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{{Infobox MOS}}
{{Infobox MOS}}


'''Shōsūshī''' - so named because of the four small steps in its diatonic MOS - is an excellent 8*-limit temperament tempering out 64/63 or an excellent 9 (18)-limit temperament tempering out 81/80.
'''Shōsūshī''' - so named because of the four small steps in its diatonic MOS - is an excellent 8*-limit temperament tempering out 64/63.


== Properties ==
== Properties ==
Line 9: Line 9:
Because shōsūshī is a Mahjong hand, its MOS has 13 tones, as in the 13 tiles in a Mahjong hand and its “13 han” Japanese value. Thus the nominals are given as Japanese kana, and to avoid confusion with traditional Japanese notations, hiragana are used.
Because shōsūshī is a Mahjong hand, its MOS has 13 tones, as in the 13 tiles in a Mahjong hand and its “13 han” Japanese value. Thus the nominals are given as Japanese kana, and to avoid confusion with traditional Japanese notations, hiragana are used.


The notation used in this article is く す つ ぬ ふ  む  ゆ  き し ち に ひ み (ku-su-tsu-nu-fu-mu-yu-ki-shi-chi-ni-hi-mi) = LLsLLLsLLsLLs (Ionian b14), #/b mostly two chromas up/down.
The notation used in this article is くすつぬふむゆきしちにひみ (ku-su-tsu-nu-fu-mu-yu-ki-shi-chi-ni-hi-mi) = LLsLLLsLLsLLs (Ionian b14), #/b mostly two chromas up/down.


Thus the [[22edXIV]] gamut is as follows:
Thus the [[22edXIV]] gamut is as follows:
Line 1,611: Line 1,611:
|M
|M
|-
|-
|Aeolian Dominant ♮6
|Aeolian Dominant ♮6
|LLsLLsLLsLLsL
|LLsLLsLLsLLsL
|<nowiki>8|4</nowiki>
|<nowiki>8|4</nowiki>
Line 1,659: Line 1,659:
|m
|m
|-
|-
|Phrygian ♮2
|Phrygian ♮2
|LsLLsLLsLLLsL
|LsLLsLLsLLLsL
|<nowiki>5|7</nowiki>
|<nowiki>5|7</nowiki>
Line 1,675: Line 1,675:
|m
|m
|-
|-
|Locrian ♮2 ♮5
|Locrian ♮2 ♮5
|LsLLsLLsLLsLL
|LsLLsLLsLLsLL
|<nowiki>4|8</nowiki>
|<nowiki>4|8</nowiki>
Line 1,691: Line 1,691:
|m
|m
|-
|-
|Locrian ♮5
|Locrian ♮5
|sLLLsLLsLLsLL
|sLLLsLLsLLsLL
|<nowiki>3|9</nowiki>
|<nowiki>3|9</nowiki>
Line 1,757: Line 1,757:


== Temperaments ==
== Temperaments ==
The '''Shōsūshī''' temperament spells its major hexad 24:30:36:45:54:64 or 84:108:126:162:189:224 <code>root-2(4g-3p)-(3g-2p)-(11g-8p)-2(3g-2p)-(1g)</code> (p = 18/5 or 7/2, g = 8/3) and its minor hexad 12:14:18:21:27:32 or 60:72:90:108:135:160 <code>root-(-5g-p)-(3g-2p)-(-2g)-2(3g-2p)-(1g)</code> (p = 18/5 or 7/2, g = 8/3).
The '''Shōsūshī''' temperament spells its major hexad 84:108:126:162:189:224 <code>root-2(4g-3p)-(3g-2p)-(11g-8p)-2(3g-2p)-(1g)</code> (p = 7/2, g = 8/3) and its minor hexad 12:14:18:21:27:32 or 60:72:90:108:135:160 <code>root-(-5g-p)-(3g-2p)-(-2g)-2(3g-2p)-(1g)</code> (p = 7/2, g = 8/3).
 
