The Overtone Series and MMA
Why the Melodic Minor Ascending scale aligns with the upper harmonic series more closely than the major scale — and what this means acoustically for dominant chord resonance.
The harmonic series is the physical source of all musical intervals. When a string or air column vibrates, it produces not just a fundamental frequency but a series of overtones at integer multiples of that fundamental. The second harmonic is twice the frequency (an octave up). The third is three times (a perfect fifth above the octave). The fourth is four times (another octave). The fifth is five times (a major third above that). And so on up through the series, with each successive harmonic becoming quieter and producing a smaller interval from the one before.
The notes of the Melodic Minor Ascending scale align with this harmonic series — particularly its upper partials — more closely than the notes of the major scale do. This alignment is not accidental. It is the acoustic basis for why MMA sounds “right” over dominant chord contexts: the scale’s notes correspond to the overtones that the dominant chord’s root naturally generates.
Bar length = relative amplitude. “~” = approximate equal temperament equivalent (within 50 cents). The 11th harmonic (≈ F#, the #11) is in MMA but not the major scale.
The Critical Difference — The 11th Harmonic
The most significant difference between the major scale and MMA in terms of harmonic series alignment is the 11th partial. The 11th harmonic of any fundamental is approximately 551 cents above an octave of the fundamental — roughly a tritone and a quarter tone above the root, or approximately a very sharp fourth. In equal temperament, the nearest note is F# (600 cents above C), which is the raised fourth — the #11 of the dominant chord, the defining note of the Lydian Dominant mode.
The major scale contains F natural (the perfect fourth), not F# (the raised fourth). The MMA scale, in its Lydian Dominant mode, contains F# — bringing the scale closer to the natural 11th harmonic of the root. This is the acoustic basis for why the #11 sounds “natural” and “resonant” over a dominant chord: it is closer to an actual overtone of the chord’s root than the natural 4th (which is why the natural 4th is an “avoid note” over dominant chords — it clashes with the natural harmonic tendency of the root).
Major Scale vs. MMA — Harmonic Series Alignment
The Altered Scale and the Upper Harmonics
The Altered scale (Mode 7 of MMA) extends this alignment into the very upper partials of the harmonic series. The b9 (minor 9th, approximately harmonic 17), the #9 (augmented 9th, approximately harmonic 19), and the b13 (minor 13th, approximately harmonic 13) all correspond to upper harmonics that are present — at low amplitude — in the natural overtone series of any vibrating string or air column.
This is why altered dominant chords, despite their surface dissonance, do not sound “wrong” — they sound tense. The alterations correspond to real overtones of the chord’s root, which means the ear recognizes them as harmonically related to the root even though they create dissonance with the chord tones. Tension, not noise. The Altered scale exploits this upper-harmonic relationship systematically: every one of its “altered” notes is an upper partial of the dominant chord’s root.
The acoustic alignment between MMA’s modes and the harmonic series is, ultimately, the physical reason why MMA works where other scales create avoid notes. It is not arbitrary that MMA passes the avoid-note test for all 12 transpositions — it is a consequence of MMA’s interval structure placing its notes closer to natural overtone positions than the major scale does. The mathematics of the previous articles and the physics of the harmonic series are the same story told in two languages.
Acoustic physics and scale theory — the same phenomenon
The 11th harmonic
The 11th partial of any fundamental falls approximately at the #11 (tritone) above the root — the note that defines Lydian Dominant. The “avoid note” status of the natural 4th over dominant chords is the acoustic rejection of a note that contradicts this natural overtone tendency.
Upper partial correspondence
The Altered scale’s “alterations” are not arbitrary dissonances — they are upper harmonics (13th, 17th, 19th partials) of the dominant chord’s root. The ear hears them as tense but related, not random. Acoustic physics is the source of the altered dominant’s characteristic sound.
Avoid notes as acoustic conflicts
An “avoid note” is a scale tone that conflicts with a natural overtone of the chord root. The major scale’s natural 4th conflicts with the 11th harmonic tendency. MMA’s #4 (raised fourth / Lydian Dominant mode) aligns with it. This acoustic alignment is why MMA avoids the avoid notes.
Resonance as harmony
When a scale’s notes align with a chord root’s overtone series, the scale resonates with the chord acoustically — the room seems to agree with the harmony. This is the physical basis of what musicians call “the scale fitting the chord.” MMA fits dominant chords because it resonates with their overtone structure.
The next article examines the acoustic properties of the Altered scale specifically — the most extreme MMA mode and the one most deeply connected to upper harmonic resonance — and how these properties make it the ideal tool for dominant chord tension and resolution.
The harmonic series and its relationship to musical intervals: Helmholtz, On the Sensations of Tone (1877); Roederer, Introduction to the Physics and Psychophysics of Music (4th ed., 2008). The 11th harmonic and the tritone: Sethares, Tuning, Timbre, Spectrum, Scale (2005). SuperScales documentation at muse-eek.com.