Douglas Blumeyer's RTT How-To: Difference between revisions

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A generator is an interval which generates a temperament. Again, if you’re already familiar with MOS scales, this is the same concept. If not, all this means is that if you repeatedly move by this interval, you will visit the pitches you can include in your tuning.

We briefly looked at generators earlier. We saw how the generator for 12-ET was about 1.059, because repeated movement is like repeated multiplication (1.059 × 1.059 × 1.059 ...) and 1.059¹² ≈ 2, 1.059¹⁹ ≈ 3, and 1.059²⁸ ≈ 5. This meantone generator is the same basic idea, but there’s a couple important differences we need to cover.

We briefly looked at generators earlier. We saw how the generator for 12-ET was about 1.059, because repeated movement is like repeated multiplication (1.059 × 1.059 × 1.059 ...) and 1.059¹² ≈ 2, 1.059¹⁹ ≈ 3, and 1.059²⁸ ≈ 5. This meantone generator is the same basic idea, but there’s a couple of important differences we need to cover.

First of all, and this difference is superficial, it’s in a different format. We were expressing 12-ET’s generator 1.059 as a frequency multiplier; it’s like 2, 3, or 5, and this could be measured in Hz, say, by multiplying by 440 if A4 was our 1/1 (1.059 away from A is 466Hz, which is #A). But the meantone generators we’re looking at now in forms like <math>\frac 25</math>, <math>\frac 37</math>, or <math>\frac{5}{12}</math>, are expressed as fractional octaves, i.e. they’re in terms of pitch, something that could be measured in cents if we multiplied by 1200 (2/5 × 1200¢ = 480¢). We have a special way of writing fractional octaves, and that’s with a backslash instead of a slash, like this: 2\5, 3\7, 5\12.

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 A generator is an interval which generates a temperament. Again, if you’re already familiar with MOS scales, this is the same concept. If not, all this means is that if you repeatedly move by this interval, you will visit the pitches you can include in your tuning.
-We briefly looked at generators earlier. We saw how the generator for 12-ET was about 1.059, because repeated movement is like repeated multiplication (1.059 × 1.059 × 1.059 ...) and 1.059¹² ≈ 2, 1.059¹⁹ ≈ 3, and 1.059²⁸ ≈ 5. This meantone generator is the same basic idea, but there’s a couple important differences we need to cover.
+We briefly looked at generators earlier. We saw how the generator for 12-ET was about 1.059, because repeated movement is like repeated multiplication (1.059 × 1.059 × 1.059 ...) and 1.059¹² ≈ 2, 1.059¹⁹ ≈ 3, and 1.059²⁸ ≈ 5. This meantone generator is the same basic idea, but there’s a couple of important differences we need to cover.
 First of all, and this difference is superficial, it’s in a different format. We were expressing 12-ET’s generator 1.059 as a frequency multiplier; it’s like 2, 3, or 5, and this could be measured in Hz, say, by multiplying by 440 if A4 was our 1/1 (1.059 away from A is 466Hz, which is #A). But the meantone generators we’re looking at now in forms like <span><math>\frac 25</math></span>, <span><math>\frac 37</math></span>, or <span><math>\frac{5}{12}</math></span>, are expressed as fractional octaves, i.e. they’re in terms of pitch, something that could be measured in cents if we multiplied by 1200 (2/5 × 1200¢ = 480¢). We have a special way of writing fractional octaves, and that’s with a backslash instead of a slash, like this: 2\5, 3\7, 5\12.