Ratios do not determine absolute pitch
For example, the ratios 1/1, 5/4, and 3/2 with a reference frequency of 220 Hz give notes at 220, 275, and 330 Hz. Changing the reference shifts all three frequencies proportionally while preserving their interval ratios.
To compare intervals independently of the reference pitch, use cents: 1200 × log₂ of the frequency ratio. A just major third of 5/4 is approximately 386.31 cents, while four equal semitones span 400 cents. The difference of about 13.69 cents describes two interval definitions; it is not a universal judgment of which sonority is better for every timbre and musical context.
A scale file stores only part of the solution
A Scala .scl file describes intervals. A .kbm map defines how scale degrees relate to MIDI notes and the reference tuning. Two synthesizers can therefore import the same scale yet respond differently to the same key if their mappings differ.
Also decide where the scale repeats, how many degrees it contains, and what happens to keys outside the selected range. A scale degree, MIDI note number, and frequency are different entities. A key label helps the performer but does not define the sound. Keep scale and mapping files with the reference frequency so the next session restores the complete assignment, not merely a list of attractive ratios.
MPE requires a matched range
In MPE, individual voices are distributed across member channels. Pitch deviation on a channel must be interpreted identically by transmitter and receiver. A pitch-bend range mismatch turns a correct message value into an incorrect interval.
Polyphony introduces state: a channel may hold a sounding note, remain sustained by a pedal, or be ready for reuse. A new note must not inherit an unintended pitch bend from its predecessor. Check the agreed bend range and the receiver’s behavior when voices run out. This applies to a particular MPE-compatible setup; a MIDI input alone does not establish support.
Verify the result
When preparing an MPE map, we first choose three reference notes and check them on the receiving instrument. We then test chords, note releases, and channel reuse. One correct note does not establish correct polyphonic behavior.
A sine wave is convenient for interval checks, while the working patch may mask its fundamental or contain strong inharmonic components. Verify frequencies with a simple source first, then listen to the musical voice. Percussive attacks and short notes need care: pitch estimators can fail during transients. Keep the recording and estimation method, rather than only the number displayed by a tuner.
The acoustic string has a life of its own
NACRE and GRAIN’s acoustic tuning is measured and adjusted separately from the electronic scale. When combining the layers, check the intervals between them. A difference can be retained as part of the composition and noted in the score.
In a shared part, decide what acts as the reference: fixed acoustic tuning, an electronic voice, or a changing harmonic center. With adaptive electronic tuning, a held note can acquire a new function as its neighbors change. Treat this as a performance decision. A static interval table and a dynamic retuning rule describe different instruments even when their first note matches.
What the research adds
Volkov’s Pivotuner describes an adaptive tuning center with locking and reset controls. It helps distinguish a static scale from tuning behavior over time. This does not mean our studio’s programs automatically implement that adaptation. [1] Volkov, 2023
Shafiei and Hakam analyze intonation in monophonic vocal recordings while accounting for performance variation. Their work distinguishes an extracted model from living practice: statistical centers should not automatically become mandatory pitches for every performer in a tradition. [2] Shafiei & Hakam, 2025
an adaptive tuning center
A practical check
Save the scale, keyboard map, reference frequency, and pitch-bend range. Test reference, third, and fifth individually, then together, with sustain and after voice reassignment. Repeat after restarting the receiving instrument. This short sequence tests both pitch arithmetic and system memory, two reasons why a correct on-screen tuning can sound unexpected.
Research references
Links point to the specified arXiv versions; publication status is available on each paper’s page. The studies concern their authors’ systems. Connections to Sagittarius A Studio instruments are our engineering and musical interpretation.