{"id":1924,"date":"2018-08-22T22:46:00","date_gmt":"2018-08-22T10:46:00","guid":{"rendered":"http:\/\/www.funk.co.nz\/blog\/?p=1924"},"modified":"2018-09-19T02:22:33","modified_gmt":"2018-09-18T14:22:33","slug":"mathematical-solution-432-vs-440","status":"publish","type":"post","link":"https:\/\/www.funk.co.nz\/blog\/music\/mathematical-solution-432-vs-440","title":{"rendered":"A potential mathematical solution to the question: 432 hz or 440 hz?"},"content":{"rendered":"

There exist 14 numbers below fifty that you can multiply up to reach 432 without the use of fractions. The number 440 has not a single whole integer factor<\/strong> below 50, and the only factor that isn't some recurring irrational number is 27 x 27.5 = 440<\/strong><\/span>. Compare this with 432 which has a whopping 14 factors in the full list at bottom of this article but they are: 1, 2, 3, 4, 5, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48. They even share the number 27 as a common factor.<\/p>\n

\"432

Whats better? 432 or 440 hz for the tuning of concert pitch middle A.<\/p><\/div>\n

It always partly annoyed me to hear that certain frequencies possibly had special significance in the universe.. more so than say other frequencies.<\/p>\n

Because frequencies are measured in hertz - cycles per second - and a second aint no thang - it's just an\u00c2\u00a086400th fraction of a solar day, which by the way is 4 minutes longer<\/strong> than Earth's actual rotation time, which I guess must be about 23 hours 56 minutes:<\/p>\n

the time taken by the earth to rotate on its axis relative to the stars, is almost four minutes shorter than the solar day because of the earth's orbital motion.<\/em><\/p><\/blockquote>\n

To put another way, it is not special nature of the universe type thing. It's artbitrary. And it is getting longer each day so I don't see why it would have any special significance. Time is something we project on the universe not the other way round. If anything I'd pick the Schumann resonance of 7.83 Hertz but that's hardly an even number nor needs to be.<\/p>\n

\n
\n
The\u00c2\u00a0Schumann resonances\u00c2\u00a0 are a set of spectrum peaks in the extremely low\u00c2\u00a0frequency\u00c2\u00a0(ELF) portion of the Earth's electromagnetic field spectrum.\u00c2\u00a0Schumann resonances\u00c2\u00a0are global electromagnetic\u00c2\u00a0resonances, generated and excited by lightning discharges in the cavity formed by the Earth's surface and the ionosphere.<\/span><\/em><\/div>\n<\/blockquote>\n<\/div>\n

The length of the second is changing: Earth doesn\u00e2\u20ac\u2122t rotate uniformly. In fact, it\u00e2\u20ac\u2122s rotation decreases being late by 20 millionths of a second every calendar year due to tidal friction caused by the Moon. Currently it is increasing the length of the day by about 2.3 milliseconds per century. A million years from now the day will be about an hour longer.<\/span><\/p>\n

