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Scale 1709: "Dorian"

Scale 1709: Dorian, 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

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
Dorian
Ancient Greek
Greek Phrygian
Medieval
Medieval Dorian
Medieval Hypomixolydian
Hindustani
Kafi That
Kafi Theta
Carnatic
Mela Kharaharapriya
Raga Bageshri
Unknown / Unsorted
Bhimpalasi
Nayaki Kanada
Sriraga
Ritigaula
Huseni
Kanara
Yu
Hyojo
Oshikicho
Nam
Schenkerian
Mischung 5
Gregorian Numbered
Gregorian Number 8
Exoticisms
Eskimo Heptatonic
Japanese
Banshikicho
Zeitler
Dorian
Dozenal
Dorian
Carnatic Melakarta
Kharaharapriya
Carnatic Numbered Melakarta
22nd Melakarta raga

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

7 (heptatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,2,3,5,7,9,10}

Forte Number

A code assigned by theorist Allen Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

7-35

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

[0]

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

yes

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

no

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

2 (dihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

0 (ancohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

1

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

6

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 1387

Generator

Indicates if the scale can be constructed using a generator, and an origin.

generator: 5
origin: 9

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

yes

Interval Structure

Defines the scale as the sequence of intervals between one tone and the next.

[2, 1, 2, 2, 2, 1, 2]

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

<2, 5, 4, 3, 6, 1>

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hanson.

p6m3n4s5d2t

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<1> = {1,2}
<2> = {3,4}
<3> = {5,6}
<4> = {6,7}
<5> = {8,9}
<6> = {10,11}

Spectra Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

0.857

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

yes

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

yes

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

2.665

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

6.035

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

yes

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

[0]

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Proper

Heteromorphic Profile

Defined by Norman Carey (2002), the heteromorphic profile is an ordered triple of (c, a, d) where c is the number of contradictions, a is the number of ambiguities, and d is the number of differences. When c is zero, the scale is Proper. When a is also zero, the scale is Strictly Proper.

(0, 1, 56)

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

Generator

This scale has a generator of 5, originating on 9.

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}231.71
F{5,9,0}231.71
A♯{10,2,5}231.71
Minor Triadscm{0,3,7}231.71
dm{2,5,9}231.71
gm{7,10,2}231.71
Diminished Triads{9,0,3}231.71
Parsimonious Voice Leading Between Common Triads of Scale 1709. Created by Ian Ring ©2019 cm cm D# D# cm->D# cm->a° dm dm F F dm->F A# A# dm->A# gm gm D#->gm F->a° gm->A#

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 1709 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1451
Scale 1451: Phrygian, Ian Ring Music TheoryPhrygian
3rd mode:
Scale 2773
Scale 2773: Lydian, Ian Ring Music TheoryLydian
4th mode:
Scale 1717
Scale 1717: Mixolydian, Ian Ring Music TheoryMixolydian
5th mode:
Scale 1453
Scale 1453: Aeolian, Ian Ring Music TheoryAeolian
6th mode:
Scale 1387
Scale 1387: Locrian, Ian Ring Music TheoryLocrianThis is the prime mode
7th mode:
Scale 2741
Scale 2741: Major, Ian Ring Music TheoryMajor

Prime

The prime form of this scale is Scale 1387

Scale 1387Scale 1387: Locrian, Ian Ring Music TheoryLocrian

Complement

The heptatonic modal family [1709, 1451, 2773, 1717, 1453, 1387, 2741] (Forte: 7-35) is the complement of the pentatonic modal family [661, 677, 1189, 1193, 1321] (Forte: 5-35)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1709 is itself, because it is a palindromic scale!

Scale 1709Scale 1709: Dorian, Ian Ring Music TheoryDorian

Transformations:

In the abbreviation, the subscript number after "T" is the number of semitones of tranposition, "M" means the pitch class is multiplied by 5, and "I" means the result is inverted. Operation is an identical way to express the same thing; the syntax is <a,b> where each tone of the set x is transformed by the equation y = ax + b

Abbrev Operation Result Abbrev Operation Result
T0 <1,0> 1709       T0I <11,0> 1709
T1 <1,1> 3418      T1I <11,1> 3418
T2 <1,2> 2741      T2I <11,2> 2741
T3 <1,3> 1387      T3I <11,3> 1387
T4 <1,4> 2774      T4I <11,4> 2774
T5 <1,5> 1453      T5I <11,5> 1453
T6 <1,6> 2906      T6I <11,6> 2906
T7 <1,7> 1717      T7I <11,7> 1717
T8 <1,8> 3434      T8I <11,8> 3434
T9 <1,9> 2773      T9I <11,9> 2773
T10 <1,10> 1451      T10I <11,10> 1451
T11 <1,11> 2902      T11I <11,11> 2902
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 3599      T0MI <7,0> 3599
T1M <5,1> 3103      T1MI <7,1> 3103
T2M <5,2> 2111      T2MI <7,2> 2111
T3M <5,3> 127      T3MI <7,3> 127
T4M <5,4> 254      T4MI <7,4> 254
T5M <5,5> 508      T5MI <7,5> 508
T6M <5,6> 1016      T6MI <7,6> 1016
T7M <5,7> 2032      T7MI <7,7> 2032
T8M <5,8> 4064      T8MI <7,8> 4064
T9M <5,9> 4033      T9MI <7,9> 4033
T10M <5,10> 3971      T10MI <7,10> 3971
T11M <5,11> 3847      T11MI <7,11> 3847

The transformations that map this set to itself are: T0, T0I

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 1711Scale 1711: Adonai Malakh, Ian Ring Music TheoryAdonai Malakh
Scale 1705Scale 1705: Raga Manohari, Ian Ring Music TheoryRaga Manohari
Scale 1707Scale 1707: Dorian Flat 2, Ian Ring Music TheoryDorian Flat 2
Scale 1701Scale 1701: Dominant Seventh, Ian Ring Music TheoryDominant Seventh
Scale 1717Scale 1717: Mixolydian, Ian Ring Music TheoryMixolydian
Scale 1725Scale 1725: Minor Bebop, Ian Ring Music TheoryMinor Bebop
Scale 1677Scale 1677: Raga Manavi, Ian Ring Music TheoryRaga Manavi
Scale 1693Scale 1693: Dogian, Ian Ring Music TheoryDogian
Scale 1741Scale 1741: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
Scale 1773Scale 1773: Blues Scale II, Ian Ring Music TheoryBlues Scale II
Scale 1581Scale 1581: Raga Bagesri, Ian Ring Music TheoryRaga Bagesri
Scale 1645Scale 1645: Dorian Flat 5, Ian Ring Music TheoryDorian Flat 5
Scale 1837Scale 1837: Dalian, Ian Ring Music TheoryDalian
Scale 1965Scale 1965: Raga Mukhari, Ian Ring Music TheoryRaga Mukhari
Scale 1197Scale 1197: Minor Hexatonic, Ian Ring Music TheoryMinor Hexatonic
Scale 1453Scale 1453: Aeolian, Ian Ring Music TheoryAeolian
Scale 685Scale 685: Raga Suddha Bangala, Ian Ring Music TheoryRaga Suddha Bangala
Scale 2733Scale 2733: Melodic Minor Ascending, Ian Ring Music TheoryMelodic Minor Ascending
Scale 3757Scale 3757: Raga Mian Ki Malhar, Ian Ring Music TheoryRaga Mian Ki Malhar

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. All other diagrams and visualizations are © Ian Ring. 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, and George Howlett for assistance with the Carnatic ragas.