Penslen: Difference between revisions
From Xenharmonic Reference
Created page with "'''Penslen''' is an aberrismic ternary scale with structure 5L5m6s. It is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024. Tuning shown is just 2.3.5, Slendric 7, tempered 11/8 offset. 7 ≈ 2^((10-log2(3))/3) {| class="wikitable" |+Mode A3 (msLsmLsmLsmsLmsL) Just-2.3.5 Tuning | |0 |1 |- |3 |702.0 |51.6 |- |2 |468.0 |1017.6 |- |1 |234.0 |783.6 |- |0 |0.0 |549.6 |- | -1 |966.0 |315.6 |- | -2 |732.0 |81.7 |- | -3 |498.0 |1047..." |
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'''Penslen''' is an aberrismic ternary scale with structure 5L5m6s. It is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity. | |||
7 | Tuning shown is just 2.3.5, Slendric 7, Keenanismic 11. | ||
<math> | |||
{}^{T} 7 = 2^{\frac{10 - \log_2(3)}{3}} | |||
</math> | |||
<math> | |||
{}^{T} 11 = \frac{384}{35} | |||
</math> | |||
{| class="wikitable" | {| class="wikitable" | ||
Revision as of 22:08, 25 December 2025
This page or section is a work in progress. It may lack sufficient justification, content, or organization, and is subject to future overhaul.
Penslen is an aberrismic ternary scale with structure 5L5m6s. It is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity.
Tuning shown is just 2.3.5, Slendric 7, Keenanismic 11.
| 0 | 1 | |
| 3 | 702.0 | 51.6 |
| 2 | 468.0 | 1017.6 |
| 1 | 234.0 | 783.6 |
| 0 | 0.0 | 549.6 |
| -1 | 966.0 | 315.6 |
| -2 | 732.0 | 81.7 |
| -3 | 498.0 | 1047.7 |
| -4 | 264.1 | 813.7 |
| 36/35 | 48.8 |
| 21/20 | 84.5 |
| 8/7 | 231.2 |
| 7/6 | 266.9 |
| 6/5 | 315.6 |
| 21/16 | 470.8 |
| 4/3 | 498.0 |
| 48/35 | 546.8 |
| 3/2 | 702.0 |
| 32/21 | 729.2 |
| 63/40 | 786.4 |
| 8/5 | 813.7 |
| 7/4 | 968.8 |
| 9/5 | 1017.6 |
| 64/35 | 1044.9 |
| 2/1 | 1200.0 |
