8019/8000: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = trimitone comma

~~| Ratio = 8019/8000~~

| Color name = L1og31, lalotrigu 1sn, Lalotrigu comma

~~| Monzo = -6 6 -3 0 1~~

| Comma = yes

~~| Cents = 4.1068~~

| Name =

| Color name =

| ~~FJS name =~~

~~| Sound~~ =

}}

'''8019/8000''' is a comma in the 2.3.5.11 subgroup~~, equal to (~~[[11/8]])/([[10/9]])3.

'''8019/8000''', the '''trimitone comma''' (for "triple minor (whole) tone"), is the [[comma]] in the 11-limit (also 2.3.5.11 [[subgroup]]) by which a stack of three instances of [[10/9]] fall short of [[11/8]], thus leading to the formulation of (11/8)/(10/9)3. It is also the interval separating the [[syntonic comma]] and the [[ptolemisma]] because of being an [[ultraparticular]].

In the 13-limit, it factors neatly into ([[729/728]])([[1001/1000]]).

== Temperaments ==

In terms of microtempering the 2.3.5.11 subgroup, it may combine well with the [[schisma]] as doing so gives lower-complexity interpretations to the [[5-limit]] "tritones" of (10/9)3 and [[729/512|(9/8)3]] and their octave-complements, which results in the 53&65 temperament in the 2.3.5.11 subgroup. (The term "tritones" is being used here in the sense of stacking 3 tones, as calling (10/9)3 a "tritone" is questionable.) For optimising this temperament, [[183edo]] is recommendable, although [[65edo]] provides a less accurate tuning at the benefit of a more manageable number of tones. If extended to the full [[11-limit|11-]] or [[13-limit]], it is closely related to [[Schismatic family#Bischismic|~~Bischismic~~]], which also tempers [[3136/3125]].

In the full 11-limit, tempering it out leads to the rank-4 [[Rank-4 temperament #Trimitone (8019/8000)|trimitone temperament]]. Due to the factorization above, it extends neatly to the 13-limit.

In terms of microtempering the 2.3.5.11 subgroup, it may combine well with the [[schisma]] as doing so gives lower-complexity interpretations to the [[5-limit]] "tritones" of (10/9)3 and [[729/512|(9/8)3]] and their octave-complements, which results in the 53&65 (or equivalently 12&53) temperament in the 2.3.5.11 subgroup. (The term "tritones" is being used here in the sense of stacking 3 tones, as calling (10/9)3 a "tritone" is questionable.) For optimising this temperament, [[183edo]] is recommendable, although [[65edo]] provides a less accurate tuning at the benefit of a more manageable number of tones (and at the benefit of being a superset of [[5edo]] and [[13edo]], thus potentially making it easier to conceptualise). This temperament is therefore great for 8:9:10:11:12 chords. If extended to the full [[11-limit|11-]] or [[13-limit]], it is closely related to [[Schismatic family #Bischismic|bischismic]], which also tempers [[3136/3125]].

== See also ==

==See also==

*[[Small comma]]

* [[Unnoticeable comma]]

[[Category:Trimitone]]

* [[Category:~~11-limit~~]]

[[Category:Commas named for the intervals they stack]]

* [[Category:~~Ratio~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = trimitone comma
-| Ratio = 8019/8000
+| Color name = L1og<sup>3</sup>1, lalotrigu 1sn,<br>Lalotrigu comma
-| Monzo = -6 6 -3 0 1
+| Comma = yes
-| Cents = 4.1068
-| Name =
-| Color name =
-| FJS name =
-| Sound =
 }}
-'''8019/8000''' is a comma in the 2.3.5.11 subgroup, equal to ([[11/8]])/([[10/9]])<sup>3</sup>.
+'''8019/8000''', the '''trimitone comma''' (for "triple minor (whole) tone"), is the [[comma]] in the 11-limit (also 2.3.5.11 [[subgroup]]) by which a stack of three instances of [[10/9]] fall short of [[11/8]], thus leading to the formulation of (11/8)/(10/9)<sup>3</sup>.  It is also the interval separating the [[syntonic comma]] and the [[ptolemisma]] because of being an [[ultraparticular]].
+In the 13-limit, it factors neatly into ([[729/728]])([[1001/1000]]).
 == Temperaments ==
-In terms of microtempering the 2.3.5.11 subgroup, it may combine well with the [[schisma]] as doing so gives lower-complexity interpretations to the [[5-limit]] "tritones" of (10/9)<sup>3</sup> and [[729/512|(9/8)<sup>3</sup>]] and their octave-complements, which results in the 53&65 temperament in the 2.3.5.11 subgroup. (The term "tritones" is being used here in the sense of stacking 3 tones, as calling (10/9)<sup>3</sup> a "tritone" is questionable.) For optimising this temperament, [[183edo]] is recommendable, although [[65edo]] provides a less accurate tuning at the benefit of a more manageable number of tones. If extended to the full [[11-limit|11-]] or [[13-limit]], it is closely related to [[Schismatic family#Bischismic|Bischismic]], which also tempers [[3136/3125]].
+In the full 11-limit, tempering it out leads to the rank-4 [[Rank-4 temperament #Trimitone (8019/8000)|trimitone temperament]]. Due to the factorization above, it extends neatly to the 13-limit.
+In terms of microtempering the 2.3.5.11 subgroup, it may combine well with the [[schisma]] as doing so gives lower-complexity interpretations to the [[5-limit]] "tritones" of (10/9)<sup>3</sup> and [[729/512|(9/8)<sup>3</sup>]] and their octave-complements, which results in the 53&65 (or equivalently 12&53) temperament in the 2.3.5.11 subgroup. (The term "tritones" is being used here in the sense of stacking 3 tones, as calling (10/9)<sup>3</sup> a "tritone" is questionable.) For optimising this temperament, [[183edo]] is recommendable, although [[65edo]] provides a less accurate tuning at the benefit of a more manageable number of tones (and at the benefit of being a superset of [[5edo]] and [[13edo]], thus potentially making it easier to conceptualise). This temperament is therefore great for 8:9:10:11:12 chords. If extended to the full [[11-limit|11-]] or [[13-limit]], it is closely related to [[Schismatic family #Bischismic|bischismic]], which also tempers [[3136/3125]].
-== See also ==
+==See also==
+*[[Small comma]]
-* [[Unnoticeable comma]]
+[[Category:Trimitone]]
-* [[Category:11-limit]]
+[[Category:Commas named for the intervals they stack]]
-* [[Category:Ratio]]