SFINX - Xenharmonic Guitar Learning App

SFINX 
Stringed Fretted Instruments Notes Explorer

This free web-based app is designed to help you explore and experiment with xenharmonic (micro/macro-tonal) guitars.

Key Features:

• Generate scales and chord diagrams for custom tunings
• Play and find chord progressions on an interactive virtual guitar
• Utilize a built-in tuner and fretboard calculator

Basic Concepts:

• Xenharmonic Tuning: SFINX specializes in exploring tunings beyond the standard 12-tone equal temperament. Users can create custom tunings using decimal ratios or equal division.
• Virtual Guitar: The app provides an interactive virtual guitar interface to visualize and experiment with different tunings, scales, and chords.
• Preset Management: Users can save and load instrument and scale presets for quick access and experimentation.

Help:

Default presets include normal 12ed2 guitar and bass.
SFINX saves presets per browser, allowing you to import and export settings. Overwriting existing presets is possible, but remember to save the instrument preset after creating or modifying scales.

Tuning System

• Strings and Frets: Define the physical parameters of your virtual instrument.
• Decimal Ratio List: The program accepts intervals in decimal ratio, comma-separated. The last ratio represents the octave equivalent.
• Equal Division: Divide the octave into a specified number of equal intervals.
• Tuning Pattern: Determine the open string note of each string relative to the previous one. This allows for various tuning configurations, including drop tunings.
  Each string you add, also adds a control on its left that sets the open string note in relation with its previous string (that is why the lowest string doesn't have one).
  The standard guitar tuning pattern is 5, 5, 5, 4, 5.
  A one step drop tuning pattern is: 7, 5, 5, 4, 5.
• Lowest Pitch: Set the fundamental frequency of the lowest open string.
  In hertz. Sets the lowest possible pitch, that is the lowest open string, the only control for setting pitch directly.
• Interval Rulers: Measure intervals and string lengths for in-depth analysis.
  - The pink ruler marks always the equave.(the last number in the interval list, or the interval used for the division in equal-division systems)
  - The fixed green 12ed2 ruler is useful to measure other tunings, since most musicians are familiar with the role of those tempered 12, is easy to relate new tunings using the ruler for quick comparison. (it can be moved)
  For deeper interval analysis and measurement beyond the basic tools provided, explore my other app, 'Interval Rulers.' It visualizes intervals as an 'abstract guitar' or interval matrix, enabling complex calculations like successive reductions and chroma finding. Unlike SFINX, which focuses on a fixed interval matrix inherent to the guitar, 'Interval Rulers' offers a more flexible and comprehensive approach to interval exploration.

Visualization and Interaction

• Highlights: Select specific notes on the fretboard to focus on particular scales or chords.
  Each interval on the list gets a control, or with the equal-division system, each division gets a control.(Note: with non-integer divisions, this gets truncated, floored. So with 11.66 divisions, it will count 11, this is non-sense, yes).
  Here is where you set the scale to be displayed on the fretboard.
  Each marked note, adds a control for arpeggiate a chord.
  
• Chord Pattern: Define the notes for each chord position.
  Each string added, adds a control for selecting a note for the chord-row.
• Colors: Customize the appearance of notes based on:
  Single: Plain color.
  Class: Notes get a unique color by its class.
  Row: Colorize by chord row, controlled by the chord pattern.
• Arpeggiator: Play notes sequentially in different patterns (up, down, converge, diverge).
• Speed: Arpeggio note separation speed in seconds.
• Synth Sound: Choose from available sounds for the virtual guitar.

Additional Controls

• Width, Length, Zoom: Adjust the visual representation of the fretboard without affecting the tuning or sound.
• Note Length: Control the duration of played notes.
• Volume: Adjust the overall volume of the virtual guitar.
• Calculator ruler: Displays a ruler (orange) with the relative size of the string when hovering a fret.
• Size: Sets the nut to bridge length for calculations. In units.

