Regular temperament: Difference between revisions
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In between lies the cornucopia of temperaments discussed in [[Paul Erlich]]'s seminal work, ''[[:File:MiddlePath2015.pdf|A Middle Path Between Just Intonation and the Equal Temperaments]]''. | In between lies the cornucopia of temperaments discussed in [[Paul Erlich]]'s seminal work, ''[[:File:MiddlePath2015.pdf|A Middle Path Between Just Intonation and the Equal Temperaments]]''. | ||
== | == Introductory materials == | ||
* [[Mike's Lectures On Regular Temperament Theory|Mike Battaglia's Lectures on RTT]] | * [[Mike's Lectures On Regular Temperament Theory|Mike Battaglia's Lectures on RTT]] | ||
* [[Keenan's explanation of vals|Keenan Pepper's explanation of vals]] | * [[Keenan's explanation of vals|Keenan Pepper's explanation of vals]] | ||
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* [[Douglas Blumeyer's RTT How-To]] | * [[Douglas Blumeyer's RTT How-To]] | ||
== How it | == How it works == | ||
* [[Monzo]] | * [[Monzo]] | ||
* [[Val]] | * [[Val]] | ||
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== A brief history == | == A brief history == | ||
The roots of '''Regular Temperament Theory''' — or '''RTT''' — can be traced back for centuries. The practice far predates the theory, and in particular [[meantone]] temperament has been known since the 15th century. Many [[Pioneers of the Regular Mapping Paradigm|early pioneers]] set the stage for the general theory to come: | |||
The roots of '''Regular Temperament Theory''' — or '''RTT''' — can be traced back for centuries. The practice far predates the theory, and in particular [[meantone]] temperament has been known since the 15th century. Many [[ | |||
* Nicola Vicentino (1511–1576): [[adaptive JI]], [[31edo|31-ET]] | * Nicola Vicentino (1511–1576): [[adaptive JI]], [[31edo|31-ET]] | ||
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In 2009 [[Kite Giedraitis]] began developing his own approach to RTT, including some noteworthy innovations. | In 2009 [[Kite Giedraitis]] began developing his own approach to RTT, including some noteworthy innovations. | ||
== Why would I want to use a regular temperament? == | == FAQ == | ||
=== Why would I want to use a regular temperament? === | |||
Regular temperaments are of most use to musicians who want their music to sound as much as possible like low-overtone just intonation, but without the difficulties normally associated with [[low-overtone JI]], such as wolf intervals, commas, and comma pumps. Specifically, if your chord progression pumps a comma, and you want to avoid pitch shifts, wolf intervals, and/or tonic drift, that comma must be tempered out. Temperaments are also of interest to musicians wishing to exploit the unique possibilities that arise when ratios that are distinct in JI become equated. For instance, 10/9 and 9/8 are equated in meantone. Equating distinct ratios through temperament allows for the construction of musical "puns", which are melodies or chord progressions that exploit the multiplicity of "meanings" of tempered intervals. Finally, some use temperaments solely for their sound. For example, one might like the sound of neutral 3rds, without caring much what ratio they are tuned to. Thus one might use Rastmic even though no commas are pumped. | Regular temperaments are of most use to musicians who want their music to sound as much as possible like low-overtone just intonation, but without the difficulties normally associated with [[low-overtone JI]], such as wolf intervals, commas, and comma pumps. Specifically, if your chord progression pumps a comma, and you want to avoid pitch shifts, wolf intervals, and/or tonic drift, that comma must be tempered out. Temperaments are also of interest to musicians wishing to exploit the unique possibilities that arise when ratios that are distinct in JI become equated. For instance, 10/9 and 9/8 are equated in meantone. Equating distinct ratios through temperament allows for the construction of musical "puns", which are melodies or chord progressions that exploit the multiplicity of "meanings" of tempered intervals. Finally, some use temperaments solely for their sound. For example, one might like the sound of neutral 3rds, without caring much what ratio they are tuned to. Thus one might use Rastmic even though no commas are pumped. | ||
== What do I need to know to understand all the numbers on the pages for individual regular temperaments? == | === What do I need to know to understand all the numbers on the pages for individual regular temperaments? === | ||
Although the concept of regular temperament is centuries old and predates much of modern mathematics, members of the Yahoo! Alternative Tuning List have developed a particular form of numerical shorthand for describing the properties of temperaments. The most important of these are [[val]]s (aka mappings) and [[tempering out|tempering out comma]]s, which any student of the modern regular temperament paradigm should become familiar with. These concepts are rather straightforward and require little math to understand. | Although the concept of regular temperament is centuries old and predates much of modern mathematics, members of the Yahoo! Alternative Tuning List have developed a particular form of numerical shorthand for describing the properties of temperaments. The most important of these are [[val]]s (aka mappings) and [[tempering out|tempering out comma]]s, which any student of the modern regular temperament paradigm should become familiar with. These concepts are rather straightforward and require little math to understand. | ||
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== External links == | == External links == | ||
* [http://x31eq.com/paradigm.html Graham Breed's "The Regular Mapping Paradigm"] | * [http://x31eq.com/paradigm.html Graham Breed's "The Regular Mapping Paradigm"] | ||
* [https://youtu.be/ZoAuVgndmbU John Moriarty – Tuning Theory 2: Temperament ("Microtonal" Theory)], a video lecture | |||
[[Category:Regular temperament theory| ]] <!-- main article --> | [[Category:Regular temperament theory| ]] <!-- main article --> | ||