Tablatures chords, scales and modes for computer systems.
This collection serves dual artistic and scientific objectives, facilitating harmonic and ethnomusicological analysis while addressing professional requirements in sound design and electroacoustic composition.
An additional aim involves advanced compositional research centered on the superposition of complex chords and sound clusters characteristic of Stockhausen, Ligeti, and Varèse—figures whose work has shaped electronic experimentation and contemporary orchestration.
Beginning during my studies at various conservatories, I systematically cataloged scales, modes, and chords. These were organized into structured lists designed for rapid retrieval and manipulation via indexing functions, supporting the development of layered harmonic structures and polychordal progressions—key elements in generative music and soundscapes.
Initial implementations commenced in May 2015, employing spreadsheets for numerical computation. At that stage, the collections comprised lists including:
• Major and minor chords
• Inversions and suspensions
• Subdominant and dominant derivatives
• Triadic superimpositions for cluster generation
During experimentation, I identified two data categories within computational systems:
• Initialized data (“i”) – precomputed and ready for use
• Generated data (“k”) – requiring calculation
To optimize performance and accelerate indexing, I manually initialized lists, enabling efficient manipulation of overlapping chord patterns and iterative polyrhythmic construction.
Because conventional chord nomenclature was not always compatible with computational syntax, I adopted a simplified nomenclature:
• D = sharp (#)
• b = flat
• M = major chords
• m = minor chords
Example: Cmi6 := {C, Eb, G, A}, where 6 denotes the sixth degree (A) of the C minor chord.
Primary progressions were denoted in Roman numerals—for instance, CIV for the subdominant chord of C major (F, A, C)—to streamline progression generation.
A pivotal development occurred with the consultation of the CookBook JazzMaster, which integrated dissonant jazz chords into the system alongside classical progressions. The capacity to concatenate poly-chordal overlaps facilitated the creation of complex soundscapes.
In 2022, a commission prompted experimentation within CSound via the CsoundQt editor to generate MIDI tracks. The simultaneous processing of three to six overlapping notes necessitated index functions such as:
• Cyclic segmentation using timeScale for extraction velocity
• Random segmentation
• Index list phase-shifting systems
In 2023, to address the constraints of CsoundQt, the system was migrated to a graphical user interface for Csound, integrated with spreadsheet software and expanded list management capabilities:
• Arpeggios: CMA = {261.63, 329.63, 392., 392., 329.63, 261.63}
• Harmonic phase shifts: CMS = {261.63, 329.63, 392., 329.63, 392., 261.63, …}
• Symmetric phase shifts: CMAS = {261.63, 329.63, 392., 392., 329.63, …}
This phase resulted in the development of the first application for managing five combinatorial triggers, establishing a foundation for a permutable pattern generator suited to multilayered and iterative compositions.
In 2024, the system was evaluated using Smalltalk syntax for Kyma, introducing the concept of PatternLag, which enables:
• Sequence generation, repetition and lagged
• Specification of repetition number
• Phase shifting after defined or variable cycle intervals
This function proved effective for iterative overlays characteristic of minimalist aesthetics while remaining adaptable to avant-garde matrix structures.
This expanded documentation is designed to:
• Disseminate musical indexing methodologies for computational systems
• Provide digital tablatures for chords, scales, and modes
• Supply tools for generative composition
• Enable harmonic exploration for experimental composers
– Establish a translation convention for existing modes: iBbaddb13add9 = B♭ with added 13th and 9th
The document includes two tables presenting corresponding values in hertz (Hz), ratio, and MIDI. Note repetition denotes the duration of note persistence within the system; difference indicates the frequency delta in Hz relative to the preceding value.
