41503/41472
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| Ratio | 41503/41472 |
| Factorization | 2-9 × 3-4 × 73 × 112 |
| Monzo | [-9 -4 0 3 2⟩ |
| Size in cents | 1.2936007¢ |
| Name | (Young's) tinge |
| Color name | 1ooz32, Lolotrizo comma |
| FJS name | [math]\text{d2}^{7,7,7,11,11}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 30.6808 |
| Weil height (log2 max(n, d)) | 30.6819 |
| Wilson height (sopfr (nd)) | 73 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.40523 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
In just intonation, 41503/41472 is the comma between three 8/7's (693.522 cents) and two 11/9's (694.816 cents), measuring 1.294 cents[1] and casually once referred to as "the tinge"[2]. So it is the difference of 1029/1024 and 243/242. Besides, it is also the difference of 385/384 and 540/539. Those two ratios make up 225/224. Therefore, tempering it out guarantees that 225/224 is split into two, each for 385/384~540/539.
It factors into two superparticular commas: 2401/2400 × 3025/3024.
See also
Notes
- ↑ Gayle Young, "The Pitch Organization of Harmonium for James Tenney", Perspectives of New Music, vol. 26, no. 2, summer 1988, pp. 204–12. Stable URL: http://www.jstor.org/stable/833190
- ↑ Gayle Young, private e-mail to Todd Harrop, 24 June 2018.