Kite's thoughts on pergens: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-02-19 03:38:03 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-02-19 04:33:11 UTC</tt>.

: The original revision id was <tt>~~626596551~~</tt>.

: The original revision id was <tt>626598157</tt>.

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If a rank-2 temperament uses the primes 2 and 3 in its comma(s), or in its prime subgroup (i.e. doesn't explicitly exclude the octave or the fifth), then the period can be expressed as the octave 2/1, or some fraction of an octave. Furthermore, the generator can usually be expressed as some 3-limit interval, or some fraction of such an interval. The fraction is always of the form 1/N, thus the octave and/or the 3-limit interval is **split** into N parts. The interval which is split into multiple generators is the **multi-gen**. The 3-limit multi-gen is referred to not by its ratio but by its conventional name, e.g. P5, M6, m7, etc.

For example, the srutal temperament (2.3.5 and 2048/2025) splits the octave in two, and its pergen name is half-octave. The pergen is written (P8/2, P5). Not only the temperament, but also the comma is said to split the octave. The dicot temperament (2.3.5 and 25/24) splits the fifth in two, and is called half-fifth, written (P8, P5/2). Porcupine is third-fourth, or perhaps third-of-a-fourth, (P8, P4/3). Semaphore, which means "semi-fourth", is of course half-fourth.

For example, the srutal temperament (2.3.5 and 2048/2025) splits the octave in two, and its spoken pergen name is half-octave. The pergen is written (P8/2, P5). Not only the temperament, but also the comma is said to split the octave. The dicot temperament (2.3.5 and 25/24) splits the fifth in two, and is called half-fifth, written (P8, P5/2). Porcupine is third-fourth, or perhaps third-of-a-fourth, (P8, P4/3). Semaphore, which means "semi-fourth", is of course half-fourth.

Many temperaments share the same pergen. This has the advantage of reducing the thousands of temperament names to fewer than perhaps a hundred categories. It focuses on the melodic properties of the temperament, not the harmonic properties. MOS scales in both srutal and injera sound the same, although they temper out different commas. In addition, the pergen tells us how to notate the temperament using [[Ups and Downs Notation|ups and downs]]. See the notation guide below, under [[pergen#Further%20Discussion-Supplemental%20materials|Supplemental materials]].

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If a rank-2 temperament uses the primes 2 and 3 in its comma(s), or in its prime subgroup (i.e. doesn't explicitly exclude the octave or the fifth), then the period can be expressed as the octave 2/1, or some fraction of an octave. Furthermore, the generator can usually be expressed as some 3-limit interval, or some fraction of such an interval. The fraction is always of the form 1/N, thus the octave and/or the 3-limit interval is split into N parts. The interval which is split into multiple generators is the multi-gen. The 3-limit multi-gen is referred to not by its ratio but by its conventional name, e.g. P5, M6, m7, etc.

For example, the srutal temperament (2.3.5 and 2048/2025) splits the octave in two, and its pergen name is half-octave. The pergen is written (P8/2, P5). Not only the temperament, but also the comma is said to split the octave. The dicot temperament (2.3.5 and 25/24) splits the fifth in two, and is called half-fifth, written (P8, P5/2). Porcupine is third-fourth, or perhaps third-of-a-fourth, (P8, P4/3). Semaphore, which means &quot;semi-fourth&quot;, is of course half-fourth.

For example, the srutal temperament (2.3.5 and 2048/2025) splits the octave in two, and its spoken pergen name is half-octave. The pergen is written (P8/2, P5). Not only the temperament, but also the comma is said to split the octave. The dicot temperament (2.3.5 and 25/24) splits the fifth in two, and is called half-fifth, written (P8, P5/2). Porcupine is third-fourth, or perhaps third-of-a-fourth, (P8, P4/3). Semaphore, which means &quot;semi-fourth&quot;, is of course half-fourth.

Many temperaments share the same pergen. This has the advantage of reducing the thousands of temperament names to fewer than perhaps a hundred categories. It focuses on the melodic properties of the temperament, not the harmonic properties. MOS scales in both srutal and injera sound the same, although they temper out different commas. In addition, the pergen tells us how to notate the temperament using <a class="wiki_link" href="/Ups%20and%20Downs%20Notation">ups and downs</a>. See the notation guide below, under <a class="wiki_link" href="/pergen#Further%20Discussion-Supplemental%20materials">Supplemental materials</a>.

