Douglas Blumeyer's RTT How-To: Difference between revisions

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What’s tempering, you ask, and why temper? I won’t be answering those questions in depth here. Plenty has been said about the “what” and “why” elsewhere<ref>And curiously little about the history.</ref>. These materials are about the “how”.

But I will at least give brief answers. In the most typical case, tempering means mistuning the primes — the harmonic building blocks of your music — only a little bit, so that you can still sense what chords and melodies are “supposed” to be, but in just such a way that the interval math “adds up” in more practical ways than it does in pure [[JI]]. This is also what [[Equal-step_tuning|EDs]] do, but where EDs go “all the way”, compromising more JI accuracy for more practicality<ref>I know that there are other reasons to use EDs besides practicality. They can create provocative or otherwise pleasant harmonic effects independent of harmonic purity. For these purposes here it’s sufficient to simply collapse all of that special ED-ness into one package called “practicality”.</ref>, RTT finds a “middle path”: minimizing the accuracies you sacrifice, while maximizing the practicalities you attain. Understanding that much of the “what”, you can refer to this table to see basically “why”:

But I will at least give brief answers. In the most typical case, tempering means mistuning the primes — the harmonic building blocks of your music — only a little bit, so that you can still sense what chords and melodies are “supposed” to be, but in just such a way that the interval math “adds up” in more practical ways than it does in pure [[JI]]. This is also what [[Equal-step_tuning|EDs]] do, but where EDs go “all the way”, compromising more JI accuracy for more practicality, RTT finds a “middle path”: minimizing the accuracies you sacrifice, while maximizing the practicalities you attain. Understanding that much of the “what”, you can refer to this table to see basically “why”:

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The point is that a tempered tuning manages to score high for both practicality and harmonic accuracy, and therefore the case can be made that it is better overall than either a straight ED or straight JI. On this table that I just made up, anyway, RTT got six total stars while ED and JI each only got five.

The point is that a tempered tuning manages to score high for both practicality and harmonic accuracy, and therefore the case can be made that it is better overall than either a straight ED or straight JI. On this table that I just made up, anyway, RTT got six total stars while ED and JI each only got five. (And this doesn't even account for the power RTT has to create fascinating new harmonic effects, like [[comma pumps]] and [[essentially tempered chords]], which EDs can do to a lesser extent.)

But, you protest: this tutorial is pretty long, and it contains a bunch of gnarly diagrams and advanced math concepts, so how could RTT possibly be more practical than JI? Well, what I’ve rated above is the practicality ''after you’ve chosen your particular ED, RTT, or JI tuning''. It’s the ease of writing, reading, reasoning about, communicating about, teaching, performing, listening to, and analyzing the music in said tuning. This is different from how simple it is to ''determine'' a desirable tuning up front.

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 What’s tempering, you ask, and why temper? I won’t be answering those questions in depth here. Plenty has been said about the “what” and “why” elsewhere<ref>And curiously little about the history.</ref>. These materials are about the “how”.
-But I will at least give brief answers. In the most typical case, tempering means mistuning the primes — the harmonic building blocks of your music — only a little bit, so that you can still sense what chords and melodies are “supposed” to be, but in just such a way that the interval math “adds up” in more practical ways than it does in pure [[JI]]. This is also what [[Equal-step_tuning|EDs]] do, but where EDs go “all the way”, compromising more JI accuracy for more practicality<ref>I know that there are other reasons to use EDs besides practicality. They can create provocative or otherwise pleasant harmonic effects independent of harmonic purity. For these purposes here it’s sufficient to simply collapse all of that special ED-ness into one package called “practicality”.</ref>, RTT finds a “middle path”: minimizing the accuracies you sacrifice, while maximizing the practicalities you attain. Understanding that much of the “what”, you can refer to this table to see basically “why”:
+But I will at least give brief answers. In the most typical case, tempering means mistuning the primes — the harmonic building blocks of your music — only a little bit, so that you can still sense what chords and melodies are “supposed” to be, but in just such a way that the interval math “adds up” in more practical ways than it does in pure [[JI]]. This is also what [[Equal-step_tuning|EDs]] do, but where EDs go “all the way”, compromising more JI accuracy for more practicality, RTT finds a “middle path”: minimizing the accuracies you sacrifice, while maximizing the practicalities you attain. Understanding that much of the “what”, you can refer to this table to see basically “why”:
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 |}
-The point is that a tempered tuning manages to score high for both practicality and harmonic accuracy, and therefore the case can be made that it is better overall than either a straight ED or straight JI. On this table that I just made up, anyway, RTT got six total stars while ED and JI each only got five.
+The point is that a tempered tuning manages to score high for both practicality and harmonic accuracy, and therefore the case can be made that it is better overall than either a straight ED or straight JI. On this table that I just made up, anyway, RTT got six total stars while ED and JI each only got five. (And this doesn't even account for the power RTT has to create fascinating new harmonic effects, like [[comma pumps]] and [[essentially tempered chords]], which EDs can do to a lesser extent.)
 But, you protest: this tutorial is pretty long, and it contains a bunch of gnarly diagrams and advanced math concepts, so how could RTT possibly be more practical than JI? Well, what I’ve rated above is the practicality ''after you’ve chosen your particular ED, RTT, or JI tuning''. It’s the ease of writing, reading, reasoning about, communicating about, teaching, performing, listening to, and analyzing the music in said tuning. This is different from how simple it is to ''determine'' a desirable tuning up front.