View source for Pseudo-semaphore

'''Pseudo-semaphore''' is a [[dual-fifth]] temperament related to [[semaphore]]. As in all dual-fifth temperaments, the third harmonic has two mappings, in this case a [[flattone]] to [[flattertone]]-sized one and a [[superpyth]] to [[ultrapyth]]-sized one.

It's called "pseudo-semaphore" because it has the same MOS structure as semaphore, but [[49/48]] is not tempered out. Perhaps it's better to think of it as [[superpyth]] in which the 4/3 generator has been split in half forming a weird interval that's neither [[8/7]] nor [[7/6]].

== Interval chain ==

{| class="wikitable"
|-
| 204.
| 448.
| 692.
| 936.
| 1180.
| 224.
| 468.
| 712.
| 956.
| 0.
| 244.
| 488.
| 732.
| 976.
| 20.
| 264.
| 508.
| 752.
| 996.
|-
| 9/8
| 9/7
| 3/2 (flat)
| 12/7
|
| 9/8~8/7
|
| 3/2 (sharp)
|
| 1/1
|
| 4/3 (flat)
|
| 7/4~16/9
|
| 7/6
| 4/3 (sharp)
| 14/9
| 16/9
|}

== MOSes ==

=== 5-note (LLLLs, proper) ===

The 5-note MOS is not much use because only one of the two different mappings shows up. You'd be better off using [[semaphore]][5] or [[superpyth]][5] (or [[5edo]]).

{| class="wikitable"
|-
| Small ("minor") interval
| 224.
| 468.
| 712.
| 956.
|-
| JI intervals represented
| 9/8~8/7
|
| 3/2
|
|-
| Large ("major") interval
| 244.
| 488.
| 732.
| 976.
|-
| JI intervals represented
|
| 4/3
|
| 7/4~16/9
|}

=== 9-note (LLsLsLsLs, improper) ===

Here's where all the action begins. Note that this nine-note scale contains nine [[4/3]]s and nine [[3/2]]s. The only way this is possible with a single mapping for 3 is an equal temperament, and all of these 4/3s and 3/2s are much more accurate than in [[9edo]].

{| class="wikitable"
|-
| Small ("minor") interval
| 20.
| 244.
| 264.
| 488.
| 508.
| 732.
| 752.
| 976.
|-
| JI intervals represented
|
|
| 7/6
| 4/3 (flat)
| 4/3 (sharp)
|
| 14/9
| 7/4~16/9
|-
| Large ("major") interval
| 224.
| 448.
| 468.
| 692.
| 712.
| 936.
| 956.
| 1180.
|-
| JI intervals represented
| 9/8~8/7
| 9/7
|
| 3/2 (flat)
| 3/2 (sharp)
| 12/7
| 
|
|}

[[Category:Temperaments]]
[[Category:Dual-fifth temperaments]]