Deeptone: Difference between revisions

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== Extensions ==

Deeptone has an accurate [[13/8]], represented by the interval notated as a minor sixth, so it is very plausible to have a 2.3.5.13 [[subgroup]] extension tempering out both [[177147/163840]] and [[1053/1024]] (the ''tridecimal comma''). This also gives a more simple interpretation of Deeptone's major and minor thirds as tridecimal neutral thirds [[16/13]] and [[39/32]] respectively. ~~This~~ extension in [[40edo]] ~~has an~~ essentially perfect tuning of 13/8 and 16/13, ~~inheriting it~~ from [[10edo]].

Deeptone has an accurate [[13/8]], represented by the interval notated as a minor sixth, so it is very plausible to have a 2.3.5.13 [[subgroup]] extension tempering out both [[177147/163840]] and [[1053/1024]] (the ''tridecimal comma''). This also gives a more simple interpretation of Deeptone's major and minor thirds as tridecimal neutral thirds [[16/13]] and [[39/32]] respectively. Tuning this Deeptone extension in [[40edo]] results in essentially perfect tuning of [[13/8]] and [[16/13]], which is inherited from [[10edo]].

== Scales ==

When properly tuned, Deeptone features [[MOS scale]]s of the families [[2L 3s]], [[5L 2s]], [[7L 5s]], [[7L 12s]], and [[7L 19s]]. Another important scale, intermediate between the [[7L 5s]] and [[7L 12s]] scales, is the "Deeptone[14]" non-MOS scale. This scale is notable for being the smallest Deeptone scale that is generally "complete" for 5-limit purposes (as noted by [[groundfault]]) since Deeptone[12] has a paucity of 5-limit triads. Deeptone[14] is essentially just two interlaced Deeptone[7] diatonic scales with one of them being offset by an augmented unison above the other.

== Interval chain ==

In the following table, prime harmonics are labeled in '''bold'''.

{| class="wikitable center-1 right-2"

|-

! #

!colspan=3| Notation

!Cents*

!Approximate Ratios

|-

| 0 || perfect unison || P1 || C || 0.0 || [[1/1]]

| 1 || perfect fifth || P5 || G || 689.879 || [[3/2]]

| 2 || perfect fifth || P5 || G || 689.879 || [[3/2]]

|}

<nowiki />* In 5-limit CTE tuning

== Notes ==

@@ Line 9: / Line 9: @@
 == Extensions ==
-Deeptone has an accurate [[13/8]], represented by the interval notated as a minor sixth, so it is very plausible to have a 2.3.5.13 [[subgroup]] extension tempering out both [[177147/163840]] and [[1053/1024]] (the ''tridecimal comma''). This also gives a more simple interpretation of Deeptone's major and minor thirds as tridecimal neutral thirds [[16/13]] and [[39/32]] respectively. This extension in [[40edo]] has an essentially perfect tuning of 13/8 and 16/13, inheriting it from [[10edo]].
+Deeptone has an accurate [[13/8]], represented by the interval notated as a minor sixth, so it is very plausible to have a 2.3.5.13 [[subgroup]] extension tempering out both [[177147/163840]] and [[1053/1024]] (the ''tridecimal comma''). This also gives a more simple interpretation of Deeptone's major and minor thirds as tridecimal neutral thirds [[16/13]] and [[39/32]] respectively. Tuning this Deeptone extension in [[40edo]] results in essentially perfect tuning of [[13/8]] and [[16/13]], which is inherited from [[10edo]].
 == Scales ==
 When properly tuned, Deeptone features [[MOS scale]]s of the families [[2L 3s]], [[5L 2s]], [[7L 5s]], [[7L 12s]], and [[7L 19s]]. Another important scale, intermediate between the [[7L 5s]] and [[7L 12s]] scales, is the "Deeptone[14]" non-MOS scale. This scale is notable for being the smallest Deeptone scale that is generally "complete" for 5-limit purposes (as noted by [[groundfault]]) since Deeptone[12] has a paucity of 5-limit triads. Deeptone[14] is essentially just two interlaced Deeptone[7] diatonic scales with one of them being offset by an augmented unison above the other.
+== Interval chain ==
+== Interval chain ==
+In the following table, prime harmonics are labeled in '''bold'''.
+{| class="wikitable center-1 right-2"
+|-
+! &#35;
+!colspan=3| Notation
+!Cents*
+!Approximate Ratios
+|-
+| 0 || perfect unison || P1 || C || 0.0 || [[1/1]]
+| 1 || perfect fifth || P5 || G || 689.879 || [[3/2]]
+| 2 || perfect fifth || P5 || G || 689.879 || [[3/2]]
+|}
+<nowiki />* In 5-limit CTE tuning
 == Notes ==