Talk:Euler–Fokker genus

Confusing: Multiset, normalized
This article says the following:
 * 3070 = 1
 * 3071 = 7
 * 3170 = 3
 * 3171 = 21
 * 3270 = 9
 * 3271 = 63
 * Normalized to fall within an octave, this is 1/1, 9/8, 21/16, 3/2, 7/4, 63/32.
 * Normalized to fall within an octave, this is 1/1, 9/8, 21/16, 3/2, 7/4, 63/32.
 * Normalized to fall within an octave, this is 1/1, 9/8, 21/16, 3/2, 7/4, 63/32.

I'm trying to see how that makes sense. Are the values of these fractions supposed to be ratios of frequencies? Or are they pitches, which are the logarithms of frequencies? How does this "fall within an octave"? The ratio of frequencies of the C above middle-C to middle-C is 2-to-1. But 63/32 is more than 2[later note: I meant of course more than 1, since I was thinking of musical intervals instead of ratios of frequencies; sorry to confuse matters.]. So is 9/8. So is 21/16. So is 74. So is 3/2.

This is not clearly written. I have no doubt that a shorter simpler explanation could be clear. This explanation is opaque. Michael Hardy (talk) 19:08, 10 October 2010 (UTC)


 * They are frequency ratios, not logarithms at all. It's a fairly standard way of expressing musical intervals in just intonation. Also, 63/32 = 1.96875 < 2. The other fractions are also in the half-open interval [1,2). (Assuming octave equivalence, any musical interval can be expressed as a number in [1,2) by multiplying by an appropriate power of 2, so just intonation theorists use that as a kind of normalization.)
 * I agree that the article could have clearer explanation, especially including appropriate links to other articles that explain the basic stuff. —Keenan Pepper 22:00, 10 October 2010 (UTC)
 * Oh.... my arithmetic is messed up because I was thinking those numbers are more than 1, as in 1 octave above wherever you start. That would make sense if these were intervals rather than ratios of frequencies.  Indeed they are less than 2. Michael Hardy (talk) 15:43, 11 October 2010 (UTC)

Tag removed. Hyacinth (talk) 08:06, 23 April 2011 (UTC)

There is a very big error in the diagram at the upper right as it has two 3/2 coming off the C instead of a E ,normally in the vertical dimension  — Preceding unsigned comment added by Banaphshu (talk • contribs) 22:53, 27 August 2023 (UTC)

The statement that it was fokker who added the 7 is mistaken if one looks at Euler's original paper. it is unclear just waht fokker added. while one can have repeated factors in eulers lattices these run in the same direction and not new ones. there is no history of this type of use of lattices and actually undeminds their use — Preceding unsigned comment added by Banaphshu (talk • contribs) 23:55, 27 August 2023 (UTC)