Magic22 as srutis: Difference between revisions

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=Magic[22] as srutis=

= Magic[22] as srutis =

:''<tt>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_63593.html#63593 Original article] by [[~~Gene_Ward_Smith|~~Gene Ward Smith]], on the Yahoo tuning forum, is quoted here.</tt>''

:''<tt>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_63593.html#63593 Original article] by [[Gene Ward Smith]], on the Yahoo tuning forum, is quoted here.</tt>''

What srutis are seems to be fairly flexible. However, reasonably authentic conditions to impose are the following:

(1) It should contain the Sa-grama, 9/~~8-5~~/~~4-4~~/~~3-3~~/~~2-27~~/~~16-15~~/~~8-2~~

(1) It should contain the Sa-grama, 9/8—5/4—4/3—3/2—27/16—15/8—2.

(2) It should give the major whole tone, 9/8, four srutis, 10/9 three srutis, and 16/15 two srutis, hence giving the octave 22 srutis.

(3) 9/8, 10/9 and 16/15 are each always of the same size, and distinguished, with 9/8>10/9>16/15.

(3) 9/8, 10/9 and 16/15 are each always of the same size, and distinguished, with 9/8 > 10/9 > 16/15.

Many scales fulfill these conditions, and one of the most interesting, I think, is Magic[22], the 22-note MOS of the [[~~Regular_Temperaments#magic~~|magic temperament]]. Using the generator of 13 steps of [[41edo|41-et]], if we take the shrutis for 10/9 to always be 222, and the srutis for 16/15 to always be 22, we are left to give three steps of size 2, and one of size 1, for the srutis given to 9/8. If we vary the pattern of doing this we can get Magic[22]:

Many scales fulfill these conditions, and one of the most interesting, I think, is Magic[22], the 22-note MOS of the [[Magic|magic temperament]]. Using the generator of 13 steps of [[41edo|41-et]], if we take the shrutis for 10/9 to always be 222, and the srutis for 16/15 to always be 22, we are left to give three steps of size 2, and one of size 1, for the srutis given to 9/8. If we vary the pattern of doing this we can get Magic[22]:

1-(2212)-9/8-(222)-5/4-(22)-4/3-(1222)-3/2-(2221)~~-27~~/~~16-~~(222)~~-15~~/8-(22)-2

1—(2212)—9/8—(222)—5/4—(22)—4/3—(1222)—3/2—(2221)—27/16—(222)—15/8—(22)—2

Here the numbers in parethesis are the scale step patters between one note of Sa-grama and the next.

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-=Magic[22] as srutis=
+= Magic[22] as srutis =
-:''<tt>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_63593.html#63593 Original article] by [[Gene_Ward_Smith|Gene Ward Smith]], on the Yahoo tuning forum, is quoted here.</tt>''
+:''<tt>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_63593.html#63593 Original article] by [[Gene Ward Smith]], on the Yahoo tuning forum, is quoted here.</tt>''
 What srutis are seems to be fairly flexible. However, reasonably authentic conditions to impose are the following:
-(1) It should contain the Sa-grama, 9/8-5/4-4/3-3/2-27/16-15/8-2
+(1) It should contain the Sa-grama, 9/8—5/4—4/3—3/2—27/16—15/8—2.
 (2) It should give the major whole tone, 9/8, four srutis, 10/9 three srutis, and 16/15 two srutis, hence giving the octave 22 srutis.
-(3) 9/8, 10/9 and 16/15 are each always of the same size, and distinguished, with 9/8&gt;10/9&gt;16/15.
+(3) 9/8, 10/9 and 16/15 are each always of the same size, and distinguished, with 9/8 &gt; 10/9 &gt; 16/15.
-Many scales fulfill these conditions, and one of the most interesting, I think, is Magic[22], the 22-note MOS of the [[Regular_Temperaments#magic|magic temperament]]. Using the generator of 13 steps of [[41edo|41-et]], if we take the shrutis for 10/9 to always be 222, and the srutis for 16/15 to always be 22, we are left to give three steps of size 2, and one of size 1, for the srutis given to 9/8. If we vary the pattern of doing this we can get Magic[22]:
+Many scales fulfill these conditions, and one of the most interesting, I think, is Magic[22], the 22-note MOS of the [[Magic|magic temperament]]. Using the generator of 13 steps of [[41edo|41-et]], if we take the shrutis for 10/9 to always be 222, and the srutis for 16/15 to always be 22, we are left to give three steps of size 2, and one of size 1, for the srutis given to 9/8. If we vary the pattern of doing this we can get Magic[22]:
--(2212)-9/8-(222)-5/4-(22)-4/3-(1222)-3/2-(2221)-27/16-(222)-15/8-(22)-2
+—(2212)—9/8—(222)—5/4—(22)—4/3—(1222)—3/2—(2221)—27/16—(222)—15/8—(22)—2
 Here the numbers in parethesis are the scale step patters between one note of Sa-grama and the next.