Mike's lectures on regular temperament theory: Difference between revisions
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= Preface = | |||
= | |||
'''These are a series of posts that explain, in the perspective I've found most useful, some of the ins and outs of tuning theory.''' I will be adding to these posts over time. | '''These are a series of posts that explain, in the perspective I've found most useful, some of the ins and outs of tuning theory.''' I will be adding to these posts over time. | ||
In these posts, I assume that you have a basic understanding of | In these posts, I assume that you have a basic understanding of | ||
* High school algebra (e.g. what a vector is), but not matrix algebra | |||
* What ratios are | |||
* What cents are | |||
* What monzos and vals are, but nothing else | |||
If you don't understand monzos and vals, check out the [[ | If you don't understand monzos and vals, check out the [[General Theory]] pages on those - they're very simple, and this is supposed to build on that. I'll keep adding to this as I write more stuff. | ||
=The Lectures= | = The Lectures = | ||
#[[Mike's_Lecture_on_Vector_Spaces_and_Dual_Spaces|Vector Spaces and Dual Spaces]] | # [[Mike's_Lecture_on_Vector_Spaces_and_Dual_Spaces|Vector Spaces and Dual Spaces]] | ||
#[[Mike's_Lecture_on_the_First_Fundamental_Law_of_Tempering|The First Fundamental Law of Tempering]] | # [[Mike's_Lecture_on_the_First_Fundamental_Law_of_Tempering|The First Fundamental Law of Tempering]] | ||
== | == Some notes on terminology == | ||
<ul><li>There are many times when more than one term has been used for the same thing, with there being no real preference one way or another. When this happens, I've picked the term that I find to be the most intuitive description of what the concept is.</li><li>Additionally, there are a number of instances where theorists disagree on various minutia involving the precise definition terms. Sometimes people have very subtle differences in their usage of "temperament," "MOS," etc. I've chosen the most middle-of-the-road naming convention possible, and where it's still unclear, I've left footnotes specifying how other people view these things.</li><li>I've seen firsthand that most people reading this are not only capable of understanding the theory as it's currently being talked about on places like tuning-math and XA, but also have interesting ideas to contribute. I believe that the lack of a resource simply stating what some of the terminology means in very clear terms is the simple greatest obstacle that this theory faces towards greater adoption. I hope that this guide can serve as such a resource, and as such I've placed an emphasis on defining "standard" terms as clearly as possible, so as to facilitate the understanding of what, exactly, everyone's saying.</li><li>There are a number of people who advocate completely scrapping the terminology commonly used, e.g. things like "val," "monzo," etc, and starting over from scratch with more intuitive terms. There is a place for that sort of argument, and consequently a separate guide I'd like to write someday for musicians who don't care about math at all and hate it. However, this is not that guide - this is meant to be a primer for the folks who aren't afraid to get a LITTLE bit mathematical, and still want to understand tuning theory. As such I've chosen to use the "standard" terminology when possible, as it's currently being used on tuning and tuning-math, on this wiki, on XA, etc. However, I have '''always''' taken the effort to define my terms in clear, intuitive ways when necessary, using lots of examples.</li></ul> | <ul><li>There are many times when more than one term has been used for the same thing, with there being no real preference one way or another. When this happens, I've picked the term that I find to be the most intuitive description of what the concept is.</li><li>Additionally, there are a number of instances where theorists disagree on various minutia involving the precise definition terms. Sometimes people have very subtle differences in their usage of "temperament," "MOS," etc. I've chosen the most middle-of-the-road naming convention possible, and where it's still unclear, I've left footnotes specifying how other people view these things.</li><li>I've seen firsthand that most people reading this are not only capable of understanding the theory as it's currently being talked about on places like tuning-math and XA, but also have interesting ideas to contribute. I believe that the lack of a resource simply stating what some of the terminology means in very clear terms is the simple greatest obstacle that this theory faces towards greater adoption. I hope that this guide can serve as such a resource, and as such I've placed an emphasis on defining "standard" terms as clearly as possible, so as to facilitate the understanding of what, exactly, everyone's saying.</li><li>There are a number of people who advocate completely scrapping the terminology commonly used, e.g. things like "val," "monzo," etc, and starting over from scratch with more intuitive terms. There is a place for that sort of argument, and consequently a separate guide I'd like to write someday for musicians who don't care about math at all and hate it. However, this is not that guide - this is meant to be a primer for the folks who aren't afraid to get a LITTLE bit mathematical, and still want to understand tuning theory. As such I've chosen to use the "standard" terminology when possible, as it's currently being used on tuning and tuning-math, on this wiki, on XA, etc. However, I have '''always''' taken the effort to define my terms in clear, intuitive ways when necessary, using lots of examples.</li></ul> | ||
== | == Some final notes about my goals with this series of articles == | ||
Sometimes tuning theorists differ subtly in the ways they like to think about tuning theory. This is a result of this field of study being a hugely interdisciplinary collaboration between mathematicians, musicians, engineers, physicists, psychoacousticians, etc. Many of these disagreements derive from the fact that different fields emphasize different skills and ways of thinking. | Sometimes tuning theorists differ subtly in the ways they like to think about tuning theory. This is a result of this field of study being a hugely interdisciplinary collaboration between mathematicians, musicians, engineers, physicists, psychoacousticians, etc. Many of these disagreements derive from the fact that different fields emphasize different skills and ways of thinking. | ||