Tritone: Difference between revisions

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The '''tritone''' is the name of a musical interval that is made up of three [[Tone|whole tones]]. In [[12edo]] the tritone is exactly 600 cents, or sqrt(2). As such, the term is also used generally to refer to any pitch in the neighborhood of 600c, or roughly halfway between [[4/3]] and [[3/2]].

In tunings other ~~tnah~~ 12edo, and particularly in [[just intonation]], there are a number of different tritones which have subtly different flavors, such as [[7/5]] and [[10/7]]. The temperament eliminating [[50/49]] is of particular interest in that it equates these two tritones, and provides a JI basis for the 12-EDO concept of the "tritone substitution."

In tunings other than 12edo, and particularly in [[just intonation]], there are a number of different tritones which have subtly different flavors, such as [[7/5]] and [[10/7]]. The temperament eliminating [[50/49]] is of particular interest in that it equates these two tritones, and provides a JI basis for the 12-EDO concept of the "tritone substitution."

The following table compares selected tritone pairs:

The following table compares selected JI tritone pairs:

{| class="wikitable ~~sortable" style="text-align: right~~"

{| class="wikitable"

! ~~class="unsortable"~~ | Ratios

! | Ratios

! p-limit

! | prime limit

! ~~delta~~

! | distance from 600c

|-

~~| style="text-align: center"~~ | [[7/5]], [[10/7]]

| [[729/512]], [[1024/729]]

| 7

| 3

| 17.~~488~~

| 11.730

|-

~~| style="text-align: center"~~ | [[45/32]], [[64/45]]

| [[45/32]], [[64/45]]

| 5

| 9.776

|-

| ~~style="text~~-~~align: center"~~ | [[13/9]], [[18/13]]

| [[7/5]], [[10/7]]

| 7

| 17.488

|-

| [[13/9]], [[18/13]]

| 13

| 36.618

|-

~~| style="text-align: center"~~ | [[24/17]], [[17/12]]

| [[24/17]], [[17/12]]

| 17

| 3.000

|-

~~| style="text-align: center"~~ | [[23/16]], [[32/23]]

| [[23/16]], [[32/23]]

| 23

| 28.274

|}

[[Category:Tritone| ]]

[[Category:Tritone]]

[[Category:Interval]]

[[Category:Stub]]

@@ Line 1: / Line 1: @@
 The '''tritone''' is the name of a musical interval that is made up of three [[Tone|whole tones]]. In [[12edo]] the tritone is exactly 600 cents, or sqrt(2). As such, the term is also used generally to refer to any pitch in the neighborhood of 600c, or roughly halfway between [[4/3]] and [[3/2]].
-In tunings other tnah 12edo, and particularly in [[just intonation]], there are a number of different tritones which have subtly different flavors, such as [[7/5]] and [[10/7]]. The temperament eliminating [[50/49]] is of particular interest in that it equates these two tritones, and provides a JI basis for the 12-EDO concept of the "tritone substitution."
+In tunings other than 12edo, and particularly in [[just intonation]], there are a number of different tritones which have subtly different flavors, such as [[7/5]] and [[10/7]]. The temperament eliminating [[50/49]] is of particular interest in that it equates these two tritones, and provides a JI basis for the 12-EDO concept of the "tritone substitution."
-The following table compares selected tritone pairs:
+The following table compares selected JI tritone pairs:
-{| class="wikitable sortable" style="text-align: right"
+{| class="wikitable"
-! class="unsortable" | Ratios
+! | Ratios
-! p-limit
+! | prime limit
-! delta
+! | distance from 600c
 |-
-| style="text-align: center" | [[7/5]], [[10/7]]
+| [[729/512]], [[1024/729]]
-| 7
+| 3
-| 17.488
+| 11.730
 |-
-| style="text-align: center" | [[45/32]], [[64/45]]
+| [[45/32]], [[64/45]]
 | 5
 | 9.776
 |-
-| style="text-align: center" | [[13/9]], [[18/13]]
+| [[7/5]], [[10/7]]
+| 7
+| 17.488
+|-
+| [[13/9]], [[18/13]]
 | 13
 | 36.618
 |-
-| style="text-align: center" | [[24/17]], [[17/12]]
+| [[24/17]], [[17/12]]
 | 17
 | 3.000
 |-
-| style="text-align: center" | [[23/16]], [[32/23]]
+| [[23/16]], [[32/23]]
 | 23
 | 28.274
 |}
-[[Category:Tritone| ]] <!-- main article -->
+[[Category:Tritone]] <!-- main article -->
 [[Category:Interval]]
 [[Category:Stub]]