=== Shōsūshī-Meantone ===
[[Subgroup]]: 18/5.2.3
 
[[Comma]] list: [[81/80]]
 
[[POL2]] generator: ~4/3 = 506.8820
 
[[Mapping]]: [{{Val|1 1 2}}, {{Val|0 -2 -5}}]
 
[[Vals]]: [[22edXIV]], [[35edXIV]], [[48edXIV]], [[61edXIV]]


=== Shōsūshī-Superpyth ===
=== Shōsūshī-Superpyth ===
Line 1,783: Line 1,772:
== Scale tree ==
== Scale tree ==
The spectrum looks like this:
The spectrum looks like this:
{| class="wikitable"
{{Scale tree | 9L 4s <7/2>}}
|+
! colspan="3" |Generator
!<u>Normalized<ref name=":0" /></u>
!''ed22\12 (→ed11\6)<ref name=":0" />''
!L
!s
!L/s
!Comments
|-
|3\13
|
|
|<u>514; 3, 2</u>
|''507; 1, 3, 3''
|1
|1
|1.000
|Equalised
|-
|
|17\74
|
|<u>510</u>
|''505; 2, 2, 7''
|6
|5
|1.200
|
|-
|
|14\61
|
|<u>509.{{Overline|09}}</u>
|''504; 1, 11, 5''
|5
|4
|1.250
|
|-
|
|
|25\109
|<u>508; 2, 9, 3</u>
|''504; 1, 1, 2, 2, 1, 2, 2''
|9
|7
|1.286
|
|-
|
|11\48
|
|<u>507; 1, 3, 3</u>
|''504.1{{Overline|6}}''
|4
|3
|1.333
|
|-
|
|
|19\83
|<u>506.{{Overline|6}}</u>
|''503; 1, 1, 1, 1, 2, 6''
|7
|5
|1.400
|
|-
|
|8\35
|
|<u>505; 3, 1, 4</u>
|''502; 1, 6''
|3
|2
|1.500
|Shōsūshī-Meantone starts here
|-
|
|
|21\92
|<u>504</u>
|''502; 5, 1, 3''
|8
|5
|1.600
|
|-
|
|
|13\57
|<u>503; 4, 2, 3</u>
|''501; 1, 3, 14''
|5
|3
|1.667
|
|-
|
|
|18\79
|<u>502; 3, 14</u>
|''501; 3, 1, 3, 5''
|7
|4
|1.750
|
|-
|
|
|23\101
|<u>501.{{Overline|81}}</u>
|''500.{{Overline|0099}}''
|9
|5
|1.800
|
|-
|
|5\22
|
|<u>500</u>
|''500''
|2
|1
|2.000
|Shōsūshī-Meantone ends, Shōsūshī-Pythagorean begins
|-
|
|
|27\119
|<u>498; 2, 6</u>
|''499; 6, 3, 1, 4''
|11
|5
|2.200
|
|-
|
|
|22\97
|<u>498; 8, 1, 5</u>
|''498; 1, 31, 3''
|9
|4
|2.250
|
|-
|
|
|17\75
|<u>497; 1, 1, 3, 1, 1, 2</u>
|''498.{{Overline|6}}''
|7
|3
|2.333
|
|-
|
|
|12\53
|<u>496; 1, 1, 4, 3</u>
|''498; 8, 1, 5''
|5
|2
|2.500
|Shōsūshī-Neogothic heartland is from here…
|-
|
|
|19\84
|<u>495; 1, 1, 1, 7</u>
|''497; 1, 1, 1, 1, 1, 2''
|8
|3
|2.667
|…to here
|-
|
|7\31
|
|<u>494; 8, 2</u>
|''496; 1, 3, 2, 3''
|3
|1
|3.000
|Shōsūshī-Pythagorean ends, Shōsūshī-Superpyth begins
|-
|
|
|30\133
|<u>493; 6, 1, 1, 1, 3</u>
|''496; 4, 6, 2, 2''
|13
|4
|3.250
|
|-
|
|
|23\102
|<u>492.8{{Overline|3}}</u>
|''496; 12, 1, 3''
|10
|3
|3.333
|
|-
|
|
|16\71
|<u>492; 3, 4</u>
|''495; 1, 3, 2, 3, 2''
|7
|2
|3.500
|
|-
|
|
|25\111
|<u>491; 1, 4, 12</u>
|''495; 2, 55''
|11
|3
|3.667
|
|-
|
|9\40
|
|<u>490.{{Overline|90}}</u>
|''495''
|4
|1
|4.000
|
|-
|
|
|20\89
|<u>489; 1, 3, 1, 9</u>
|''494; 2, 1, 1, 1, 1, 1, 1, 2''
|9
|2
|4.500
|
|-
|
|11\49
|
|<u>488.{{Overline|8}}</u>
|''493; 1, 7, 6''
|5
|1
|5.000
|Shōsūshī-Superpyth ends
|-
|
|13\58
|
|<u>487.5</u>
|''493; 9, 1, 2''
|6
|1
|6.000
|
|-
|2\9
|
|
|<u>480</u>
|''488.{{Overline|8}}''
|1
|0
|→ inf
|Paucitonic
|}
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