 'real' world. This doesn't mean the notation is bad, just that thinking that it somehow represents sounds better than standard notation is wrong.

By the end of the section I can see that the squares represent simply and proportionally the time values of notes on the X-axis, but I cannot yet see the point of the square wave form. In other words, why have a representation of phase snaking up and down when a line with point markings would convey the same information?

Is a note represented by an 'n' shaped waveform somehow different from a note represented by a 'u' shaped waveform? If not, why are they different in the graph notation?
wow thats really cool, im looking forward to the next chapter
all the best.
(insert self-aggrandizing quote here)
Quote by Jehannum
I'm going to be somewhat critical I'm afraid.
Glad to have feedback, even critical ones!

At first sight the graph notation doesn't make a lot of sense.

The terminology is outdated from a current scientific perspective.

Oh yes, I am aware of this, It is the most common criticism I see. The problem is, that I am not aware of what the current correct terminology is, so I don’t know the specifics of where the discrepancies are.

The link between the physical form of sound waves and this notation is tenuous. Sound travels as longitudinal waves, the notation is transverse. Many other details don't survive the analogy either: the 'periodicity' of true sound waves is orders of magnitude higher than the graph shows, and the phase of those waves is not relevant to composition.

The translation of expressions is not to establish a link connecting the composition of music to the actual structure of sound waves, it is merely to provide an example in which a regularly recurring event may be notated in different ways: graphically, numerically, and using musical notation. It is not an attempt to translate the entirety of the information provided by the original graph of the wave, but only a very specific aspect: the points in time at which certain events occur. While a sound wave is heard by us instantaneously, maybe a more apt example would be a slower moving wave, such as an ocean wave. If a hypothetic ocean wave continued in a regular pattern, you could notate with this system the intervals at which you pass a particular point on the wave if you were floating in it.

I might be rambling, but does that help clarify? Or have I missed your point?

So, there's no real link from the notation to musical sounds in the 'real' world. This doesn't mean the notation is bad, just that thinking that it somehow represents sounds better than standard notation is wrong.

It doesn’t represents sound any better, but it does, in Schillinger’s opinion, represent rhythms better. Schillinger’s primary problem with current standard musical notation is that it is based off of a system of 2s. A whole note is divided in half to produce a half note, which is divided in half to produce a quarter note, etc etc. This makes sense if you are dealing in a 2-based system of rhythm, but if you are not, it is counter-intuitive. In 4/4 time, a quarter note is indeed 1/4 of the entire measure, however in 3/4 time, it is only 1/3 of the measure, but we still call it a quarter note, and, according to schillinger, we still think of it in a system of two, rather then in a system of three, as it should be thought of in 3/4 (to show this, the most common way of dividing a quarter note in a 3/4 measure is into two eighth notes, meaning that we are dividing 3 notes into 6 notes, rather then turning quarter notes into three tripelets, which is how a pure system of 3-based rhythms should be divided)

Yet another problem Schillinger has with this system is the clumsy way we must notate rhythms that are not based upon two or three. If we were to write a duration of 5, we would have to write either a whole note tied to a quarter note, or a half note tied to a dotted half note. Schilinger believes this has conditioned us to understand five in relationship to two and three (this can be easily demonstrated by the way we count a 5 rhythm, which is ONE two three FOUR five, or ONE two THREE four five, ie, as 2 + 3). However, the graphic notation provided doesn’t have the same setbacks. When we look at a graph that has a line five squares long, we do not have to see the line as 2 + 3, or 4 + 1, we can just simply see it as 5.

This is really getting ahead of ourselves, however. This isn’t explained until about 4 or 5 chapters later.

why have a representation of phase snaking up and down when a line with point markings would convey the same information?

Is a note represented by an 'n' shaped waveform somehow different from a note represented by a 'u' shaped waveform? If not, why are they different in the graph notation?

