User:Ganaram inukshuk/Sandbox: Difference between revisions

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===Generalized ET/ED intro===

~~For nonoctave equaves~~: '''k equal divisions of ~~p/q~~''' (abbreviated '''~~kedp/q~~'''~~) is a non-octave tuning system based on dividing p/q into k equal pieces of exactly/about s¢ each. Each step of kedp/q represents the frequency ratio of (p/q)1/k or the kth root of p/q.~~

The intro displayed depends on the equave being divided.

* Common abbreviations

~~For edos:~~ '''~~k equal divisions of the octave~~''' ~~(abbreviated~~ '''~~kedo~~'''), also called '''k-tone equal temperament''' ('''~~ktet~~''') or '''k equal temperament''' ('''~~ket~~''') when viewed under a regular temperament perspective, is the tuning system that divides the octave into k equal parts of exactly/about r¢ each. Each step of kedo represents a frequency ratio of 21/k, or the ~~kth~~ root of 2.

** edo: '''''k'' equal divisions of the octave''' (abbreviated '''''k''edo''' or '''''k''ed2'''), also called '''''k''-tone equal temperament''' ('''''k''tet''') or '''''k'' equal temperament''' ('''''k''et''') when viewed under a regular temperament perspective, is the tuning system that divides the octave into ''k'' equal parts of exactly/about s¢ each. Each step of kedo represents a frequency ratio of 21/''k'', or the ''k''th root of 2.

** edt: '''''k'' equal divisions of the tritave''' or '''twelfth''' (abbreviated '''''k''edt''' or '''''k''ed3''') is a non-octave tuning system that divides the 3rd harmonic, or 3/1, into ''k'' equal parts of exactly/about s¢ each. Each step of ''k''edo represents a frequency ratio of 31/''k'', or the ''k''th root of 3.

~~For edts~~: '''k equal divisions of the tritave''' or '''twelfth''' (abbreviated '''~~kedt~~''' or '''~~ked3~~''') is a non-octave tuning system that divides the 3rd harmonic, or 3/1, into k equal parts of exactly/about r¢ each. Each step of ~~kedo~~ represents a frequency ratio of 31/k, or the ~~kth~~ root of 3.

** edf: '''''k'' equal divisions of the fifth''' (abbreviated '''''k''edf''' or '''''k''ed3/2''') is a non-octave tuning system that divides the perfect fifth, or 3/2, into ''k'' equal parts of exactly/about s¢ each. Each step of ''k''edo represents a frequency ratio of (3/2)1/''k'', or the ''k''th root of 3/2.

* Equal divisions of a harmonic

~~For edfs~~: '''k equal divisions of the fifth''' (abbreviated '''~~kedf~~''' or '''~~ked3~~/2''') is a non-octave tuning system that divides the perfect fifth, or 3/2, into k equal parts of exactly/about r¢ each. Each step of ~~kedo~~ represents a frequency ratio of (3/2)1/k, or the ~~kth~~ root of 3/2.

** ed2: same as edo

** ed3: same as edt

~~For nonoctave equaves~~: '''k equal divisions of p/q''' (abbreviated '''~~kedp~~/q''') is a non-octave tuning system that divides p/q into k equal pieces of exactly/about s¢ each. Each step of ~~kedp~~/q represents the frequency ratio of (p/q)1/k or the ~~kth~~ root of p/q.

** ed''h'': '''''k'' equal divisions of the ''h''th harmonic''' (abbreviated '''''k''ed''h''''') is a non-octave tuning system that divides the ''h''th harmonic, or ''h''/1, into ''k'' equal parts of exactly/about s¢ each. Each step of ''k''edh represents a frequency ratio of ''h''1/''k'', or the ''k''th root of ''h''.

* Equal divisions of an arbitrary ratio ''p''/''q''

** ed''p''/''q'': '''''k'' equal divisions of ''p''/''q''''' (abbreviated '''''k''ed''p''/''q''''') is a non-octave tuning system that divides ''p''/''q'' into ''k'' equal pieces of exactly/about s¢ each. Each step of ''k''ed''p''/''q'' represents the frequency ratio of (''p''/''q'')1/''k'', or the ''k''th root of ''p''/''q''.

* Equal divisions of an arbitrary constant c

** ed''c'': '''''k'' equal divisions of ''c''''' (abbreviated '''''k''edc''') is a non-octave tuning system where the interval of r¢ is divided into ''k'' equal pieces of exactly/about s¢ each. Each step of ''k''ed''c'' represents the frequency ratio of ''c''1/''k'', or the ''k''th root of ''c''.

* Equal-step tunings - special cases of the above where there is only one division of the harmonic, ratio, or cent value; more typical of intervals smaller than 2/1.

** 1ed''p''/''q'' - '''1 equal division of ''p''/''q''''' (abbreviated '''1ed''p''/''q'''''), also known as '''ambitonal sequence of ''p''/''q''''' (abbreviated '''AS''p''/''q''''') or '''''p''/''q'' equal-step tuning''', is a non-octave tuning system where adjacent pitches are ''p''/''q'', or exactly/about s¢, apart.

** 1ed''c''¢ - '''1 equal division of ''c''¢''' (abbreviated '''1ed''c''¢''' or '''1ed''c''c'''), also known as '''arithmetic pitch sequence of c¢''' (abbreviated '''APS''c''¢''') or '''''c''cET''', is a non-octave tuning system where adjacent pitches are ''c''¢, apart.

