Harmonic entropy of just intervals: Difference between revisions

Line 1:

This is a procedurally generated table of several hundred [[just intonation]] intervals between [[1/1]] and [[16/1]]: roughly evenly spaced with about one interval every ~~4-5~~ [[cents]].

This is a procedurally generated table of several hundred [[just intonation]] intervals between [[1/1]] and [[16/1]]: roughly evenly spaced with about one interval every 4–5 [[cents]].

The table shows how wide each interval is in cents, as well as showing its [[harmonic entropy]].

Line 6:

== Methodology ==

This table was made with [[Scale Workshop]]. It was made by starting with 1080ed16 ([[270edo]] but treating 16/1 as the [[period]]), then using "convert interval values>fraction" with a tolerance of 4.4 ~~cents~~ to convert all the intervals into the nearest simple just interval (according to Scale Workshop's default settings).

This table was made with [[Scale Workshop]]. It was made by starting with 1080ed16 ([[270edo]] but treating 16/1 as the [[period]]), then using "convert interval values > fraction" with a tolerance of 4.4{{c}} to convert all the intervals into the nearest simple just interval (according to Scale Workshop's default settings).

Then Scale Workshop's built-in harmonic entropy table was used to get the cents and the harmonic entropy, with all parameters left as default for the column "%, Rényi order 1.0", and all set to default except Réyni order for the column "%, Rényi order 7.0" (which was as the name suggests).

== Table of intervals ==

=== 1/1 to 2/1 ===

{| class="wikitable mw-collapsible sortable"

|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 0 to ~~1200¢~~

|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 0 to 1200{{c}}

|-

! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)

Line 427:

Line 426:

=== 2/1 to 4/1 ===

{| class="wikitable mw-collapsible sortable"

|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 1200 to ~~2400¢~~

|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 1200 to 2400{{c}}

|-

! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)

Line 844:

Line 843:

=== 4/1 to 8/1 ===

{| class="wikitable mw-collapsible sortable"

|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 2400 to ~~3600¢~~

|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 2400 to 3600{{c}}

|-

! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)

Line 1,267:

Line 1,266:

=== 8/1 to 16/1 ===

{| class="wikitable mw-collapsible sortable"

|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 3600 to ~~4800¢~~

|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 3600 to 4800{{c}}

|-

! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)

@@ Line 1: / Line 1: @@
-This is a procedurally generated table of several hundred [[just intonation]] intervals between [[1/1]] and [[16/1]]: roughly evenly spaced with about one interval every 4-5 [[cents]].
+This is a procedurally generated table of several hundred [[just intonation]] intervals between [[1/1]] and [[16/1]]: roughly evenly spaced with about one interval every 4–5 [[cents]].
 The table shows how wide each interval is in cents, as well as showing its [[harmonic entropy]].
@@ Line 6: / Line 6: @@
 == Methodology ==
-This table was made with [[Scale Workshop]]. It was made by starting with 1080ed16 ([[270edo]] but treating 16/1 as the [[period]]), then using "convert interval values>fraction" with a tolerance of 4.4 cents to convert all the intervals into the nearest simple just interval (according to Scale Workshop's default settings).
+This table was made with [[Scale Workshop]]. It was made by starting with 1080ed16 ([[270edo]] but treating 16/1 as the [[period]]), then using "convert interval values &gt; fraction" with a tolerance of 4.4{{c}} to convert all the intervals into the nearest simple just interval (according to Scale Workshop's default settings).
 Then Scale Workshop's built-in harmonic entropy table was used to get the cents and the harmonic entropy, with all parameters left as default for the column "%, Rényi order 1.0", and all set to default except Réyni order for the column "%, Rényi order 7.0" (which was as the name suggests).
 == Table of intervals ==
 === 1/1 to 2/1 ===
 {| class="wikitable mw-collapsible sortable"
-|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 0 to 1200¢
+|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 0 to 1200{{c}}
 |-
 ! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
@@ Line 427: / Line 426: @@
 === 2/1 to 4/1 ===
 {| class="wikitable mw-collapsible sortable"
-|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 1200 to 2400¢
+|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 1200 to 2400{{c}}
 |-
 ! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
@@ Line 844: / Line 843: @@
 === 4/1 to 8/1 ===
 {| class="wikitable mw-collapsible sortable"
-|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 2400 to 3600¢
+|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 2400 to 3600{{c}}
 |-
 ! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
@@ Line 1,267: / Line 1,266: @@
 === 8/1 to 16/1 ===
 {| class="wikitable mw-collapsible sortable"
-|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 3600 to 4800¢
+|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 3600 to 4800{{c}}
 |-
 ! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)