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Jan. 17th, 2005 08:52 am*looks at tax return pages* eeep.
I managed this fine last year, why am I finding it so intimidating this year?
Anyway, not doing it until tomorrow, because today we have![[livejournal.com profile]](https://www.dreamwidth.org/img/external/lj-userinfo.gif)
deralte and sylk visiting.
It still feels *really* sodding weird to be wearing a ring.
And further to last post, a brief explanation of the Pythagorean comma:
As I recall, the equal-temperament scale is designed so that each semitone rise corresponds to an increase in frequency by a factor of 2 ^ (1/12) . This means that if you go up a fifth, in equal temperament, the increase in frequency will always be by a factor of 1.4983 [ =2^(7/12) ] instead of by a factor of 1.5 as it would be for a perfect fifth. Other intervals suffer from the same problem. Octaves are perfectly in tune, of course. The frequency discrepancy between using powers of the twelfth root of 2 and exact harmonic ratios is known as the Pythagorean comma. I have no idea what Pythagoras had to do with it, though.
To return briefly to the minor third problem: a minor third in equal temperament will have the ratio 1.1892:1. A minor third as the first two notes of a minor chord will have the ratio 19:16 = 1.1875:1. A minor third as the top two notes of a major chord will have the ratio 6:5 = 1.2:1.
(the discrepancy between the minor thirds in minor and major chords is 0.0125, which is about 1 part in 96, or about 1/32 of a semitone. The equal-temperament version is off by 0.0108 from the major chord, about 1/40 of a semitone flatter, and the minor chord is another 0.0017 flat, or about 1/160 of a semitone. So equal temperament means that minor thirds in minor chords are fairly accurate, whereas minor thirds at the tops of major chords are )
Similarly, a major third has the ratio 5:4 = 1.25:1 (major chord), 1.2599:1 (equal temperament) or 24:19 = 1.2632:1 (minor chord).
(discrepancy between major chord and equal temperament = 1 part in 125, or about 1/30 of a semitone; discrepancy between equal and minor = 1 part in 375)
It's interesting to note that in both cases, equal temperament tuning falls midway between the tuning in a harmonic-sequence major and minor chord.
I managed this fine last year, why am I finding it so intimidating this year?
Anyway, not doing it until tomorrow, because today we have
deralte and sylk visiting.It still feels *really* sodding weird to be wearing a ring.
And further to last post, a brief explanation of the Pythagorean comma:
As I recall, the equal-temperament scale is designed so that each semitone rise corresponds to an increase in frequency by a factor of 2 ^ (1/12) . This means that if you go up a fifth, in equal temperament, the increase in frequency will always be by a factor of 1.4983 [ =2^(7/12) ] instead of by a factor of 1.5 as it would be for a perfect fifth. Other intervals suffer from the same problem. Octaves are perfectly in tune, of course. The frequency discrepancy between using powers of the twelfth root of 2 and exact harmonic ratios is known as the Pythagorean comma. I have no idea what Pythagoras had to do with it, though.
To return briefly to the minor third problem: a minor third in equal temperament will have the ratio 1.1892:1. A minor third as the first two notes of a minor chord will have the ratio 19:16 = 1.1875:1. A minor third as the top two notes of a major chord will have the ratio 6:5 = 1.2:1.
(the discrepancy between the minor thirds in minor and major chords is 0.0125, which is about 1 part in 96, or about 1/32 of a semitone. The equal-temperament version is off by 0.0108 from the major chord, about 1/40 of a semitone flatter, and the minor chord is another 0.0017 flat, or about 1/160 of a semitone. So equal temperament means that minor thirds in minor chords are fairly accurate, whereas minor thirds at the tops of major chords are )
Similarly, a major third has the ratio 5:4 = 1.25:1 (major chord), 1.2599:1 (equal temperament) or 24:19 = 1.2632:1 (minor chord).
(discrepancy between major chord and equal temperament = 1 part in 125, or about 1/30 of a semitone; discrepancy between equal and minor = 1 part in 375)
It's interesting to note that in both cases, equal temperament tuning falls midway between the tuning in a harmonic-sequence major and minor chord.
