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Scale 3577: "Loptygic"

Scale 3577: Loptygic, 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
Loptygic

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

{0,3,4,5,6,7,8,10,11}

Forte Number

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

9-4

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: 1015

Hemitonia

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

7 (multihemitonic)

Cohemitonia

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

5 (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: 959

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.

[3, 1, 1, 1, 1, 1, 2, 1, 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.

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

Interval Spectrum

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

p7m7n6s6d7t3

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> = {1,2,3}
<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> = {9,10,11}

Spectra Variation

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

2

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.

2.683

Polygon Perimeter

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

6.038

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}342.07
D♯{3,7,10}352.4
E{4,8,11}442.07
G♯{8,0,3}342.2
B{11,3,6}352.4
Minor Triadscm{0,3,7}442
d♯m{3,6,10}263
em{4,7,11}431.87
fm{5,8,0}263
g♯m{8,11,3}332
Augmented TriadsC+{0,4,8}452.27
D♯+{3,7,11}541.8
Diminished Triads{0,3,6}252.6
{4,7,10}242.47
{5,8,11}252.8
Parsimonious Voice Leading Between Common Triads of Scale 3577. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ em em C->em E E C+->E fm fm C+->fm C+->G# d#m d#m D# D# d#m->D# d#m->B D#->D#+ D#->e° D#+->em g#m g#m D#+->g#m D#+->B e°->em em->E E->f° E->g#m f°->fm g#m->G#

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.

Diameter6
Radius3
Self-Centeredno
Central Verticesem, g♯m
Peripheral Verticesd♯m, fm

Modes

Modes are the rotational transformation of this scale. Scale 3577 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 959
Scale 959: Katylygic, Ian Ring Music TheoryKatylygicThis is the prime mode
3rd mode:
Scale 2527
Scale 2527: Phradygic, Ian Ring Music TheoryPhradygic
4th mode:
Scale 3311
Scale 3311: Mixodygic, Ian Ring Music TheoryMixodygic
5th mode:
Scale 3703
Scale 3703: Katalygic, Ian Ring Music TheoryKatalygic
6th mode:
Scale 3899
Scale 3899: Katorygic, Ian Ring Music TheoryKatorygic
7th mode:
Scale 3997
Scale 3997: Dogygic, Ian Ring Music TheoryDogygic
8th mode:
Scale 2023
Scale 2023: Zodygic, Ian Ring Music TheoryZodygic
9th mode:
Scale 3059
Scale 3059: Madygic, Ian Ring Music TheoryMadygic

Prime

The prime form of this scale is Scale 959

Scale 959Scale 959: Katylygic, Ian Ring Music TheoryKatylygic

Complement

The enneatonic modal family [3577, 959, 2527, 3311, 3703, 3899, 3997, 2023, 3059] (Forte: 9-4) is the complement of the tritonic modal family [35, 385, 2065] (Forte: 3-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3577 is 1015

Scale 1015Scale 1015: Ionodygic, Ian Ring Music TheoryIonodygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3577 is chiral, and its enantiomorph is scale 1015

Scale 1015Scale 1015: Ionodygic, Ian Ring Music TheoryIonodygic

Transformations:

T0 3577  T0I 1015
T1 3059  T1I 2030
T2 2023  T2I 4060
T3 4046  T3I 4025
T4 3997  T4I 3955
T5 3899  T5I 3815
T6 3703  T6I 3535
T7 3311  T7I 2975
T8 2527  T8I 1855
T9 959  T9I 3710
T10 1918  T10I 3325
T11 3836  T11I 2555

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 3579Scale 3579: Zyphyllian, Ian Ring Music TheoryZyphyllian
Scale 3581Scale 3581: Epocryllian, Ian Ring Music TheoryEpocryllian
Scale 3569Scale 3569: Aeoladyllic, Ian Ring Music TheoryAeoladyllic
Scale 3573Scale 3573: Kaptygic, Ian Ring Music TheoryKaptygic
Scale 3561Scale 3561: Pothyllic, Ian Ring Music TheoryPothyllic
Scale 3545Scale 3545: Thyptyllic, Ian Ring Music TheoryThyptyllic
Scale 3513Scale 3513: Dydyllic, Ian Ring Music TheoryDydyllic
Scale 3449Scale 3449: Bacryllic, Ian Ring Music TheoryBacryllic
Scale 3321Scale 3321: Epagyllic, Ian Ring Music TheoryEpagyllic
Scale 3833Scale 3833: Dycrygic, Ian Ring Music TheoryDycrygic
Scale 4089Scale 4089: Decatonic Chromatic Descending, Ian Ring Music TheoryDecatonic Chromatic Descending
Scale 2553Scale 2553: Aeolaptyllic, Ian Ring Music TheoryAeolaptyllic
Scale 3065Scale 3065: Zothygic, Ian Ring Music TheoryZothygic
Scale 1529Scale 1529: Kataryllic, Ian Ring Music TheoryKataryllic

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.