Breedsmic temperaments: Difference between revisions

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This page ~~discusses miscellaneous~~ [[rank-2 temperament|rank-2]] ~~[[regular temperament|~~temperaments]] [[tempering out]] the [[breedsma]] ({{monzo|legend=1| -5 -1 -2 4 }}, [[ratio]]: 2401/2400). This is the amount by which two [[49/40]] intervals exceed [[3/2]], and by which two [[60/49]] intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system ([[12edo]], for example) which does not possess a neutral third cannot be tempering out the breedsma.

This page collects [[rank-2 temperament|rank-2]] '''breedsmic temperaments''', which [[tempering out|temper out]] the [[breedsma]] ({{monzo|legend=1| -5 -1 -2 4 }}, [[ratio]]: 2401/2400). This is the amount by which two [[49/40]] intervals exceed [[3/2]], and by which two [[60/49]] intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system ([[12edo]], for example) which does not possess a neutral third cannot be tempering out the breedsma.

The breedsma is also the amount by which four stacked [[10/7]] intervals exceed 25/6: (10000/2401)⋅(2401/2400) = 10000/2400 = 25/6, which is two octaves above the classic chromatic semitone, [[25/24]]. We might note also that (49/40)⋅(10/7) = 7/4 and (49/40)⋅(10/7)<sup>2</sup> = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40~60/49 neutral third and the 7/5 and 10/7 ~~intervals~~ tend to have relatively low complexity in a breedsmic system.

The breedsma is also the amount by which four stacked [[10/7]] intervals exceed 25/6: (10000/2401)⋅(2401/2400) = 10000/2400 = 25/6, which is two octaves above the classic chromatic semitone, [[25/24]]. We might note also that (49/40)⋅(10/7) = 7/4 and (49/40)⋅(10/7)<sup>2</sup> = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40~60/49 neutral third and the 7/5 and 10/7 tritones tend to have relatively low complexity in a breedsmic system.

Temperaments discussed elsewhere include:

* ''[[Beatles]]'' (+64/63) → [[Archytas clan #Beatles|Archytas clan]]

* ''[[Newt]]'' (+33554432/33480783) → [[~~Garischismic~~ clan #Beatles|~~Garischismic~~ clan]]

* ''[[Newt]]'' (+33554432/33480783) → [[Septischismic clan #Beatles|Septischismic clan]]

* [[Decimal]] (+25/24, 49/48 or 50/49) → [[Dicot family #Decimal|Dicot family]]

* [[Squares]] (+81/80) → [[Meantone family #Squares|Meantone family]]

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 {{Technical data page}}
-This page discusses miscellaneous [[rank-2 temperament|rank-2]] [[regular temperament|temperaments]] [[tempering out]] the [[breedsma]] ({{monzo|legend=1| -5 -1 -2 4 }}, [[ratio]]: 2401/2400). This is the amount by which two [[49/40]] intervals exceed [[3/2]], and by which two [[60/49]] intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system ([[12edo]], for example) which does not possess a neutral third cannot be tempering out the breedsma.
+This page collects [[rank-2 temperament|rank-2]] '''breedsmic temperaments''', which [[tempering out|temper out]] the [[breedsma]] ({{monzo|legend=1| -5 -1 -2 4 }}, [[ratio]]: 2401/2400). This is the amount by which two [[49/40]] intervals exceed [[3/2]], and by which two [[60/49]] intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system ([[12edo]], for example) which does not possess a neutral third cannot be tempering out the breedsma.
-The breedsma is also the amount by which four stacked [[10/7]] intervals exceed 25/6: (10000/2401)⋅(2401/2400) = 10000/2400 = 25/6, which is two octaves above the classic chromatic semitone, [[25/24]]. We might note also that (49/40)⋅(10/7) = 7/4 and (49/40)⋅(10/7)<sup>2</sup> = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40~60/49 neutral third and the 7/5 and 10/7 intervals tend to have relatively low complexity in a breedsmic system.
+The breedsma is also the amount by which four stacked [[10/7]] intervals exceed 25/6: (10000/2401)⋅(2401/2400) = 10000/2400 = 25/6, which is two octaves above the classic chromatic semitone, [[25/24]]. We might note also that (49/40)⋅(10/7) = 7/4 and (49/40)⋅(10/7)<sup>2</sup> = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40~60/49 neutral third and the 7/5 and 10/7 tritones tend to have relatively low complexity in a breedsmic system.
 Temperaments discussed elsewhere include:
 * ''[[Beatles]]'' (+64/63) → [[Archytas clan #Beatles|Archytas clan]]
-* ''[[Newt]]'' (+33554432/33480783) → [[Garischismic clan #Beatles|Garischismic clan]]
+* ''[[Newt]]'' (+33554432/33480783) → [[Septischismic clan #Beatles|Septischismic clan]]
 * [[Decimal]] (+25/24, 49/48 or 50/49) → [[Dicot family #Decimal|Dicot family]]
 * [[Squares]] (+81/80) → [[Meantone family #Squares|Meantone family]]

Breedsmic temperaments: Difference between revisions

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