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 ease of use, RTT finds a “middle path”: minimizing the accuracies you sacrifice, while maximizing ease of use. 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|equal divisions]] (EDs) do, but where EDs go “all the way”, compromising more JI accuracy for more ease of use, RTT finds a “middle path”: minimizing the accuracies you sacrifice, while maximizing ease of use. Understanding that much of the “what”, you can refer to this table to see basically “why”:

{| class="wikitable"

|+ '''Table 1a.''' Why RTT

!

!~~EDs~~

!equal divisions

!RTT (middle path)

!JI

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The point is that a tempered tuning manages to score high for both usability 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 easier to use than JI? Well, what I’ve rated above is the ease of use ''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.

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 easier to use than JI? Well, what I’ve rated above is the ease of use ''after you’ve chosen your particular equal division, 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.

Determining desirable tunings is a whole other beast. Perhaps contrary to popular belief, xenharmonic musicians — composers and performers alike — can mostly insulate themselves from this stuff if they like. It’s fine to nab a popular and well-reviewed tuning off the shelf, without deeply understanding how or why it’s there, and just pump, jam, or riff away. There's a good chance you could naturally pick up what's cool about a tuning without ever learning the definition of "temper out" or "generator". But if you do want to be deliberate about it, to mod something, rifle through the obscure section, or even discover your own tuning, then you must prepare to delve deeper into the xenharmonic fold. That’s why this resource is here, for RTT.

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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 ease of use, RTT finds a “middle path”: minimizing the accuracies you sacrifice, while maximizing ease of use. 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|equal divisions]] (EDs) do, but where EDs go “all the way”, compromising more JI accuracy for more ease of use, RTT finds a “middle path”: minimizing the accuracies you sacrifice, while maximizing ease of use. Understanding that much of the “what”, you can refer to this table to see basically “why”:
 {| class="wikitable"
 |+ '''Table 1a.''' Why RTT
 !
-!EDs
+!equal divisions
 !RTT (middle path)
 !JI
@@ Line 30: / Line 30: @@
 The point is that a tempered tuning manages to score high for both usability 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 easier to use than JI? Well, what I’ve rated above is the ease of use ''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.
+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 easier to use than JI? Well, what I’ve rated above is the ease of use ''after you’ve chosen your particular equal division, 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.
 Determining desirable tunings is a whole other beast. Perhaps contrary to popular belief, xenharmonic musicians — composers and performers alike — can mostly insulate themselves from this stuff if they like. It’s fine to nab a popular and well-reviewed tuning off the shelf, without deeply understanding how or why it’s there, and just pump, jam, or riff away. There's a good chance you could naturally pick up what's cool about a tuning without ever learning the definition of "temper out" or "generator". But if you do want to be deliberate about it, to mod something, rifle through the obscure section, or even discover your own tuning, then you must prepare to delve deeper into the xenharmonic fold. That’s why this resource is here, for RTT.