79MOS 159edo: Difference between revisions

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

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

My tuning scheme involves [[33ed4/3|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

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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: @@
 :''<tt>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_64170.html#64171 Original article] by Ozan Yarman, on the Yahoo tuning forum, is quoted here.</tt>''
-My tuning scheme involves 33 equal divisions of the pure fourth.
+My tuning scheme involves [[33ed4/3|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 171: / 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]]