Fractional-octave temperaments: Difference between revisions

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A particularly strong offender of this is the [[landscape microtemperaments]] list, which features temperaments which are all supersets of 3edo, but from a composer's perspective it contains wildly different temperaments due to the fact that edo multiples of 3 themselves are different. For example, magnesium (12), and zinc (30), are both landscape systems due to being multiples of 3, but 30edo is drastically different from 12edo in terms of composition, and therefore such temperaments are not alike at all.

== Octave-splitting comma ==

An '''octave-splitting comma''' is a rational [[interval]] which induces a fractional-octave temperament. If tempering out the comma leads to splitting the [[octave]] into ''N'' equal parts (''N'' > 1), the comma is an octave-splitting comma which induces an ''N''th-octave temperament. This terminology was developed by [[Xenllium]].

=== Examples ===

Below is a list of octave-splitting commas for common temperaments:

{| class="wikitable"

|-

! Comma !! Associated <br>temperament !! Harmonic <br>limit !! Splitting <br>order

|-

| [[256/243]] || [[Limmic temperaments|Blackwood]] || 3 || 5

|-

| [[2187/2048]] || [[Apotome family|Whitewood]] || 3 || 7

|-

| [[531441/524288]] || [[Compton family|Compton]] || 3 || 12

|-

| [[2048/2025]] || [[Diaschismic family|Diaschismic]] || 5 || 2

|-

| [[128/125]] || [[Augmented family|Augmented]] || 5 || 3

|-

| [[648/625]] || [[Diminished family|Diminished]] || 5 || 4

|-

| [[50/49]] || [[Jubilismic clan|Jubilismic]] || 7 || 2

|-

| [[250047/250000]] || [[Landscape microtemperaments|Landscape]] || 7 || 3

|-

| [[9801/9800]] || [[Kalismic temperaments|Kalismic]] || 11 || 2

|-

| [[289/288]] || [[Semitonismic]] || 17 || 2

|}

== Individual pages of temperaments by subtending equal division ==

=== 2 to 100 ===

{| class="wikitable center-all"

@@ Line 15: / Line 15: @@
 A particularly strong offender of this is the [[landscape microtemperaments]] list, which features temperaments which are all supersets of 3edo, but from a composer's perspective it contains wildly different temperaments due to the fact that edo multiples of 3 themselves are different. For example, magnesium (12), and zinc (30), are both landscape systems due to being multiples of 3, but 30edo is drastically different from 12edo in terms of composition, and therefore such temperaments are not alike at all.
+== Octave-splitting comma ==
+An '''octave-splitting comma''' is a rational [[interval]] which induces a fractional-octave temperament. If tempering out the comma leads to splitting the [[octave]] into ''N'' equal parts (''N'' > 1), the comma is an octave-splitting comma which induces an ''N''th-octave temperament. This terminology was developed by [[Xenllium]].
+=== Examples ===
+Below is a list of octave-splitting commas for common temperaments:
+{| class="wikitable"
+|-
+! Comma !! Associated <br>temperament !! Harmonic <br>limit !! Splitting <br>order
+|-
+| [[256/243]] || [[Limmic temperaments|Blackwood]] || 3 || 5
+|-
+| [[2187/2048]] || [[Apotome family|Whitewood]] || 3 || 7
+|-
+| [[531441/524288]] || [[Compton family|Compton]] || 3 || 12
+|-
+| [[2048/2025]] || [[Diaschismic family|Diaschismic]] || 5 || 2
+|-
+| [[128/125]] || [[Augmented family|Augmented]] || 5 || 3
+|-
+| [[648/625]] || [[Diminished family|Diminished]] || 5 || 4
+|-
+| [[50/49]] || [[Jubilismic clan|Jubilismic]] || 7 || 2
+|-
+| [[250047/250000]] || [[Landscape microtemperaments|Landscape]] || 7 || 3
+|-
+| [[9801/9800]] || [[Kalismic temperaments|Kalismic]] || 11 || 2
+|-
+| [[289/288]] || [[Semitonismic]] || 17 || 2
+|}
 == Individual pages of temperaments by subtending equal division ==
 === 2 to 100 ===
 {| class="wikitable center-all"