Pseudo-semaphore: Difference between revisions

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Pseudo-semaphore is a weird temperament in which the third harmonic does not have a single consistent mapping. If you want to force it into the regular mapping paradigm you have to think of it as a 2.3.3'.7 temperament.
'''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|semaphore]], but 49/48 is not tempered out. Perhaps it's better to think of it as [[Superpyth|superpyth]] in which the 4/3 generator has been split in half forming a weird interval that's neither 8/7 nor 7/6.
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==
== Interval chain ==


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


==MOSes==
== MOSes ==


===5-note (LLLLs, proper)===
=== 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|semaphore]][5] or [[Superpyth|superpyth]][5] (or [[5edo|5edo]]).
 
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"
{| class="wikitable"
|-
|-
| | Small ("minor") interval
| Small ("minor") interval
| | 224.
| 224.
| | 468.
| 468.
| | 712.
| 712.
| | 956.
| 956.
|-
|-
| | JI intervals represented
| JI intervals represented
| | 9/8~8/7
| 9/8~8/7
| |  
|
| | 3/2
| 3/2
| |  
|
|-
|-
| | Large ("major") interval
| Large ("major") interval
| | 244.
| 244.
| | 488.
| 488.
| | 732.
| 732.
| | 976.
| 976.
|-
|-
| | JI intervals represented
| JI intervals represented
| |  
|
| | 4/3
| 4/3
| |  
|
| | 7/4~16/9
| 7/4~16/9
|}
|}


===9-note (LLsLsLsLs, improper)===
=== 9-note (LLsLsLsLs, improper) ===
Here's where all the action begins. Note that this nine-note scale contains nine 4/3s and nine 3/2s. 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|9edo]].
 
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"
{| class="wikitable"
|-
|-
| | Small ("minor") interval
| Small ("minor") interval
| | 20.
| 20.
| | 244.
| 244.
| | 264.
| 264.
| | 488.
| 488.
| | 508.
| 508.
| | 732.
| 732.
| | 752.
| 752.
| | 976.
| 976.
|-
|-
| | JI intervals represented
| JI intervals represented
| |  
|
| |  
|
| | 7/6
| 7/6
| | 4/3 (flat)
| 4/3 (flat)
| | 4/3 (sharp)
| 4/3 (sharp)
| |  
|
| | 14/9
| 14/9
| | 7/4~16/9
| 7/4~16/9
|-
|-
| | Large ("major") interval
| Large ("major") interval
| | 224.
| 224.
| | 448.
| 448.
| | 468.
| 468.
| | 692.
| 692.
| | 712.
| 712.
| | 936.
| 936.
| | 956.
| 956.
| | 1180.
| 1180.
|-
|-
| | JI intervals represented
| JI intervals represented
| | 9/8~8/7
| 9/8~8/7
| | 9/7
| 9/7
| |  
|
| | 3/2 (flat)
| 3/2 (flat)
| | 3/2 (sharp)
| 3/2 (sharp)
| | 12/7
| 12/7
| |  
|  
| |  
|
|}
|}
[[Category:Temperaments]]
[[Category:Dual-fifth temperaments]]

Latest revision as of 23:38, 19 April 2025

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

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).

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 4/3s and nine 3/2s. 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.

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
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