79MOS 159edo: Difference between revisions

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Line 1:

[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_64170.html#64171 Original article] by Ozan Yarman, on the Yahoo tuning forum, is quoted here.

:''<tt>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_64170.html#64171 Original article] by Ozan Yarman, on the Yahoo tuning forum, is quoted here.</tt>''

<nowiki>--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------</~~nowiki>~~

My tuning scheme involves [[33ed4/3|33 equal divisions of the pure fourth]].

~~My tuning scheme involves~~ 33 ~~equal divisions of the pure fourth~~.

1. [log (4/3) * 1200]/(log 2) divided by 33 = 15.092272701048866128954947492807 [[cents]].

~~1. [log (4/3) * 1200]/(log 2) divided by 33 = 15.092272701048866128954947492807 cents.~~

2. Carry the [[comma]] to the 79th step and you reach 1192.2895433828604241874408519317 cents.

2. Carry the comma to the 79th step and you reach 1192.2895433828604241874408519317 cents.

3. Complete the octave to 1200 cents and move the 22.802729318188441941514095561079 cent comma between steps 45-46. You do this by key transposing the tuning to the -46th step.

Voila! You now have a circulating temperament which is practically a subset of 159-tET. There are three sizes of fifths by which one can formulate diatonical scales:

Voila! You now have a [[circulating temperament]] which is practically a subset of [[159edo|159-tET]]. There are three sizes of fifths by which one can formulate [[diatonic|diatonical]] scales:

0: 1/1 C RAST

Line 17:

Line 15:

1: 15.092 cents C/

2: 30.185 cents C

2: 30.185 cents C//

3: 45.277 cents C^ Db(

Line 29:

Line 27:

7: 105.646 cents C#/ Db

8: 120.738 cents C#'' Db/''

8: 120.738 cents C#// Db/

9: 135.830 cents C#^ D(

Line 55:

Line 53:

20: 301.845 cents D#/ Eb

21: 316.938 cents D#'' Eb/''

21: 316.938 cents D#// Eb/

22: 332.030 cents D#^ E(

Line 83:

Line 81:

34: 513.137 cents F/

35: 528.230 cents F

35: 528.230 cents F//

36: 543.322 cents F^ Gb(

Line 95:

Line 93:

40: 603.691 cents F#/ Gb

41: 618.783 cents F#'' Gb/''

41: 618.783 cents F#// Gb/

42: 633.875 cents F#^ G(

Line 109:

Line 107:

47: 717.047 cents G/

48: 732.140 cents G

48: 732.140 cents G//

49: 747.232 cents G^ Ab(

Line 121:

Line 119:

53: 807.601 cents G#/ Ab

54: 822.693 cents G#'' Ab/''

54: 822.693 cents G#// Ab/

55: 837.785 cents G#^ A(

Line 135:

Line 133:

60: 913.247 cents A/ Huseyni again

61: 928.339 cents A

61: 928.339 cents A//

62: 943.431 cents A^ Bb(

Line 147:

Line 145:

66: 1003.800 cents A#/ Bb

67: 1018.893 cents A#'' Bb/''

67: 1018.893 cents A#// Bb/

68: 1033.985 cents A#^ B(

Line 161:

Line 159:

73: 1109.446 cents B/ Cb Mahur

74: 1124.539 cents B'' Cb/ Mahurek (my proposal)''

74: 1124.539 cents B// Cb/ Mahurek (my proposal)

75: 1139.631 cents B^ C(

Line 173:

Line 171:

79: 1200.000 cents C GERDANIYE

Some degrees yield excellent 11 limit results, while others produce adorable 5 limit and sufficiently close 7 limit intervals. I had implemented this tuning on my special Qanun, and also installed Wittner fine-tuners to the strings for accuracy of pitch. Although my hands are still numb from all that tuning, I am very pleased, and so are Qanun performers who were "unfortunate" enough to have met me.

Some degrees yield excellent [[11 limit]] results, while others produce adorable [[5-limit|5 limit]] and sufficiently close [[7-limit|7 limit]] intervals.

I had implemented this tuning on my special Qanun, and also installed Wittner fine-tuners to the strings for accuracy of pitch. Although my hands are still numb from all that tuning, I am very pleased, and so are Qanun performers who were "unfortunate" enough to have met me.