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-02-19 03:38:03 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-02-19 04:33:11 UTC</tt>.<br>
-: The original revision id was <tt>626596551</tt>.<br>
+: The original revision id was <tt>626598157</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 15: / Line 15: @@
 If a rank-2 temperament uses the primes 2 and 3 in its comma(s), or in its prime subgroup (i.e. doesn't explicitly exclude the octave or the fifth), then the period can be expressed as the octave 2/1, or some fraction of an octave. Furthermore, the generator can usually be expressed as some 3-limit interval, or some fraction of such an interval. The fraction is always of the form 1/N, thus the octave and/or the 3-limit interval is **split** into N parts. The interval which is split into multiple generators is the **multi-gen**. The 3-limit multi-gen is referred to not by its ratio but by its conventional name, e.g. P5, M6, m7, etc.
-For example, the srutal temperament (2.3.5 and 2048/2025) splits the octave in two, and its pergen name is half-octave. The pergen is written (P8/2, P5). Not only the temperament, but also the comma is said to split the octave. The dicot temperament (2.3.5 and 25/24) splits the fifth in two, and is called half-fifth, written (P8, P5/2). Porcupine is third-fourth, or perhaps third-of-a-fourth, (P8, P4/3). Semaphore, which means "semi-fourth", is of course half-fourth.
+For example, the srutal temperament (2.3.5 and 2048/2025) splits the octave in two, and its spoken pergen name is half-octave. The pergen is written (P8/2, P5). Not only the temperament, but also the comma is said to split the octave. The dicot temperament (2.3.5 and 25/24) splits the fifth in two, and is called half-fifth, written (P8, P5/2). Porcupine is third-fourth, or perhaps third-of-a-fourth, (P8, P4/3). Semaphore, which means "semi-fourth", is of course half-fourth.
 Many temperaments share the same pergen. This has the advantage of reducing the thousands of temperament names to fewer than perhaps a hundred categories. It focuses on the melodic properties of the temperament, not the harmonic properties. MOS scales in both srutal and injera sound the same, although they temper out different commas. In addition, the pergen tells us how to notate the temperament using [[Ups and Downs Notation|ups and downs]]. See the notation guide below, under [[pergen#Further%20Discussion-Supplemental%20materials|Supplemental materials]].
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 If a rank-2 temperament uses the primes 2 and 3 in its comma(s), or in its prime subgroup (i.e. doesn't explicitly exclude the octave or the fifth), then the period can be expressed as the octave 2/1, or some fraction of an octave. Furthermore, the generator can usually be expressed as some 3-limit interval, or some fraction of such an interval. The fraction is always of the form 1/N, thus the octave and/or the 3-limit interval is &lt;strong&gt;split&lt;/strong&gt; into N parts. The interval which is split into multiple generators is the &lt;strong&gt;multi-gen&lt;/strong&gt;. The 3-limit multi-gen is referred to not by its ratio but by its conventional name, e.g. P5, M6, m7, etc.&lt;br /&gt;
 &lt;br /&gt;
-For example, the srutal temperament (2.3.5 and 2048/2025) splits the octave in two, and its pergen name is half-octave. The pergen is written (P8/2, P5). Not only the temperament, but also the comma is said to split the octave. The dicot temperament (2.3.5 and 25/24) splits the fifth in two, and is called half-fifth, written (P8, P5/2). Porcupine is third-fourth, or perhaps third-of-a-fourth, (P8, P4/3). Semaphore, which means &amp;quot;semi-fourth&amp;quot;, is of course half-fourth.&lt;br /&gt;
+For example, the srutal temperament (2.3.5 and 2048/2025) splits the octave in two, and its spoken pergen name is half-octave. The pergen is written (P8/2, P5). Not only the temperament, but also the comma is said to split the octave. The dicot temperament (2.3.5 and 25/24) splits the fifth in two, and is called half-fifth, written (P8, P5/2). Porcupine is third-fourth, or perhaps third-of-a-fourth, (P8, P4/3). Semaphore, which means &amp;quot;semi-fourth&amp;quot;, is of course half-fourth.&lt;br /&gt;
 &lt;br /&gt;
 Many temperaments share the same pergen. This has the advantage of reducing the thousands of temperament names to fewer than perhaps a hundred categories. It focuses on the melodic properties of the temperament, not the harmonic properties. MOS scales in both srutal and injera sound the same, although they temper out different commas. In addition, the pergen tells us how to notate the temperament using &lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;ups and downs&lt;/a&gt;. See the notation guide below, under &lt;a class="wiki_link" href="/pergen#Further%20Discussion-Supplemental%20materials"&gt;Supplemental materials&lt;/a&gt;.&lt;br /&gt;