The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 2699: "Sythimic"

Scale 2699: Sythimic, 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
Sythimic
Dozenal
Scuian

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

{0,1,3,7,9,11}

Forte Number

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

6-21

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: 2603

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.

1 (uncohemitonic)

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.

5

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: 349

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, 4, 2, 2, 1]

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, 4, 2, 4, 1, 2>

Interval Spectrum

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

pm4n2s4d2t2

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

Spectra Variation

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

3

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.

(18, 20, 61)

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
Minor Triadscm{0,3,7}210.67
Augmented TriadsD♯+{3,7,11}121
Diminished Triads{9,0,3}121

The following pitch classes are not present in any of the common triads: {1}

Parsimonious Voice Leading Between Common Triads of Scale 2699. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ cm->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.

Diameter2
Radius1
Self-Centeredno
Central Verticescm
Peripheral VerticesD♯+, a°

Modes

Modes are the rotational transformation of this scale. Scale 2699 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3397
Scale 3397: Sydimic, Ian Ring Music TheorySydimic
3rd mode:
Scale 1873
Scale 1873: Dathimic, Ian Ring Music TheoryDathimic
4th mode:
Scale 373
Scale 373: Epagimic, Ian Ring Music TheoryEpagimic
5th mode:
Scale 1117
Scale 1117: Raptimic, Ian Ring Music TheoryRaptimic
6th mode:
Scale 1303
Scale 1303: Epolimic, Ian Ring Music TheoryEpolimic

Prime

The prime form of this scale is Scale 349

Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic

Complement

The hexatonic modal family [2699, 3397, 1873, 373, 1117, 1303] (Forte: 6-21) is the complement of the hexatonic modal family [349, 1111, 1489, 1861, 2603, 3349] (Forte: 6-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2699 is 2603

Scale 2603Scale 2603: Gadimic, Ian Ring Music TheoryGadimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2699 is chiral, and its enantiomorph is scale 2603

Scale 2603Scale 2603: Gadimic, Ian Ring Music TheoryGadimic

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> 2699       T0I <11,0> 2603
T1 <1,1> 1303      T1I <11,1> 1111
T2 <1,2> 2606      T2I <11,2> 2222
T3 <1,3> 1117      T3I <11,3> 349
T4 <1,4> 2234      T4I <11,4> 698
T5 <1,5> 373      T5I <11,5> 1396
T6 <1,6> 746      T6I <11,6> 2792
T7 <1,7> 1492      T7I <11,7> 1489
T8 <1,8> 2984      T8I <11,8> 2978
T9 <1,9> 1873      T9I <11,9> 1861
T10 <1,10> 3746      T10I <11,10> 3722
T11 <1,11> 3397      T11I <11,11> 3349
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2729      T0MI <7,0> 683
T1M <5,1> 1363      T1MI <7,1> 1366
T2M <5,2> 2726      T2MI <7,2> 2732
T3M <5,3> 1357      T3MI <7,3> 1369
T4M <5,4> 2714      T4MI <7,4> 2738
T5M <5,5> 1333      T5MI <7,5> 1381
T6M <5,6> 2666      T6MI <7,6> 2762
T7M <5,7> 1237      T7MI <7,7> 1429
T8M <5,8> 2474      T8MI <7,8> 2858
T9M <5,9> 853      T9MI <7,9> 1621
T10M <5,10> 1706      T10MI <7,10> 3242
T11M <5,11> 3412      T11MI <7,11> 2389

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 2697Scale 2697: Katagitonic, Ian Ring Music TheoryKatagitonic
Scale 2701Scale 2701: Hawaiian, Ian Ring Music TheoryHawaiian
Scale 2703Scale 2703: Galian, Ian Ring Music TheoryGalian
Scale 2691Scale 2691: Rahian, Ian Ring Music TheoryRahian
Scale 2695Scale 2695: Rakian, Ian Ring Music TheoryRakian
Scale 2707Scale 2707: Banimic, Ian Ring Music TheoryBanimic
Scale 2715Scale 2715: Kynian, Ian Ring Music TheoryKynian
Scale 2731Scale 2731: Neapolitan Major, Ian Ring Music TheoryNeapolitan Major
Scale 2763Scale 2763: Mela Suvarnangi, Ian Ring Music TheoryMela Suvarnangi
Scale 2571Scale 2571: Pukian, Ian Ring Music TheoryPukian
Scale 2635Scale 2635: Gocrimic, Ian Ring Music TheoryGocrimic
Scale 2827Scale 2827: Runian, Ian Ring Music TheoryRunian
Scale 2955Scale 2955: Thorian, Ian Ring Music TheoryThorian
Scale 2187Scale 2187: Ionothitonic, Ian Ring Music TheoryIonothitonic
Scale 2443Scale 2443: Panimic, Ian Ring Music TheoryPanimic
Scale 3211Scale 3211: Epacrimic, Ian Ring Music TheoryEpacrimic
Scale 3723Scale 3723: Myptian, Ian Ring Music TheoryMyptian
Scale 651Scale 651: Golitonic, Ian Ring Music TheoryGolitonic
Scale 1675Scale 1675: Raga Salagavarali, Ian Ring Music TheoryRaga Salagavarali

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.