Chromatic Solfége
Using the Harken Music System to Teach and Learn Chromatic Solfége
The Harken Music system provides a unique way to learn and use solfége, or sight singing, by replacing the traditional major-scale “fixed do” system with a fully chromatic, cycle-based sequence. This method introduces all twelve notes of the chromatic scale equally, encouraging students to perceive accidentals (sharp and flat notes) as integral to the musical language, rather than mere deviations. This provides an effective framework for developing pitch recognition, interval accuracy, and chromatic ear-training, skills often limited by traditional seven-note systems.
Ascending and Descending Chromatic Solfége
With traditional solfége, musical pitches are assigned distinct syllables based on their note relationships with the tonic: ascending through the cycle we sing: do, sol, re, la, mi, ti, fi, ri, si, me, li, fa, do; descending we sing: do, fa, te, me, le, ra, se, ti, mi, la, re, sol, do.
Solfége was created to allow vocalizing of the various pitches using a single syllable for each note. It’s not possible to sing the words “A-sharp” or “B-flat” without using two syllables, so we sing “li” or “te” instead.
Solfége follows traditional note-naming conventions, where enharmonically equivalent pitches do not share the same letter name or accidental. For example: D♯ and E♭ represent the same pitch. This can and does cause confusion, as there are 17 names for just 12 notes, 7 letter names for “natural” notes and 10 (5 x 2) names for “accidental” notes, and it’s even more when double flats and double sharps are used.
It is much easier to simply sing the 12 pitches using just 12 numbers: zero, one, two, three, four, five, six, seven, eight, nine, ten, eleven. And while “se•ven” and “e•le•ven” are clearly multiple-syllable words, we can phonetically slur them to make one-syllable sounds, e.g., “sevn” and “leven”. And although “twelve” is also a single-syllable word, which may occasionally substitute for “zero” in this system, larger numbers are never used for sight singing, due to the increasing number of syllables, e.g., thir•teen, four•teen, fif•teen, and so on.
So if preferred, students may skip traditional solfége altogether and just sing pitches using the numbers 0-11 instead. As notated above, we can ascend through the cycle singing: zero, seven, two, nine, four, eleven, six, one, eight, three, ten, five, repeating zero one octave above the starting point or tonic pitch; and descend through the cycle singing: zero, five, ten, three, eight, one, six, eleven, four, nine, two, seven, repeating zero one octave below.
The cycle order provides an accessible bi-directional sequence that’s easy to memorize and sing, fostering confidence with chromaticism from an early stage. Students also learn interval relationships within a chromatic framework, making it easier to apply this knowledge across musical contexts, including improvisation, composition, and analysis.
Teaching Chromatic Solfége with the Harken System
To implement this system, students start by learning the cycle order, focusing on accurate intonation and pitch matching for each syllable. Teachers may introduce the sequence slowly, using call-and-response exercises to reinforce both ascending and descending patterns. The use of colors or visual aids to represent each syllable and note can further enhance students' memory and pitch association, adding a visual dimension that supports auditory learning.
Additionally, the Harken Music system emphasizes practicing intervals beyond simple stepwise motion, incorporating leaps across the chromatic cycle. For example, a teacher might ask students to sing from do to si, introducing the augmented fifth, or from do to ti, presenting a major seventh. This builds comfort with chromatic intervals, strengthening the ear’s capacity to identify pitches within the full 12-tone palette.
Expanding Ear-Training Beyond Traditional Scales
The Harken Music system enables students to explore beyond major and minor tonality, engaging with a broader range of intervals and harmonic colors from the chromatic scale. This structure prepares students for modern musical contexts, including jazz and contemporary classical music, where chromaticism is encouraged. This method also aids in developing "relative pitch" by solidifying each pitch’s identity within the cycle, enhancing students' adaptability to different keys and tonalities.
In summary, chromatic solfége offers a well-rounded method for teaching ear-training. By integrating all twelve notes, it promotes a holistic view of pitch, cultivates interval recognition, and equips students with a robust skill set for navigating the full chromatic spectrum. This approach not only enriches musical understanding but fosters flexibility and creativity, essential tools for any musician today.
Please try our free open-source demo* at harkenmusic.com, where you can choose any combination size (from 1 to 12 notes) from the pull-down menu; then select any particular combination from the numbered list, to see and hear all permutations, reflections (inversions), and rotations (transpositions).
*Note: a desktop or laptop computer and current web browser (Chrome, Safari, etc.) are required for using the demo; however there are no downloads, sign-up, or subscription requirements.
It cannot be overstated that the Harken Music system uses only mathematics and math related programming code. The programming does not include or use any databases, lookup tables, or other sources of data. Everything—nearly 1.2 billion musical combinations and permutations—is calculated on the fly.
For a detailed explanation of the high-school-level math used in creating the Harken Music system, please read, “The Future of Music is Math” by Mitch Kahle.
See also: “Harken Music: A New Mathematical Framework for 12-Tone Harmony”, by ChatGPT 4o, and for an even deeper dive into the mathematics, read Factorials and Fractions “Navigating the 12-tone matrix,” by Mitch Kahle.
This information and related software code are now available for free on Harken Music and Github as open-source software under the standard MIT License set forth below.
Copyright 2024 Mitchell Kahle and Holly J. Huber
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