Concluding recommendation: indexing across two octaves is advised using ListNote{Hz or Sys or Ratio}.
| ListNote | Hz | RATIO | MIDI | Differences in Hz; |
|---|---|---|---|---|
| iC2; | 523.25" | 2.000; | 72; | 29.37 |
| iCD2; | 554.37" | 2.118; | 73; | 31.12 |
| iDb2; | 554.37" | 2.118; | 73; | |
| iD2; | 587.33" | 2.244; | 74; | 32.96 |
| iDD2; | 622.25" | 2.378; | 75; | 34.92 |
| iEb2; | 622.25" | 2.378; | 75; | |
| iE2; | 659.25" | 2.519; | 76; | 37 |
| iED2; | 698.46" | 2.669; | 77; | 39.21 |
| iFb2; | 659.25" | 2.519; | 76; | |
| iF2; | 698.46" | 2.669; | 77; | |
| iFD2; | 739.99" | 2.828; | 78; | 41.53 |
| iGb2; | 739.99" | 2.828; | 78; | |
| iG2; | 783.99" | 2.996; | 79; | 44 |
| iGD2; | 830.61" | 3.174; | 80; | 46.62 |
| iAb2; | 830.61" | 3.174; | 80; | |
| iA2; | 880.00" | 3.363; | 81; | 49.39 |
| iAD2; | 932.33" | 3.563; | 82; | 52.33 |
| iBb2; | 932.33" | 3.563; | 82; | |
| iB2; | 987.77" | 3.775; | 83; | 55.44 |
| CHORD SCALE Name | ListNote | HarmonicMean Hz | Differences Hz | |
|---|---|---|---|---|
| MAJOR | ||||
| 1 | C | iC, iE, iG. | 318.914 | 68., 62.37 |
| 2 | C6 | iC, iE, iG, iA. | 342.476 | 68., 62.37, 48 |
| 3 | C6|9 | iC, iE, iG, iA, iD. | 373.629 | 68., 62.37, 48., 147.33 |
| 4 | C(add9) | iC, iE, iG, iD. | 360.051 | 68., 62.37, 195.33 |
| 5 | CMA7 | iC, iE, iG, iB. | 349.904 | 68., 62.37, 101.88 |
| 6 | CMA7(add13) | iC, iE, iG, iA, iB. | 364.846 | 68., 62.37, 48., 53.88 |
| 7 | CMA9 | iC, iE, iG, iB, iD. | 380.682 | 68., 62.37, 101.88, 93.45 |
| 8 | CMA13 | iC, iE, iG, iB, iD, iA. | 420.442 | 68., 62.37, 101.88, 93.45, 292.67 |
| 9 | C7 | iC, iE, iG, iBb. | 346.257 | 68., 62.37, 74.16 |
| 10 | C9 | iC, iE, iG, iBb, iD. | 377.224 | 68., 62.37, 74.16, 121.17 |
| 11 | C13 | iC, iE, iG, iBb, iD, iA. | 416.925 | 68., 62.37, 74.16, 121.17, 292.67 |
| 12 | CMA7(b5) | iC, iE, iGb, iB. | 354.34 | 68., 85.67, 78.58 |
| 13 | CMa7(#5) | iC, iE, iGD, iB. | 345.32 | 68., 40.36, 123.89 |
| 14 | CMa7(#11) | iC, iE, iG, iB, iFD. | 391.143 | 68., 62.37, 101.88, 246.12 |
| 15 | CMA9(#11) | iC, iE, iG, iB, iD, iFD. | 414.202 | 68., 62.37, 101.88, 93.45, 152.67 |
| 16 | CMa13 (#11) | iC, iE, iG, iB, iD, iFD, iA. | 353.312 | 68., 62.37, 101.88, 93.45, 152.66, 140.01 |
| 17 | C7(b5) | iC, iE, iGb, iBb. | 341.768 | 68., 40.36, 96.17 |
