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Scale 1583: "Salian"

Scale 1583: Salian, 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

Zeitler
Salian
Dozenal
Julian

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

{0,1,2,3,5,9,10}

Forte Number

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

7-11

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.

none

Palindromicity

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

no

Chirality

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

yes
enantiomorph: 3725

Hemitonia

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

4 (multihemitonic)

Cohemitonia

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

2 (dicohemitonic)

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.

3

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: 379

Generator

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

none

Deep Scale

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

no

Interval Structure

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

[1, 1, 1, 2, 4, 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.

<4, 4, 4, 4, 4, 1>

Interval Spectrum

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

p4m4n4s4d4t

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

Spectra Variation

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

3.143

Maximally Even

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

no

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.

no

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.

2.299

Polygon Perimeter

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

5.803

Myhill Property

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

no

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.

none

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".

Improper

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.

(43, 27, 92)

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.

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 TriadsF{5,9,0}231.5
A♯{10,2,5}241.83
Minor Triadsdm{2,5,9}231.5
a♯m{10,1,5}231.5
Augmented TriadsC♯+{1,5,9}321.17
Diminished Triads{9,0,3}142.17
Parsimonious Voice Leading Between Common Triads of Scale 1583. Created by Ian Ring ©2019 C#+ C#+ dm dm C#+->dm F F C#+->F a#m a#m C#+->a#m A# A# dm->A# F->a° a#m->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.

Diameter4
Radius2
Self-Centeredno
Central VerticesC♯+
Peripheral Verticesa°, A♯

Modes

Modes are the rotational transformation of this scale. Scale 1583 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2839
Scale 2839: Lyptian, Ian Ring Music TheoryLyptian
3rd mode:
Scale 3467
Scale 3467: Katonian, Ian Ring Music TheoryKatonian
4th mode:
Scale 3781
Scale 3781: Gyphian, Ian Ring Music TheoryGyphian
5th mode:
Scale 1969
Scale 1969: Stylian, Ian Ring Music TheoryStylian
6th mode:
Scale 379
Scale 379: Aeragian, Ian Ring Music TheoryAeragianThis is the prime mode
7th mode:
Scale 2237
Scale 2237: Epothian, Ian Ring Music TheoryEpothian

Prime

The prime form of this scale is Scale 379

Scale 379Scale 379: Aeragian, Ian Ring Music TheoryAeragian

Complement

The heptatonic modal family [1583, 2839, 3467, 3781, 1969, 379, 2237] (Forte: 7-11) is the complement of the pentatonic modal family [157, 929, 1063, 2579, 3337] (Forte: 5-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1583 is 3725

Scale 3725Scale 3725: Kyrian, Ian Ring Music TheoryKyrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1583 is chiral, and its enantiomorph is scale 3725

Scale 3725Scale 3725: Kyrian, Ian Ring Music TheoryKyrian

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> 1583       T0I <11,0> 3725
T1 <1,1> 3166      T1I <11,1> 3355
T2 <1,2> 2237      T2I <11,2> 2615
T3 <1,3> 379      T3I <11,3> 1135
T4 <1,4> 758      T4I <11,4> 2270
T5 <1,5> 1516      T5I <11,5> 445
T6 <1,6> 3032      T6I <11,6> 890
T7 <1,7> 1969      T7I <11,7> 1780
T8 <1,8> 3938      T8I <11,8> 3560
T9 <1,9> 3781      T9I <11,9> 3025
T10 <1,10> 3467      T10I <11,10> 1955
T11 <1,11> 2839      T11I <11,11> 3910
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 1583       T0MI <7,0> 3725
T1M <5,1> 3166      T1MI <7,1> 3355
T2M <5,2> 2237      T2MI <7,2> 2615
T3M <5,3> 379      T3MI <7,3> 1135
T4M <5,4> 758      T4MI <7,4> 2270
T5M <5,5> 1516      T5MI <7,5> 445
T6M <5,6> 3032      T6MI <7,6> 890
T7M <5,7> 1969      T7MI <7,7> 1780
T8M <5,8> 3938      T8MI <7,8> 3560
T9M <5,9> 3781      T9MI <7,9> 3025
T10M <5,10> 3467      T10MI <7,10> 1955
T11M <5,11> 2839      T11MI <7,11> 3910

The transformations that map this set to itself are: T0, T0M

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 1581Scale 1581: Raga Bagesri, Ian Ring Music TheoryRaga Bagesri
Scale 1579Scale 1579: Sagimic, Ian Ring Music TheorySagimic
Scale 1575Scale 1575: Zycrimic, Ian Ring Music TheoryZycrimic
Scale 1591Scale 1591: Rodian, Ian Ring Music TheoryRodian
Scale 1599Scale 1599: Pocryllic, Ian Ring Music TheoryPocryllic
Scale 1551Scale 1551: Jorian, Ian Ring Music TheoryJorian
Scale 1567Scale 1567: Jobian, Ian Ring Music TheoryJobian
Scale 1615Scale 1615: Sydian, Ian Ring Music TheorySydian
Scale 1647Scale 1647: Polyllic, Ian Ring Music TheoryPolyllic
Scale 1711Scale 1711: Adonai Malakh, Ian Ring Music TheoryAdonai Malakh
Scale 1839Scale 1839: Zogyllic, Ian Ring Music TheoryZogyllic
Scale 1071Scale 1071: Gorian, Ian Ring Music TheoryGorian
Scale 1327Scale 1327: Zalian, Ian Ring Music TheoryZalian
Scale 559Scale 559: Lylimic, Ian Ring Music TheoryLylimic
Scale 2607Scale 2607: Aerolian, Ian Ring Music TheoryAerolian
Scale 3631Scale 3631: Gydyllic, Ian Ring Music TheoryGydyllic

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.