8edo: Difference between revisions

Line 479:

~~== Scales ==~~

== Octave stretch and compression ==

~~=== Scala file ===~~

~~Here is a .scl file of 8edo: [[:File:08-EDO.scl|08-edo.scl]]~~

~~<pre>~~

~~! 08-EDO.scl~~

!

~~8 EDO~~

8

!

~~150.00~~

~~300.00~~

~~450.00~~

~~600.00~~

~~750.00~~

~~900.00~~

~~1050.00~~

~~2/1~~

~~</pre>~~

~~=== Temperaments ===~~

8edo is fairly composite, so the only step that generates a [[mos]] scale that covers every interval other than the 1 is the 3, producing scales of 332 and [[3L 2s|21212]]. In terms of temperaments, in the 5-limit this is best interpreted as [[father]], as 8edo is the highest edo that tempers out the diatonic semitone in it's [[patent val]], merging 5/4 and 4/3 into a single interval, which is also the generator. This means major and minor chords are rotations of each other, making them inaccurate but very simple, with even the 5 note mos having 3 of both and providing a functional skeleton of 5-limit harmony, albeit with some very strange enharmonic equivalences. In terms of 7-limit extensions things get even more inaccurate, as the patent val supports [[mother]], but the ideal tuning for that is much closer to [[5edo]]. The 8d val supports septimal father and [[pater]], and is much closer to the ideal tuning for both, as the extremely sharp 7 works better with the {{nowrap| 3 & 5 }}. In terms of multi-period temperaments, it makes for a near perfect [[walid]] or a much less accurate [[diminished (temperament)|diminished]] scale.

=== Octave stretch and compression ===

8edo's approximation of [[JI]] can be improved via [[octave shrinking]]. Compressing 8edo's octave from 1200 [[cent]]s down to 1187 cents gives the tuning called [[ed12|29ed12]].

Line 527:

Line 504:

* Step size: 148.343{{c}}, octave size: 1186.746{{c}}

{{Harmonics in equal|29|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 29ed12}}

{{Harmonics in equal|29|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 29ed12 (continued)}}

== Scales ==

=== Scala file ===

Here is a .scl file of 8edo: [[:File:08-EDO.scl|08-edo.scl]]

<pre>

! 08-EDO.scl

!

8 EDO

8

!

150.00

300.00

450.00

600.00

750.00

900.00

1050.00

2/1

</pre>

=== Temperaments ===

8edo is fairly composite, so the only step that generates a [[mos]] scale that covers every interval other than the 1 is the 3, producing scales of 332 and [[3L 2s|21212]]. In terms of temperaments, in the 5-limit this is best interpreted as [[father]], as 8edo is the highest edo that tempers out the diatonic semitone in it's [[patent val]], merging 5/4 and 4/3 into a single interval, which is also the generator. This means major and minor chords are rotations of each other, making them inaccurate but very simple, with even the 5 note mos having 3 of both and providing a functional skeleton of 5-limit harmony, albeit with some very strange enharmonic equivalences. In terms of 7-limit extensions things get even more inaccurate, as the patent val supports [[mother]], but the ideal tuning for that is much closer to [[5edo]]. The 8d val supports septimal father and [[pater]], and is much closer to the ideal tuning for both, as the extremely sharp 7 works better with the {{nowrap| 3 & 5 }}. In terms of multi-period temperaments, it makes for a near perfect [[walid]] or a much less accurate [[diminished (temperament)|diminished]] scale.

== Instruments ==

@@ Line 479: / Line 479: @@
 <references/>
-== Scales ==
+== Octave stretch and compression ==
-=== Scala file ===
-Here is a .scl file of 8edo: [[:File:08-EDO.scl|08-edo.scl]]
-<pre>
-! 08-EDO.scl
-!
-EDO
-!
-.00
-.00
-.00
-.00
-.00
-.00
-.00
-/1
-</pre>
-=== Temperaments ===
-edo is fairly composite, so the only step that generates a [[mos]] scale that covers every interval other than the 1 is the 3, producing scales of 332 and [[3L 2s|21212]]. In terms of temperaments, in the 5-limit this is best interpreted as [[father]], as 8edo is the highest edo that tempers out the diatonic semitone in it's [[patent val]], merging 5/4 and 4/3 into a single interval, which is also the generator. This means major and minor chords are rotations of each other, making them inaccurate but very simple, with even the 5 note mos having 3 of both and providing a functional skeleton of 5-limit harmony, albeit with some very strange enharmonic equivalences. In terms of 7-limit extensions things get even more inaccurate, as the patent val supports [[mother]], but the ideal tuning for that is much closer to [[5edo]]. The 8d val supports septimal father and [[pater]], and is much closer to the ideal tuning for both, as the extremely sharp 7 works better with the {{nowrap| 3 & 5 }}. In terms of multi-period temperaments, it makes for a near perfect [[walid]] or a much less accurate [[diminished (temperament)|diminished]] scale.
-=== Octave stretch and compression ===
 edo's approximation of [[JI]] can be improved via [[octave shrinking]]. Compressing 8edo's octave from 1200 [[cent]]s down to 1187 cents gives the tuning called [[ed12|29ed12]].
@@ Line 527: / Line 504: @@
 * Step size: 148.343{{c}}, octave size: 1186.746{{c}}
 {{Harmonics in equal|29|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 29ed12}}
 {{Harmonics in equal|29|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 29ed12 (continued)}}
+== Scales ==
+=== Scala file ===
+Here is a .scl file of 8edo: [[:File:08-EDO.scl|08-edo.scl]]
+<pre>
+! 08-EDO.scl
+!
+EDO
+!
+.00
+.00
+.00
+.00
+.00
+.00
+.00
+/1
+</pre>
+=== Temperaments ===
+edo is fairly composite, so the only step that generates a [[mos]] scale that covers every interval other than the 1 is the 3, producing scales of 332 and [[3L 2s|21212]]. In terms of temperaments, in the 5-limit this is best interpreted as [[father]], as 8edo is the highest edo that tempers out the diatonic semitone in it's [[patent val]], merging 5/4 and 4/3 into a single interval, which is also the generator. This means major and minor chords are rotations of each other, making them inaccurate but very simple, with even the 5 note mos having 3 of both and providing a functional skeleton of 5-limit harmony, albeit with some very strange enharmonic equivalences. In terms of 7-limit extensions things get even more inaccurate, as the patent val supports [[mother]], but the ideal tuning for that is much closer to [[5edo]]. The 8d val supports septimal father and [[pater]], and is much closer to the ideal tuning for both, as the extremely sharp 7 works better with the {{nowrap| 3 & 5 }}. In terms of multi-period temperaments, it makes for a near perfect [[walid]] or a much less accurate [[diminished (temperament)|diminished]] scale.
 == Instruments ==