| 18 | C9(b5) | iC, iE, iGb, iBb, iD. | 372.954 | 68., 40.36, 96.17, 121.17 |
| MINOR | ||||
| 19 | Cmi | iC, iEb, iG. | 312.914 | 49.5, 80.87 |
| 20 | Cmi6 | iC, iEb, iG, iA. | 337.267 | 49.5, 80.87, 48. |
| 21 | Cmi6|9 | iC, iEb, iG, iA, iD. | 368.66 | 49.5, 80.87, 48., 147.33 |
| 22 | Cmi (add9) | iC, iEb, iG, iD. | 354.298 | 49.5, 80.87, 195.33 |
| 23 | Cmi7 | iC, iEb, iG, iBb. | 340.934 | 49.5, 80.87, 74.16 |
| 24 | Cmi7(add11) | iC, iEb, iG, iBb, iF. | 379.818 | 49.5, 80.87, 74.16, 232.3 |
| 25 | Cmi7(add13) | iC, iEb, iG, iA, iBb. | 357.01 | 49.5, 80.87, 48., 26.16 |
| 26 | Cmi9 | iC, iEb, iG, iBb, iD. | 372.159 | 49.5, 80.87, 74.16, 121.17 |
| 27 | Cmi11 | iC, iEb, iG, iBb, iD, iF. | 333.311 | 49.5, 80.87, 74.16, 121.17, 111.13 |
| 28 | Cmi13 | iC, iEb, iG, iBb, iD, iF, iA. | 437.413 | 49.5, 80.87, 74.16, 121.17, 111.13, 181.54 |
| 29 | Cmi(Ma7) | iC, iEb, iG, iB. | 344.469 | 49.5, 80.87, 101.88 |
| 30 | Cmi9(Ma7) | iC, iEb, iG, iB, iD. | 375.525 | 49.5, 80.87, 101.88, 93.45 |
| 31 | Cmi7(b5) | iC, iEb, iGb, iBb. | 336.58 | 49.5, 58.86, 96.17 |
| 32 | Cmi9(b5) | iC, iEb, iGb, iBb, iD. | 368.002 | 49.5, 58.86, 96.17, 121.17 |
| 33 | Cmi11(b5) | iC, iEb, iGb, iBb, iD, iF. | 399.505 | 49.5, 58.86, 96.17, 121.17, 111.13 |
| Diminuiti e Sus | ||||
| 34 | Cdim. | iC, iEb, iGb. | 308.038 | 49.5, 58.86 |
| 35 | C°7 | iC, iEb, iGb, iA. | 336.58 | 49.5, 58.86, 96.17 |
| 36 | C°7(addMa7) | iC, iEb, iGb, iA, iB. | 356.212 | 49.5, 58.86, 70.01, 53.88 |
| 37 | C+ | iC, iE, iGD. | 323.841 | 68., 85.67 |
| 38 | Csus4 | iC, iF, iG. | 324.793 | 87.6, 42.77 |
| 39 | C7sus4 | iC, iF, iG, iBb. | 351.437 | 87.6, 42.77, 74.16 |
| 40 | C9sus4 | iC, iF, iG, iBb, iD. | 382.133 | 87.6, 42.77, 74.16, 121.17 |
| 41 | C13sus4 | iC, iF, iG, iBb, iD, iA. | 421.916 | 87.6, 42.77, 74.16, 121.17, 292.67 |
| 42 | C7sus4-3 | iC, iG, iBb, iF, iE. | 436.034 | 130.37, 74.16, 193.09, 39.21 |
| 43 | C7(#5) | iC, iE, iGD, iBb. | 350.601 | 68., 85.67, 50.86 |
| 44 | C9(#5) | iC, iE, iGD, iBb, iD. | 372.954 | 68., 40.36, 96.17, 121.17 |
| 45 | C7(b9) | iC, iE, iG, iBb, iDb. | 329.818 | 68., 62.37, 74.16, 88.21 |
| 46 | C7(#9) | iC, iE, iG, iBb, iDD. | 379.963 | 68., 62.37, 74.16, 156.09 |
| 47 | C7(b9b5) | iC, iE, iGb, iBb, iDb. | 326.549 | 68., 40.36, 96.17, 88.21 |
