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Scale 1645: "Dorian Flat 5"

Scale 1645: Dorian Flat 5, 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

Western Altered
Dorian Flat 5
Locrian Natural Sharp 2 Sharp 6
Jazz and Blues
Blues Heptatonic
Turkish
Makam Karcigar
Arabic
Maqam Nahawand Murassah
Unknown / Unsorted
Kiourdi ascending
Kartzihiar
Zeitler
Katagian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,5,6,9,10}
Forte Number7-32
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1741
Hemitonia3 (trihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes6
Prime?no
prime: 859
Deep Scaleno
Interval Vector335442
Interval Spectrump4m4n5s3d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {8,9}
<6> = {9,10,11}
Spectra Variation1.429
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
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{2,6,9}431.6
F{5,9,0}331.8
A♯{10,2,5}232
Minor Triadsdm{2,5,9}331.7
d♯m{3,6,10}331.8
Augmented TriadsD+{2,6,10}331.7
Diminished Triads{0,3,6}232
d♯°{3,6,9}231.9
f♯°{6,9,0}231.9
{9,0,3}232
Parsimonious Voice Leading Between Common Triads of Scale 1645. Created by Ian Ring ©2019 d#m d#m c°->d#m c°->a° dm dm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° D+->d#m D+->A# d#°->d#m 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 1645 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1435
Scale 1435: Makam Huzzam, Ian Ring Music TheoryMakam Huzzam
3rd mode:
Scale 2765
Scale 2765: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
4th mode:
Scale 1715
Scale 1715: Harmonic Minor Inverse, Ian Ring Music TheoryHarmonic Minor Inverse
5th mode:
Scale 2905
Scale 2905: Aeolian Flat 1, Ian Ring Music TheoryAeolian Flat 1
6th mode:
Scale 875
Scale 875: Locrian Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 7
7th mode:
Scale 2485
Scale 2485: Harmonic Major, Ian Ring Music TheoryHarmonic Major

Prime

The prime form of this scale is Scale 859

Scale 859Scale 859: Ultralocrian, Ian Ring Music TheoryUltralocrian

Complement

The heptatonic modal family [1645, 1435, 2765, 1715, 2905, 875, 2485] (Forte: 7-32) is the complement of the pentatonic modal family [595, 665, 805, 1225, 2345] (Forte: 5-32)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1645 is 1741

Scale 1741Scale 1741: Lydian Diminished, Ian Ring Music TheoryLydian Diminished

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1645 is chiral, and its enantiomorph is scale 1741

Scale 1741Scale 1741: Lydian Diminished, Ian Ring Music TheoryLydian Diminished

Transformations:

T0 1645  T0I 1741
T1 3290  T1I 3482
T2 2485  T2I 2869
T3 875  T3I 1643
T4 1750  T4I 3286
T5 3500  T5I 2477
T6 2905  T6I 859
T7 1715  T7I 1718
T8 3430  T8I 3436
T9 2765  T9I 2777
T10 1435  T10I 1459
T11 2870  T11I 2918

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 1647Scale 1647: Polyllic, Ian Ring Music TheoryPolyllic
Scale 1641Scale 1641: Bocrimic, Ian Ring Music TheoryBocrimic
Scale 1643Scale 1643: Locrian Natural 6, Ian Ring Music TheoryLocrian Natural 6
Scale 1637Scale 1637: Syptimic, Ian Ring Music TheorySyptimic
Scale 1653Scale 1653: Minor Romani Inverse, Ian Ring Music TheoryMinor Romani Inverse
Scale 1661Scale 1661: Gonyllic, Ian Ring Music TheoryGonyllic
Scale 1613Scale 1613: Thylimic, Ian Ring Music TheoryThylimic
Scale 1629Scale 1629: Synian, Ian Ring Music TheorySynian
Scale 1581Scale 1581: Raga Bagesri, Ian Ring Music TheoryRaga Bagesri
Scale 1709Scale 1709: Dorian, Ian Ring Music TheoryDorian
Scale 1773Scale 1773: Blues Scale II, Ian Ring Music TheoryBlues Scale II
Scale 1901Scale 1901: Ionidyllic, Ian Ring Music TheoryIonidyllic
Scale 1133Scale 1133: Stycrimic, Ian Ring Music TheoryStycrimic
Scale 1389Scale 1389: Minor Locrian, Ian Ring Music TheoryMinor Locrian
Scale 621Scale 621: Pyramid Hexatonic, Ian Ring Music TheoryPyramid Hexatonic
Scale 2669Scale 2669: Jeths' Mode, Ian Ring Music TheoryJeths' Mode
Scale 3693Scale 3693: Stadyllic, Ian Ring Music TheoryStadyllic

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. Special thanks to Richard Repp for helping with technical accuracy.