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Semaphore and godzilla: Difference between revisions

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'''Semaphore''', of the [[Slendro clan]], is characterized by the vanishing of [[49/48]], so the generator represents [[8/7]] and [[7/6]] equally. This results in a very low [[complexity]] 2.3.7 [[temperament]], with the drawback that most intervals of 7 must be out of tune by at least half of the comma 49/48, or about 18 [[cent]]s. Semaphore is a play on the words "semi-" and "fourth."
'''Semaphore''', of the [[Slendro clan]], is characterized by [[49/48]] being tempered out, so the generator represents [[8/7]] and [[7/6]] equally. This results in a very low [[complexity]] 2.3.7 [[temperament]], with the drawback that most intervals of 7 must be out of tune by at least half of the comma 49/48, or about 18 [[cent]]s. Semaphore is a play on the words "semi-" and "fourth."


If 5 is mapped at all, it can be sensibly mapped to -8 [[generator]]s by [[tempering out]] [[81/80]], making it a [[Meantone family #Godzilla|meantone temperament]]. This temperament is called '''godzilla'''. A more accurate but complex mapping of 5 can be found in [[immunity]], or you can make 5/4 itself the period by tempering out [[128/125]], resulting in [[triforce]].
If the 5th harmonic's intervals are desired, 5/4 can be sensibly mapped to −8 [[generator]]s by [[tempering out]] [[81/80]], making it a [[Meantone family#Godzilla|meantone temperament]]. This temperament is called '''Godzilla'''. A more accurate but complex mapping of 5 can be found in [[immunity]], or 5/4 itself can be made the period by tempering out [[128/125]], resulting in [[triforce]].


== Temperament data ==
== Temperament data ==
Line 13: Line 13:


=== Godzilla (19&24, 2.3.5.7) ===
=== Godzilla (19&24, 2.3.5.7) ===
Period: 1\1
Period: 1\1


Line 24: Line 23:
== Interval chains ==
== Interval chains ==
=== Semaphore ===
=== Semaphore ===
{| class="wikitable"
{| class="wikitable"
|-
|-
| | 198.46
| 198.46
| | 448.85
| 448.85
| | 699.23
| 699.23
| | 949.62
| 949.62
| | 0
| 0
| | 250.38
| 250.38
| | 500.77
| 500.77
| | 751.15
| 751.15
| | 1001.54
| 1001.54
|-
|-
| | [[9/8|9/8]]
| [[9/8|9/8]]
| | [[9/7|9/7]]
| [[9/7|9/7]]
| | [[3/2|3/2]]
| [[3/2|3/2]]
| | 12/7~7/4
| 12/7~7/4
| | [[1/1|1/1]]
| [[1/1|1/1]]
| | 8/7~7/6
| 8/7~7/6
| | [[4/3|4/3]]
| [[4/3|4/3]]
| | [[14/9|14/9]]
| [[14/9|14/9]]
| | [[16/9|16/9]]
| [[16/9|16/9]]
|}
|}


Line 52: Line 50:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | 378.92
| 378.92
| | 631.56
| 631.56
| | 884.19
| 884.19
| | 1136.83
| 1136.83
| | 189.46
| 189.46
| | 442.10
| 442.10
| | 694.73
| 694.73
| | 947.37
| 947.37
| | 0
| 0
| | 252.63
| 252.63
| | 505.27
| 505.27
| | 757.90
| 757.90
| | 1010.54
| 1010.54
| | 63.17
| 63.17
| | 315.81
| 315.81
| | 568.44
| 568.44
| | 821.08
| 821.08
|-
|-
| | [[5/4|5/4]]~16/13
| [[5/4|5/4]]~16/13
| | [[10/7|10/7]]~13/9
| [[10/7|10/7]]~13/9
| | [[5/3|5/3]]
| [[5/3|5/3]]
| | 27/14
| 27/14
| | 10/9~9/8
| 10/9~9/8
| | 9/7~13/10
| 9/7~13/10
| | 3/2
| 3/2
| | 12/7~7/4~26/15
| 12/7~7/4~26/15
| | 1/1
| 1/1
| | 8/7~7/6~15/13
| 8/7~7/6~15/13
| | 4/3
| 4/3
| | 14/9~20/13
| 14/9~20/13
| | 16/9~9/5
| 16/9~9/5
| | 28/27~21/20
| 28/27~21/20
| | [[6/5|6/5]]
| [[6/5|6/5]]
| | [[7/5|7/5]]~18/13
| [[7/5|7/5]]~18/13
| | [[8/5|8/5]]~13/8
| [[8/5|8/5]]~13/8
|}
|}


== MOS scales ==
== MOS scales ==
=== 5-note (proper) ===
=== 5-note (proper) ===
{| class="wikitable"
{| class="wikitable"
|-
|-
| | Small ("minor") interval
| Small ("minor") interval
| | 198.46
| 198.46
| | 448.85
| 448.85
| | 699.23
| 699.23
| | 949.62
| 949.62
|-
|-
| | [[JI|JI]] intervals represented
| [[JI|JI]] intervals represented
| | 9/8
| 9/8
| | 9/7~13/10
| 9/7~13/10
| | 3/2
| 3/2
| | 12/7~7/4~26/15
| 12/7~7/4~26/15
|-
|-
| | Large ("major") interval
| Large ("major") interval
| | 250.38
| 250.38
| | 500.77
| 500.77
| | 751.15
| 751.15
| | 1001.54
| 1001.54
|-
|-
| | JI intervals represented
| JI intervals represented
| | 8/7~7/6~15/13
| 8/7~7/6~15/13
| | 4/3
| 4/3
| | 14/9~20/13
| 14/9~20/13
| | 16/9
| 16/9
|}
|}


=== 9-note (improper) ===
=== 9-note (improper) ===
see [[5L 4s]]
See [[5L 4s]]
{| class="wikitable"
{| class="wikitable"
|-
|-
| | Small ("minor") interval
| Small ("minor") interval
| | 63.17
| 63.17
| | 252.63
| 252.63
| | 315.81
| 315.81
| | 505.27
| 505.27
| | 568.44
| 568.44
| | 757.90
| 757.90
| | 821.08
| 821.08
| | 1010.54
| 1010.54
|-
|-
| | JI intervals represented
| JI intervals represented
| |  
|  
| | 8/7~7/6~15/13
| 8/7~7/6~15/13
| | 6/5
| 6/5
| | 4/3
| 4/3
| | 7/5~18/13
| 7/5~18/13
| | 14/9~20/13
| 14/9~20/13
| | 8/5~13/8
| 8/5~13/8
| | 16/9~9/5
| 16/9~9/5
|-
|-
| | Large ("major") interval
| Large ("major") interval
| | 189.46
| 189.46
| | 378.92
| 378.92
| | 442.10
| 442.10
| | 631.56
| 631.56
| | 694.73
| 694.73
| | 884.19
| 884.19
| | 947.37
| 947.37
| | 1136.83
| 1136.83
|-
|-
| | JI intervals represented
| JI intervals represented
| | 10/9~9/8
| 10/9~9/8
| | 5/4
| 5/4
| | 9/7~13/10
| 9/7~13/10
| | 10/7~13/9
| 10/7~13/9
| | 3/2
| 3/2
| | 5/3
| 5/3
| | 12/7~7/4~26/15
| 12/7~7/4~26/15
| |  
|  
|}
|}


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