Trienstonic clan: Difference between revisions

Line 1:

The '''trienstonic clan''' of [[rank-2 temperament|rank-2]] [[temperament]]s are low-complexity, high-error temperaments that [[tempering out|temper out]] [[28/27]], the septimal third-tone or trienstonic comma. This equates very different intervals with each other; in particular, [[9/8]] with [[7/6]], [[8/7]] with [[32/27]], and [[4/3]] with [[9/7]]. Trienstonian is close to the edge of what can be sensibly called a temperament at all; in other words, it is an [[exotemperament]].

~~Adding 16/15 to 28/27 leads to father, 256/245 gives uncle, 50/49 gives octokaidecal, and 35/32 gives wallaby. Other members of the clan discussed elsewhere are:~~

* ''[[Sharptone]]'' (+21/20) → [[Meantone family #Sharptone|Meantone family]]

* ''[[Wallaby]]'' (+35/32) → [[Very low accuracy temperaments #Wallaby|Very low accuracy temperaments]]

* ''[[Sharpie]]'' (+25/24) → [[Dicot family #Sharpie|Dicot family]]

* ''[[Mite]]'' (+27/25) → [[Bug family #Mite|Bug family]]

* ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated|Augmented family]]

* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum|Porcupine family]]

* [[Blackwood]] (+49/48) → [[Limmic temperaments #Blackwood|Limmic temperaments]]

== Trienstonian ==

Line 31:

Line 22:

[[Badness]] (Sintel): 0.235

=== Overview to extensions ===

Adding 16/15 to 28/27 leads to father, 21/20 gives sharptone, 256/245 gives uncle, and 35/32 gives wallaby. These all use the same generators as trienstonian.

50/49 gives octokaidecal with a semi-octave period. 25/24 gives sharpie; 27/25 gives mite. Those split the generator in two. 1029/1000 gives parakangaroo; 126/125 gives opossum. Those split the generator in three. 128/125 gives inflated with a 1/3-octave period. Finally, 49/48 gives blackwood, with a 1/5-octave period.

Members of the clan discussed elsewhere are:

* ''[[Wallaby]]'' (+35/32) → [[Very low accuracy temperaments #Wallaby|Very low accuracy temperaments]]

* ''[[Sharpie]]'' (+25/24) → [[Dicot family #Sharpie|Dicot family]]

* ''[[Mite]]'' (+27/25) → [[Bug family #Mite|Bug family]]

* ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated|Augmented family]]

* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum|Porcupine family]]

* [[Blackwood]] (+49/48) → [[Limmic temperaments #Blackwood|Limmic temperaments]]

Considered below are father, sharptone, uncle, octokaidecal, and parakangaroo.

== Father ==

Line 36:

Line 42:

See [[Father family #Septimal father]].

== Sharptone ==

See [[Meantone family #Sharptone]].

== Uncle ==

Line 118:

Line 127:

== Parakangaroo ==

: ''For the 5-limit version of this temperament, see [[~~High badness~~ temperaments #Kangaroo]].''

: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Kangaroo]].''

This temperament used to be known as '''kangaroo'''.

@@ Line 1: / Line 1: @@
 {{Technical data page}}
 The '''trienstonic clan''' of [[rank-2 temperament|rank-2]] [[temperament]]s are low-complexity, high-error temperaments that [[tempering out|temper out]] [[28/27]], the septimal third-tone or trienstonic comma. This equates very different intervals with each other; in particular, [[9/8]] with [[7/6]], [[8/7]] with [[32/27]], and [[4/3]] with [[9/7]]. Trienstonian is close to the edge of what can be sensibly called a temperament at all; in other words, it is an [[exotemperament]].
-Adding 16/15 to 28/27 leads to father, 256/245 gives uncle, 50/49 gives octokaidecal, and 35/32 gives wallaby. Other members of the clan discussed elsewhere are:
-* ''[[Sharptone]]'' (+21/20) → [[Meantone family #Sharptone|Meantone family]]
-* ''[[Wallaby]]'' (+35/32) → [[Very low accuracy temperaments #Wallaby|Very low accuracy temperaments]]
-* ''[[Sharpie]]'' (+25/24) → [[Dicot family #Sharpie|Dicot family]]
-* ''[[Mite]]'' (+27/25) → [[Bug family #Mite|Bug family]]
-* ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated|Augmented family]]
-* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum|Porcupine family]]
-* [[Blackwood]] (+49/48) → [[Limmic temperaments #Blackwood|Limmic temperaments]]
 == Trienstonian ==
@@ Line 31: / Line 22: @@
 [[Badness]] (Sintel): 0.235
+=== Overview to extensions ===
+Adding 16/15 to 28/27 leads to father, 21/20 gives sharptone, 256/245 gives uncle, and 35/32 gives wallaby. These all use the same generators as trienstonian.
+/49 gives octokaidecal with a semi-octave period. 25/24 gives sharpie; 27/25 gives mite. Those split the generator in two. 1029/1000 gives parakangaroo; 126/125 gives opossum. Those split the generator in three. 128/125 gives inflated with a 1/3-octave period. Finally, 49/48 gives blackwood, with a 1/5-octave period.
+Members of the clan discussed elsewhere are:
+* ''[[Wallaby]]'' (+35/32) → [[Very low accuracy temperaments #Wallaby|Very low accuracy temperaments]]
+* ''[[Sharpie]]'' (+25/24) → [[Dicot family #Sharpie|Dicot family]]
+* ''[[Mite]]'' (+27/25) → [[Bug family #Mite|Bug family]]
+* ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated|Augmented family]]
+* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum|Porcupine family]]
+* [[Blackwood]] (+49/48) → [[Limmic temperaments #Blackwood|Limmic temperaments]]
+Considered below are father, sharptone, uncle, octokaidecal, and parakangaroo.
 == Father ==
@@ Line 36: / Line 42: @@
 See [[Father family #Septimal father]].
+== Sharptone ==
+See [[Meantone family #Sharptone]].
 == Uncle ==
@@ Line 118: / Line 127: @@
 == Parakangaroo ==
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Kangaroo]].''
+: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Kangaroo]].''
 This temperament used to be known as '''kangaroo'''.