User talk:Cam Taylor

Why do people keep calling 70 cents a minor second when it's clearly an augmented unison? Here are close–ups of 19edo, 31edo and 43edo:

C   C#  Db  D
0   63  126 189

C   .   C#  Db  .   D
0   39  77  116 155 194

C   .   .   C#  Db  .   .   D
0   28  56  84  112 140 167 195

It's clearly seen, that the 70—80 cent interval is C to C#, or an augmented unison. PiotrGrochowski (talk) 05:15, 29 September 2018 (UTC)

Unsure how to respond with a private message here, but you can get me easier on Facebook if you have it. C-C#, or an augmented unison is only the small semitone where perfect fifths are less than 700c. In every tuning where the perfect fifth is more than 700c (as here), the interval from C-C# will be greater than the interval from C#-D (minor second). This includes 17, 22, 27, 29, 34, 37, 41, 44, 46edos, which are not meantone tunings, like those you referred to, where the augmented unison is indeed the smaller semitone and the minor second the larger part. That is the case for all tunings within (4\7, 7\12), "negative tunings", as opposed to the "positive tunings" with fifths between (7\12, 3\5). Hope this helps to clarify. -Cam

But I've seen "minor second" named so in situations where a pythagorean or superpyth fifth size is not applicable, like naming 80 cents that damn "minor second" name in 15edo-interval names, where the fifth is 5edo. Also, meantone is the intuitive 5–limit tuning; 5/4 will usually be considered to be a major third, not a diminished fourth as in schismic or an augmented second as in superpyth. This meantone logic continues to other 5–limit intervals; 25/24 (which is about 70 cents) is an augmented unison (consistent with 6/5 being a minor third and 5/4 being a major third), and 16/15 (117 cents) is a minor second. Trying to base note names on pythagorean or superpyth leads to failures and inconsistences as soon as you try to name intervals with 5. Quarter comma meantone is the best trusted tuning when it comes to note naming for that reason. You cannot name 6/5 a minor third and 5/4 a major third, then throw in the inconsistency that the inbetween 25/24 is some sort of minor second because of superpyth. PiotrGrochowski (talk) 06:41, 29 September 2018 (UTC)

70 cents as "minor second"

I agree with everything said so far about minor seconds or diatonic semitones and chromatic semitones or augmented primes in the context of regular tunings, negative, neutral (5th=700 cents), or positive.

With 15-ed2, a nondiatonic tuning, I might guess that 80 cents tends to be deemed the minor second because 160 cents, around 23:21 and between 11:10 and 12:11, seems too large, a large middle or Zalzalian second maybe closer to a major second than a minor second.

In a rank-3 tuning like MET-24, there are regular diatonic semitones at 81.445 cents and chromatic semitones at 125.977 cents. Additionally there are intervals involving notes from both 12-note chains of fifths, so without a simple diatonic or chromatic reference.

For example, a small thirdtone or spacing at 57.422 cents, the distance between the two chains of fifths, can serve musically as a minor second in a realization of a permutation of the Archytas

1/1--9/8-7/6-4/3---3/2--22/13-7/4-2/1 D----E--E^----G----A----B--B^----D 0-207-265-496-704-911-969-1200

Here we have a minor second step at a tempered 28:27, 57.4 cents, with whole-tone steps at 9:8 or a tempered 207.4 cents and 8:7 or a tempered 231.4 cents. Intuitively I would regard the small thirdtone or spacing to be playing the role of minor second or "diatonic semitone," although it is not derived from -5 fifths. Mschulter1325 02:46, 22 December 2023 (UTC)