Comparison of temperaments
Comparison of temperaments
1:2 is "different octave, same note name"
By doing 3:2 up and down three times from some appropriate note D, a scale consisting of seven notes can be formed.
This is within about 6% of a semitone deviation from the white keys of the modern average scale.
https://gyazo.com/e77e2c0792fae93b1231feae47372f95
More repetition of this will produce "a little higher" and "a little lower" notes than the whole tone scale
It turned out sharp and flat.
At this point, the sharp on the Do and the flat on the Re sounded different.
https://gyazo.com/7d0f483d34c2d19a09201958c90205fa
G# - Ab = log(3, 2) * 12 % 1 = 0.01955000865387646
If this is zero, we can consider them to be the same note in different octaves, but in reality, there is a discrepancy.
_ * 12 = 0.23460010384651753
I can tell this discrepancy is about a quarter semitone.
pure tone 1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2 If C is used as a reference, then E is 3 degrees above C, G is 5 degrees above C, B is 3 degrees above G, D is 5 degrees above G, F is 5 degrees below C, and A is 3 degrees above F. The whole C major scale is obtained by arranging these within one octave. Pure law - Wikipedia https://gyazo.com/5820277b801d1dfd83bf42fbbc5d72c9
Multiplying by 5/4 from the stem note yields a sharp semitone, and multiplying by 4/5 yields a flat semitone.
https://gyazo.com/b0c842b797808a84e4b078de35495d13
Am I correct in understanding that the sharp of la and the flat of so do not exist?nishio.icon
I guess this is why I still don't write that way very often.
Write Bb instead of A#, F# instead of Gb
Sharp on a Do and flat on a Re are of course different sounds.
The twelve-means rule is a temperament in which one octave is divided into twelve equal parts. The frequency ratio of adjacent notes (semitones) is equal $ (\sqrt[12]{2})^n : 1 . Mean law - Wikipedia Considering that "an octave is 12 semitones," we averaged the frequency ratios of the semitones to arrive at the same ratio.
The sharp on the Do and the flat on the Re sounded the same.
Q: "Q: Why are there two different notations for the same sound? A: It used to be different."
In fretted instruments and monochords, the mean rule can be realized by geometrically setting the division points of the strings. In fretted instruments, the fret intervals for each string are not aligned with respect to each other, which is inconvenient for the use of straight frets in temperaments where the pitch of semitones other than the mean rule is not constant. I seenishio.icon
table::
Average Rhythm Pure Rhythm Pita
D 0 0 1/1 0 1/1
Eb 100 90 256/243
E 200 204 9/8 204 9/8
F 300 294 32/27
F# 400 386 5/4 408 81/64
G 500 498 4/3 498 4/3
G# 600 612 729/512
A 700 702 3/2 702 3/2
Bb 800 792 128/81
B 900 884 5/3 906 27/16
C 1000 996 16/9
C# 1100 1088 15/8 1110 243/128
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