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Scale 1727: "Sydygic"

Scale 1727: Sydygic, 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

Zeitler
Sydygic

Analysis

Cardinality

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

9 (enneatonic)

Pitch Class Set

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

{0,1,2,3,4,5,7,9,10}

Forte Number

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

9-7

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: 4013

Hemitonia

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

6 (multihemitonic)

Cohemitonia

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

4 (multicohemitonic)

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.

2

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.

8

Prime Form

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

no
prime: 1471

Deep Scale

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

no

Interval Formula

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

[1, 1, 1, 1, 1, 2, 2, 1, 2] 9

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.

<6, 7, 7, 6, 7, 3>

Interval Spectrum

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

p7m6n7s7d6t3

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

Spectra Variation

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

1.778

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.

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.

2.799

Polygon Perimeter

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

6.106

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

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 TriadsC{0,4,7}442.31
D♯{3,7,10}342.44
F{5,9,0}242.38
A{9,1,4}442.13
A♯{10,2,5}342.44
Minor Triadscm{0,3,7}342.44
dm{2,5,9}242.56
gm{7,10,2}342.44
am{9,0,4}442.19
a♯m{10,1,5}442.31
Augmented TriadsC♯+{1,5,9}442.19
Diminished Triadsc♯°{1,4,7}242.44
{4,7,10}242.56
{7,10,1}242.56
{9,0,3}242.56
a♯°{10,1,4}242.44
Parsimonious Voice Leading Between Common Triads of Scale 1727. Created by Ian Ring ©2019 cm cm C C cm->C D# D# cm->D# cm->a° c#° c#° C->c#° C->e° am am C->am A A c#°->A C#+ C#+ dm dm C#+->dm F F C#+->F C#+->A a#m a#m C#+->a#m A# A# dm->A# D#->e° gm gm D#->gm F->am g°->gm g°->a#m gm->A# a°->am am->A a#° a#° A->a#° a#°->a#m 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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1727 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2911
Scale 2911: Katygic, Ian Ring Music TheoryKatygic
3rd mode:
Scale 3503
Scale 3503: Zyphygic, Ian Ring Music TheoryZyphygic
4th mode:
Scale 3799
Scale 3799: Aeralygic, Ian Ring Music TheoryAeralygic
5th mode:
Scale 3947
Scale 3947: Ryptygic, Ian Ring Music TheoryRyptygic
6th mode:
Scale 4021
Scale 4021: Raga Pahadi, Ian Ring Music TheoryRaga Pahadi
7th mode:
Scale 2029
Scale 2029: Kiourdi, Ian Ring Music TheoryKiourdi
8th mode:
Scale 1531
Scale 1531: Styptygic, Ian Ring Music TheoryStyptygic
9th mode:
Scale 2813
Scale 2813: Zolygic, Ian Ring Music TheoryZolygic

Prime

The prime form of this scale is Scale 1471

Scale 1471Scale 1471: Radygic, Ian Ring Music TheoryRadygic

Complement

The enneatonic modal family [1727, 2911, 3503, 3799, 3947, 4021, 2029, 1531, 2813] (Forte: 9-7) is the complement of the tritonic modal family [37, 641, 1033] (Forte: 3-7)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1727 is 4013

Scale 4013Scale 4013: Raga Pilu, Ian Ring Music TheoryRaga Pilu

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1727 is chiral, and its enantiomorph is scale 4013

Scale 4013Scale 4013: Raga Pilu, Ian Ring Music TheoryRaga Pilu

Transformations:

T0 1727  T0I 4013
T1 3454  T1I 3931
T2 2813  T2I 3767
T3 1531  T3I 3439
T4 3062  T4I 2783
T5 2029  T5I 1471
T6 4058  T6I 2942
T7 4021  T7I 1789
T8 3947  T8I 3578
T9 3799  T9I 3061
T10 3503  T10I 2027
T11 2911  T11I 4054

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 1725Scale 1725: Minor Bebop, Ian Ring Music TheoryMinor Bebop
Scale 1723Scale 1723: JG Octatonic, Ian Ring Music TheoryJG Octatonic
Scale 1719Scale 1719: Lyryllic, Ian Ring Music TheoryLyryllic
Scale 1711Scale 1711: Adonai Malakh, Ian Ring Music TheoryAdonai Malakh
Scale 1695Scale 1695: Phrodyllic, Ian Ring Music TheoryPhrodyllic
Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic
Scale 1791Scale 1791: Aerygyllian, Ian Ring Music TheoryAerygyllian
Scale 1599Scale 1599: Pocryllic, Ian Ring Music TheoryPocryllic
Scale 1663Scale 1663: Lydygic, Ian Ring Music TheoryLydygic
Scale 1855Scale 1855: Gaptygic, Ian Ring Music TheoryGaptygic
Scale 1983Scale 1983: Soryllian, Ian Ring Music TheorySoryllian
Scale 1215Scale 1215, Ian Ring Music Theory
Scale 1471Scale 1471: Radygic, Ian Ring Music TheoryRadygic
Scale 703Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllic
Scale 2751Scale 2751: Sylygic, Ian Ring Music TheorySylygic
Scale 3775Scale 3775: Loptyllian, Ian Ring Music TheoryLoptyllian

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. 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.