Deeptone: Difference between revisions

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 quartertone). 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]].

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 quartertone). 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 ==

Line 15:

== Interval chain ==

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

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

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

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

|-

| 1 || perfect 5th || P5 || G || 689.879 || [[3/2]] ||

| 1 || perfect 5th || P5 || G || 689.879 || '''[[3/2]]''' ||

|-

| 2 || major 2nd || M2 || D || 179.758 || [[9/8]] || [[128/117]]

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| 3 || major 6th || M6 || A || 869.637 || [[27/16]] || [[64/39]]

|-

| 4 || major 3rd || M3 || E || 359.516 || [[81/64]] || [[16/13]]

| 4 || major 3rd || M3 || E || 359.516 || [[81/64]] || '''[[16/13]]'''

|-

| 5 || major 7th || M7 || B || 1049.395 || [[243/128]], || [[24/13]]

| 5 || major 7th || M7 || B || 1049.395 || [[243/128]] || [[24/13]]

|-

| 6 || aug 4th || A4 || G# || 539.274 || [[729/512]], [[320/243]] || [[18/13]]

|-

| 7 || aug unison || A1 || C# || 29.153 || [[2187/2048]], [[81/80|80/81]] || [[27/26]]

|-

| 8 || aug 5th || A5 || G# || 719.032 || [[40/27]] ||

|-

| 9 || aug 2nd || A2 || D# || 208.911 || [[10/9]] ||

|-

| 10 || aug 6th || A6 || A# || 898.79 || [[5/3]] ||

|-

| 11 || aug 3rd || A3 || E# || 388.67 || '''[[5/4]]''' ||

|-

| 12 || aug 7th || A7 || B# || 1078.55 || [[15/8]] ||

|}

<nowiki/>* In 5-limit CTE tuning

@@ 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 quartertone). 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]].
+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 quartertone). 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 ==
@@ Line 15: / Line 15: @@
 == Interval chain ==
-In the following table, prime harmonics are labeled in '''bold'''.
+In the following table, prime harmonics and subharmonics are labeled in '''bold'''.
 {| class="wikitable center-1 right-2"
@@ Line 27: / Line 27: @@
 | 0 || perfect unison || P1 || C || 0.0 || [[1/1]] ||
 |-
-| 1 || perfect 5th || P5 || G || 689.879 || [[3/2]] ||
+| 1 || perfect 5th || P5 || G || 689.879 || '''[[3/2]]''' ||
 |-
 | 2 || major 2nd || M2 || D || 179.758 || [[9/8]] || [[128/117]]
@@ Line 33: / Line 33: @@
 | 3 || major 6th || M6 || A || 869.637 || [[27/16]] || [[64/39]]
 |-
-| 4 || major 3rd || M3 || E || 359.516 || [[81/64]] || [[16/13]]
+| 4 || major 3rd || M3 || E || 359.516 || [[81/64]] || '''[[16/13]]'''
 |-
-| 5 || major 7th || M7 || B || 1049.395 || [[243/128]], || [[24/13]]
+| 5 || major 7th || M7 || B || 1049.395 || [[243/128]] || [[24/13]]
 |-
 | 6 || aug 4th || A4 || G# || 539.274 || [[729/512]], [[320/243]] || [[18/13]]
 |-
 | 7 || aug unison || A1 || C# || 29.153 || [[2187/2048]], [[81/80|80/81]] || [[27/26]]
+|-
+| 8 || aug 5th || A5 || G# || 719.032 || [[40/27]] ||
+|-
+| 9 || aug 2nd || A2 || D# || 208.911 || [[10/9]] ||
+|-
+| 10 || aug 6th || A6 || A# || 898.79 || [[5/3]] ||
+|-
+| 11 || aug 3rd || A3 || E# || 388.67 || '''[[5/4]]''' ||
+|-
+| 12 || aug 7th || A7 || B# || 1078.55 || [[15/8]] ||
 |}
 <nowiki/>* In 5-limit CTE tuning