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"Sagittal" temperaments

🔗Gene Ward Smith <genewardsmith@juno.com> <genewardsmith@juno.com>

2/5/2003 10:43:51 AM

Here is a list of 11-limit temperaments which arise from triplets of commas, each of which is either one of the 11-limit sagittal notation commas, or a quotient of such commas. They all, therefore, should simplfy the sagittal notation in their case.

Septimal
[0, 0, 7, 0, 0, 11, 0, 16, 0, -24]
rms 22.636347 comp 26.058106 bad 5184.550161

[1, -3, -2, -1, -7, -6, -5, 4, 8, 4]
rms 54.982509 comp 15.875495 bad 5513.617843

Porcupine
[3, 5, -6, 4, 1, -18, -4, -28, -8, 32]
rms 11.793935 comp 41.067070 bad 5765.207400

[2, 1, 3, 5, -3, -1, 1, 4, 8, 4]
rms 55.689539 comp 16.340735 bad 5859.936955

[2, 1, 3, -2, -3, -1, -10, 4, -8, -16]
rms 52.234534 comp 17.254513 bad 6018.139493

Arnold
[1, 4, -2, -1, 4, -6, -5, -16, -16, 4]
rms 39.863722 comp 21.483576 bad 6618.437353

[2, 1, -4, 5, -3, -12, 1, -12, 8, 28]
rms 27.107413 comp 27.157168 bad 6651.131418

[1, 4, -2, 6, 4, -6, 6, -16, 0, 24]
rms 28.872265 comp 26.432118 bad 6771.748430

[2, 1, -4, -2, -3, -12, -10, -12, -8, 8]
rms 42.344437 comp 21.310039 bad 6935.909992

Semififth
[2, 8, -11, 5, 8, -23, 1, -48, -16, 52]
rms 6.681355 comp 64.720989 bad 6970.647533

[3, 5, 1, 4, 1, -7, -4, -12, -8, 8]
rms 37.194175 comp 23.910689 bad 7381.224379

Hexidecimal
[1, -3, 5, -1, -7, 5, -5, 20, 8, -20]
rms 30.938504 comp 27.201522 bad 7611.810986

[6, 17, -26, 15, 13, -58, 3, -108, -24, 132]
rms 1.860428 comp 152.101752 bad 8063.122648

Flattone
[1, 4, -9, 6, 4, -17, 6, -32, 0, 48]
rms 13.051258 comp 48.332860 bad 8369.956700

[1, 4, 5, 6, 4, 5, 6, 0, 0, 0]
rms 55.787056 comp 20.476771 bad 8550.061093

[4, 9, -15, 10, 5, -35, 2, -60, -8, 80]
rms 5.007160 comp 88.019435 bad 8720.788247

[2, 8, -4, 5, 8, -12, 1, -32, -16, 28]
rms 17.726670 comp 43.670435 bad 9600.039564

Amity
[5, 13, -17, 9, 9, -41, -3, -76, -24, 84]
rms 4.265603 comp 104.931875 bad 9957.709517