Breedsmic temperaments: Difference between revisions

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This page discusses miscellaneous [[~~Rank~~-2 temperament|rank-2]] [[temperament]]s [[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 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.

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.

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* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]

* ''[[Octacot]]'' (+245/243) → [[Tetracot family #Octacot|Tetracot family]]

* ''[[Greenwood]]'' (+405/392 or 1323/1280) → [[~~Greenwoodmic temperaments~~ #Greenwood|~~Greenwoodmic temperaments~~]]

* ''[[Greenwood]]'' (+405/392 or 1323/1280) → [[Whitewood family #Greenwood|Whitewood family]]

* ''[[Quasitemp]]'' (+875/864) → [[Keemic temperaments #Quasitemp|Keemic temperaments]]

* ''[[Quadrasruta]]'' (+2048/2025) → [[Diaschismic family #Quadrasruta|Diaschismic family]]

* ''[[Quadrimage]]'' (+3125/3072) → [[Magic family #Quadrimage|Magic family]]

* ''[[Hemiwürschmidt]]'' (+3136/3125 or 6144/6125) → [[Hemimean clan #Hemiwürschmidt|Hemimean clan]]

* [[Ennealimmal]] (+4375/4374) → [[~~Ragismic microtemperaments~~ #Ennealimmal|~~Ragismic microtemperaments~~]]

* [[Ennealimmal]] (+4375/4374) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]]

* ''[[Quadritikleismic]]'' (+15625/15552) → [[Kleismic family #Quadritikleismic|Kleismic family]]

* [[Harry]] (+19683/19600) → [[Gravity family #Harry|Gravity family]]

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 {{Technical data page}}
-This page discusses miscellaneous [[Rank-2 temperament|rank-2]] [[temperament]]s [[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 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.
 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.
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 * [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]
 * ''[[Octacot]]'' (+245/243) → [[Tetracot family #Octacot|Tetracot family]]
-* ''[[Greenwood]]'' (+405/392 or 1323/1280) → [[Greenwoodmic temperaments #Greenwood|Greenwoodmic temperaments]]
+* ''[[Greenwood]]'' (+405/392 or 1323/1280) → [[Whitewood family #Greenwood|Whitewood family]]
 * ''[[Quasitemp]]'' (+875/864) → [[Keemic temperaments #Quasitemp|Keemic temperaments]]
 * ''[[Quadrasruta]]'' (+2048/2025) → [[Diaschismic family #Quadrasruta|Diaschismic family]]
 * ''[[Quadrimage]]'' (+3125/3072) → [[Magic family #Quadrimage|Magic family]]
 * ''[[Hemiwürschmidt]]'' (+3136/3125 or 6144/6125) → [[Hemimean clan #Hemiwürschmidt|Hemimean clan]]
-* [[Ennealimmal]] (+4375/4374) → [[Ragismic microtemperaments #Ennealimmal|Ragismic microtemperaments]]
+* [[Ennealimmal]] (+4375/4374) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]]
 * ''[[Quadritikleismic]]'' (+15625/15552) → [[Kleismic family #Quadritikleismic|Kleismic family]]
 * [[Harry]] (+19683/19600) → [[Gravity family #Harry|Gravity family]]