They are not different at all. When graphing rhythms, the up-and-down sides of the graph are only a convenience to allow us to more easily discern points of attack (since the points of attack are represented by a full line, instead of a dot), however, when we deal with melodic graphs later, and different pitch levels are included (so that specific y axis movement is actually meaningful), we do indeed use straight lines with a dot or line through it to indicate repetition on the same pitch. The only reason we don’t do so here, is that graphing on a two-y-unit level makes the attack placement seem more obvious then a straight line with several lines through it. In short, it exists only as a convenience to make the graphs easier to read and understand.
Last edited by nmitchell076 at Aug 25, 2011,
I'm sorry to miss this post, I'll answer it now.
Quote by felakutihimself
Looks very good man. I'm still trying to get my head around the rhythmic variables but maybe if I go over it again, it will click. You've done a good job of explaining the material in a clear way.
Thanks for you effort man.

Any issues still? I'll be happy to clarify anything

Mind if I ask a question.
Does studying this system require thorough knowledge of conventional music theory (Harmony, Counterpoint) or only the basics?
Not particularly, in fact, it attempts to create a new foundation for those very ideas. Music theory begins with an examination of the major and harmonic minor scales and the harmonies (and, in advanced cases, modes) derived therefrom. However, this begins at an even more basic level.

Also, I'm thinking of getting the 2 volumes of the original book and studying from them by myself, and maybe revise off your wiki. Do you I can do it alone, or does this need some guidance?

Well, if you're looking for guidance, you won't find any. I'm working my way through Schillinger's theory all on my own, and let me tell you it was (and still is) one of the most difficult readings I've ever done. It's primarily because Schillinger's first language was not English, and it shows in his writings. I find the way he explains many of his ideas damn near impossible to understand until you do your own investigations and put them into practice. That's why I took such extensive notes on it, because reading it alone did not allow me to understand it. It's also why I put this wiki together, as I feel I can bring his ideas into a language that is a bit easier to comprehend without loosing any ideas in the process.

It's not a matter of faulty or overly difficult ideas that makes it tough, its a matter of poorly worded representations of these ideas. But if you do get it, then I hope my wiki will provide enough guidance to get through it.
Quote by nmitchell076

It doesn’t represents sound any better, but it does, in Schillinger’s opinion, represent rhythms better. Schillinger’s primary problem with current standard musical notation is that it is based off of a system of 2s. A whole note is divided in half to produce a half note, which is divided in half to produce a quarter note, etc etc. This makes sense if you are dealing in a 2-based system of rhythm, but if you are not, it is counter-intuitive. In 4/4 time, a quarter note is indeed 1/4 of the entire measure, however in 3/4 time, it is only 1/3 of the measure, but we still call it a quarter note, and, according to schillinger, we still think of it in a system of two, rather then in a system of three, as it should be thought of in 3/4 (to show this, the most common way of dividing a quarter note in a 3/4 measure is into two eighth notes, meaning that we are dividing 3 notes into 6 notes, rather then turning quarter notes into three tripelets, which is how a pure system of 3-based rhythms should be divided)

I think you're thinking of 9/8, where you would have three dotted quarter notes to a bar where each dotted quarter note gets divided into three eighths. The only reason we use a dotted quarter rather than a regular quarter for this is to avoid writing the eighths as triplets.

And really, alot of why we write things how we do is simply just to standardize notation. We could always write little 2's above duplets like we write 3's above triplets, etc.. but we've left them out for convenience, in the same way you would write t1+t2 instead of 1t1+1t2.

Quote by nmitchell076
Yet another problem Schillinger has with this system is the clumsy way we must notate rhythms that are not based upon two or three. If we were to write a duration of 5, we would have to write either a whole note tied to a quarter note, or a half note tied to a dotted half note. Schilinger believes this has conditioned us to understand five in relationship to two and three (this can be easily demonstrated by the way we count a 5 rhythm, which is ONE two three FOUR five, or ONE two THREE four five, ie, as 2 + 3). However, the graphic notation provided doesn’t have the same setbacks. When we look at a graph that has a line five squares long, we do not have to see the line as 2 + 3, or 4 + 1, we can just simply see it as 5.

