What is a scale degree?

A scale degree is the position of a pitch within a scale, counted from 1 (the tonic or root) upward. In a 7-note scale the tonic is degree 1 and the leading tone is degree 7. Each degree has a traditional name — tonic, supertonic, mediant, subdominant, dominant, submediant and subtonic or leading tone — and a Roman numeral label used in harmonic analysis.

How do you calculate the notes in a major scale?

The major scale follows the whole-step/half-step pattern W W H W W W H, which in semitones is 0, 2, 4, 5, 7, 9, 11. Add each value (mod 12) to the root pitch class to get each note. For C major: C(0) D(2) E(4) F(5) G(7) A(9) B(11).

What is the difference between a mode and a scale?

A mode is a rotation of the diatonic (major) scale starting from a different degree. Dorian starts on degree 2, Phrygian on degree 3, and so on through Lydian, Mixolydian, Aeolian (Natural Minor) and Locrian. Each rotation has the same seven pitches as its parent key but a different tonal centre, producing a distinct emotional colour.

What do the Roman numerals mean?

Roman numerals label each degree and hint at the chord built on it. Upper-case (I, IV, V) implies a major chord; lower-case (ii, iii, vi) implies minor; a degree symbol (vii°) means diminished; a plus sign (III+) means augmented. This system lets musicians communicate harmonic function across different keys — "go to the V" means the dominant chord regardless of root.

How does the frequency ratio work for each degree?

In 12-tone equal temperament every semitone multiplies frequency by the twelfth root of two (2^(1/12)). A degree n semitones above the root has frequency ratio 2^(n/12). The perfect fifth (7 semitones) gives 2^(7/12) ≈ 1.4983, very close to the pure ratio 3:2 = 1.5000.

What scales are included?

The calculator covers 15 scales: Major (Ionian), Natural Minor (Aeolian), Harmonic Minor, Melodic Minor (ascending), Dorian, Phrygian, Lydian, Mixolydian, Locrian, Major Pentatonic, Minor Pentatonic, Blues Hexatonic, Whole Tone, Diminished (whole-half octatonic) and Chromatic.

Scale Degree Calculator

The scale degree calculator shows you every note in any musical scale or mode, labelled by degree number, Roman numeral, note name and interval quality. Select a root pitch and a scale type and the full degree table — plus a mini piano diagram — updates instantly. It is built for songwriters, music theory students, guitarists, pianists and anyone learning how keys and modes work.

How it works

A musical scale is defined by a set of semitone intervals above the root. The major scale uses the pattern 0 – 2 – 4 – 5 – 7 – 9 – 11 semitones; the natural minor (Aeolian) uses 0 – 2 – 3 – 5 – 7 – 8 – 10. Given a root pitch class R (0 = C through 11 = B), degree i has pitch class:

pitch = (R + semitones[i]) mod 12

The tool stores the interval formula for each of 15 scales, applies the modular arithmetic to every step, and maps the resulting pitch class to a note name (and enharmonic equivalent where applicable). Roman numerals are pre-assigned per scale type — upper-case for major-quality chords, lower-case for minor, with ° for diminished and + for augmented.

Frequency ratios

In 12-tone equal temperament each semitone multiplies frequency by 2^(1/12). A scale degree s semitones above the root has ratio:

ratio = 2^(s / 12)

Clicking any row in the degree table displays this ratio alongside the interval name. The perfect fifth (7 semitones) gives 2^(7/12) ≈ 1.4983, extremely close to the just-intonation ratio 3:2 = 1.5. The major third (4 semitones) gives 2^(4/12) ≈ 1.2599 versus the pure 5:4 = 1.25 — a small but audible difference that drove centuries of tuning debate.

Worked example — D Dorian

Root: D Scale: Dorian (intervals: 0, 2, 3, 5, 7, 9, 10 semitones)

Degree	Roman	Note	Semitones	Interval
1	i	D	0	P1 (Unison)
2	ii	E	2	M2
3	III	F	3	m3
4	IV	G	5	P4
5	v	A	7	P5
6	vi	B	9	M6
7	VII	C	10	m7

Dorian is the second mode of the C major scale. Its characteristic sound comes from the major 6th on degree 6 (B natural in D Dorian) contrasted against the minor third and minor seventh. This makes it ideal for jazz and funk — Miles Davis’s “So What” and Carlos Santana’s playing are canonical examples.

Formula note

Scale degree frequency ratio (equal temperament):

f(s) = f_root × 2^(s / 12)

where s is the number of semitones above the root. The piano diagram highlights active pitch classes across one octave so you can instantly see whether a scale clusters around the white keys or crosses between natural and accidental notes.

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