User:Plumtree/Sandbox/Interval
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Audio demonstrations use:
| Ratio | 3/2 |
| Factorization | 2-1 × 3 |
| Monzo | [-1 1⟩ |
| Size in cents | 701.955¢ |
| Name | just perfect fifth |
| Color name | w5, wa 5th |
| FJS name | [math]\text{P5}[/math] |
| Special properties | superparticular, reduced, reduced harmonic |
| Tenney height (log2 nd) | 2.58496 |
| Weil height (log2 max(n, d)) | 3.16993 |
| Wilson height (sopfr (nd)) | 5 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~3.42385 bits |
[sound info] | |
| open this interval in xen-calc | |
| Ratio | 110/81 |
| Factorization | 2 × 3-4 × 5 × 11 |
| Monzo | [1 -4 1 0 1⟩ |
| Size in cents | 529.81165¢ |
| Name | undecimal grave paramajor fourth |
| FJS name | [math]\text{P4}^{5,11}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 13.1212 |
| Weil height (log2 max(n, d)) | 13.5627 |
| Wilson height (sopfr (nd)) | 30 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.27727 bits |
Audio demonstration | |
| open this interval in xen-calc | |
| Ratio | 211/103 |
| Subgroup monzo | 103.211 [-1 1⟩ |
| Size in cents | 1241.5184¢ |
| Name(s) | missing ? |
| FJS name | [math]\text{A8}^{211}_{103}[/math] |
| Tenney height (log2 nd) | 14.4076 |
| Weil height (log2 max(n, d)) | 15.4422 |
| Wilson height (sopfr (nd)) | 314 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.40293 bits |
Audio demonstration | |
| open this interval in xen-calc | |
| Ratio | 2/1 |
| Factorization | 2 |
| Monzo | [1⟩ |
| Size in cents | 1200¢ |
| Name(s) | missing ? |
| FJS name | [math]\text{P8}[/math] |
| Special properties | superparticular, harmonic |
| Tenney height (log2 nd) | 1 |
| Weil height (log2 max(n, d)) | 2 |
| Wilson height (sopfr (nd)) | 2 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~2.24202 bits |
Audio demonstration | |
| open this interval in xen-calc | |
| Ratio | 33/32 |
| Factorization | 2-5 × 3 × 11 |
| Monzo | [-5 1 0 0 1⟩ |
| Size in cents | 53.272943¢ |
| Names | al-Farabi quarter tone, undecimal quarter tone, undecimal comma, Alpharabian parachroma, Alpharabian ultraprime |
| Color name | 1o1, ilo unison |
| FJS name | [math]\text{P1}^{11}[/math] |
| Special properties | superparticular, reduced, reduced harmonic |
| Tenney height (log2 nd) | 10.0444 |
| Weil height (log2 max(n, d)) | 10.0888 |
| Wilson height (sopfr (nd)) | 24 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.44702 bits |
| Comma size | medium |
| S-expression | S9 × S10 × S11 |
Audio demonstration | |
| open this interval in xen-calc | |
| Ratio | 1/1 |
| Factorization | n/a |
| Monzo | [0⟩ |
| Size in cents | 0¢ |
| Names | (perfect) unison, (perfect) prime, 1st harmonic, 1st subharmonic, fundamental |
| FJS name | [math]\text{P1}[/math] |
| Special properties | reduced, harmonic |
| Tenney height (log2 nd) | 0 |
| Weil height (log2 max(n, d)) | 0 |
| Wilson height (sopfr (nd)) | 0 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.19982 bits |
Audio demonstration | |
| open this interval in xen-calc | |
| Ratio | 0/1 |
| Factorization | n/a |
| Name(s) | missing ? |
| Ratio | 1/0 |
| Factorization | n/a |
| Name(s) | missing ? |
| Ratio | 0/0 |
| Factorization | n/a |
| Name(s) | missing ? |
| Ratio | -1/2 |
| Factorization | -2-1 |
| Name(s) | missing ? |
| Expression | [math]\pi/3[/math] |
| Size in cents | 79.840355¢ |
| Names | engineer's comma, pi over 3 |
| Special properties | reduced |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.32957 bits |
| Comma size | medium |
Audio demonstration | |
| Expression | [math]\sqrt{25/24}[/math] |
| Monzo | [-3/2 -1/2 1⟩ |
| Size in cents | 35.336213¢ |
| Name | square root of 25/24 |
| Special properties | reduced |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.51942 bits |
Audio demonstration | |
| open this interval in xen-calc | |
| Factorization | 2-263 × 388 × 744 |
| Monzo | [-263 88 0 44⟩ |
| Size in cents | 0.3799608¢ |
| Names | septimal ruthenia, septiruthenia |
| FJS name | [math]\text{P8}^{7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7}[/math] |
| Special properties | reduced, reduced harmonic |
| Tenney height (log2 nd) | 526 |
| Weil height (log2 max(n, d)) | 526.001 |
| Wilson height (sopfr (nd)) | 1098 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.20044 bits |
| Comma size | unnoticeable |
Audio demonstration | |
| open this interval in xen-calc | |