I think of things based on accents. So if its a bar of five that's being accented as a group of three then a group of two that's how I think of it. If I were to have a bar of 2 or 3 or 4 or whatever where all the quarters were being divided into fifthtuplets, I would count ONE two three four five Two two three four five THREE two three four five, etc...
Quote by nmitchell076
I'm sorry to miss this post, I'll answer it now.

Any issues still? I'll be happy to clarify anything

Mind if I ask a question.
Does studying this system require thorough knowledge of conventional music theory (Harmony, Counterpoint) or only the basics?
Not particularly, in fact, it attempts to create a new foundation for those very ideas. Music theory begins with an examination of the major and harmonic minor scales and the harmonies (and, in advanced cases, modes) derived therefrom. However, this begins at an even more basic level.

Well, if you're looking for guidance, you won't find any. I'm working my way through Schillinger's theory all on my own, and let me tell you it was (and still is) one of the most difficult readings I've ever done. It's primarily because Schillinger's first language was not English, and it shows in his writings. I find the way he explains many of his ideas damn near impossible to understand until you do your own investigations and put them into practice. That's why I took such extensive notes on it, because reading it alone did not allow me to understand it. It's also why I put this wiki together, as I feel I can bring his ideas into a language that is a bit easier to comprehend without loosing any ideas in the process.

It's not a matter of faulty or overly difficult ideas that makes it tough, its a matter of poorly worded representations of these ideas. But if you do get it, then I hope my wiki will provide enough guidance to get through it.

Thanks for answering my questions. Seems like I'll be counting on your wiki to learn this system . Thanks anyway for taking the time to do this.
Have you composed anything using this method or are you still learning it?
Quote by isaac_bandits
I think you're thinking of 9/8, where you would have three dotted quarter notes to a bar where each dotted quarter note gets divided into three eighths. The only reason we use a dotted quarter rather than a regular quarter for this is to avoid writing the eighths as triplets.

And really, alot of why we write things how we do is simply just to standardize notation. We could always write little 2's above duplets like we write 3's above triplets, etc.. but we've left them out for convenience, in the same way you would write t1+t2 instead of 1t1+1t2.

Right, but still, how do you divide eighth notes in 9/8? Usually into two sixteenth notes. so you have a whole measure divided into three divided into 9 divided into 18, ie. it is still not purely in a three system (which would divide 9 notes into 27), it is a hybrid between 9 and 2. Schillinger believes standard musical notation has hindered our rhythmic development because it is more used to creating hybrids between a system and 2, rather then allowing for pure rhythmic systems in which all subdivisions occur through the same number. For example, a pure rhythmic system of five would be a whole divided into 5 notes, divided into 25 notes, divided into 125 notes.

Schillinger believes this whole "hybrid with 2" stems from the nature of our musical notation, which is developed from a pure 2 system (whole divided into 2 divided into 4 divided into 8 divided into 16 etc.). It was developed in a system that only required those types of divisions, and ever since we have moved passed a rhythmic system based solely on 2, we have been looking for ways around the 2 notation (the notation of tripelets, or any -plet being one example, as well as dots).

I think of things based on accents. So if its a bar of five that's being accented as a group of three then a group of two that's how I think of it. If I were to have a bar of 2 or 3 or 4 or whatever where all the quarters were being divided into fifthtuplets, I would count ONE two three four five Two two three four five THREE two three four five, etc...

Right, but it has become standard for five to be thought of as 2 + 3. If you look at most scores written in 5/8, for example, the grouping of eighth notes occurs as a set of 2 eighth notes. If you watch conductors conduct 5/8, they also inherently think about it as 2 + 3, as their conducting of 5 is always divided into that pattern. So in reality, 5/8 does not in fact mean "5 beats per measure, with the eighth note getting the beat," but rather has come to mean "2 beats per measure, with one beat being a quarter note and another being a dotted quarter note."

