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Scale 1769: "Blues Heptatonic II"

Scale 1769: Blues Heptatonic II, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

41161837294116105072918310504116183
Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

Common Names

Jazz and Blues
Blues Heptatonic II
Zeitler
Rythian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,3,5,6,7,9,10}
Forte Number7-25
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 749
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 733
Deep Scaleno
Interval Vector345342
Interval Spectrump4m3n5s4d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,9,10}
<6> = {9,10,11}
Spectra Variation2.286
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsD♯{3,7,10}231.75
F{5,9,0}231.88
Minor Triadscm{0,3,7}331.63
d♯m{3,6,10}331.63
Diminished Triads{0,3,6}231.75
d♯°{3,6,9}231.75
f♯°{6,9,0}231.88
{9,0,3}231.75
Parsimonious Voice Leading Between Common Triads of Scale 1769. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m D# D# cm->D# cm->a° d#° d#° d#°->d#m f#° f#° d#°->f#° d#m->D# F F F->f#° F->a°

view full size

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1769 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 733
Scale 733: Donian, Ian Ring Music TheoryDonianThis is the prime mode
3rd mode:
Scale 1207
Scale 1207: Aeoloptian, Ian Ring Music TheoryAeoloptian
4th mode:
Scale 2651
Scale 2651: Panian, Ian Ring Music TheoryPanian
5th mode:
Scale 3373
Scale 3373: Lodian, Ian Ring Music TheoryLodian
6th mode:
Scale 1867
Scale 1867: Solian, Ian Ring Music TheorySolian
7th mode:
Scale 2981
Scale 2981: Ionolian, Ian Ring Music TheoryIonolian

Prime

The prime form of this scale is Scale 733

Scale 733Scale 733: Donian, Ian Ring Music TheoryDonian

Complement

The heptatonic modal family [1769, 733, 1207, 2651, 3373, 1867, 2981] (Forte: 7-25) is the complement of the pentatonic modal family [301, 721, 1099, 1673, 2597] (Forte: 5-25)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1769 is 749

Scale 749Scale 749: Aeologian, Ian Ring Music TheoryAeologian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1769 is chiral, and its enantiomorph is scale 749

Scale 749Scale 749: Aeologian, Ian Ring Music TheoryAeologian

Transformations:

T0 1769  T0I 749
T1 3538  T1I 1498
T2 2981  T2I 2996
T3 1867  T3I 1897
T4 3734  T4I 3794
T5 3373  T5I 3493
T6 2651  T6I 2891
T7 1207  T7I 1687
T8 2414  T8I 3374
T9 733  T9I 2653
T10 1466  T10I 1211
T11 2932  T11I 2422

Nearby Scales:

These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.

Scale 1771Scale 1771, Ian Ring Music Theory
Scale 1773Scale 1773: Blues Scale II, Ian Ring Music TheoryBlues Scale II
Scale 1761Scale 1761, Ian Ring Music Theory
Scale 1765Scale 1765: Lonian, Ian Ring Music TheoryLonian
Scale 1777Scale 1777: Saptian, Ian Ring Music TheorySaptian
Scale 1785Scale 1785: Tharyllic, Ian Ring Music TheoryTharyllic
Scale 1737Scale 1737: Raga Madhukauns, Ian Ring Music TheoryRaga Madhukauns
Scale 1753Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major
Scale 1705Scale 1705: Raga Manohari, Ian Ring Music TheoryRaga Manohari
Scale 1641Scale 1641: Bocrimic, Ian Ring Music TheoryBocrimic
Scale 1897Scale 1897: Ionopian, Ian Ring Music TheoryIonopian
Scale 2025Scale 2025, Ian Ring Music Theory
Scale 1257Scale 1257: Blues Scale, Ian Ring Music TheoryBlues Scale
Scale 1513Scale 1513: Stathian, Ian Ring Music TheoryStathian
Scale 745Scale 745: Kolimic, Ian Ring Music TheoryKolimic
Scale 2793Scale 2793: Eporian, Ian Ring Music TheoryEporian
Scale 3817Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.