[[Category:159edo]]

@@ Line 1: / Line 1: @@
-[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_64170.html#64171 Original article] by Ozan Yarman, on the Yahoo tuning forum, is quoted here.
+:''<tt>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_64170.html#64171 Original article] by Ozan Yarman, on the Yahoo tuning forum, is quoted here.</tt>''
-<nowiki>--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------</nowiki>
+My tuning scheme involves [[33ed4/3|33 equal divisions of the pure fourth]].
-My tuning scheme involves 33 equal divisions of the pure fourth.
+. [log (4/3) * 1200]/(log 2) divided by 33 = 15.092272701048866128954947492807 [[cents]].
-. [log (4/3) * 1200]/(log 2) divided by 33 = 15.092272701048866128954947492807 cents.
+. Carry the [[comma]] to the 79th step and you reach 1192.2895433828604241874408519317 cents.
-. Carry the comma to the 79th step and you reach 1192.2895433828604241874408519317 cents.
 . Complete the octave to 1200 cents and move the 22.802729318188441941514095561079 cent comma between steps 45-46. You do this by key transposing the tuning to the -46th step.
-Voila! You now have a circulating temperament which is practically a subset of 159-tET. There are three sizes of fifths by which one can formulate diatonical scales:
+Voila! You now have a [[circulating temperament]] which is practically a subset of [[159edo|159-tET]]. There are three sizes of fifths by which one can formulate [[diatonic|diatonical]] scales:
 : 1/1 C RAST
@@ Line 17: / Line 15: @@
 : 15.092 cents C/
-: 30.185 cents C
+: 30.185 cents C//
 : 45.277 cents C^ Db(
@@ Line 29: / Line 27: @@
 : 105.646 cents C#/ Db
-: 120.738 cents C#'' Db/''
+: 120.738 cents C#// Db/
 : 135.830 cents C#^ D(
@@ Line 55: / Line 53: @@
 : 301.845 cents D#/ Eb
-: 316.938 cents D#'' Eb/''
+: 316.938 cents D#// Eb/
 : 332.030 cents D#^ E(
@@ Line 83: / Line 81: @@
 : 513.137 cents F/
-: 528.230 cents F
+: 528.230 cents F//
 : 543.322 cents F^ Gb(
@@ Line 95: / Line 93: @@
 : 603.691 cents F#/ Gb
-: 618.783 cents F#'' Gb/''
+: 618.783 cents F#// Gb/
 : 633.875 cents F#^ G(
@@ Line 109: / Line 107: @@
 : 717.047 cents G/
-: 732.140 cents G
+: 732.140 cents G//
 : 747.232 cents G^ Ab(
@@ Line 121: / Line 119: @@
 : 807.601 cents G#/ Ab
-: 822.693 cents G#'' Ab/''
+: 822.693 cents G#// Ab/
 : 837.785 cents G#^ A(
@@ Line 135: / Line 133: @@
 : 913.247 cents A/ Huseyni again
-: 928.339 cents A
+: 928.339 cents A//
 : 943.431 cents A^ Bb(
@@ Line 147: / Line 145: @@
 : 1003.800 cents A#/ Bb
-: 1018.893 cents A#'' Bb/''
+: 1018.893 cents A#// Bb/
 : 1033.985 cents A#^ B(
@@ Line 161: / Line 159: @@
 : 1109.446 cents B/ Cb Mahur
-: 1124.539 cents B'' Cb/ Mahurek (my proposal)''
+: 1124.539 cents B// Cb/ Mahurek (my proposal)
 : 1139.631 cents B^ C(
@@ Line 173: / Line 171: @@
 : 1200.000 cents C GERDANIYE
-Some degrees yield excellent 11 limit results, while others produce adorable 5 limit and sufficiently close 7 limit intervals. I had implemented this tuning on my special Qanun, and also installed Wittner fine-tuners to the strings for accuracy of pitch. Although my hands are still numb from all that tuning, I am very pleased, and so are Qanun performers who were "unfortunate" enough to have met me.
+Some degrees yield excellent [[11 limit]] results, while others produce adorable [[5-limit|5 limit]] and sufficiently close [[7-limit|7 limit]] intervals.
+I had implemented this tuning on my special Qanun, and also installed Wittner fine-tuners to the strings for accuracy of pitch. Although my hands are still numb from all that tuning, I am very pleased, and so are Qanun performers who were "unfortunate" enough to have met me.
+[[Category:159edo]]