Further, Schillinger has a different way of thinking about accents as well, but we will get to that later.

it is not that notating 5 as three plus two is wrong, its that if that is the primary way our musical notation has conditioned us to think about it, then it is limiting our thoughts about rhythm in a way that is cumbersome to get around.

If this discussion goes much further, I might just do the chapter where he discusses this more as my next chapter
Last edited by nmitchell076 at Aug 27, 2011,
Quote by felakutihimself
Thanks for answering my questions. Seems like I'll be counting on your wiki to learn this system . Thanks anyway for taking the time to do this.
Have you composed anything using this method or are you still learning it?

I havent gotten to a point where I can compose full systems of music. I have composed a single melodic line as well as created the formal proportions of a violin piece I'm doing. But I've yet to expand upon that melodic line or fill out the formal proportions yet.

I actually uploaded the creation of the melodic line for another thing, so I can post that as an example of application here. But I haven't uploaded the formal proportion creation yet, I might later, however.

you can see at the very top of the page the rhythmic graph of the piece, and how that translates to the musical notation of the rhythm of the composed melody. You can also see the difference between melodic and rhythmic graphs here.
Looks interesting. I'll be waiting for the final outcome .
Until then keep up the great work.

For now I'll be studying conventional theory as that seems more useful to me at the moment. But when I reach a far enough level, I'll be coming back to study this system. It has sparked my interest, since I have always thought of ways to make music more logical, and this seems to be a definite method. Hopefully, when I come back to studying this, the wiki page will be complete or with a lot of material then.

Thank you again
Quote by nmitchell076
Right, but still, how do you divide eighth notes in 9/8? Usually into two sixteenth notes. so you have a whole measure divided into three divided into 9 divided into 18, ie. it is still not purely in a three system (which would divide 9 notes into 27), it is a hybrid between 9 and 2. Schillinger believes standard musical notation has hindered our rhythmic development because it is more used to creating hybrids between a system and 2, rather then allowing for pure rhythmic systems in which all subdivisions occur through the same number. For example, a pure rhythmic system of five would be a whole divided into 5 notes, divided into 25 notes, divided into 125 notes.

I get what your saying and I think you have somewhat of a point. It still is possible to divide the eighth notes in 9/8 into 16th note triplets, and then divide those into 32nd ninetuplets etc... but then the notation does get really messy. However if you start doing that with 32nd note ninetuplets you'd have 81 to a bar of nine. That's an extremely short duration of time, which I would argue would not be useful to write anyways (in the same way that we don't use 64th notes in a bar of 4/4). With five its even worse. You can divide a bar of 5/4 into 25 eighth note fifthtuplets but then the 16th note 25-tuplets are going to be so fast you wouldn't actually write them.

The reason why we use a system where 2 is the basic divisor is because it is the smallest so we can actually divide by it many times before the notes become too short to be practical.

So I do see your point but I don't think it would affect composition much anyways.

Quote by nmitchell076
Right, but it has become standard for five to be thought of as 2 + 3. If you look at most scores written in 5/8, for example, the grouping of eighth notes occurs as a set of 2 eighth notes. If you watch conductors conduct 5/8, they also inherently think about it as 2 + 3, as their conducting of 5 is always divided into that pattern. So in reality, 5/8 does not in fact mean "5 beats per measure, with the eighth note getting the beat," but rather has come to mean "2 beats per measure, with one beat being a quarter note and another being a dotted quarter note."

But that's all assuming 5/8 is being used as hybrid duple time, which it most often is. If someone was writing in simple pentuple time, which would be more likely written as 5/4 then you would have 5 equal length beats in a bar.

Quote by nmitchell076
Further, Schillinger has a different way of thinking about accents as well, but we will get to that later.

I'd be interested to see it. All the things with accenting patterns in different time signatures make alot of sense to me, since I've played with them alot, but I know they can be difficult to explain, so if he has a more elegant system I'd like to see it.
Quote by isaac_bandits
That's an extremely short duration of time, which I would argue would not be useful to write anyways (in the same way that we don't use 64th notes in a bar of 4/4). With five its even worse. You can divide a bar of 5/4 into 25 eighth note fifthtuplets but then the 16th note 25-tuplets are going to be so fast you wouldn't actually write them.

