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Scale 1579: "Sagimic"

Scale 1579: Sagimic, 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
Sagimic
Dozenal
Jujian

Analysis

Cardinality

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

6 (hexatonic)

Pitch Class Set

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

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

Forte Number

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

6-Z24

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: 2701

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.

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.

5

Prime Form

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

no
prime: 347

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, 2, 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.

<2, 3, 3, 3, 3, 1>

Interval Spectrum

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

p3m3n3s3d2t

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

Spectra Variation

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

2.667

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.

2.232

Polygon Perimeter

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

5.767

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.

(14, 11, 59)

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}221
Minor Triadsa♯m{10,1,5}131.5
Augmented TriadsC♯+{1,5,9}221
Diminished Triads{9,0,3}131.5
Parsimonious Voice Leading Between Common Triads of Scale 1579. Created by Ian Ring ©2019 C#+ C#+ F F C#+->F a#m a#m C#+->a#m F->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
Radius2
Self-Centeredno
Central VerticesC♯+, F
Peripheral Verticesa°, a♯m

Triad Polychords

Also known as Bi-Triadic Hexatonics (a term coined by mDecks), and related to Generic Modality Compression (a method for guitar by Mick Goodrick and Tim Miller), these are two common triads that when combined use all the tones in this scale.

There is 1 way that this hexatonic scale can be split into two common triads.


Diminished: {9, 0, 3}
Minor: {10, 1, 5}

Modes

Modes are the rotational transformation of this scale. Scale 1579 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2837
Scale 2837: Aelothimic, Ian Ring Music TheoryAelothimic
3rd mode:
Scale 1733
Scale 1733: Raga Sarasvati, Ian Ring Music TheoryRaga Sarasvati
4th mode:
Scale 1457
Scale 1457: Raga Kamalamanohari, Ian Ring Music TheoryRaga Kamalamanohari
5th mode:
Scale 347
Scale 347: Barimic, Ian Ring Music TheoryBarimicThis is the prime mode
6th mode:
Scale 2221
Scale 2221: Raga Sindhura Kafi, Ian Ring Music TheoryRaga Sindhura Kafi

Prime

The prime form of this scale is Scale 347

Scale 347Scale 347: Barimic, Ian Ring Music TheoryBarimic

Complement

The hexatonic modal family [1579, 2837, 1733, 1457, 347, 2221] (Forte: 6-Z24) is the complement of the hexatonic modal family [599, 697, 1481, 1829, 2347, 3221] (Forte: 6-Z46)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1579 is 2701

Scale 2701Scale 2701: Hawaiian, Ian Ring Music TheoryHawaiian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1579 is chiral, and its enantiomorph is scale 2701

Scale 2701Scale 2701: Hawaiian, Ian Ring Music TheoryHawaiian

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> 1579       T0I <11,0> 2701
T1 <1,1> 3158      T1I <11,1> 1307
T2 <1,2> 2221      T2I <11,2> 2614
T3 <1,3> 347      T3I <11,3> 1133
T4 <1,4> 694      T4I <11,4> 2266
T5 <1,5> 1388      T5I <11,5> 437
T6 <1,6> 2776      T6I <11,6> 874
T7 <1,7> 1457      T7I <11,7> 1748
T8 <1,8> 2914      T8I <11,8> 3496
T9 <1,9> 1733      T9I <11,9> 2897
T10 <1,10> 3466      T10I <11,10> 1699
T11 <1,11> 2837      T11I <11,11> 3398
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 559      T0MI <7,0> 3721
T1M <5,1> 1118      T1MI <7,1> 3347
T2M <5,2> 2236      T2MI <7,2> 2599
T3M <5,3> 377      T3MI <7,3> 1103
T4M <5,4> 754      T4MI <7,4> 2206
T5M <5,5> 1508      T5MI <7,5> 317
T6M <5,6> 3016      T6MI <7,6> 634
T7M <5,7> 1937      T7MI <7,7> 1268
T8M <5,8> 3874      T8MI <7,8> 2536
T9M <5,9> 3653      T9MI <7,9> 977
T10M <5,10> 3211      T10MI <7,10> 1954
T11M <5,11> 2327      T11MI <7,11> 3908

The transformations that map this set to itself are: T0

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 1577Scale 1577: Raga Chandrakauns (Kafi), Ian Ring Music TheoryRaga Chandrakauns (Kafi)
Scale 1581Scale 1581: Raga Bagesri, Ian Ring Music TheoryRaga Bagesri
Scale 1583Scale 1583: Salian, Ian Ring Music TheorySalian
Scale 1571Scale 1571: Lagitonic, Ian Ring Music TheoryLagitonic
Scale 1575Scale 1575: Zycrimic, Ian Ring Music TheoryZycrimic
Scale 1587Scale 1587: Raga Rudra Pancama, Ian Ring Music TheoryRaga Rudra Pancama
Scale 1595Scale 1595: Dacrian, Ian Ring Music TheoryDacrian
Scale 1547Scale 1547: Jopian, Ian Ring Music TheoryJopian
Scale 1563Scale 1563: Joyian, Ian Ring Music TheoryJoyian
Scale 1611Scale 1611: Dacrimic, Ian Ring Music TheoryDacrimic
Scale 1643Scale 1643: Locrian Natural 6, Ian Ring Music TheoryLocrian Natural 6
Scale 1707Scale 1707: Dorian Flat 2, Ian Ring Music TheoryDorian Flat 2
Scale 1835Scale 1835: Byptian, Ian Ring Music TheoryByptian
Scale 1067Scale 1067: Gopian, Ian Ring Music TheoryGopian
Scale 1323Scale 1323: Ritsu, Ian Ring Music TheoryRitsu
Scale 555Scale 555: Aeolycritonic, Ian Ring Music TheoryAeolycritonic
Scale 2603Scale 2603: Gadimic, Ian Ring Music TheoryGadimic
Scale 3627Scale 3627: Kalian, Ian Ring Music TheoryKalian

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.