2401/2400: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Ratio = 2401/2400
| Monzo = -5 -1 -2 4
| Cents = 0.72120
| Name = breedsma
| Name = breedsma
| Color name = z<sup>4</sup>gg3, bizozogu 3rd
| Color name = z<sup>4</sup>gg3, bizozogu 3rd,<br>Bizozogu comma
| FJS name =
| Comma = yes
| Sound =  
}}
}}


'''2401/2400''', the '''breedsma''', is a [[7-limit]] [[unnoticeable comma]]. It is the second smallest 7-limit [[superparticular]] comma, being the difference between [[49/48]] and [[50/49]], and between [[49/40]] and [[60/49]].  
'''2401/2400''', the '''breedsma''', is an [[unnoticeable comma|unnoticeable]] [[7-limit]] [[comma]]. It is the second smallest 7-limit [[superparticular]] comma, being the difference between [[49/48]] and [[50/49]], and between [[49/40]] and [[60/49]].  


== Temperaments ==
== Temperaments ==
The breedsma is tempered out in the rank-3 [[breed family]] and all rank-2 [[breedsmic temperaments]], all of which feature a neutral third interval for 49/40~60/49, and in which the classic chromatic semitone, [[25/24]], is split into two, each representing 49/48~50/49.  
The breedsma is tempered out in the rank-3 [[breed family]] and all rank-2 [[breedsmic temperaments]], all of which feature a neutral third interval for 49/40~60/49, and in which the classic chromatic semitone, [[25/24]], is split into two, each representing 49/48~50/49.  
== Etymology ==
The corresponding temperament was named ''breed'' by [[Gene Ward Smith]] in 2004 after [[Graham Breed]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10058.html Yahoo! Tuning Group | ''Breeding'']</ref>. The term ''breedsma'' appeared shortly after<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10195.html Yahoo! Tuning Group | ''Comma names'']</ref>.


== See also ==
== See also ==
* [[Breed family]], the rank-3 family where it is tempered out
* [[Breedsmic temperaments]], a collection of rank-2 temperaments where it is tempered out
* [[Unnoticeable comma]]
* [[List of superparticular intervals]]
* [[List of superparticular intervals]]


[[Category:7-limit]]
== Notes ==
[[Category:Unnoticeable commas]]
 
[[Category:Superparticular]]
[[Category:Breed]]
[[Category:Breed]]
[[Category:Commas named after music theorists]]

Latest revision as of 02:01, 4 November 2024

Interval information
Ratio 2401/2400
Factorization 2-5 × 3-1 × 5-2 × 74
Monzo [-5 -1 -2 4
Size in cents 0.7211973¢
Name breedsma
Color name z4gg3, bizozogu 3rd,
Bizozogu comma
FJS name [math]\displaystyle{ \text{dd3}^{7,7,7,7}_{5,5} }[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 22.4582
Weil height (log2 max(n, d)) 22.4588
Wilson height (sopfr(nd)) 51
Comma size unnoticeable
S-expression S49
Open this interval in xen-calc

2401/2400, the breedsma, is an unnoticeable 7-limit comma. It is the second smallest 7-limit superparticular comma, being the difference between 49/48 and 50/49, and between 49/40 and 60/49.

Temperaments

The breedsma is tempered out in the rank-3 breed family and all rank-2 breedsmic temperaments, all of which feature a neutral third interval for 49/40~60/49, and in which the classic chromatic semitone, 25/24, is split into two, each representing 49/48~50/49.

Etymology

The corresponding temperament was named breed by Gene Ward Smith in 2004 after Graham Breed[1]. The term breedsma appeared shortly after[2].

See also

Notes