 <\/p>\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Factor<\/strong><\/span><\/td>\n432<\/strong><\/span><\/td>\n440<\/strong><\/span><\/td>\n<\/tr>\n
1<\/span><\/td>\n432<\/strong><\/td>\n1.018518519<\/td>\n<\/tr>\n
2<\/span><\/td>\n216<\/strong><\/td>\n2.037037037<\/td>\n<\/tr>\n
3<\/span><\/td>\n144<\/strong><\/td>\n3.055555556<\/td>\n<\/tr>\n
4<\/span><\/td>\n108<\/strong><\/td>\n4.074074074<\/td>\n<\/tr>\n
5<\/span><\/td>\n86.4<\/strong><\/td>\n5.092592593<\/td>\n<\/tr>\n
6<\/span><\/td>\n72<\/strong><\/td>\n6.111111111<\/td>\n<\/tr>\n
7<\/span><\/td>\n61.71428571<\/td>\n7.12962963<\/td>\n<\/tr>\n
8<\/span><\/td>\n54<\/strong><\/td>\n8.148148148<\/td>\n<\/tr>\n
9<\/span><\/td>\n48<\/strong><\/td>\n9.166666667<\/td>\n<\/tr>\n
10<\/span><\/td>\n43.2<\/td>\n10.18518519<\/td>\n<\/tr>\n
11<\/span><\/td>\n39.27272727<\/td>\n11.2037037<\/td>\n<\/tr>\n
12<\/span><\/td>\n36<\/strong><\/td>\n12.22222222<\/td>\n<\/tr>\n
13<\/span><\/td>\n33.23076923<\/td>\n13.24074074<\/td>\n<\/tr>\n
14<\/span><\/td>\n30.85714286<\/td>\n14.25925926<\/td>\n<\/tr>\n
15<\/span><\/td>\n28.8<\/td>\n15.27777778<\/td>\n<\/tr>\n
16<\/span><\/td>\n27<\/strong><\/td>\n16.2962963<\/td>\n<\/tr>\n
17<\/span><\/td>\n25.41176471<\/td>\n17.31481481<\/td>\n<\/tr>\n
18<\/span><\/td>\n24<\/strong><\/td>\n18.33333333<\/td>\n<\/tr>\n
19<\/span><\/td>\n22.73684211<\/td>\n19.35185185<\/td>\n<\/tr>\n
20<\/span><\/td>\n21.6<\/td>\n20.37037037<\/td>\n<\/tr>\n
21<\/span><\/td>\n20.57142857<\/td>\n21.38888889<\/td>\n<\/tr>\n
22<\/span><\/td>\n19.63636364<\/td>\n22.40740741<\/td>\n<\/tr>\n
23<\/span><\/td>\n18.7826087<\/td>\n23.42592593<\/td>\n<\/tr>\n
24<\/span><\/td>\n18<\/strong><\/td>\n24.44444444<\/td>\n<\/tr>\n
25<\/span><\/td>\n17.28<\/td>\n25.46296296<\/td>\n<\/tr>\n
26<\/span><\/td>\n16.61538462<\/td>\n26.48148148<\/td>\n<\/tr>\n
27<\/span><\/td>\n16<\/strong><\/td>\n27.5<\/td>\n<\/tr>\n
28<\/span><\/td>\n15.42857143<\/td>\n28.51851852<\/td>\n<\/tr>\n
29<\/span><\/td>\n14.89655172<\/td>\n29.53703704<\/td>\n<\/tr>\n
30<\/span><\/td>\n14.4<\/td>\n30.55555556<\/td>\n<\/tr>\n
31<\/span><\/td>\n13.93548387<\/td>\n31.57407407<\/td>\n<\/tr>\n
32<\/span><\/td>\n13.5<\/td>\n32.59259259<\/td>\n<\/tr>\n
33<\/span><\/td>\n13.09090909<\/td>\n33.61111111<\/td>\n<\/tr>\n
34<\/span><\/td>\n12.70588235<\/td>\n34.62962963<\/td>\n<\/tr>\n
35<\/span><\/td>\n12.34285714<\/td>\n35.64814815<\/td>\n<\/tr>\n
36<\/span><\/td>\n12<\/strong><\/td>\n36.66666667<\/td>\n<\/tr>\n
37<\/span><\/td>\n11.67567568<\/td>\n37.68518519<\/td>\n<\/tr>\n
38<\/span><\/td>\n11.36842105<\/td>\n38.7037037<\/td>\n<\/tr>\n
39<\/span><\/td>\n11.07692308<\/td>\n39.72222222<\/td>\n<\/tr>\n
40<\/span><\/td>\n10.8<\/td>\n40.74074074<\/td>\n<\/tr>\n
41<\/span><\/td>\n10.53658537<\/td>\n41.75925926<\/td>\n<\/tr>\n
42<\/span><\/td>\n10.28571429<\/td>\n42.77777778<\/td>\n<\/tr>\n
43<\/span><\/td>\n10.04651163<\/td>\n43.7962963<\/td>\n<\/tr>\n
44<\/span><\/td>\n9.818181818<\/td>\n44.81481481<\/td>\n<\/tr>\n
45<\/span><\/td>\n9.6<\/td>\n45.83333333<\/td>\n<\/tr>\n
46<\/span><\/td>\n9.391304348<\/td>\n46.85185185<\/td>\n<\/tr>\n
47<\/span><\/td>\n9.191489362<\/td>\n47.87037037<\/td>\n<\/tr>\n
48<\/span><\/td>\n9<\/strong><\/td>\n48.88888889<\/td>\n<\/tr>\n
49<\/span><\/td>\n8.816326531<\/td>\n49.90740741<\/td>\n<\/tr>\n
50<\/span><\/td>\n8.64<\/td>\n50.92592593<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

I believe the great Pythagoras was well aware of such matters, hence his choice of 432.<\/p>\n","protected":false},"excerpt":{"rendered":"

There exist 14 numbers below fifty that you can multiply up to reach 432 without the use of fractions. The number 440 has not a single whole integer factor below 50, and the only factor that isn’t some recurring irrational number is 27 x 27.5 = 440. Compare this with 432 which has a whopping […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10,36],"tags":[],"class_list":["post-1924","post","type-post","status-publish","format-standard","hentry","category-music","category-science"],"_links":{"self":[{"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/posts\/1924","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/comments?post=1924"}],"version-history":[{"count":0,"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/posts\/1924\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/media?parent=1924"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/categories?post=1924"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/tags?post=1924"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}