Xenharmonikon 18 — Lydia Ayers
Making Scales from Mathematical Means
40 scales
| File | Description | Notes | Period (¢) | Limit |
|---|---|---|---|---|
| xen18-ayers-table-04 | 7 Iterated Arithmetic Means between 1/1 and 2/1 | 8 | 1200.0 | 13 |
| xen18-ayers-table-05 | 6 Generalized Arithmetic Means between 1/1 and 2/1 | 7 | 1200.0 | 13 |
| xen18-ayers-table-11 | 7 Iterated Harmonic Means between 1/1 and 2/1 | 8 | 1200.0 | 13 |
| xen18-ayers-table-12 | 5 Generalized Harmonic Means between 1/1 and 2/1 | 6 | 1200.0 | 11 |
| xen18-ayers-table-13-14 | Generalized Harmonic Mean scale from Table 13 and Table 14 | 12 | 1200.0 | 19 |
| xen18-ayers-table-16 | 2nd Iteration of Musical Proportion between 1/1 and 2/1 | 7 | 1200.0 | 7 |
| xen18-ayers-table-18 | 7 Iterated Subcontraries to the Harmonic Mean | 8 | 1200.0 | 3373 |
| xen18-ayers-table-19 | 3 Iterated Harmonic Means and 3 Iterated Subcontraries to the Harmonic Mean | 7 | 1200.0 | 61 |
| xen18-ayers-table-20 | 7 Iterated Geometric Means Between 1/1 and 2/1 (8-tone Equal Temperament) | 8 | 1200.0 | |
| xen18-ayers-table-23 | Inverted Geometric Means Between 1/1 and 2/1 Produce a Symmetrical Scale | 9 | 1200.0 | 3 |
| xen18-ayers-table-24 | Generalized Geometric Means in Slendro Between 1/1 and 2/1 | 5 | 1200.0 | |
| xen18-ayers-table-26 | 7 Iterated First Subcontraries to Geometric Means between 1/1 and 2/1 | 8 | 1200.0 | |
| xen18-ayers-table-28 | 7 Iterated Second Subcontraries to Geometric Means between 1/1 and 2/1 | 8 | 1200.0 | |
| xen18-ayers-table-30 | 7 Iterated Logarithmic Means between 1/1 and 2/1 | 8 | 1200.0 | |
| xen18-ayers-table-32 | 7 Iterated Counter-Logarithmic Means between 1/1 and 2/1 | 8 | 1200.0 | |
| xen18-ayers-table-33 | Logarithmic Means scale from Table 33 | 7 | 1200.0 | |
| xen18-ayers-table-34 | 7 Iterated Root Mean Squares between 1/1 and 2/1 | 8 | 1200.0 | |
| xen18-ayers-table-35 | 7 Generalized Root Mean Squares between 1 and 2.5 | 8 | 1586.3 | |
| xen18-ayers-table-37 | 7 Iterated Harmonic Square Means between 1/1 and 2/1 | 8 | 1200.0 | 14321 |
| xen18-ayers-table-38 | Harmonic Square Means in Tetrachords between 1/1 and 4/3 and 3/2 and 2/1 | 7 | 1200.0 | 1201 |
| xen18-ayers-table-39 | 7 Iterated Root Harmonic Square Means between 1/1 and 2/1 | 8 | 1200.0 | |
| xen18-ayers-table-40 | 7 Generalized Root Harmonic Square Means between 1.0 and 1.6 | 8 | 813.7 | |
| xen18-ayers-table-41-42 | Fibonacci-Type Means scale from Table 41 and Table 42 | 7 | 1200.0 | 5 |
| xen18-ayers-table-43 | 7 Fibonacci-Type Means between 1/1 and 2/1 | 8 | 1200.0 | 17 |
| xen18-ayers-table-44 | Transposing 3 Fibonacci-Type Means to Lower Tetrachord Between 1/1 and 4/3 | 7 | 1200.0 | 13 |
| xen18-ayers-table-45 | Complementary Ratios to 3 Fibonacci-Type Means for Lower Tetrachord Between 1/1 and 4/3 | 7 | 1200.0 | 13 |
| xen18-ayers-table-46 | Reciprocals of Golden Mean in P4 | 3 | 498.0 | |
| xen18-ayers-table-47 | Reciprocals of Golden Mean in Octave | 5 | 1200.0 | |
| xen18-ayers-table-48 | 7 Iterated Reciprocals of Golden Means between 1/1 and 2/1 | 8 | 1200.0 | |
| xen18-ayers-table-49 | 7 Iterated First Unnamed Means between 1/1 and 2/1 | 8 | 1200.0 | 17 |
| xen18-ayers-table-54 | 7 Iterated First Unnamed Means between 1/1 and 2/1, Weighted by Ratio 3/2 | 8 | 1200.0 | 53 |
| xen18-ayers-table-55 | First Unnamed Mean scale from window in Table 55 | 7 | 1200.0 | 13 |
| xen18-ayers-table-56 | 7 Iterated Second Unnamed Means between 1/1 and 2/1 | 8 | 1200.0 | 157 |
| xen18-ayers-table-59 | 7 Iterated Second Unnamed Means between 1/1 and 2/1, Weighted by Ratio 3/2 | 8 | 1200.0 | 23 |
| xen18-ayers-table-61 | 7 Iterated Third Unnamed Means between 1/1 and 2/1 | 8 | 1200.0 | |
| xen18-ayers-table-62 | 7 Iterated Fourth Unnamed Means between 1/1 and 2/1 | 8 | 1200.0 | 17 |
| xen18-ayers-table-63 | Didymos' Chromatic Tetrachord | 3 | 498.0 | 5 |
| xen18-ayers-table-64 | Archytas' Enharmonic Tetrachord | 3 | 498.0 | 7 |
| xen18-ayers-table-65 | 7 Iterated Mediants between 1/1 and 2/1 | 8 | 1200.0 | 7 |
| xen18-ayers-table-71 | 7 Weighted Mediants between 1/1 and 2/1 | 8 | 1200.0 | 7 |