m17EDO-2306
Modified 17-EDO tuning system (June 2023 revision). Three steps are replaced with just-intonation-derived or equal-temperament intervals: step 9 uses 11/8 (551.3¢), step 10 uses the tritone at 600.0¢, and step 12 uses 8/5 (813.6¢). First used in Prelude X (2023) for piano tuned to a unique 17-tone temperament.
| Step | Cents | Ratio | 17-EDO ref | Deviation | Note |
|---|---|---|---|---|---|
| 1 | 0.0 | 1/1 | 0.0 | 0.0 | unison |
| 2 | 70.6 | 70.6 | 0.0 | ||
| 3 | 141.2 | 141.2 | 0.0 | ||
| 4 | 211.8 | 211.8 | 0.0 | ||
| 5 | 282.4 | 282.4 | 0.0 | ||
| 6 | 352.9 | 352.9 | 0.0 | ||
| 7 | 423.5 | 423.5 | 0.0 | ||
| 8 | 494.1 | 494.1 | 0.0 | ||
| 9 | 551.3 | 11/8 | 564.7 | −13.4 | * MODIFIED |
| 10 | 600.0 | 635.3 | −35.3 | * MODIFIED | |
| 11 | 705.9 | 705.9 | 0.0 | ||
| 12 | 813.6 | 8/5 | 776.5 | +37.1 | * MODIFIED |
| 13 | 847.1 | 847.1 | 0.0 | ||
| 14 | 917.6 | 917.6 | 0.0 | ||
| 15 | 988.2 | 988.2 | 0.0 | ||
| 16 | 1058.8 | 1058.8 | 0.0 | ||
| 17 | 1129.4 | 1129.4 | 0.0 | ||
| 1 | 1200.0 | 2/1 | 1200.0 | 0.0 | octave |
m17EDO-2311
Modified 17-EDO tuning system (November 2023 revision). Five steps are modified from standard 17-EDO: steps 6, 9, 10, 12, and 16. First used in Lunar Fantasia (2023) for microtonal piano.
| Step | Cents | 17-EDO ref | Deviation | Note |
|---|---|---|---|---|
| 1 | 0.0 | 0.0 | 0.0 | unison |
| 2 | 70.6 | 70.6 | 0.0 | |
| 3 | 141.2 | 141.2 | 0.0 | |
| 4 | 211.8 | 211.8 | 0.0 | |
| 5 | 282.4 | 282.4 | 0.0 | |
| 6 | 377.0 | 352.9 | +24.1 | * MODIFIED |
| 7 | 423.5 | 423.5 | 0.0 | |
| 8 | 494.1 | 494.1 | 0.0 | |
| 9 | 536.9 | 564.7 | −27.8 | * MODIFIED |
| 10 | 603.0 | 635.3 | −32.3 | * MODIFIED |
| 11 | 705.9 | 705.9 | 0.0 | |
| 12 | 813.6 | 776.5 | +37.1 | * MODIFIED |
| 13 | 847.1 | 847.1 | 0.0 | |
| 14 | 917.6 | 917.6 | 0.0 | |
| 15 | 988.2 | 988.2 | 0.0 | |
| 16 | 1088.2 | 1058.8 | +29.4 | * MODIFIED |
| 17 | 1129.4 | 1129.4 | 0.0 | |
| 1 | 1200.0 | 1200.0 | 0.0 | octave |
m17EDO-2306 vs m17EDO-2311
Circular pitch-space visualization. Grey ticks = standard 17-EDO positions. Red = m17EDO-2306, blue = m17EDO-2311. Open circles with cent labels = modified steps. 0¢ (unison) at 12 o'clock; pitch ascends clockwise.
Side-by-side comparison of the two modified 17-EDO variants. Differences are highlighted in the table below.
| Step | 2306 (cents) | 2311 (cents) | Diff (2311−2306) |
|---|---|---|---|
| 1 | 0.0 | 0.0 | 0.0 |
| 2 | 70.6 | 70.6 | 0.0 |
| 3 | 141.2 | 141.2 | 0.0 |
| 4 | 211.8 | 211.8 | 0.0 |
| 5 | 282.4 | 282.4 | 0.0 |
| 6 | 352.9 | 377.0 | +24.1 |
| 7 | 423.5 | 423.5 | 0.0 |
| 8 | 494.1 | 494.1 | 0.0 |
| 9 | 551.3 | 536.9 | −14.4 |
| 10 | 600.0 | 603.0 | +3.0 |
| 11 | 705.9 | 705.9 | 0.0 |
| 12 | 813.6 | 813.6 | 0.0 |
| 13 | 847.1 | 847.1 | 0.0 |
| 14 | 917.6 | 917.6 | 0.0 |
| 15 | 988.2 | 988.2 | 0.0 |
| 16 | 1058.8 | 1088.2 | +29.4 |
| 17 | 1129.4 | 1129.4 | 0.0 |
| 1 | 1200.0 | 1200.0 | 0.0 |
Piano Opera — 51-Note Tuning
Piano Opera in 4 Acts — The Asteroidal Sequence of Metaphysical Ulysses (2024–2025). Three microtonal pianos tuned to a unique system of 17 notes each, yielding 51 notes per octave. Piano 1 is the Prelude X tuning (= m17EDO-2306). Base pitch: 312 Hz (octave at 624 Hz).
