Semaphore and godzilla: Difference between revisions
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'''Semaphore''', of the [[ | '''Semaphore''', of the [[slendro clan]], is characterized by [[49/48]] being [[tempering out|tempered out]], so the [[generator]] represents [[8/7]] and [[7/6]] equally. This results in a very low [[complexity]] 2.3.7-[[subgroup]] [[regular temperament|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 the 5th harmonic's intervals are desired, 5/4 can be sensibly mapped to −8 | If the [[5/1|5th harmonic]]'s intervals are desired, [[5/4]] can be sensibly mapped to −8 generators by tempering out [[81/80]], making it a [[Meantone family #Extensions|meantone temperament]]. This temperament is '''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]]. | ||
See [[Slendro clan #Semaphore]] and [[Slendro clan #Godzilla|#Godzilla]] for technical data. | |||
== Interval chains == | == Interval chains == | ||
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|} | |} | ||
== | == Scales == | ||
Scala files: | |||
* [[semaphore5]] | |||
* [[semaphore9]] | |||
* [[semaphore14]] | |||
=== 5-note (proper) === | === 5-note (proper) === | ||
{| class="wikitable" | {| class="wikitable" | ||
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Like supra[7], godzilla[9] is well stocked with subminor and supermajor triads; in this case they can be viewed as 6:7:9 and 10:13:15 since 19edo is a [[The_Biosphere|biome]] temperament. Godzilla[9] has only ''one'' each of the more stable 5-limit major and minor triads, which might be considered a drawback, but could also be considered a strength for helping to establish a clearer tonal center (since all triads other than the tonic have tension in them). | Like supra[7], godzilla[9] is well stocked with subminor and supermajor triads; in this case they can be viewed as 6:7:9 and 10:13:15 since 19edo is a [[The_Biosphere|biome]] temperament. Godzilla[9] has only ''one'' each of the more stable 5-limit major and minor triads, which might be considered a drawback, but could also be considered a strength for helping to establish a clearer tonal center (since all triads other than the tonic have tension in them). | ||
== Music == | == Music == | ||
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* [http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/S__no_Contratempo_by_Roncevaux_on_SoundCloud___Hear_the_world_s_sounds.mp3 Só no Contratempo] | * [http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/S__no_Contratempo_by_Roncevaux_on_SoundCloud___Hear_the_world_s_sounds.mp3 Só no Contratempo] | ||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/__O_que_a_gente_quer__em_19_TET__temperamento_Godzilla__9___by_Roncevaux.mp3 O que a gente quer] | * [http://micro.soonlabel.com/gene_ward_smith/Others/Roncevaux/__O_que_a_gente_quer__em_19_TET__temperamento_Godzilla__9___by_Roncevaux.mp3 O que a gente quer] | ||
== See also == | |||
* [[Diasem]], a [[maximum variety|max-variety-3]] JI [[detempering]] of semaphore | |||
[[Category:Temperaments]] | [[Category:Temperaments]] | ||
Revision as of 12:53, 30 July 2024
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-subgroup 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 cents. Semaphore is a play on the words "semi-" and "fourth."
If the 5th harmonic's intervals are desired, 5/4 can be sensibly mapped to −8 generators by tempering out 81/80, making it a meantone temperament. This temperament is 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.
See Slendro clan #Semaphore and #Godzilla for technical data.
Interval chains
Semaphore
| 198.46 | 448.85 | 699.23 | 949.62 | 0 | 250.38 | 500.77 | 751.15 | 1001.54 |
| 9/8 | 9/7 | 3/2 | 12/7~7/4 | 1/1 | 8/7~7/6 | 4/3 | 14/9 | 16/9 |
Godzilla
| 378.92 | 631.56 | 884.19 | 1136.83 | 189.46 | 442.10 | 694.73 | 947.37 | 0 | 252.63 | 505.27 | 757.90 | 1010.54 | 63.17 | 315.81 | 568.44 | 821.08 |
| 5/4~16/13 | 10/7~13/9 | 5/3 | 27/14 | 10/9~9/8 | 9/7~13/10 | 3/2 | 12/7~7/4~26/15 | 1/1 | 8/7~7/6~15/13 | 4/3 | 14/9~20/13 | 16/9~9/5 | 28/27~21/20 | 6/5 | 7/5~18/13 | 8/5~13/8 |
Scales
Scala files:
5-note (proper)
| Small ("minor") interval | 198.46 | 448.85 | 699.23 | 949.62 |
| JI intervals represented | 9/8 | 9/7~13/10 | 3/2 | 12/7~7/4~26/15 |
| Large ("major") interval | 250.38 | 500.77 | 751.15 | 1001.54 |
| JI intervals represented | 8/7~7/6~15/13 | 4/3 | 14/9~20/13 | 16/9 |
9-note (improper)
| Small ("minor") interval | 63.17 | 252.63 | 315.81 | 505.27 | 568.44 | 757.90 | 821.08 | 1010.54 |
| JI intervals represented | 8/7~7/6~15/13 | 6/5 | 4/3 | 7/5~18/13 | 14/9~20/13 | 8/5~13/8 | 16/9~9/5 | |
| Large ("major") interval | 189.46 | 378.92 | 442.10 | 631.56 | 694.73 | 884.19 | 947.37 | 1136.83 |
| JI intervals represented | 10/9~9/8 | 5/4 | 9/7~13/10 | 10/7~13/9 | 3/2 | 5/3 | 12/7~7/4~26/15 |
In 19edo, godzilla[9] has steps 3 3 1 3 1 3 1 3 1, and contains the following useful scales as subsets:
- Meantone pentatonic (5 3 5 3 3)
- Altered diatonic I (3 4 3 1 3 4 1)
- Altered diatonic II (3 4 3 1 4 3 1)
- Altered diatonic III (4 3 3 1 4 3 1)
- Altered diatonic IV (3 3 4 1 3 4 1)
It does not, however, contain the ordinary diatonic scale. Godzilla[9] thus expands on the pentatonic scale, but in a different way than diatonic scales do.
The four heptatonic subsets can be regarded as chromatic alterations of the diatonic scale, or alternatively as variants of Archytas' septimal diatonic scale, but with a greatly exaggerated difference between the two different whole tone sizes. All five of these subsets are very expressive melodically. Godzilla[9] combines all of these and is expressive in its own right; it could even be thought of as 19edo's answer to the well-loved supra[7] diatonic scale of 17edo, as both are improper and made up of whole-tones and third-tones.
Like supra[7], godzilla[9] is well stocked with subminor and supermajor triads; in this case they can be viewed as 6:7:9 and 10:13:15 since 19edo is a biome temperament. Godzilla[9] has only one each of the more stable 5-limit major and minor triads, which might be considered a drawback, but could also be considered a strength for helping to establish a clearer tonal center (since all triads other than the tonic have tension in them).
Music
- "Change is on the Wind" in Godzilla[9]
See also
- Diasem, a max-variety-3 JI detempering of semaphore