| 48 | C7(#9#5) | iC, iE, iGD, iBb, iDD. | 384.141 | 68., 85.67, 50.86, 156.09 |
| 49 | C7(b9#5) | iC, iE, iGD, iBb, iDb. | 332.962 | 68., 85.67, 50.86, 88.21 |
| 50 | C7(#11) | iC, iE, iG, iBb, iFD. | 387.493 | 68., 62.37, 74.16, 273.84 |
| 51 | C9(#11) | iC, iE, iG, iBb, iD, iFD. | 410.788 | 68., 62.37, 74.16, 121.17, 152.67 |
| 52 | C7(#11b9) | iC, iE, iG, iBb, iDb, iFD. | 363.389 | 68., 62.37, 74.16, 88.21, 185.63 |
| 53 | C7(#11#9) | iC, iE, iG, iBb, iDD, iFD. | 413.493 | 68., 62.37, 74.16, 156.09, 117.75 |
| 54 | C13(b5) | iC, iE, iGb, iBb, iFD, iA. | 420.405 | 68., 40.36, 96.17, 232.3, 181.54 |
| 55 | C13(b9) | iC, iE, iG, iBb, iDb, iA. | 368.183 | 68., 62.37, 74.16, 88.21, 325.63 |
| 56 | C13(#11) | iC, iE, iG, iBb, iD, iFD, iA. | 444.658 | 68., 62.37, 74.16, 121.17, 152.67, 140. |
| 57 | C7sus4(b9) | iC, iF, iG, iBb, iDb. | 333.565 | 87.6, 42.77, 74.16, 88.21 |
| RIVOLTI / INVERSION | ||||
| 58 | C13sus4(b9) | iC, iF, iG, iBb, iDb, iA. | 372.071 | 87.6, 42.77, 74.16, 88.21, 325.63 |
| 59 | C|E | iE, iG, iC2. | 318.914 | 62.37, 131.25 |
| 60 | C|G | iG, iC, iE. | 312.914 | 131.25, 136. |
| 61 | E|C | iE, iGD, iB, iC2. | 354.34 | 85.67, 78.58, 29.37 |
| 62 | Bb|C | iC, iD, iF, iBb. | 326.901 | 32.03, 55.57, 144.65 |
| 63 | C|E (add9) | iE, iG, iC2, iD2. | 434.855 | 62.37, 131.25, 64.08 |
| 64 | C(add9 omit3) | iC, iG, iD2. | 371.479 | 130.37, 195.33 |
| 65 | C7(omit3) | iC, iG, iBb. | 433.205 | 130.37, 101.88 |
| 66 | Cmi7(omit5) | iC, iEb, iBb. | 364.7 | 49.5, 182.75 |
| 67 | C# Ma7 sus4 (b5) | iCD, iFD, iG, iBD. | 378.638 | 92.81, 22.01, 131.25 |
| 68 | F#7 sus (add3) | iFD, iAD, iB, iCD2, iE2. | 416.758 | 96.17, 27.72, 60.49, 104.88 |
| 69 | Bb (add b13 add9) | iBb, iD2, iF2, iGb2, iC3. | 516.266 | 93.45, 111.13, 41.53, 306.51 |
| 70 | A+ (add #9 add b9) | iA, iCD2, iED2, iBb2, iC3. | 668.785 | 114.37, 144.09, 233.87, 114.17 |
| 71 | G#mi7 (add11 omit5) | iGD, iB, iCD2, iFD2. | 527.156 | 78.58, 60.49, 185.62 |
| 72 | F/F# | iFD, iA, iC2, iF2. | 480.864 | 70.01, 83.25, 175.21 |
| 73 | E+/G | iG, iE2, iGD2, iBD2. | 516.514 | 267.25, 171.36, 215.89 |
| 74 | G7sus/A | iA, iC2, iD2, iF2, iG2. | 498.731 | 83.25, 64.08, 111.13, 85.53 |
| 75 | GMA7(#5) / F# | iFD, iG, iB, iDD2, iFD2. | 381.219 | 22.01, 101.88, 128.37, 117.74 |
