Tp tuning: Difference between revisions

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For an example, consider [[Chromatic_pairs#Indium|indium temperament]], with group 2.5/3.7/3.11/3 and comma basis 3025/3024 and 3125/3087. The corresponding full 11-limit temperament is of rank three, and using the [[Tenney-Euclidean_Tuning|usual methods]], in particular the pseudoinverse, we find that the T2 (TE) tuning map is <1199.552 1901.846 2783.579 3371.401 4153.996|. Applying that to 12/11 gives a generator of 146.995, and multiplying that by 1200.0/1199.552 gives a POT2 tuning, or extended POTE tuning, of 147.010. Converting the tuning map to weighted coordinates and subtracting <1200 1200 1200 1200 1200| gives <-0.4475 -.0685 -1.1778 0.9172 0.7741|. The ordinary Euclidean norm of this, ie the square root of the dot product, is 1.7414, and dividing by sqrt(5) gives the RMS error, 0.77879 cents.

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	For an example, consider [[Chromatic_pairs#Indium\|indium temperament]], with group 2.5/3.7/3.11/3 and comma basis 3025/3024 and 3125/3087. The corresponding full 11-limit temperament is of rank three, and using the [[Tenney-Euclidean_Tuning\|usual methods]], in particular the pseudoinverse, we find that the T2 (TE) tuning map is <1199.552 1901.846 2783.579 3371.401 4153.996\|. Applying that to 12/11 gives a generator of 146.995, and multiplying that by 1200.0/1199.552 gives a POT2 tuning, or extended POTE tuning, of 147.010. Converting the tuning map to weighted coordinates and subtracting <1200 1200 1200 1200 1200\| gives <-0.4475 -.0685 -1.1778 0.9172 0.7741\|. The ordinary Euclidean norm of this, ie the square root of the dot product, is 1.7414, and dividing by sqrt(5) gives the RMS error, 0.77879 cents.		For an example, consider [[Chromatic_pairs#Indium\|indium temperament]], with group 2.5/3.7/3.11/3 and comma basis 3025/3024 and 3125/3087. The corresponding full 11-limit temperament is of rank three, and using the [[Tenney-Euclidean_Tuning\|usual methods]], in particular the pseudoinverse, we find that the T2 (TE) tuning map is <1199.552 1901.846 2783.579 3371.401 4153.996\|. Applying that to 12/11 gives a generator of 146.995, and multiplying that by 1200.0/1199.552 gives a POT2 tuning, or extended POTE tuning, of 147.010. Converting the tuning map to weighted coordinates and subtracting <1200 1200 1200 1200 1200\| gives <-0.4475 -.0685 -1.1778 0.9172 0.7741\|. The ordinary Euclidean norm of this, ie the square root of the dot product, is 1.7414, and dividing by sqrt(5) gives the RMS error, 0.77879 cents.

			{{todo\|review\|categorize\|improve readability}}