User:PiotrGrochowski/User:PiotrGrochowski: Difference between revisions

← Older edit

VisualWikitext

@@ Line 1: / Line 1: @@
-Nice edos to start with are 7edo, 9edo, 10edo, 12edo, 15edo, 17edo, 19edo, 22edo, 26edo, 29edo, 31edo, 34edo, 41edo, 43edo, 46edo, 48edo, 50edo, 53edo, 55edo and 60edo. They offer nice approximations to some of the intervals.
+<span style="font-family: 'Consolas';"><div><big>''Do not ban this user''</big></div>
-Meantone: 7edo, 12edo, 19edo, 26edo, 31edo, 43edo, 50edo, 55edo. These allow unambiguous notation and have a generally familiar diatonic scale, except for 7edo which is slightly out of tune.
+<div><big>''He did nothing wrong''</big></div>
-Superpyth: 10edo, 15edo, 17edo, 22edo. These edos are worthy of mention avoiding the 81/80 comma instead sharpening the fifth to temper out the 64/63 comma. The diatonic scale will sound out of tune, and it's harder to notate, but the xenharmonic musical possibilities may help.
+Edos are for calculating approximate logarithms in mathematics. The right choice of an edo (such as [[53edo]] or even [[612edo]] for 5-limit numbers) would give accurate results.
-Schismic: 12edo, 17edo, 29edo, 41edo, 53edo. These edos go eight fifths down to get the 5/4 ratio, which potentially allows greater accuracy in both 3/2 and 5/4 than meantone, as 53edo shows.
+<pre>Which number is the biggest?
+A. 81^56
+B. 9^100
+C. 27^72
+D. 2^224</pre>
-Modified 12edo: 48edo, 60edo. These offer the intervals of 12edo, while also offering more accurate 5 and 7, detaching from meantone and schismic instead into different temperaments.
+log₂(81^56)≈18816<br>
+log₂(9^100)≈16800<br>
+log₂(27^72)≈18144<br>
+log₂(2^224)=11872
-edo is a macrotonal edo that accurately represents 7/6.
+<b>A.</b>
-edo is notable for its 5–limit accuracy.
+(calculated successfully with [[53edo]])
-edo is notable for its 13–limit accuracy.
+<pre>³√(2 7/9)÷³√(3/5) rounded to the nearest integer is
+A. 1
+B. 2
+C. 3
+D. 4</pre>
+log₂(³√(25/9)÷³√(3/5))≈39
+^(39÷53)≈5÷3
+round(5÷3)=2
+<b>B.</b>
+(calculated successfully with [[53edo]])
+<pre>Which number is the smallest?
+A. 5√3
+B. 4√7
+C. 8√2
+D. 3√11</pre>
+log₂(5√3)≈127.5<br>
+log₂(4√7)≈139.5<br>
+log₂(8√2)=143.5<br>
+log₂(3√11)≈136
+<b>A.</b>
+(calculated successfully with [[41edo]])
+</span>
+<!--For information about me, see [[Editor PiotrGrochowski]]
+<span style="font-family: 'Consolas';">'''DO NOT MOVE [[Editor PiotrGrochowski]] HERE. THIS IS A PERSONAL [[SandBox]].'''</span>
+making up interval names
+\94 0 unison
+\94 12.766
+\94 25.532
+\94 38.298
+\94 51.064
+\94 63.830
+\94 76.596
+\94 89.362
+\94 102.128
+\94 114.894
+\94 127.660
+\94 140.426
+\94 153.191
+\94 165.957
+\94 178.723
+\94 191.489
+\94 204.255
+experimenting with 94edo version of partch (I like to keep using 94edo for everything...)
+/1
+/143
+/80
+/48
+/35
+/24
+Will write down the commas of 15–odd–limit below
+{{list
+|[[16/15]], [[15/8]]
+|[[15/14]], [[28/15]]
+|[[14/13]], [[13/7]]
+|[[13/12]], [[24/13]]
+|[[12/11]], [[11/6]]
+|[[11/10]], [[20/11]]
+|[[10/9]], [[9/5]]
+|[[9/8]], [[16/9]]
+|[[8/7]], [[7/4]]
+|[[15/13]], [[26/15]]
+|[[7/6]], [[12/7]]
+|[[13/11]], [[22/13]]
+|[[6/5]], [[5/3]]
+|[[11/9]], [[18/11]]
+|[[16/13]], [[13/8]]
+|[[5/4]], [[8/5]]
+|[[14/11]], [[11/7]]
+|[[9/7]], [[14/9]]
+|[[13/10]], [[20/13]]
+|[[4/3]], [[3/2]]
+|[[15/11]], [[22/15]]
+|[[11/8]], [[16/11]]
+|[[18/13]], [[13/9]]
+|[[7/5]], [[10/7]]
+}}
+<pre>16/15 and 15/14 — '''225/224'''
+/15 and 14/13 — '''105/104'''
+/15 and 13/12 — '''65/64'''
+/15 and 12/11 — '''45/44'''
+/15 and 11/10 — '''33/32'''
+/15 and 10/9 — '''25/24'''
+/15 and 9/8 — '''135/128'''
+/14 and 14/13 — '''196/195'''
+/14 and 13/12 — '''91/90'''
+/14 and 12/11 — '''56/55'''
+/14 and 11/10 — '''77/75'''
+/14 and 10/9 — '''28/27'''
+/14 and 9/8 — '''21/20'''
+/13 and 13/12 — '''169/168'''
+-->