| 76 | EbMA7(#5) / F | iF, iG, iB, iD2, iEb2. | 472.876 | 42.77, 101.88, 93.45, 34.92 |
| 77 | BMA7sus / F# | iFD, iAD, iB, iE2, iFD2. | 476.78 | 96.17, 27.72, 165.37, 80.74 |
| MODI ANTICHI | ||||
| 78 | Ionico | iC, iD, iE, iF, iG, iA, iB. | 350.47 | 32.03, 35.97, 19.6, 42.77, 48., 53.88 |
| 79 | Dorico | iD, iE, iF, iG, iA, iB, iC2. | 387.552 | 35.97, 19.6, 42.77, 48., 53.88, 29.37 |
| 80 | Frigio | iE, iF, iG, iA, iB, iC2, iD2. | 427.888 | 19.6, 42.77, 48., 53.88, 29.37, 64.08 |
| 81 | Lidio | iF, iG, iA, iB, iC2, iD2, iE2. | 471.615 | 42.77, 48., 53.88, 29.37, 64.08, 71.92 |
| 82 | Misolidio | iG, iA, iB, iC2, iD2, iE2, iF2. | 521.964 | 48., 53.88, 29.37, 64.08, 71.92, 39.21 |
| 83 | Eolio | iA, iB, iC2, iD2, iE2, iF2, iG2. | 356.667 | 53.88, 29.37, 64.08, 71.92, 39.21, 85.53 |
| 84 | Locrio | iB, iC2, iD2, iE2, iF2, iG2, iA2. | 636.42 | 29.37, 64.08, 71.92, 39.21, 85.53, 96.01 |
| 85 | Scala Armonica | iA, iB, iC2, iD2, iE2, iF2, iGD2, iA2. | 606.053 | 53.88, 29.37, 64.08, 71.92, 39.21, 132.15, 49.39 |
| 86 | Scala Melodica | iA, iB, iC2, iD2, iE2, iFD2, iGD2. | 584.139 | 53.88, 29.37, 64.08, 71.92, 80.74, 90.62 |
| 87 | Blues | iC, iEb, iF, iFD, iG, iBb. | 346.847 | 49.5, 38.1, 20.76, 22.01, 101.88 |
| 88 | C diminuita (T-S) | iC, iD, iEb, iF, iFD, iGD, iA, iB. | 352.218 | 32.03, 17.47, 38.1, 20.76, 45.31, 24.7, 53.88 |
| 89 | C diminuita (S-T) | iC, iDb, iEb, iFb, iFD, iG, iA, iBb. | 342.62 | 15.55, 33.95, 38.1, 20.76, 22.01, 48., 53.88 |
| SIX TONE | ||||
| 90 | Modo1 (Messiaen) | iC, iD, iE, iFD, iGD, iAD. | 342.523 | 32.03, 35.97, 40.36, 45.31, 50.86 |
| 91 | Modo2 (Messiaen) | iC, iDb, iEb, iE, iFD, iG, iA, iBb. | 342.62 | 15.55, 33.95, 18.5, 40.36, 22.01, 48., 53.88 |
| 92 | Modo3 (Messiaen) | iC, iD, iEb, iE, iFD, iG, iAb, iBb, iB. | 355.634 | 32.03, 17.47, 18.5, 40.36, 22.01, 23.3, 78.58, 0. |
| 93 | Modo4 (Messiaen) | iC, iDb, iD, iF, iFD, iG, iAb, iB. | 342.097 | 15.55, 16.48, 55.57, 20.76, 22.01, 23.3, 78.58 |
| 94 | Modo5 (Messiaen) | iC, iDb, iF, iFD, iG, iB. | 341.453 | 15.55, 72.05, 20.76, 22.01, 101.88 |
| 95 | Modo6 (Messiaen) | iC, iDb, iD, iEb, iF, iFD, iG, iA, iAD, iB. | 349.537 | 15.55, 16.48, 17.47, 38.1, 20.76, 22.01, 48., 26.16, 27.72 |