But we aren't talking about playing a straight 25-tuplet pattern, we use those 25 notes as the basic units to create rhythmic structures out of. Once you combine those 25 notes in various ways into longer durations, then it does become useful.
The reason why we use a system where 2 is the basic divisor is because it is the smallest so we can actually divide by it many times before the notes become too short to be practical.

Right, and that is what Schillinger believes as well. He just feels as though a composer needs to have it known to him that other systems of rhythm are available. You don't have to work in a system that uses two. You can work in a pure system of 3, 4, 5, 6, 7, 8, 9 etc. Or you could work in other hybrid forms, such as a hybrid between 5 and 3, or between 7 and 5. It is making these options apparent, available, and easy to conceptualize to the composer, then allowing him to use his or her own creative judgment to select the system that suits the composition.

So I do see your point but I don't think it would affect composition much anyways.

Well, another thing we have to think about is looking in the opposite direction. Two and three also dominate the construction of large-scale forms (Binary/Ternary form, antecedent/consequent phrases, which often consist of 4 bar phrases each, the 32 bar form). But again, this is working in a pure 2 form or in a hybrid form with 2. But with other systems, you can work with other large scale time construction options.
Quote by felakutihimself
For now I'll be studying conventional theory as that seems more useful to me at the moment. But when I reach a far enough level, I'll be coming back to study this system.

I think you wouldn't get hurt learning this theory at the same time. We don't get to anything that is difficult to reconcile with standard theory until book 2. But Book 1 deals with issues that, for the most part, lie outside of traditional theory. So you don't have to worry about doing anything that would make learning normal theory any more difficult.
Guys, I think we should wait for the next (few) chapters, before criticizing the method. Granted, I don't 'get' it yet, but that doesn't make it something obsolete. Same thing goes for Schenkerian analysis, I still don't 'get' it (at all), but it's very valuable for the people who do get it.

Keep up the work Nmitchell!
Quote by nmitchell076
Well, another thing we have to think about is looking in the opposite direction. Two and three also dominate the construction of large-scale forms (Binary/Ternary form, antecedent/consequent phrases, which often consist of 4 bar phrases each, the 32 bar form). But again, this is working in a pure 2 form or in a hybrid form with 2. But with other systems, you can work with other large scale time construction options.

This is true, but I don't think it comes out of our notation system. With our system writing phrases of 5 bars is not difficult to write or to read. I don't really know though why very few songs use phrases of 5 or 7 bars.
Quote by Keth
Guys, I think we should wait for the next (few) chapters, before criticizing the method. Granted, I don't 'get' it yet, but that doesn't make it something obsolete. Same thing goes for Schenkerian analysis, I still don't 'get' it (at all), but it's very valuable for the people who do get it.

Keep up the work Nmitchell!

You can LEARN by 'criticising' or questioning and listening to the feedback.
Quote by Jehannum
You can LEARN by 'criticising' or questioning and listening to the feedback.

Indeed, I really appreciate the criticism actually. Although I also thank you for your support, Keth.

by the way, Jehannum, did I answer your points sufficiently both in my direct responses and the ones to isaac? In particular, I'd enjoy hearing some of the specific incidents of missuse of scientific terminology, learn what the actual terminology of such things are, and correct it in the wiki, if you'd be willing to show them to me.
Jehannum, I think you missed the point of his post. If we wait for a few more chapters we'll probably begin to see why Schillinger chose certain methods to convey ideas. I'd prefer Mr. Mitchell (that is your name right?) was spending his time writing the next chapters rather than answering questions which possibly wouldn't need answering anyway.
Last edited by Jesse Clarkson at Aug 29, 2011,
Quote by Jesse Clarkson
Jehannum, I think you missed the point of his post. If we wait for a few more chapters we'll probably begin to see why Schillinger chose certain methods to convey ideas. I'd prefer Mitchell (that is your name right?) was spending his time writing the next chapters rather than answering questions which possibly wouldn't need answering anyway.