===JI ratio intro===

@@ Line 4: / Line 4: @@
 ===Generalized ET/ED intro===
-For nonoctave equaves: '''k equal divisions of p/q''' (abbreviated '''kedp/q''') is a non-octave tuning system based on dividing p/q into k equal pieces of exactly/about s¢ each. Each step of kedp/q represents the frequency ratio of (p/q)<sup>1/k</sup> or the kth root of p/q.
+The intro displayed depends on the equave being divided.
+* Common abbreviations
-For edos: '''k equal divisions of the octave''' (abbreviated '''kedo'''), also called '''k-tone equal temperament''' ('''ktet''') or '''k equal temperament''' ('''ket''') when viewed under a regular temperament perspective, is the tuning system that divides the octave into k equal parts of exactly/about r¢ each. Each step of kedo represents a frequency ratio of 21/k, or the kth root of 2.
+** edo: '''''k'' equal divisions of the octave''' (abbreviated '''''k''edo''' or '''''k''ed2'''), also called '''''k''-tone equal temperament''' ('''''k''tet''') or '''''k'' equal temperament''' ('''''k''et''') when viewed under a regular temperament perspective, is the tuning system that divides the octave into ''k'' equal parts of exactly/about s¢ each. Each step of kedo represents a frequency ratio of 2<sup>1/''k''</sup>, or the ''k''th root of 2.
+** edt: '''''k'' equal divisions of the tritave''' or '''twelfth''' (abbreviated '''''k''edt''' or '''''k''ed3''') is a non-octave tuning system that divides the 3rd harmonic, or 3/1, into ''k'' equal parts of exactly/about s¢ each. Each step of ''k''edo represents a frequency ratio of 3<sup>1/''k''</sup>, or the ''k''th root of 3.
-For edts: '''k equal divisions of the tritave''' or '''twelfth''' (abbreviated '''kedt''' or '''ked3''') is a non-octave tuning system that divides the 3rd harmonic, or 3/1, into k equal parts of exactly/about r¢ each. Each step of kedo represents a frequency ratio of 3<sup>1/k</sup>, or the kth root of 3.
+** edf: '''''k'' equal divisions of the fifth''' (abbreviated '''''k''edf''' or '''''k''ed3/2''') is a non-octave tuning system that divides the perfect fifth, or 3/2, into ''k'' equal parts of exactly/about s¢ each. Each step of ''k''edo represents a frequency ratio of (3/2)<sup>1/''k''</sup>, or the ''k''th root of 3/2.
+* Equal divisions of a harmonic
-For edfs: '''k equal divisions of the fifth''' (abbreviated '''kedf''' or '''ked3/2''') is a non-octave tuning system that divides the perfect fifth, or 3/2, into k equal parts of exactly/about r¢ each. Each step of kedo represents a frequency ratio of (3/2)<sup>1/k</sup>, or the kth root of 3/2.
+** ed2: same as edo
+** ed3: same as edt
-For nonoctave equaves: '''k equal divisions of p/q''' (abbreviated '''kedp/q''') is a non-octave tuning system that divides p/q into k equal pieces of exactly/about s¢ each. Each step of kedp/q represents the frequency ratio of (p/q)<sup>1/k</sup> or the kth root of p/q.
+** ed''h'': '''''k'' equal divisions of the ''h''th harmonic''' (abbreviated '''''k''ed''h''''') is a non-octave tuning system that divides the ''h''th harmonic, or ''h''/1, into ''k'' equal parts of exactly/about s¢ each. Each step of ''k''edh represents a frequency ratio of ''h''<sup>1/''k''</sup>, or the ''k''th root of ''h''.
+* Equal divisions of an arbitrary ratio ''p''/''q''
+** ed''p''/''q'': '''''k'' equal divisions of ''p''/''q''''' (abbreviated '''''k''ed''p''/''q''''') is a non-octave tuning system that divides ''p''/''q'' into ''k'' equal pieces of exactly/about s¢ each. Each step of ''k''ed''p''/''q'' represents the frequency ratio of (''p''/''q'')<sup>1/''k''</sup>, or the ''k''th root of ''p''/''q''.
+* Equal divisions of an arbitrary constant c
+** ed''c'': '''''k'' equal divisions of ''c''''' (abbreviated '''''k''edc''') is a non-octave tuning system where the interval of r¢ is divided into ''k'' equal pieces of exactly/about s¢ each. Each step of ''k''ed''c'' represents the frequency ratio of ''c''<sup>1/''k''</sup>, or the ''k''th root of ''c''.
+* Equal-step tunings - special cases of the above where there is only one division of the harmonic, ratio, or cent value; more typical of intervals smaller than 2/1.
+** 1ed''p''/''q'' - '''1 equal division of ''p''/''q''''' (abbreviated '''1ed''p''/''q'''''), also known as '''ambitonal sequence of ''p''/''q''''' (abbreviated '''AS''p''/''q''''') or '''''p''/''q'' equal-step tuning''', is a non-octave tuning system where adjacent pitches are ''p''/''q'', or exactly/about s¢, apart.
+** 1ed''c''¢ - '''1 equal division of ''c''¢''' (abbreviated '''1ed''c''¢''' or '''1ed''c''c'''), also known as '''arithmetic pitch sequence of c¢''' (abbreviated '''APS''c''¢''') or '''''c''cET''', is a non-octave tuning system where adjacent pitches are ''c''¢, apart.
 ===JI ratio intro===