Limitations Regarding Fretboard Customization

The application presents certain inherent limitations regarding the direct creation of highly customized fretboard configurations, specifically:

1. Unique Individual Frets: It is not possible to directly add a single, unique fret at a specific position on only one string without incorporating that interval into the underlying pitch set definition for the entire instrument.
2. Fret-Skipping Patterns: Creating patterns where entire frets are omitted across all strings cannot be achieved through a direct fret-removal function.

These limitations are not arbitrary but stem from the application's core design philosophy, which prioritizes the generation and analysis of scales and patterns based on consistent, underlying pitch sets. Allowing arbitrary fret additions or removals would undermine this analytical framework. However, practical workarounds exist, grounded in established music theory principles. Understanding these limitations and their justifications clarifies the application's logic, which shares conceptual roots with historical approaches to instrument notation.

Historical Precedent and Theoretical Foundation

The methodology adopted finds a parallel in historical solutions developed during the Middle Ages for fretted instruments like the cittern. As instrument makers experimented with different fretting patterns (including microtonal variations, just intonation, and skipped frets), tablatures became inconsistent and difficult to interpret across instruments. A crucial development, particularly coinciding with the standardization towards 12-tone temperament, was to number frets according to their position within the complete theoretical chromatic scale, even if the physical fret was absent.

For instance, if a string only possessed a single fret precisely at its midpoint (the octave), it was labeled "fret 12," not "fret 1." This indicated its position within the 12-tone system. This elegant solution not only standardized tablature but also facilitated theoretical understanding. It implicitly treated transposition algebraically (akin to coset shifts in modern terminology), ensuring that musical patterns like chord shapes remained consistent conceptually, even when physical frets varied. Attempting to transpose patterns based solely on naive fret counting on irregularly fretted instruments would quickly lead to inconsistencies.

Application Context: Timbre and Octave Equivalence

It is pertinent to note that while the application offers various synthesized guitar timbres, all are fundamentally harmonic. This guarantees the perceptual validity of the octave as the primary cycle of pitch repetition. Consequently, the application's chroma-based color-coding system is fixed to octave equivalence, reinforcing the focus on cyclical pitch structures. (For manipulation of more abstract pitch/timbre relationships, the generalized interval matrix tool should be utilized).

Workaround: Simulating Unique Fret Additions

Consider the scenario of adding a single extra fret to a standard 12-tone guitar – for example, a quarter-tone fret between the 3rd and 4th traditional frets on one string. This might represent a neutral third, a specific microtonal inflection, or serve another modal/contextual purpose.

Directly modeling this single fret addition is not supported. The required workaround involves redefining the instrument's fundamental pitch set to include the desired new interval. This means the interval will be replicated at octave-equivalent positions across the entire fretboard. While a single physical fret might be intended as ornamental, incorporating its pitch interval categorically into the underlying set maintains theoretical consistency.

This approach offers significant advantages:

• It preserves a coherent, cyclical pitch structure, which is easier to implement computationally.
• It results in a more intuitive playing and analysis experience, as patterns remain consistent.
• Chord progressions and scale analyses remain valid across the fretboard. Integrating the new note reveals its systematic relationship within the established structures.

To implement this, you would define the new pitch set using cents notation, incorporating the new interval. For instance, adding a quarter tone (50 cents) near the beginning of the scale: {50, 100, 200, 300, ... , 1200}. Tuning shifts can then be used to position this interval relative to the open string as desired.

Workaround: Simulating Fret-Skipping

Fret-skipping, common in constructing instruments based on subsets of larger microtonal systems (e.g., selecting specific pitches from 31-EDO), presents a different challenge. It's crucial to distinguish between:

• Removing specific notes from a system: This is how regular temperaments are often realized (e.g., a 7-note diatonic scale derived from 12-EDO). On a guitar, this might appear as skipped frets, but the same set of notes remains available across the entire fretboard, just spaced differently.
• Skipping entire frets across all strings: This creates a complex scenario where the availability of specific pitches becomes inconsistent across different positions and octaves.

