Naming System

PhizMusic uses a dual naming system for pitches: step-numbers for precision and arithmetic, Dodeka syllables for speaking and singing. Both name all 12 chromatic steps equally — no pitch is treated as an alteration of another. There are no sharps, no flats, no enharmonic confusion.

🎯 Simple version: Instead of 7 note names with sharps and flats (confusing), we use 12 names — one for each key on the piano, no exceptions. Do, Ka, Re, Xo, Mi, Fa, Hu, So, Bi, La, Ve, Si. For math and precision, we use numbers 0-11 plus an octave number: 4.7 means “octave 4, step 7.”

Design Principles

The PhizMusic naming system solves three problems with conventional Western note names:

1. Asymmetric treatment of pitches. Western names treat 7 pitches as “natural” (C D E F G A B) and 5 as “altered” (C♯/D♭, D♯/E♭, etc.). In 12-TET, all 12 chromatic steps are physically equal — the distinction is a historical artifact of the diatonic scale, not physics. PhizMusic gives every step equal status.

2. Enharmonic confusion. In Western notation, C♯ and D♭ are the same frequency in 12-TET but have different names, different staff positions, and different theoretical implications. This doubles the vocabulary without adding information. PhizMusic: one step = one name, period.

3. Opaque arithmetic. In Western names, “a major third above C” requires knowing that C + major third = E (not intuitive). In PhizMusic: step 0 + the 4-step-interval = step 4. Transposition is addition. Inversion is subtraction from 12. The naming system makes the math visible.

Step-Numbers: Formal Notation

A pitch is identified by two numbers:

octave.step

• Octave (0-8): which octave register (matching the standard scientific octave numbering)
• Step (0-11): position within the chromatic octave

Examples:

• 4.0 = octave 4, step 0 = “middle C” area = 261.63 Hz
• 4.7 = octave 4, step 7 = 392.00 Hz
• 4.9 = octave 4, step 9 = 440.00 Hz (the standard tuning reference)
• 5.0 = octave 5, step 0 = 523.25 Hz (one octave above 4.0)

Arithmetic Properties

Step-numbers make musical operations trivial:

No lookup tables. No special cases. Just integer arithmetic modulo 12.

Frequency from Step-Number

Any pitch’s frequency can be computed from its step-number and octave:

MIDI number:  n = (octave + 1) × 12 + step
Frequency:    f = 440 × 2^((n - 69) / 12)

See Reference Table for the complete mapping.

Dodeka Syllables: Casual Notation

For speaking, singing, and informal reference, each step has a unique syllable adapted from the Dodeka Music system by Jacques-Daniel Rochat:

Click any row to hear the pitch for that step in octave 4.

In casual use, a syllable plus octave number identifies a pitch: So4 = step 7, octave 4 = G4 in Western notation.

Key differences from Western solfège (Do Re Mi Fa Sol La Ti):

• Western solfège has 7 syllables for a 12-note system — the 5 “in-between” pitches get no dedicated name
• Dodeka syllables give 12 unique names — every chromatic pitch has an equally simple name
• The 12th syllable is Si (not “Ti” as in Western solfège)

When to Use Which

Anchoring Convention: Do = C

The assignment of step 0 (Do) to the Western pitch C is arbitrary but conventional. We adopt it for pragmatic compatibility:

• Do4 (4.0) = C4 = 261.63 Hz
• La4 (4.9) = A4 = 440.00 Hz (the universal tuning standard)

Nothing in the PhizMusic system depends on this choice. If you wanted to anchor Do to A (step 0 = 440 Hz), every formula and relationship would still hold — only the absolute frequencies in the Reference Table would shift. The anchoring is a convention for interoperability, not a property of the system.

Categorical Perception

The brain does not perceive pitch as a smooth continuum. Trained listeners — and even untrained ones to some extent — perceive pitch categorically: continuous frequency changes are heard as discrete steps, with sharp boundaries between categories. This is the same phenomenon that makes you hear phonemes in speech rather than a smooth acoustic stream.

The PhizMusic naming system aligns with this perceptual reality: 12 equal categories, each with a unique label, matching the 12-TET chromatic grid. The Western system’s 7+5 asymmetry (7 “natural” notes, 5 “accidentals”) conflicts with the actual perceptual symmetry of 12-TET, where all 12 categories have equal status.

Complete Mapping

Note that Western notation has 17 names for 12 pitches (C, C♯, D♭, D, D♯, E♭, E, F, F♯, G♭, G, G♯, A♭, A, A♯, B♭, B). PhizMusic has exactly 12 names for 12 pitches. The redundancy is gone.

Translation Table

Connections

• Glossary — definitions of step-number and syllable
• Reference Table — complete octave × step → frequency mapping
• Intervals — step-intervals between pitches
• Scales — step-subsets using the naming system
• Translation Tables — comprehensive cross-system lookup