| 96 | Modo7 (Messiaen) | iC, iD, iE, iF, iFD, iGD, iAD, iB. | 357.059 | 32.03, 35.97, 19.6, 20.76, 45.31, 50.86, 27.72 |
| 97 | Esatonale1 | iCD, iD, iF, iG, iA, iB. | 362.892 | 16.48, 55.57, 42.77, 48., 53.88 |
| 98 | Esatonale2 | iC, iD, iE, iFD, iGD, iAD. | 342.523 | 32.03, 35.97, 40.36, 45.31, 50.86 |
| 99 | Enigmatica (Verdi) | iC, iDb, iE, iFD, iGD, iAD, iB. | 354.533 | 15.55, 52.45, 40.36, 45.31, 50.86, 27.72 |
| 97 | Esatonale1 | iCD, iD, iF, iG, iA, iB. | 362.892 | 16.48, 55.57, 42.77, 48., 53.88 |
| 98 | Esatonale2 | iC, iD, iE, iFD, iGD, iAD. | 342.523 | 32.03, 35.97, 40.36, 45.31, 50.86 |
| 99 | Enigmatica (Verdi) | iC, iDb, iE, iFD, iGD, iAD, iB. | 354.533 | 15.55, 52.45, 40.36, 45.31, 50.86, 27.72 |
| INDIAN SCALE | ||||
| 100 | Bhairav thaat | iC, iDb, iE, iF, iG, iAb, iB. | 344.644 | 15.55, 52.45, 19.6, 42.77, 23.3, 78.58 |
| 101 | Todi thaat | iC, iDb, iEb, iFD, iG, iAb, iB. | 344.31 | 15.55, 33.95, 58.86, 22.01, 23.3, 78.58 |
| 102 | Purvi thaat | iC, iDb, iE, iFD, iG, iAb, iB. | 347.392 | 15.55, 52.45, 40.36, 22.01, 23.3, 78.58 |
| 103 | Marva thaat | iC, iDb, iE, iFD, iG, iA, iB. | 349.738 | 15.55, 52.45, 40.36, 22.01, 48., 53.88 |
| 104 | raga Nat Bhairav | iC, iD, iE, iF, iG, iAb, iB. | 348.114 | 32.03, 35.97, 19.6, 42.77, 23.3, 78.58 |
| 105 | raga Charukeshi | iC, iD, iE, iF, iG, iAb, iBb. | 346.042 | 32.03, 35.97, 19.6, 42.77, 23.3, 78.58 |
| 106 | raga Ahir Bhairav | iC, iDb, iE, iF, iG, iA, iBb. | 344.895 | 15.55, 52.45, 19.6, 42.77, 48., 53.88 |
| 107 | raga Saugandh | iC, iD, iEb, iFD, iG, iA, iBb. | 348.029 | 32.03, 17.47, 58.86, 22.01, 48., 53.88 |
| 108 | raga Vachaspati | iC, iD, iE, iFD, iG, iA, iBb. | 351.178 | 32.03, 35.97, 40.36, 22.01, 48., 53.88 |
| PentatoniX Scale | ||||
| 109 | raga Bhupali | iC, iD, iE, iG, iA. | 331.456 | 32.03, 35.97, 62.37, 48 |
| 110 | raga Durga | iC, iD, iF, iG, iA. | 335.24 | 32.03, 55.57, 42.77, 48. |
| 111 | raga Megh | iC, iD, iF, iG, iBb. | 338.132 | 32.03, 55.57, 42.77, 101.88 |
| 112 | raga Dhani | iC, iEb, iF, iG, iBb. | 342.561 | 49.5, 38.1, 42.77, 101.88 |
| 113 | raga Malkauns | iC, iEb, iF, iA, iBb. | 349.22 | 49.5, 38.1, 90.77, 53.88 |
| 114 | Pentatonica Maggiore | iC,iD, iE, iG, iA. | 331.456 | 32.03, 35.97, 62.37, 48. |
| 115 | Pentatonica Minore | iC, iEb, iF, iG, iBb. | 333.565 | 49.5, 38.1, 42.77, 101.88 |