Actually, its nate, mitchell is my last name.

But I really don't mind the questions, they aren't really preventing me from writing, in fact, they're encouraging. YOu can thank school beginning again and a double major for preventing the next chapter. I will promise to get some work done on it in the coming week, however. I'll definitely get it done before Labor Day weekend.
Quote by nmitchell076
Indeed, I really appreciate the criticism actually. Although I also thank you for your support, Keth.

by the way, Jehannum, did I answer your points sufficiently both in my direct responses and the ones to isaac? In particular, I'd enjoy hearing some of the specific incidents of missuse of scientific terminology, learn what the actual terminology of such things are, and correct it in the wiki, if you'd be willing to show them to me.

Yes, you answered the points sufficiently.

Regarding the section on the physics of sound:

1. What exactly is a "standard" wave? I've not come across this terminology.

2. The diagram of the transverse sine wave with the As and Bs is somewhat unclear, as are the written explanations which depend on it - particularly for "phase". It might be better to start explaining sound waves with an illustration of compression and rarefaction, and to explain that these are the two phases of a soundwave. At the moment your explanation of "phase" is confusing. In any case, is "phase" necessary for the method?

3. "Periodicity of phases" is a nonstandard term for sound waves. "Period" is the time taken between repetitions of a wave at a certain point in space. Wouldn't it be simpler to just explain "frequency" anyway?

In particular, I didn't understand "the periodicity of any wave's phases can be represented as a uniform rhythmic group, for example an infinite sequence of quarter-notes.", which seems to mix different timescales - the period of an individual soundwave and the repetition of a group of notes in a musical rhythm.

After this section, it's fine.
1. What exactly is a "standard" wave? I've not come across this terminology.

A wave with constant peak-to-peak amplitude and wavelength

2. The diagram of the transverse sine wave with the As and Bs is somewhat unclear, as are the written explanations which depend on it - particularly for "phase". It might be better to start explaining sound waves with an illustration of compression and rarefaction, and to explain that these are the two phases of a soundwave. At the moment your explanation of "phase" is confusing. In any case, is "phase" necessary for the method?

A phase, by Schillingers understanding is the distance between repetitions of a wave. For example if you have the following wave:

then it would be the distance between the points at which the wave crosses the x axis. So, in a wave with constant wavelength and peak-to-peak amplitude amplitude, it would be equivalent to half of the total wavelength (if I'm understanding wavelength correctly)

3. "Periodicity of phases" is a nonstandard term for sound waves. "Period" is the time taken between repetitions of a wave at a certain point in space. Wouldn't it be simpler to just explain "frequency" anyway?

By periodicity of phases, he means the regular recurrence (periodicity by his terminology) of the phases (by the definition I gave above) of the wave. For example, if we were to look at the wave in the picture above, where a "phase" is the distance between where the wave crosses the x axis, then the "periodicity of the waves phases" would be a representation of all of the instances of when it crosses the x axis.

So if the distance between the points of intersection with the x axis were designated "z," then a wave (that has a constant wavelength) could have the "periodicity of its phases" represented as z + z + z + z + z + ... etc.

In particular, I didn't understand "the periodicity of any wave's phases can be represented as a uniform rhythmic group, for example an infinite sequence of quarter-notes.", which seems to mix different timescales - the period of an individual soundwave and the repetition of a group of notes in a musical rhythm.

Well, were the x axis to represent time, then then any wave (not just sound) could have the above expression z + z + z + z + z + ... mean "a certain amount of time + the same amount of time + the same amount of time + the same amount of time" etc. Since musical notation rhythm is the representation of a duration within a space of time, we could then assign "a certain amount of time" to a rhythmic value, such as an eighth note, a quarter note, a half note, or really anything we wanted to.

I'm sorry to reuse Schillinger's terminology yet again, but since I really don't know about actual terminology, I can't really explain myself with that terminology
Last edited by nmitchell076 at Aug 29, 2011,