While it is technically possible to pre-calculate the exact pitches resulting from a fret-skipping pattern and input them as a fixed, non-repeating scale into the application, this is highly impractical for analysis. It essentially defines a unique, non-standard instrument configuration, limiting the applicability of standard analytical tools and pattern recognition.

The recommended and more practical approach mirrors the historical solution: analyze the instrument based on the full, underlying pitch set (e.g., the complete 31-EDO scale if the physical instrument omits some 31-EDO frets). Although diagrams might show chords or scales utilizing frets physically absent on the specific instrument, this method allows:

• Understanding the underlying theoretical structure and harmony.
• Identifying alternative voicings or inversions of desired chords/patterns that are physically playable.
• Avoiding the creation of highly specific notation tied exclusively to one instrument's unique fretting.

Conclusion

The application's limitations on direct, arbitrary fret manipulation encourage users to work within consistent theoretical frameworks. By defining instruments based on complete, cyclical pitch sets (standard or custom), the application facilitates robust musical analysis, pattern recognition, and understanding of transposition and harmony, echoing effective principles developed historically for managing complex fretting systems. The focus remains on the underlying musical structure rather than idiosyncratic physical layouts.

Understanding Chroma, Pitch Class, and Equave in Scale Generation

To navigate the application's scale generation and analysis effectively, it's crucial to distinguish between three types of equivalence: Perceptual (Chroma), Analytical (Class-Based Equave), and Geometrical (Interval of Repetition).

1. Perceptual Equivalence (Chroma)

• Definition: The equivalence of pitches separated by intervals that are perceived by humans as functionally the "same note" at different registers.
• Context: For harmonic timbres (like those of the synthesized guitars), the primary chroma is the octave (1200 cents).

2. Analytical Equivalence (Class-Based Equave)

• Definition: An equivalence established by the chosen number of pitch classes. This defines the modular space within which musical elements (like scales and chords) are analyzed and manipulated. The Equave in this context refers to the interval spanning the chosen number of classes, often a musically significant interval that serves as the boundary of the analytical cycle.
• Relationship to Class: The Equave here is derived from the chosen number of classes. If you choose 12 classes for 12-EDO, the Equave of the class system is the octave. If you choose 13 classes for 13-EDT, the Equave of the class system is the tritave.
• Flexibility: The application allows you to set the number of classes (and thus the "Equave" of the analytical system) independently of the scale's inherent geometrical properties or perceptual chroma. This allows for diverse analytical perspectives.

3. Geometrical Equivalence (Interval of Repetition)

• Definition: The smallest pitch interval within the scale's structure such that transposition by this interval (or multiples of it) results in a repetition of the intervallic pattern or transpositional invariance of musical figures (like chords). This is an inherent property of the scale's construction.
• Examples:
• 12-EDO: The geometrical interval of repetition is the 100 cent step. Transposing any interval or chord by 100 cents (or multiples) within the 12-note octave will maintain the same intervallic structure relative to the steps of the scale. The octave (1200 cents) is the Equave of the 12-class system.
• 12-tone Pythagorean: The geometrical intervals between scale degrees are not uniform. While the octave is the perceptual chroma and also the interval after which the scale repeats in terms of its seven degrees, the exact intervallic relationships within each octave (and thus the sound of transposed chords) are not identical across different starting pitches (due to the nature of just intervals). In this case, the octave is the Equave (class-based) and also a period of repetition for the scale degrees, but not for the precise sonic character of transposed chords.
• 13-EDT: The geometrical interval of repetition is the single, uniform step size of approximately 146.3 cents. Transposing by this amount maintains the intervallic structure. The tritave is the Equave of the 13-class system.

In Summary:

• Chroma: Perceptual octave equivalence.
• Equave (Class-Based): The interval spanning the chosen number of pitch classes, defining the analytical cycle.
• Interval of Repetition (Geometrical): The smallest pitch interval that produces transpositional invariance of patterns within the scale's structure.

This distinction, especially between the class-based "Equave" (for analytical purposes) and the inherent "Interval of Repetition" (a structural property), is very important for understanding how scales behave and how transposition affects musical elements within them.