| # | Cents | Piano | Step |
|---|---|---|---|
| 1 | 0.0 | P1 | — |
| 2 | 12.5 | P3 | 12.5 |
| 3 | 50.0 | P2 | 37.5 |
| 4 | 70.6 | P1 | 20.6 |
| 5 | 83.1 | P3 | 12.5 |
| 6 | 120.6 | P2 | 37.5 |
| 7 | 141.2 | P1 | 20.6 |
| 8 | 153.7 | P3 | 12.5 |
| 9 | 191.2 | P2 | 37.5 |
| 10 | 211.8 | P1 | 20.6 |
| 11 | 224.3 | P3 | 12.5 |
| 12 | 261.8 | P2 | 37.5 |
| 13 | 282.4 | P1 | 20.6 |
| 14 | 294.9 | P3 | 12.5 |
| 15 | 332.4 | P2 | 37.5 |
| 16 | 352.9 | P1 | 20.5 |
| 17 | 386.5 | P3 | 33.6 |
| 18 | 403.0 | P2 | 16.5 |
| 19 | 423.5 | P1 | 20.5 |
| 20 | 436.0 | P3 | 12.5 |
| 21 | 473.6 | P2 | 37.6 |
| 22 | 494.1 | P1 | 20.5 |
| 23 | 506.6 | P3 | 12.5 |
| 24 | 544.1 | P2 | 37.5 |
| 25 | 547.5 | P3 | 3.4 |
| 26 | 551.3 | P1 | 3.8 |
| # | Cents | Piano | Step |
|---|---|---|---|
| 27 | 600.0 | P1 | 48.7 |
| 28 | 612.5 | P3 | 12.5 |
| 29 | 614.7 | P2 | 2.2 |
| 30 | 674.5 | P3 | 59.8 |
| 31 | 685.3 | P2 | 10.8 |
| 32 | 705.9 | P1 | 20.6 |
| 33 | 743.0 | P3 | 37.1 |
| 34 | 755.9 | P2 | 12.9 |
| 35 | 813.6 | P1 | 57.7 |
| 36 | 826.5 | P2 | 12.9 |
| 37 | 847.1 | P1 | 20.6 |
| 38 | 870.5 | P3 | 23.4 |
| 39 | 897.1 | P2 | 26.6 |
| 40 | 917.6 | P1 | 20.5 |
| 41 | 920.5 | P3 | 2.9 |
| 42 | 967.7 | P2 | 47.2 |
| 43 | 988.2 | P1 | 20.5 |
| 44 | 999.0 | P3 | 10.8 |
| 45 | 1033.5 | P3 | 34.5 |
| 46 | 1038.3 | P2 | 4.8 |
| 47 | 1058.8 | P1 | 20.5 |
| 48 | 1108.9 | P2 | 50.1 |
| 49 | 1129.4 | P1 | 20.5 |
| 50 | 1142.9 | P3 | 13.5 |
| 51 | 1179.5 | P2 | 36.6 |
| 1 | 1200.0 | P1 | 20.5 |
Step size = interval from previous note in cents. Minimum step: 2.2¢ (#28→#29). Maximum step: 59.8¢ (#29→#30).
Analysis
Scala Files
All three tuning systems as Scala (.scl) files for import into Pianoteq, Surge, and other microtonal-capable synthesizers.
piano-opera-51note.scl is provided for reference and analysis purposes. In practice, the Piano Opera tuning should be implemented as 3 separate instances of a 17-tone piano (each using its own modified 17-EDO tuning), not as a single 51-note scale loaded into one instrument. Loading all 51 notes into a single Pianoteq instance will produce a keyboard mapping that does not reflect the intended 3-piano layout of the composition.
All tuning data, analyses, and descriptions on this page are the intellectual property of Hiroki Naito / UTIE Instruments Inc. Unauthorized reproduction is prohibited.